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This is to certify that the

diSsertation entitled

FLUORESCENT PROBES FOR MONITORING AND
CHARACTERIZING THE CRYSTALLIZATION
CONDITIONS OF LYSOZYME

presented by

Borlan Pan

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Chemical Engineering

 

 

7230

Major professor

Date Sept. 27, 1995

 

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

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MSU le An Afflrmdlve ActloNEquel Opportunlty lnetttuton
Wt

FLUORESCENT PROBES FOR MONITORING AND
CHARACTERIsz THE CRYSTALLIZATION
CONDITIONS OF LYSOZYME
By

Borlan Pan

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemical Engineering

1995

ABSTRACT

FLUORESCENT PROBES FOR MONITORING AND
CHARACTERIsz THE CRYSTALLIZATION
CONDITIONS OF LYSOZYME

By
Borlan Pan

The production of protein crystals for crystallographic structural
determination largely relies on trial and error methods for determining
optimal crystallization conditions. To expedite the screening and optimization
of the protein crystallization process, methods are required that are able to
monitor the molecular scale interactions occurring during nucleation and
subsequent crystal growth in supersaturated solutions. Steady-state and
time-resolved fluorescence and anisotropy measurements of protein-coupled
fluorescent probes are applied to monitor and characterize the crystallization
behavior of hen egg-white lysozyme (HEL).

The X-ray crystallographic structure of HEL co-crystallized with the
organic anion orange II is first examined. The decreased amount of NaCl
required to crystallize HEL and the decreased extent of the solvent structure
indicate the participation of orange 11 in the crystallization process. Further
investigations using l-pyrene butyric acid (PBA) as a covalently bound
fluorescence probe demonstrate that the fluorescence lifetimes of PBA and
the rotational correlation times of HEL are dependent on the crystallization
conditions.

The fluorescence from the non-covalently bound probe, 1-anilino-8-
naphthalene sulfonic acid (ANS), is demonstrated to be a more practical
method to dynamically monitor protein crystallization conditions of HEL in

situ. The use of this technique for the optimization of protein crystallization
conditions is discussed. Finally, a comparison of the efl‘ects of various ionic
precipitants on the fluorescence behavior of the AN S/HEL system provides
information on the chemical mechanisms of HEL crystallization and is shown
to be useful for the screening of crystallization conditions.

The results indicate that specific interactions between the HEL and
anions are the central phenomenon involved in nucleation and crystallization.
The binding of these anions is found to cause increased interactions between
the protein and leads to a decrease in the rotational mobility. Subsequent
nucleation and crystallization depends on the ability of these bound anions to
participate in the formation of crystalline contacts between HEL molecules.

ACKNOWLEDGMENTS

The encouragement and support provided by the people associated
with Michigan State University have contributed to my development over the
years and made this work possible. I would like to thank my graduate
advisor, Dr. Kris Berglund for his exceptional enthusiasm, dedication and
guidance. I would also like to thank my parents, Dr. Keh-Ming and Su-Mei
Pan and my dear friend, Elizabeth Gibson for being there throughout.

Thanks are also given to Dr. Daina Briedis, Dr. Daniel Nocera and
Dr. Patrick Oriel for their useful suggestions, comments and criticisms while
serving as my committee members. I would like to thank Dr. John Merrill
and Dr. Donna Koslowsky for providing valuable discussions and assistance
on protein separations. Dr. Mali Yin’s work on the crystallographic
refinement of the protein structures is also appreciated as is the assistance of
Dr. Alexander Tulinsky and his coworkers. I would also like to acknowledge
Dr. Tom Carter for his assistance with the spectroscopic instrumentation.

iv

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................. viii
LIST OF FIGURES .......................................................................................... ix
Chapter 1. Introduction and Background on Protein Crystallization
Processes ........................................................................................................... 1
Introduction ........................................................................................... 1
Background on Protein crystallization ................................................. 4
History of Protein Crystal Growth and Crystallography ......... 4
The Crystallization Process ........................................................ 7
Nucleation ................................................................................... 8
Crystal Growth ............................................................................ 12
Cessation of Crystal Growth ...................................................... 15
Intermolecular Interactions in Protein Association ............................. 16
Chapter 2. Current Experimental Techniques for Investigations on
Protein Crystallization ..................................................................................... 24
Introduction ........................................................................................... 24
Macroscopic Methods ............................................................................. 25
Static Light Scattering .......................................................................... 3 1
Dynamic Light Scattering ..................................................................... 32
Chapter 3. Fluorescence Techniques for Investigations on Protein
Crystallization .................................................................................................. 40
Introduction ........................................................................................... 40
Fluorescence and Anisotropy Processes ............................................... 42
Experimental Determination of Fluorescence Parameters ................. 47
Applications of Fluorescence ................................................................. 50
Fluorescence of HEL .............................................................................. 52
Chapter 4. The Effects of Co-Crystallization with Orange II on the
Structure of Lysozyme ...................................................................................... 57
Abstract .................................................................................................. 57
Introduction ........................................................................................... 57
Material and Methods ........................................................................... 59
Results .................................................................................................... 63
Effects on Crystallization ........................................................... 63
Comparison of the Structure of OHEL with lHEL ................... 63

V

Discussion .............................................................................................. 65

Chapter 5. Time-Resolved Fluorescence and Anisotropy of Covalently
Coupled PBA for Monitoring the Crystallization Conditions of

Lysozyme ........................................................................................................... 70
Abstract .................................................................................................. 70
Introduction ........................................................................................... 71
Experimental Methods .......................................................................... 73

Labeling of HEL with PBA ......................................................... 73
Sample Preparation .................................................................... 74
Fluorescence Measurements ...................................................... 74
Data Analysis .............................................................................. 75
Results .................................................................................................... 77
Chromatography and PAGE of PBA-Lys ................................... 77
Fluorescence Measurements of PBA-HEL ................................. 78
Effects of NaCl ............................................................................ 80
Efl‘ects of Ammonium Acetate and Ammonium Sulfate ........... 83
Discussion ...................................................................... . ........................ 86

Chapter 6. Time-Resolved Fluorescence and Anisotropy of N on-
Covalently Bound ANS for Monitoring the Crystallization Conditions

of Lysozyme ....................................................................................................... 90
Abstract .................................................................................................. 90
Introduction ........................................................................................... 90
Experimental .......................................................................................... 93

Solution Preparation ................................................................... 93
Fluorescence Measurements ...................................................... 93
Results .................................................................................................... 95
Response of ANS Fluorescence to Solution Conditions ............ 95
Response of the Rotational Correlation Times to Solution
Conditions .................................................................................... 99
Monitoring the Progress of Batch Crystallization ..................... 102
Monitoring of Vapor Diffusion Crystallization .......................... 104
Discussion .............................................................................................. 105

Chapter 7 . The Effects of Precipitants on the Time-Resolved
Fluorescence and Anisotropy of ANS for Characterizing Lysozyme

Crystallization .................................................................................................. l 10
Abstract .................................................................................................. 1 10
Introduction ........................................................................................... 1 10
Experimental .......................................................................................... 1 12

Solution Preparation ................................................................... 1 12
Fluorescence Measurements ...................................................... 1 13
Results .................................................................................................... 1 l4
Fluorescence Properties of ANS in HEL solutions .................... 1 14
Comparison of Salt Effects at 3.6 % HEL .................................. 115
Efl'ects of HEL Concentration .................................................... 1 19
Discussion .............................................................................................. 121

Chapter 8. Summary and Conclusions ............................................................ 127

Conclusions ............................................................................................ 127
Recommendations for Further Research .............................................. 130
APPENDIX A. Tabulated Data for Chapter 5 ................................................ 133
APPENDIX B. Tabulated Data for Chapter 6 ................................................ 146
APPENDDI C. Tabulated Data for Chapter 7 ................................................ 169
LIST OF REFERENCES .................................................................................. 190

LIST OF TABLES

Page
Table 3. 1. Amino acid sequence of hen egg white lysozyme. 52
Table 3.2. Tryptophan fluorescence parameters for 0. 1% HEL. 54

Table 4.1. Summary of x-ray diffraction and refinement
statistics for orange 11 lysozyme (OHEL) and lysozyme (1HEL,
from [98]). 60

Table 4.2. Co-crystallization of HEL with orange 11. Values of
[NaCl] are the concentrations in the reservoir and values of
[Orange II] are the initial concentrations in the hanging drop.
Xn indicates the presence of crystals where n is the number of
crystals, ppt indicates precipitate and + indicates relatively
many. Qualitative descriptions are given in the parenthesis
indicating small (sm), large (lg) and irregular (irr) crystals. 61

viii

LIST OF FIGURES

Figure 1.1. Schematic illustration of the processes involved in
nucleation and amorphous precipitation as described by classical
nucleation theory.

Figure 1.2. The morphology of tetragonal HEL crystals. The
faces are labeled as (101) and (110).

Figure 2.1. Schematic diagram of vapor diffusion trial. Typically
a 4x6 grid of these trials are performed in one tray.

Figure 2.2. Schematic illustration of the crystallization behavior
for HEL. The data points are measured solubility data at pH 4.6,
25° C [36]. The line through the points represent the solubility
limit. Above this is a metastable zone where nucleation does not
occur. In the X region, crystallization occurs. Above this region,
immediate precipitation is observed. (Adapted from reference

[8])

Figure 3.1. Photochemical processes in fluorescence

spectroscopy.

Figure 3.2. Photoselection in fluorescence anisotropy. The
arrows in the box represent the absorption dipole moments of
the fluorescent probes. Bold arrows indicate that absorption
occurs.

Figure 3.3. Time-resolved fluorescence and anisotropy
instrumentation.

Figure 3.4. HEL a-carbon atoms showing the main polypeptide
chain (from reference [91]).

Figure 3.5. Effect of NaCl concentrations on the tryptophan a)
fluorescence lifetimes and b) rotational correlation times of 2%
HEL solutions.

Figure 4.1 Structure of Orange II.

Page

14

26

28

42

45

48

53

55
59

Figure 4.2. Structures of a) OHEL co-crystallized with orange II
and b) lHEL (from Reference [98]) showing the protein and
associated solvent atoms.

Figure 4.3. a) Average root mean square difl'erence between the
residues of OHEL and lHEL. The models were overlaid by a
least-squares procedure minimizing the rms difference between
the backbone atoms. b) Thermal factors for OHEL and lHEL.

Figure 5.1. The structure of 1-pyrene butyric acid (PBA).

Figure 5.2. Time-dependent fluorescence intensity decays of free
PBA at 23°C in 50 mM sodium borate buffer at pH 8.5. Also
shown is the fit through the total fluorescence decay data. Ivv
and Iva are virtually indistinguishable because of the fast
rotational rate of the relatively small PBA. Each channel
represents a time interval of 0.197 ns.

Figure 5.3. Time-dependent fluorescence intensity decays of
0.02% PBA-HEL at 23°C in 50 mM sodium acetate buffer at pH
4.6. The fits are shown as the solid lines through the data points.
The difference in Ivv and Iv H is due to the fluorescence
anisotropy of the conjugated PBA. Each channel represents a
time interval of 0.197 ns.

Figure 5.4. Dependence of the a) fluorescence lifetimes of and b)
rotational correlation times of PBA-HEL on NaCl concentrations
at 2% ( El ) and 4% ( O ) HEL. The X and ppt symbols represents
crystallization or precipitation, respectively. The + symbols
represent the relative amounts formed to show increasing
supersaturation.

Figure 5.5. Efl‘ects of the ionic strength of NaCl on the rotational
correlation times of PBA-HEL at 2% (D ) and 4% (O ) HEL.

Figure 5.6. Dependence of the a) fluorescence lifetimes and b)
rotational correlation times of PBA-HEL on HEL concentrations
at 2% (U ) and 5% ( O ) NaCl. See Figure 5.4 for an explanation
of the X and ppt symbols.

Figure 5.7. Dependence of the a) fluorescence lifetimes and b)
rotational correlation times of PBA-HEL on salt concentrations

at 4% HEL. The (O ), (A) and ( [3) represent solutions
containing NaCl, NAc and NS, respectively.

Figure 5.8. Effects of the ionic strength with NaCl (0 ), NAc
(A) and NS (D) on the rotational correlation times of PBA-
HEL at 4% HEL.

Figure 6.1. Structure of ANS.

62

73

78

79

81

82

83

84

85
92

Figure 6.2. Time resolved fluorescence decay curves for 10'4 M
ANS in 3.6 % HEL.

Figure 6.3. Response of the fractional pre-exponential factors A1
(0 ), A2 (' ), A3 (D) and A4 (I) on NaCl concentrations for
3.6 % HEL.

Figure 6.4. Response of the combined fractional contributions
from A1 and A2 (FA12) of HEL associated ANS to the ionic
strength of NaCl (a) and NS (b). For a), symbols represent
1.0 ( A ), 2.0 ( 0 ), 3.6 ( Cl ) and 5.0 % ( O ) HEL. For b), symbols
represent 2.1 ( O ), 3.6 ( D ) and 4.3 % ( O ) HEL. X indicates the
formation of crystals, XC indicates crystalline spherulites and
ppt indicates precipitation. The + symbols represent relative
amounts formed.

Figure 6.5. Response of the long rotational correlation times (p1)
of HEL associated ANS to the ionic strength of NaCl (a) and NS
(b). For a), symbols represent 1.0 ( A ), 2.0 ( O ), 3.6 ( D) and
5.0 % (O) HEL. For b), symbols represent 2.1(0), 3.6 ( D)
and 4.3 % (O) HEL. See Figure 6.4 for explanations of the
other symbols.

Figure 6.6. Monitoring the batch crystallization of HEL. The
(O ) symbols represents HEL concentrations from A28 1
measurements of diluted aliquots taken at the indicated times.
The ( CI) symbols are the FA12 values in a) and the p1 values in
b) from in situ fluorescence measurements.

Figure 6.7. Monitoring the progress of a HEL vapor diffusion
crystallization trial using ANS fluorescence with a) FA12 and b)

91-

Figure 7.1. Effects of the ionic strength of NS ( O ), NaP ( [3),
pH 4.6 NAc(<>), NaCl(A) and NaSCN(V) salts on the

a) FA12 and b) p1 fluorescence parameters and crystallization
behavior of 3.6% HEL solutions. X indicates the formation of
crystals and X0 indicates crystalline clusters. The 4» symbols
represent relative amounts formed.

Figure 7.2. Efl'ects of the ionic strengths on the a) FA12 and b) p 1
fluorescence parameters and crystallization behavior of
3.6% HEL solutions at pH 7.7 (O ), 6.4 (CI) and 4.6 (O ). See
Figure 7.1 for an explanation of the other symbols.

96

97

98

101

103

105

117

118

Figure 7.3. Efl'ects of HEL concentrations on the a) FA12 and the

b) m fluorescence parameters and crystallization behavior of
0.86 ionic strength NS(O), NaP(l:|), pH6.4 NAc(<>),
NaCl(A), NaSCN (V) and 0.86M concentration NS ( 0)
solutions. See Figure 7 .1 for an explanation of the other

symbols.

 

119

Chapter 1

Introduction and Background on Protein
Crystallization Processes

lntroductlon

To determine the three dimensional structure of proteins using X-ray
crystallography, diffraction quality protein crystals must be obtained. The
goal is to find conditions that will gradually increase the level of
supersaturation until only a few nuclei are formed that will grow into single
crystals. Presently, the production of these crystals largely relies on trial and
error methods for determining optimal crystallization conditions. Although
this method has produced many suitable crystals in the past, the
disadvantages of the trial and error approach are well known [1]. Typically,
the search for optimal conditions is performed by screening a multitude of
conditions among which include the choice of precipitants, the protein
concentrations, pH and temperature. The choice of successive experimental
trials is governed by a combination of skill, intuition and chance. Protein
crystallization is at present still an art more than it is a science.

In these empirical trials, suitable conditions for crystallization are
known only after the crystals are formed. Evaluating the efficacy of these
conditions relies on macroscopic observations on which further crystallization
trials are based. Only limited information on the physico-chemical process of
crystallization is obtained from macroscopic observations and results in an
ineficient strategy for finding optimal conditions. These traditional methods
are particularly disadvantaged by the long experimental time periods,

1

2

ranging from days to months, or occasionally years, before the results of the
trials are known. Furthermore, the optimization of conditions once a suitable
precipitant is found is hindered by the lack of active control over the solution
properties which mediate nucleation and subsequent crystal growth. A better
understanding of the interactions occurring between the protein, solvent and
precipitant components is required to achieve a more rational and emcient
search of protein crystal growth conditions.

To expedite the screening and optimization of the protein
crystallization process, methods are required that are able to monitor the
molecular scale interactions occurring during nucleation and subsequent
crystal growth in supersaturated solutions. Measurements of the
microenvironmental properties of fluorescence probes provide a means by
which the dynamic interactions between protein molecules, the solvent and
other additives can be measured prior to the actual appearance of crystals.

The microenvironments of fluorescence probes are strongly influenced
by solution conditions. In turn, the fluorescence lifetimes and rotational
correlation times of these probes are affected by the probe microenvironment.
Hence, measurements of these fluorescence properties are able to provide
information on the solution conditions leading to supersaturation. Time-
resolved techniques allow the direct measurement of the fluorescence
lifetimes and rotational correlation times. Time-correlated single photon
counting is a high resolution method that is often used to measure the time-
dependent fluorescence decays. From these decays, the fluorescence and
rotational parameters can be extracted. In this work, in situ techniques using
the steady-state and time-resolved fluorescence of probe molecules are
developed and demonstrated to be a flexible and sensitive alternative to

current methods.

reviewed. A summary of the techniques used to investigate and screen
protein crystallization conditions then follows. From this background

information, the predominant issues and needs involved in protein

3
The fundamental processes involved in protein crystal growth are first

crystallization are illustrated. Much of the previous work has focused on the

crystallization properties of hen egg-white lysozyme (HEL) and results
concerning this protein will be emphasized in the review. To enable
comparison with the available chemical, structural and crystallization data,
HEL has also been chosen for the current work. The results are presented in

the following studies:

1) The X-ray crystallographic structure of HEL co-crystallized with the

2)

3)

organic anion orange II is examined. The effects of this co-
crystallization agent on the determined structure of HEL itself was
found to be minimal. However, the perturbed crystallization
behavior and the decreased extent of the solvent structure indicate
the participation of orange II in the crystallization process.
Investigations using l-pyrene butyric acid (PBA) as a covalently
bound fluorescence probe demonstrate that the fluorescence
lifetimes of PBA and the rotational correlation times of HEL are
dependent on the crystallization conditions.

Fluorescence measurements of the non-covalently bound probe, 1-
anilino-8-naphthalene sulfonic acid (ANS), are demonstrated to be a
practical method to dynamically monitor protein crystallization
conditions of HEL in situ. The use of this technique for the
optimization of protein crystallization conditions is discussed.

4

4) A comparison of the effects of various ionic precipitants on the
fluorescence behavior of ANS in HEL solutions provides information
on the chemical mechanisms of HEL crystallization and is shown to
be useful for the screening of crystallization conditions.

In summary, methods using fluorescence spectroscopy have been
developed to monitor the interactions of proteins for a more efficient
screening and optimization of protein crystallization conditions. Through
these studies, the mechanisms of HEL crystallization have also been
investigated. These mechanisms most likely involve the neutralization of the
repulsive pOsitive potential on the surface of HEL by anion binding and a
subsequent chemically specific nucleation step mediated by the bound anions.
A combination of physical measurement techniques and chemical knowledge
of protein-solvent and protein-protein interactions promises to be a more
rational and efficient strategy than the traditional methods for the
production of protein crystals.

Background on Protein crystallization

History of Protein Crystal Growth and Crystallography

The history of protein crystallization is replete with serendipitous and
inadvertent discoveries using trial and error approaches for obtaining protein
crystals. This situation has not presently changed, although the need for
more rational and efficient methods is now being realized. A comprehensive
survey of the historical progress of protein crystallization is found in
MacPherson's review [2]. Here, we present a summary of the empirical

progress made in protein crystallization.

5

In the mid to late 1800's, hemoglobin became the first subject for the
systematic study of protein crystallization. By pressing the blood of
earthworms between two glass slides and allowing the liquid to slowly
evaporate, flat plate-like crystals were obtained [3]. The crystallization of
hemoglobin from several other animal species was accomplished by more or
less fortuitous means. Subsequent studies on the crystallization of plant
reserve proteins and albumins produced several procedures for protein
crystallization that are now common. These procedures include temperature
variation, dialysis against solutions of low ionic strength and the use of
organic additives. Another common procedure, salting-out with ammonium
sulfate and magnesium sulfate, originated in the crystallization of hen egg
and horse serum albumins [4].

Efl‘orts to crystallize enzymes made by J .B. Sumner in the early 1900's
demonstrated that enzymes were in fact proteins. Through this work,
Sumner successfully crystallized concavallin A, concavallin B and urease
from the Jack Bean [5]. An illustration of the serendipitous nature of protein
crystallization is seen in Stacey Howell’s accidental crystallization of
canavallin [6]. After leaving a beaker containing a solution of canavallin on
his bench top for a week, Howell returned to find a disagreeable odor along
with rhombohedral crystals growing on the bottom of the beaker. The native
canavallin molecules had apparently been cleaved by bacterial proteases into
products that would crystallize whereas the native canavallin would not. This
ability of proteolytic products to crystallize has since been found to occur with
many other proteins.

Further incentive for progress in understanding protein crystallization
processes was provided by the advent of X-ray crystallography for structural
determination. Until the development of X-ray crystallography, protein

6

crystallization was primarily used for purifying proteins from extracts or
demonstrating the purity of protein preparations [2]. Since the 1930's, the
growth of large single crystals for use in X-ray diffraction studies has largely
supplanted the use of crystallization for separations. Until the 1970's, the
supply of protein crystals was more than adequate for the needs of structural
determination.

However, advances in the methodology and instrumentation of X-ray
crystallography have greatly reduced the effort and time required to solve
protein structures [1]. Recombinant DNA technology now allows the
production of sufficient quantities of protein for study. Synchrotron radiation
sources are able to provide X-ray beams with greater intensities and a wider
range of specific wavelengths to produce clearer diffraction patterns.
Electronic area detectors and automated difi'actometers also allow the rapid
collection of diffraction patterns into digital form. In probably the most
significant advancement, improved computer hardware, algorithms and
graphics allow for the amenable analysis and visualization of difl'raction data.
These advances have resulted in the rapid determination and refinement of
the three-dimensional coordinates of proteins. However, this is the case only
after large and well-ordered protein crystals have been obtained.

Unfortunately, the progress seen in the methodology of X-ray
structural determination has not paralleled progress in the fundamental and
technical aspects of protein crystallization. Hence, the growth of suitable
crystals has become the "bottle-neck" in the determination of protein
structures. Most current efforts to crystallize proteins rely on the same
methods used early in the history of protein crystal growth. That is, by trial
and error methods where hundreds or thousands of experimental trials are

conducted to find the optimal conditions. Investigators have tried many

7

varied means such as subjecting the protein solution to the addition of metal
ions, the addition of polymers, gels, containerless growth cells, and
microgravity environments in space in efforts to grow protein crystals.
Through these empirical macroscopic studies heuristic rules have been
developed but protein crystallization remains a process involving more
intuition and chance than scientific methodology. The situation is such
because an understanding of the fundamental aspects of the association and
aggregation processes in protein crystallization is lacking.

The Crystallization Process

Protein crystallization is a complex process affected by a variety of
interacting parameters in a continuously evolving and non-ideal
multicomponent system. By considering the processes that are common to
protein crystallization, the pertinent parameters and effects can be isolated.
The growth of protein crystals involves three distinct interdependent stages:
1) Nucleation of crystals 2) Post-nucleation crystal growth and 3) Cessation of
crystal growth. Although the theoretical treatment of protein crystallization
is by no means complete, the current views on protein crystallization
processes are presented as a starting point for further investigations. For a
more comprehensive survey of the various aspects of protein crystallization,
reviews are found in Arakawa and Timasheffs theoretical treatment of
protein solubility [7], Feher and Kam's article on nucleation and growth [8],
Boistelle and Astier's article on crystallization mechanisms [9], Mcpherson's
treatment of the general principles [9-11] and Ollis and Whites article from a
more utilitarian viewpoint [12].

Nucleation

A necessary condition for the nucleation and growth of crystals is that
the concentration of protein in the growth solution must be greater than the
solubility concentration. This non-equilibrium supersaturated condition
results in a chemical potential of the protein solute that is greater than at
equilibrium conditions and provides the driving force for phase transition.
The parameter 8 = C/Cs is commonly used to describe the degree of
supersaturation in a protein solution where C; is the solubility concentration
and C is the actual concentration of the protein. With this relationship, the
chemical potential driving force, Au, is,

An = k,Tln(fl) (1.1)

where k; and T are Boltzman's constant and temperature, respectively.

Several means of achieving supersaturation are available which
decrease solubility limit of the protein by changing the solution properties [9,
13]. These methods include 1) the increase or decrease of the temperature,
2) evaporation of the solvent, 3) the addition of other soluble species or 4) a
change of pH. Although these methods are the most commonly used, many
variants to these methods are also seen. Not only is the supersaturation
important in the final quality of the crystals, but also the path taken towards
this state.

Regardless of the specific technique used, once supersaturation is
achieved, this far from equilibrium condition causes the association of protein
molecules. Nucleation occurs as the protein molecules aggregate into a
suitable structural configuration that will continue to grow into protein
crystals. Nucleation theory was first applied to proteins by Feher and Kam

[8] and is now the most commonly accepted view of the initial events in

 

 

 

 

 

 

Criicel
Size

Poctnucieetion
(9" Crystal Growth
<
S
u:
8 mm,
5 ”"°'. P'. '°"’.
u.

Aggregate Size, i

Figure 1.1. Schematic illustration of the processes involved in
nucleation and amorphous precipitation as described by classical
nucleation theory.

protein crystallization. Two possibilities in the tendency towards equilibrium
are the nucleation of crystal growth centers and the formation of amorphous
aggregates.

According to the classical nucleation theory, a distribution of small
aggregates initially forms to produce a state of quasi-equilibrium. To form a
crystal nucleus that continues into post-nucleation growth, the aggregate size
must surmount a free energy barrier formed by two competing fi'ee-energy

terms as illustrated in Figure 1.1,

A0} = -ij, + fij’Gs (1.2)

where G3 is the bulk energy/unit volume and Gs is the energy/unit surface

area relative to the values in solution. 1) is the volume of the molecule and uj
gives the total volume of the aggregate. The total surface area is given by Bj’f,
where B and y depend on the shape of the aggregate. For a spherical

10

aggregate, B=(361m2)1’3 and 7:2/3. The first term on the right hand side
represents the bulk driving force for nucleation and increases as the size of
the nucleus increases. The second term arises as a consequence of dangling
bonds on the surface of the nucleus causing inhibition of further nucleus
growth. This surface energy term increases with an increase in the surface
area of the nucleus. As the nucleus develops through local fluctuations in the
local concentration, the ratio of the surface area to volume decreases allowing
the volume term to dominate.

Under this framework, the mechanism encountered with crystal
nucleation contrasts with the formation of an amorphous precipitate [14].
Amorphous aggregates are assumed to be approximated by a one dimensional
chain of protein molecules where the addition of monomers only occur at the
ends. Because the bulk driving force dominates throughout the range of
aggregate sizes, a small surface free energy term contributes little to the total
fi'ee energy. Hence, no free energy barrier is present and the amorphous
aggregate rapidly forms without the need for a nucleation event as seen in
Figure 1.1. The precise chemical nature of the structural configuration is
unclear at this time, but is crucial to understanding the formation of protein
crystals.

Application of the theory of homogenous vapor phase nucleation to the
batch crystallization of lysozyme leads to a rationalization for conditions
leading to either crystallization or amorphous aggregation. The protein
aggregation process has been described as the successive association and
dissociation of monomers to a growing aggregate, A,, composed of j monomers

by the reaction,

A; +A%AM (1.3)

11

For a crystalline aggregate, the structure of the nucleus is assumed to be a
compact spherical cluster, while for amorphous precipitation, a linear

polymer is formed. The equilibrium constants for the crystalline j-mer is then

given by.
I o
Ki = 33’ = ELL = CXO[-§A€L/kar]
1M qq d; (1.4)

= exp{-{ v0, + yfij"‘G,]/k,T}

where C, is the concentration of the j-mer. Assuming that the aggregate is
spherical so that 7:1/3, K can be expresses in terms of K1 and K»,
«vs

I-i'V’ J
K, = 14%) = LES-J (1.5)
l

From this relation, it is expected that Kaox'rt'W/le'rAL >> 1 under
crystallizing conditions. Under conditions favoring amorphous aggregation, it
is expected that Kj~K1~K.., or KmAMOR/KlAMORd since the free energy does
not depend on the size of the aggregate. It has been suggested that by
measuring K1 and K... for a particular condition, it is possible to predict
whether crystals will grow or an amorphous aggregate will be formed.

By considering the kinetics of the aggregation process, further
information on the time dependence of the nucleation process is obtained.
Results from the numerical calculations indicated that after a relatively short
time period, a quasi-equilibrium is attained where C5 remains constant for j
less than the critical nucleus size of j*. For the crystallizing solution, Cj(t)
must then proceed toward the true equilibrium values. Once a critical

nucleus size is reached, the rate of monomer association becomes equal to the

rate of dissociation. Thus, the growth of the nucleus is governed by a random

12

addition process rather than being driven by a free energy gradient. From
vapor phase nucleation theory, the estimated delay time is then,

1,, ~ (Aj *)’(k;’.)'1 (1.6)

where Aj“ is the number of monomer additions to the critical nucleus needed
for the energy difference to become of the order kBT and the approximate
time of each addition is given by (113.5)‘1. As the protein concentration is
increased, the Aj“ that must be accomplished for the energy difference to
become of the order kBT decreases drastically and nucleation occurs more
readily. For the formation of amorphous aggregates, no time delay should
occur.

There are two principle mechanisms of crystal nucleation. Homogenous
nucleation occurs when nuclei spontaneously form in the bulk phase as
described above. In the case of heterogeneous nucleation, the nuclei form onto
solid substrates such as the walls of the container, a dust particle or a seed
crystal. The degree of supersaturation required to produce homogenous
nucleation is generally greater than with heterogeneous nucleation. This
efi'ect occurs because contact with the solid substrate decreases the surface
area in contact with the solution and subsequently decreases the surface free
energy term. Eventually, a critical nucleus size may be achieved and
depending on random fluctuation events, either the nucleus will continue to
grow into a crystal or dissipate back into a prenucleation cluster.

Crystal Growth

After a nucleus has been formed, the postnucleation growth of protein
crystals continues by the transport of protein to the crystal surface followed
by their ordered incorporation into the crystal lattice. According to the

13
periodic boundary chain theory [15-17], crystal growth can occur at three

different types of faces: 1) flat faces, where growth occurs in a two
dimensional plane, 2) stepped faces, where growth occurs along a linear array
and 3) kinked faces, where growth occurs by the direct incorporation of the
molecule onto the lattice corner. No nucleation mechanism is required for
growth onto kinked faces, whereas a one dimensional nucleation mechanism
is needed for growth onto stepped faces and a two dimensional nucleation
event is required for the flat faces. Consequently, the growth rates of the flat
faces are less than the growth rates of the stepped faces which are, in turn,
less than the growth rates of the kinked faces. Since the kinked and stepped
faces grow at a relatively faster rate than the flat faces, the kinked and
stepped faces eventually disappear and the growth rate of the crystal is
determined by the growth rate of the flat faces.

Two primary mechanisms are involved with the growth of flat faces.
These mechanisms are growth by two dimensional nucleation and growth by
spiral dislocation. With the two dimensional nucleation mechanism,
molecules must diffuse onto the surface of the crystal and become adsorbed.
Once the two dimensional nucleus has formed a large enough layer,
additional molecules can then be incorporated along the edges. More than one
nucleation event can occur so that multiple layers may eventually intersect or
grow on top of one another. The spiral dislocation mechanism occurs when a
screw dislocation appears on the flat face providing a step or a sequence of
steps that can spread from the center. Growth occurs by the lateral growth
from the spiral steps until the crystal edge is reached where upon a new layer
has been added to the crystal face.

14

(110)

Figure 1.2. The morphology of tetragonal HEL crystals. The faces are
labeled as (101) and (110).

 

(101)

 

 

 

 

 

 

 

Most of the theories on protein crystal growth have been derived from
the small molecule crystal growth theories. However, there are important
differences involved with proteins [18]. Because of the larger size and greater
complexity, there are relatively few specific contact sites and more possible
non-specific contact points. The energies per bond are also much lower if the
surface area is taken into account. Several attempts at understanding the
mechanism of HEL crystallization have been made by measuring the growth
of the tetragonal crystal form. The classical form of the HEL crystal used in
many protein crystallization studies is illustrated in Figure 1.2. Growth rate
measurements are made on the 101 and 110 faces which define the
morphology of this crystal.

Fiddis et. al. [19] concluded that tetragonal lysozyme crystals grew by
a mechanism of spontaneous surface nucleation instead of by screw
dislocation. In subsequent growth studies using electron microscopy, Durban
and Feher found that growth by the two dimensional mechanism only occurs
at higher values of supersaturation (> 1% HEL) [20]. At lower protein
supersaturations (<0.8% HEL) growth occurred by a defect mediated
mechanism. These results were in agreement with their studies using visual

15

examination of growth rates where the efi'ect of NaCl concentration was also
investigated [18]. At greater N aCl concentrations, the solubility of HEL
decreases. This lower solubility indicates stronger bonding in the crystals and
thus should predict a greater surface energy. However, the surface energy
was found to decrease as the solubility decreased. Similar results were found
by Forsythe and Pusey [21] with the efl'ect of decreased temperatures. The
reasons for these observations are not clear, but may involve the formation of
preformed aggregates which are directly incorporated into the crystal.
Although crystal growth mechanisms determine the growth rate of the
flat faces, they do not define the actual structure of the crystal. Both internal
and external factors play crucial roles in determining the actual crystal
morphology or habit. Internal factors include the structure of the protein
molecule along with the bonds in the crystal. External factors include the
level of supersaturation and the solution composition including salt
concentration, pH, temperature and impurities in the protein preparation.
For example, HEL may exist in a variety of forms depending on the
crystallization conditions and the composition of the solution [22]. Aside from
the tetragonal form, orthorhombic, monoclinic, and triclinic crystal forms may
also result under different growth conditions. Many of the internal and
external factors may be modified to produce protein crystals of a suitable

morphology and size.

Cessation of Crystal Growth

A problem encountered in obtaining large crystals is the eventual
cessation of protein crystal growth even when the protein concentration is not
depleted. This behavior has been observed experimentally, but the cause is

not well understood. Previous studies have shown that proteins crystals

16

grown under similar conditions reach approximately the same terminal size
depending on the rate of crystal growth [8]. Crystals that were reduced in size
by cutting or dissolving grew again to approximately the same size when
placed in the original growth conditions. Furthermore, impure protein
preparations produce smaller crystals than pure protein solutions. Several
explanations have been given to explain this behavior. The most generally
accepted reason for the cessation of growth is through the poisoning of growth
sites by impurities in solution. Errors would be successively incorporated into
the lattice until growth could no longer occur. However, this would not
explain why a microgravity environment can produce larger crystals. Hence,
convection current in the protein solution should also play a role in causing
cessation of growth [23]. A scenario where both impurities and convection
synergistically contribute has been suggested [20]. Another explanation
involves colloid stability theory, where the electrostatic interface potential
between the crystal and the solution builds up to a point where further
incorporation is inhibited [24]. As with the other aspects of protein
crystallization, a thorough understanding and the ability to control cessation
of growth is as of yet lacln'ng.

intennoiecular Interactions in Protein Association

Further investigations of the forces and dynamics involved in protein
association needs to be accomplished in order to understand and control the
complex processes involved in protein crystallization. By examining the
microscopic aggregation and ordering behavior responsible, a connection with
the macroscopic behavior may be made. This connection is made possible by
modeling the molecular processes involved and relating these processes to the
bulk macroscopic behavior. The extent of the models must be compromised by

17

the limitations of an incomplete theory on the fundamental nature of
intermolecular forces and dynamics, the finite computational resources
available and insufiicient experimental techniques for measuring these
molecular interactions. To begin, the molecular forces involved in protein
association are examined.

Four general types of molecular interactions are responsible for the
structure and function of biological molecules as well as the aggregation
behavior. These are electrostatic forces, dispersion forces, hydrogen bonding
interactions and so called hydrophobic interactions. Together, through the
actions of these forces, the interaction of protein solutes with the aqueous
solvent lead to dynamic association and organization and ultimately, the
macroscopic thermodynamic and kinetic behavior of crystallizing protein
solutions. Protein-solvent interactions balance against protein-protein
interactions to determine whether the protein molecules will remain in
solution, randomly aggregate to form amorphous precipitate or spontaneously
order to form crystals.

The most dominant and long-range interactions are due to electrostatic
forces. These interactions originate from the attraction or repulsion of
charges particles in a particular environment. Actually, all four of the types
of interactions mentioned above are ultimately due to charge effects, but in
the context of protein association, electrostatic forces are considered to arise
only fi'om ionic species. Attempts to model behavior of ions in dilute ionic
solution has lead to some degree of success, although a complete
understanding at higher ionic concentrations is yet to be obtained.

In a salt solution, where the ions are presumably dissociated, a central
ion causes a local polarization in the concentration of ions with opposite

charge so that the concentration of oppositely charged ions is higher near the

canl

3V

18

central ion and decays to the bulk value away from the central ion. The
fundamental relationship between charge density, pr, and electrostatic
potential, w, is given by the Poisson-Boltzmann (PB) equation,

ii 2 9K) — _4_” 1 7

r2 dr (r dr 8 p, ( . )
given here for a spherically symmetric geometry, where r is the distance from
a central ion and sis the dielectric permittivity of the solvent. By solving the
linearized form of the PB equation with the assumption that the charge
polarization caused by a central reference ion can be approximated with an
average charge distribution profile, the first successful model of ionic

behavior in solutions was arrived at with the Debye-Huckel equation,

logf. = -%§f)ztl: (1.8)

where f: is the activity coefficient of the ion, 2+ and z- are the respective

positive and negative valences of an ionic salt, I is the ionic strength given by,

= ézqz} (1.9)

and A and B are constants. The finite size of an ion is taken into account with
the parameter a, representing the radius of the central ion. This equation
provides an adequate theoretical description for dilute solutions of ions but at
higher concentrations the theory fails.

An examination of the effects of salt concentration on the experimental
solubility of protein solution may provides an explanation as to why the
simple treatment is inadequate. In general, the solubility of proteins is
enhanced with low salt concentrations. This behavior is termed salting-in and
can be explained by treating the protein as a charged species with the Debye-

19

Hiickel theory. The ionic atmosphere surrounding the protein decreases the
electrostatic free energy causing an increase in the solubility. As the salt
concentration is increased, however, a point is reached where the solubility
begins to decrease [25]. The solubility of proteins in this regime can be
described by modifying the Debye-Hiickel equation,

log%=%%-K,I (1.10)
The salting-out behavior with higher salt concentrations is due to two efi'ects
[7]. First, the addition of salt ions to aqueous solutions causes the formation
of hydration sheaths of ordered water molecules around the ions. This
binding of water molecules by the salt ions decreases the amount of water
available for the primary solvation of the protein molecules. The second effect
is due to the secondary solvation of the protein molecules [26]. The
replacement of water molecules by a protein solute of lower dielectric
constant causes an effective decrease in the orientational polarizability of the
solvent that leads to a repulsion of the salt ions. Consequently, an increase in
the free energy causes a decreased solubility of the protein.

London dispersion or Van Der Waals interactions cause a short range
attraction between protein molecules. While electrostatic forces are caused by
discrete charged species, dispersion forces arise from fluctuations in the
electron densities within molecules and can be termed electrodynamic.
Dispersion forces arise when an instantaneous fluctuation in the electron
density of one molecule forms an dipole moment. This dipole moment induces
the formation of an instantaneous dipole moment in another molecule. The
dipole moments of the two molecules become correlated and lead to an overall
attractive force. Dispersion forces vary with the distance, r, between two

20

molecules as r6. At very close distances, the electronic densities of the
molecules overlap and repulsion occurs. At greater distances, the phases of
the electromagnetic field propagating between dipoles become out of phase
and causes a retardation efi'ect so that the dispersion forces vary with r7.
Although dispersion forces are small for small molecules, the strength of
dispersion interactions become significant in the case of macromolecules.

In aqueous solutions, hydrogen bonding and hydrophobic interactions
become significant. The resemblance of the average structure of water to a
diamond lattice results from the intermolecular hydrogen bonding between
water molecules. Intramolecular and intermolecular bonds within proteins
are also determined by direct hydrogen bonding. Hydrogen bonding forces
arise fi'om the interactions between the permanent dipole moments of polar
molecules. Because of this geometric constraint, hydrogen bonds are
dependent on the orientation of the dipoles, the strongest interaction
occurring with a linear alignment of the dipoles. Generally, the optimal
distances occur at around 3 A with an energy between -3 and -6 kcal/mol.

Hydrophobic interactions are an indirect result of hydrogen bonding.
Although not completely understood, these interactions between nonpolar
molecules are entropic in origin and are a consequence of the structuring of
water around a nonpolar molecule. Aggregation of nonpolar molecules cause a
relative increase in the entropy of water because of the greater number of
microstates that unstructured water molecules possess. The hydrophobic
interaction is involved in protein folding, the specific association of
multimeric proteins and also the nonspecific crystallization and precipitation
behavior of proteins.

Protein molecules, with sizes larger than 1 nm in diameter, may be
regarded as colloidal particles. Hence, colloid stability theory may be applied

21

to protein associations [24, 27 , 28] by approximating globular proteins as
lyophobic particles or sols. According to this model, whether protein
molecules will remain in solution as a stable suspension or will aggregate
depends on a balance between the repulsive electrostatic forces and the
attractive dispersion forces. The theoretical treatment was developed
independently by Derjaguin and Landau and by Verwey and Overbeek and is
known as the DLVO theory.

In the DLVO theory, the electrostatic interaction of charged colloid
particles is due to a diffuse double layer of opposite charge surrounding the
particle [29]. For two spheres of equal radius, a, at a center to center
distance, r, the potential energy due to electrostatic repulsion , Ur(r), is given

U,(r) = 27t£avlfi ln[l + cxp(-xx)] (1.11)

where W0 is the surface potential of the particle and s=r-2a. Dispersion forces
are responsible for the attractive interactions. The potential energy due to the
dispersion interactions may be approximated by the expression

- -fl
U.(r) - 125 (1.12)

where A is known as the Hamaker constant, which is dependent on the
material of the particles.

Three distinct cases are possible: 1) At low salt concentrations, a
primary potential energy minimum is present at the surface of the particle
with a large potential barrier gradually decreasing away fi-om the particle. In
this case, the particles repel each other and can not aggregate. 2) At
intermediate ionic strengths, a secondary minimum is present with a smaller

potential energy barrier. The particles may more easily approach each other

22

to the distance of the secondary potential energy well. 3) At high ionic
strengths, the potential energy barrier is nonexistent and aggregation occurs
rapidly. In addition to changing the ionic strength, the behavior of aqueous
colloid dispersions may be manipulated by altering the dielectric constant by
mixing other solvents such as ethanol and by altering surface charge with the
binding of charged species or changing the pH.

In analogy with protein solutions, these three cases correspond to l) a
stable protein solution, 2) a metastable protein solution and 3) amorphous
precipitation of the protein. For the second case, the secondary potential well
may allow interacting protein molecules to orient in a more favorable position
for crystallization to proceed [28]. A configuration may be achieved where a
collection of protein molecules are held together in the secondary potential
well. Nucleation may occur as the favorably oriented particles in the
collection collapses into the primary well.

This model of protein crystallization is most likely an
oversimplification of the actual process. The structure of proteins are not well
described as simple spherical objects with a uniformly charged surface.
Protein surfaces are rough, with crevices and convolutions. The dynamic
structural fluctuations observed in proteins also affect crystallization
behavior. Charged amino acids and other polar groups are distributed non-
uniformly and interact with one depending on the stereospecificty and
chemical properties. Proteins are composed of flexible structural domains
with segments that are mobile and loose. For example, the structure of
lysozyme can be approximated with two lobes that bend at a hinge [30]. Even
this model oversimplifies the reality. The molecular forces that drive protein
association must be coupled with the dynamic aspects of protein polypeptide
chains in order to achieve a complete physical picture.

23

Protein crystallization must involve the interaction of the different
processes examined above. Electrostatic forces are long range interactions
that may enhance or decrease the solubility of proteins. In the colloid picture
of particle interactions, electrostatic forces only cause a repulsion between
protein particles. Dispersion forces, on the other hand, result in an attractive
interaction between protein particles. The structuring of water by hydrogen
bonding is exerted indirectly through hydrophobic interactions. Hydrogen
bonding also occur between protein molecules and with the solvent
constituents. All of these more fundamental structural and chemical
mechanisms are coupled with the dynamic motions of proteins to determine
whether crystals can be produced. At this time, theoretical and computational
limitations preclude the prediction of the crystallization behavior of proteins.
Hence, a mechanistic understanding of nucleation, crystal growth and
cessation of growth lies in the domain of experimental methods.

Chapter 2

Current Experimental Techniques for
Investigations on Protein Crystallization

Introduction

Since the realization that a trial and error approach to the
crystallization of proteins has proven to be inadequate, there has been an
impetus towards developing improved techniques and a deeper
understanding of this process. Many of these studies have been geared
towards the development of assays to predict whether given crystallization
conditions will promote favorable crystal growth. Some workers have
investigated methods to predict crystallization conditions, while others have
focused on a more fundamental understanding of the processes involved. All
of these approaches require techniques to probe or deduce the interactions of
proteins in the solution phase. In this chapter, the methods used for
screening, characterizing and measuring aggregation behavior are reviewed
along with a presentation of selected results obtained by previous studies.
Macroscopic measurements of protein and solute concentrations and
thermodynamics have provided information on the solubility and solute
behavior of crystallizing protein solutions.

Spectroscopic methods, including light scattering and fluorescence,
provide a microscopic view of the solution behavior of interacting proteins.
Such methods provide details on the space and time scales that are not
accessible to traditional macroscopic techniques and are thus valuable in

understanding the mechanisms of protein crystal growth. Light scattering

24

25

has been extensively used to monitor and characterize the protein
crystallization process. However, this method is inherently limited in its
specificity and sensitivity. In contrast, fluorescence spectroscopy is a highly
sensitive technique that is able monitor the behavior of specific components
in solution. More recently, investigations have used electron microscopy and
scanning microscope techniques to investigate the surface [20, 31, 32] and
internal properties in protein crystals. X-ray crystallography also provides
means by which the specific interactions between protein molecules and the
associated solvent shell including other solutes may be visualized. The
principles of the macroscopic, light scattering and, in the following chapter,
fluorescence methods are presented along with applications pertinent to

protein crystallization.

Macroscopic Methods

The screening, characterization and analysis of protein crystallization
processes has overwhelmingly relied on macroscopic measurements. These
traditional methods use the visual inspection of crystal growth to screen a
wide array of experimental conditions in the hopes that some form of crystals
will result. In the event that crystals are obtained, successive trials are
conducted to progressively narrow the range of conditions needed to optimize
the crystal growth properties. However, many important proteins still may
not form well ordered crystals under the screened conditions and the
structural determination is subsequently abandoned. This situation makes
the development of techniques able to crystallize such proteins crucial and
demonstrates the importance of understanding the mechanisms involved in
protein crystal growth.

26

Sealed cover glass

Drop containing
Protein + Diluted Reservoir
Solutions

Solvent evaporation
from drop to Reservoir

Reservoir
Well

 

Figure 2.1. Schematic diagram of vapor diffusion trial. Typically
a 4x6 grid of these trials are performed in one tray.

The hanging drop method, as illustrated in Figure 2.1, is by far the
most common technique used to grow crystals because of the gradual
attainment of supersaturation. This method involves a combination of solvent
evaporation and the addition of a soluble precipitant. A hanging drop
containing the protein and diluted reservoir solution is suspended above the
reservoir well which contains a higher concentration of the precipitant. In
this way, the water in the drop and in the reservoir will equilibrate by vapor
diffusion. Consequently, the protein and precipitant concentrations in the
drop will gradually increase to create supersaturating conditions. The soluble
precipitant is usually a salt such as ammonium sulfate, but polymers such as
polyethylene glycol (PEG) and organic solvents such as methanol or 2-methyl-
2,4-pentanediol (MPD) are often used. Variants to the hanging drop method
include dialysis, gel growth and the use of controlled evaporation.

The traditional methods for the screening of crystal growth conditions
has been classified into two groups. The so called “brute force” technique
relies on the assumption that if enough combinations of parameters are

tested, crystals will eventually result [33]. The use of robotics is particularly

27

amenable to this strategy. Although many crystals have been obtained using
this method, the primary disadvantage is the large amounts of protein which
must be consumed. For the 20 independent variables that may affect the
crystallization behavior, 106 different conditions are possible if only two
difi'erent values are assumed for each variable [8]. This technique has also
been criticized in that the value of human intelligence and skill is minimized.
The other traditional approach, which has gained wide acceptance, is
the “multiple factorial” [34] method. This procedure involves screening a set
of conditions which have been successful in crystallizing other proteins. For
the purpose of choosing conditions, a Biological Macromolecule
Crystallization Database is available for more than 1000 crystal forms and
over 600 macromolecules [35]. The selected conditions represent a statistical
sampling of precipitants, buffers and the other parameters known to afi'ect
crystallization. Because of the randomness associated with this technique, it
has also been termed the “shotgun” approach. A major disadvantage of this
method lies in the difficulty of interpreting the outcomes. If no crystals result,
the trials do not provide adequate physico-chemical information for a further
choice of conditions. Proteins preparations are diverse in their crystallization
behavior, even among those that appear to be closely related. It is likely that
the small subset of possible conditions used in the statistical screening
methods will not lead to the crystallization of some or possibly most proteins.
Because of the complexity of the protein crystallization process, it is
unlikely that the empirical screening approach will be completely supplanted.
However, knowledge of the efi'ects of the physical and chemical properties of
the protein and the interactions with the precipitants and solutions on
crystallization behavior will be helpful in choosing proper experimental

conditions. For example, it is generally conceded that hydrophobic

28

 

PPT.

HEL (mg/ml)
{3

 

 

fiUndersaturated
o .-,.s-,...

o 2 4
%NaC|

 

 

O-n
d
D
d
0

Figure 2.2. Schematic illustration of the crystallization behavior
for HEL. The data points are measured solubility data at pH 4.6,
25° C [36]. The line through the points represent the solubility
limit. Above this is a metastable zone where nucleation does not
occur. In the X region, crystallization occurs. Above this region,
immediate precipitation is observed. (Adapted from reference

[8])

interactions are non-specific, while hydrogen bonding and electrostatic
interactions require specific complementary. If the surface interaction
properties of the proteins can be characterized, the choice of possible
conditions may be reduced. Macroscopic methods have played an important
role in characterizing some of the interactions involved in protein
crystallization.

The crystallization of hen egg-white lysozyme (HEL) by sodium
chloride illustrates the progress made by macroscopic measurements and
observations. The primary means of characterizing the behavior of protein
solutions is the phase diagram as illustrated in Figure 2.2. The solubility
relationships for tetragonal HEL in sodium chloride solutions has been
determined [36]. From direct observations of batch HEL solutions, the protein

association behavior ranges from immediate precipitation within seconds at

29

high supersaturation to the formation of well ordered crystals within hours
near the metastable limit to a completely stable solution at low levels of
supersaturation.

Using solubility measurements, direct ion pairing has been found to
play an important role in the crystallization of HEL. The crystallization of the
basic proteins HEL and erabutoxin b did not show behavior that was
characteristic of salting out when thiocyanate and other organic anions were
used as the precipitants [37]. In fact, the effectiveness of salts for
crystallizing HEL was found to follow the reverse order of the lyotropic (or
Hofineister) series. This result may be an indication that crystallization and
amorphous precipitation proceed by different mechanisms. At pH 4.5,
histidine, lysine, arginine and terminal amino groups are generally
protonated to give basic proteins a positive charge [38, 39]. Presumably, the
positive charges on the protein were neutralized by the negatively charged
precipitants thereby decreasing the protein solubility. Subsequent data
showed that the binding of Cl' is highly exothermic [40]. The ensuing protein
aggregation involved the release of 01' into the solution with a lower rate of
heat release. Such results show the significance of anion binding in the
crystallization of HEL.

Recently, the use of ligands for the co-crystallization of proteins have
resulted in an improvement in crystal growth techniques. Studies on the use
of organic anions to induce the precipitation of HEL show a strong
electrostatic binding of these ligands to HEL [41]. This binding was also
accompanied by heat production and resulted in the co-crystallization of HEL
with the ligands. Many examples illustrate the use of small organic ligands to
facilitate the crystallization of proteins [11]. These include the use of phenol
for the crystallization of insulin [42] and thymol for the crystallization of

30

chymotrypsin [43]. An example that not only illustrates the use of
macromolecular ligand binding for crystallization, but also underscores the
importance of understanding protein crystallization processes, is seen in the
crystallization of the reverse transcriptase protein from the human
immunodeficiency virus (HIV- 1) [44]. Attempts to crystallize the homogenous
protein with salts had only yielded crystals that diffracted to 9 A resolution.
Upon the introduction of oligonucleotide ligands, crystals diffracting to 2.6 A
could be obtained. Another interesting use of ligands, involves the
co-crystallization of the glycoprotein tissue factor with the Fab fi'agment from
immunoglobins [45, 46]. With this method, crystals were obtained that
diffracted to about 2.0 A resolution.

From such studies, it is possible to postulate the mechanisms
responsible for ligand induced crystal growth [41]. The conformational
mobility of many proteins leads to a high water content both in the protein
and in crystals, resulting in their inability to form high quality crystals.
Ligands may act to reduce the repulsive forces between protein particles,
provide contact points as well as tighten the conformation of proteins.
Additionally, ligands may become incorporated into the crystal, forming a
scaffolding to further reduce mobility.

Macroscopic methods have long been the primary technique for the
analysis of protein crystallization trials and experiments. Although many
important results have been obtained using these methods, the macroscopic
viewpoint is only able to detect the bulk properties of the solution and provide
subjective visual observations of the outcomes of crystallization trials.
Because of these limitations, the causative microscopic and molecular

processes responsible for protein crystallization and aggregation can only be

31

inferred. Thus, other techniques better suited to investigating the small scale
structure and interaction are required

Static Light Scattering

Of the methods used to investigate the microscopic solution behavior
involved in the crystallization of proteins, light scattering has been the most
common. Through the use of light scattering techniques, information on the
molecular weight, aggregate size and polydispersity may be obtained. Static
light scattering measures the intensity of light scattered fi‘om a population of
particles as detected at an angle from the incident beam [47]. Dynamic light
scattering (DLS), also known as photon correlation spectroscopy or quasi-
elastic light scattering, measures the molecular motions due to thermal
fluctuations. Both techniques have been widely used to investigate protein-
protein interactions and predict conditions that are favorable for protein
crystallization.

Although static light scattering is commonly used to measure the
molecular weight of non-interacting macromolecules, this technique has had
some successes for the study of interacting particles. For protein
crystallization the molecular interactions at high protein concentrations can
not be neglected and other analyses must be used. By comparing the relative
intensity of scattered light fi'om crystallizing HEL solutions, Pusey was able
to estimate the equilibrium constants for the formation of dimers and
tetramers [48]. The concentration of monomers, dimers and tetramers could
then be estimated as a function of the total protein concentration.

It was found that the monomer and dimer concentrations eventually
reached a constant value while the tetramer concentration continued to

increase as the total protein concentration increased. Comparison of the

32

aggregate concentration profiles with the crystal face growth rate showed
that the constant monomer and dimer concentrations did not correlate with
the increasing crystal face growth rate. This result suggested that HEL
crystal growth proceeds by the addition of pre-formed tetrameric or higher
aggregates rather than by the addition of monomers or dimers. Although the
simplifying assumptions made in this study limited the amount of
information that could be obtained, it demonstrated the importance of the
solution behavior not only on nucleation, but also the crystal growth process.

Dynamic Light Scattering

DLS is able to detect the brownian motion of particles in solution by
measuring the time dependent fluctuations of the scattered light intensity
[49]. These fluctuations are analyzed by using the autocorrelation function,

 

G20). given by.
(I(q.t + r)I(q.t))
G r = ' 2.1
2( ) (101.0)? ( )
In its generalized form, G2(t) can be expressed as,
02(1) = A + b[<;,(z)]2 (2.2)

where A is the baseline, b is an instrument constant which depends on the
geometry of the optics and G1(r) is the first order autocorrelation function.
For a polydisperse mixture of N aggregates or particle sizes, G1(t) is a sum of
exponential terms given by,

N
G,(r)=2a,exp(-q’p,r) (2.3)

ill

33

where ai is the contribution from species i and Di is the translational
difl'usion coeficient of species i. The hydrodynamic radius of species i, Rm, is
often expressed in terms of the Di by the Stokes equation,

Ru = Fig-E (2.4)
where k}; is the Boltzmann constant, T is the temperature and 11 is the
hydrodynamic viscosity. From these relations, it is possible to obtain the
particle size distribution in a solution provided that the individual decay
components can be extracted from the experimentally measured
autocorrelation function.

The use of DLS in the study of protein crystallization and aggregation
has become widespread. Studies begun in the late 1970’s first offered a
kinetic explanation of how equilibrium constants of association influenced
whether the outcome of a crystallization trial would result in crystal growth
or amorphous aggregation. Subsequent studies have investigated the use of
DLS as a diagnostic method for predicting the outcome of particular
crystallization conditions. Recently, the focus has shifted to the goal of
obtaining a deeper understanding of the molecular interactions involved in
crystallization. The progression fi'om early findings to the current state is
outlined here.

The pioneering work of Kam, Shore and Feher laid the groundwork for
the use of DLS in further studies of protein crystallization [14]. Using
classical nucleation theory, as outlined in chapter 1, to study the
prenucleation behavior of HEL solutions, they rationalized the formation of
crystalline and amorphous aggregates under different conditions. 5% (w/v)
sodium chloride was used as the precipitant in the solutions promoting the
growth of tetragonal crystals, while 30% (w/v) ammonium sulfate was used

34

for the formation of amorphous aggregates. Conditions were at pH=4.2 and a
temperature of 20°C. Values of the equilibrium constants for the addition of a
monomer to another monomer, K1, and for addition to large aggregates, Koo,
were determined using dynamic light scattering for both conditions [50].

For the case of crystallization, it was found that K1-0.065 (% w/v)'1,
K..-2.3 (% w/v)'1 and K../ K1~35. For amorphous precipitation,
K1~0.5 (% w/v)'1, Koo~7.5 (% w/v)‘1 and K.JK1~1.5. These results are
consistent with the theoretical model that KJKpl for crystallization and
KoJKr-l for amorphous precipitation. However, this simple model may not
completely describe crystallization behavior, as the conditions that were
compared could be considered to be limited. In experiments with
phosphoglucomutase, both crystallizing conditions using polyethylene glycol
400 and amorphous precipitating conditions using ammonium sulfate gave
KoJK1~30 [50].

Several subsequent studies have examined the use of DLS as an
general diagnostic method for predicting whether a particular solution would
form crystals. Mikol, et. al. applied DLS to investigate the crystallization of
aminoacyl-tRNA synthetase [51]. The average diffusion coefficient was
measured and by the Stokes-Einstein equation the apparent hydrodynamic
radius, Rh, was calculated. Interactions between protein molecules that were
detected before reaching saturation were indicative that conditions were not
favorable for crystallization. Similar results were reported with HEL and jack
bean concanavalin A. It was concluded that a monodisperse distribution is a
necessary but not sufficient condition for crystal growth. Other studies by
Kadima, et. al. comparing the aggregation behavior of insan [52] and
canavalin [53] showed similar results.

35

More recent uses of DLS as a diagnostic of protein crystallization have
refined the data analysis procedures. Zulaf and D'Arcy used the obtained
particle size distributions for the aggregation behavior of 15 difl‘erent proteins
[54]. In all cases where narrow unimodal (monodisperse) distributions were
observed, crystals resulted, while in no cases where more complicated
multimodal distributions were observed did crystals grow. Thibault, et. al.
used DLS to measure the particle size distributions for the crystallization of
several aminoacyl-tRNA synthetases. Two effects were observed in
amorphously aggregating systems as the precipitant concentrations
increased: A) an increase in the scattering intensity corresponding to large
aggregates and B) a shift in the monomer peak. Under conditions where
either efi‘ect A or B occurred crystallization was not observed.

Subsequent studies have focused on the use of DLS to follow the
dynamics of nucleation in an effort to diagnose whether conditions are
favorable for crystallization. Mikol, et. al. used DLS to follow the
crystallization of HEL [55]. In this case, nucleation was achieved by lowering
the temperature of the solution. As crystallization proceeded, the apparent
hydrodynamic radius, Rhflpp, increased from ~22A to a maximum value of
~33A and then decreased as tetragonal crystals became visible. The variance
of the measurements remained small indicating that the distribution of
aggregate sizes was fairly monodisperse. These results did not reveal the
presence of a measurable number of large critical nuclei. Thus, it was
suggested that protein crystal growth occurs by the addition of either
monomers or small aggregates.

Another study using DLS with the cumulant method of analysis also
followed the course of HEL crystallization, but instead, the results were
interpreted in terms of the measured friction factor [56]. In this case,

36

supersaturation was achieved by using sodium chloride as the precipitant.
The increase in the friction factor from undersaturated solutions to
supersaturated solutions was attributed to an increase in molecular
interactions rather than the presence of large aggregates.

Skouri, et. al. have investigated DLS from HEL solutions for conditions
that favor crystallization and amorphous aggregation [57]. The
intermolecular interactions were found to be greater in undersaturated
solutions of ammonium sulfate as compared to undersaturated solutions of
sodium chloride. Again, ammonium sulfate was used as the solution favoring
amorphous aggregation and sodium chloride as the solution favoring
crystallization. A temperature quenching of HEL solutions containing sodium
chloride showed a bimodal distribution. The fast relaxation mode was
attributed to the monomer, while the slow relaxation mode was attributed to
the presence of aggregates with a radius of about 260 nm. The time evolution
of the modes indicated a slow growth in the aggregates whereas the monomer
concentration remained constant over a long period of time.

In other studies by Georgalis, et. al., a bimodal distribution was also
observed for crystallizing conditions with sodium chloride and for
precipitating conditions with ammonium sulfate [58, 59]. The slow relaxation
mode was attributed to the growth of a fractal aggregates while the fast
relaxation mode was attributed to the presence of the monomer. These
aggregates were classified as either CRAGGS (precrystalline aggregates) or
PRAGGS (Precipitating aggregates) [60]. The CRAGGS exhibited a fi'actal
dimension close to that expected for diffusion limited cluster aggregation. A
maximum in R}. was also observed as the concentration of sodium chloride

increased.

37

Malkin and Mcpherson applied DLS to the investigation of aggregates
of satellite tobacco mosaic virus (STMV), ferritin, apoferritin and pumpkin
seed globulin [61]. Under conditions favoring crystallization, there were no
observed increases in R}, during an initial induction period. After this period,
a sharp increase in the aggregate sizes up to um R}, values were observed. In
the case of amorphous precipitation, a slow increase in R}, of the aggregates
took place followed by a sharp increase to um sizes.

Sazaki, et. al. combined DLS with scanning electron microscopy (SEM)
in their studies on the crystallization of thermolysin [62]. A linear increase in
the average size of the aggregates was observed using DLS as the
crystallization progressed. The size distribution showed three peaks at 3-
6 nm, 100 nm, and >500 nm diameter. From the SEM images, crystalline
precipitates were found to be composed of small spherical particles that
roughly corresponded to the size of the 100 nm peak. They proposed a
mechanism for thermolysin growth which proceeded through the initial
formation of primary particles of 15-200 nm diameter. This is followed by
crystal growth occurring through the attachment of the primary particles.

To summarize, the DLS results have shown that there are typically
two or more peaks in the size distribution of supersaturated solutions. The
diameter corresponding to the largest sized peaks increases as time
progresses. There is also some evidence that the aggregation pathways
leading to amorphous precipitation are different than those leading to
amorphous precipitation. However, this evidence is not conclusive. Further
data is required to determine the properties of the interacting proteins and
the structures that are formed during nucleation and crystal growth.
Although DLS has provided a large amount of data concerning protein
crystallization, this technique is becoming limited with respect to

38

characterizing the chemical features involved in solutions of associating
proteins.

A more complete physico—chemical description of protein crystal growth
is required to explain the behavior of supersaturated solutions. The most
compelling limitations for the practical implementation of DLS are the low
sensitivity, low specificity and inflexibility of this technique for
measurements of a range of protein interactions under crystallization
conditions. Because the primary transport property measured by DLS is the
bulk translational diffusion, changes in protein dynamics due to molecular
scale interactions with protein and solvent molecules may not be adequately
resolved. Although measurements of rotational motions may be much more
sensitive to such interactions, DLS is not generally suitable for such
measurements [63]. A lack of specificity is another characterizing feature of
DLS that is due to the nature of measuring bulk fluctuations of optical
inhomogeneities. These effects are manifested in the undesired scattering of
light from sources such as reflections, convection currents, large particles and
scattering from the solvent itself [64]. Although some of these effects may be
ameliorated by careful sample preparation, interference from the solvent and
other constituents represents the most severe limitation to protein
crystallization applications.

The solutions used for protein crystallization contain a complex and
concentrated mixture of interacting protein, precipitant and buffer agents
that may confound DLS measurements [65]. Crystallization trials typically
contain additives, including high concentrations of inorganic salts or organic
precipitants, high molecular weight polymers, such as polyethylene glycol,
and detergents in the case of membrane and otherwise hydrophobic proteins,

that may interfere with DLS measurements. Furthermore, the appearance of

39

crystals, precipitates and other sources of turbidity intrinsic to the process of
protein crystallization may give rise to multiply scattered light [59]. The
feasibility of monitoring and controlling protein crystal growth techniques
depends on the development of other methods that are able to circumvent the
practical limitations of DLS. Steady-state fluorescence and time-resolved
fluorescence (TRF) spectroscopy provide techniques that are able to
supplement or supplant current techniques in the ability to measure a wider
range of protein interaction parameters with molecular scale sensitivity and

resolution.

Chapter 3

Fluorescence Techniques for Investigations on
Protein Crystallization

introduction

The methodology and techniques associated with fluorescence
spectroscopy have now been developing for over thirty years and is in wide
use for investigating a diverse variety of phenomena including protein
conformation and dynamics, lipid membrane dynamics, polymer dynamics
and salvation interactions [66-77]. Fluorescence methods are able to probe
many aspects of biophysical systems including the structure and dynamics of
the interactions seen in protein crystallization. However, it is surprising that
a technique like fluorescence that is well suited to the study of molecular
behavior in solutions has been applied to such a limited extent for the study
of protein crystallization. In this section, the aspects of protein crystallization
behavior that can be determined using fluorescence spectroscopy will be
examined.

Information on the local environmental, structural and dynamic
influences acting on a fluorescent probe is obtained through the use of
fluorescence spectroscopy. For the study of protein dynamics, the fluorescent
probe may be an intrinsic chromophore, such as the amino acids tryptophan,
tyrosine and phenylalanine, incorporated in the native structure of the
protein itself. Alternatively, it may be associated covalently or non-covalently
by conjugating an extrinsic fluorophore to the protein. A wide variety of

40

41

extrinsic probes are available and the particular choice that is used depends
on matching the probe properties to the specific application.

The microenvironment in which the probe is located also exerts its
influence on the fluorescence behavior. For example, the polarity of the
solvent and collisional quenchers in solution influences the fluorescence
behavior of the probe. The efi‘ects of difi'erent probe environments may then
be interpreted in terms of solvent accessibility. Additionally, the rotational
motion of the fluorophore influences the relative intensities of the vertically
and horizontally polarized emission. By conjugating the probe to protein
molecules, the rotational dynamics of the probe are influenced by the
rotational motions of the protein and its interactions. It is evident that
fluorescence methods can provide a wealth of structural and dynamic
information pertinent to protein crystallization.

Although steady-state fluorescence measurements are able to provide
some information on the probe environment and dynamics, time-resolved
fluorescence techniques are able to more directly quantify the relevant
parameters. Complicating experimental factors due to contaminating
emissions, temperature and viscosity variations can be more directly
separated from the physical effects of interest. With time-resolved
fluorescence techniques, the decay profile of the probe is measured and the
extracted decay lifetimes related to photophysical processes. Similarly, the
time dependent difl'erence of the vertical and horizontal polarization results
in the rotational correlation times of the probe. In the case of heterogeneous
samples, multiple lifetimes and rotational correlation times may be obtained.

Here, the theoretical and experimental aspects of measuring
fluorescence lifetimes and rotational correlation times are discussed. It will

be demonstrated how time-resolved fluorescence spectroscopy can be used to

42

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

S 1 k: Vibrational
M L Relaxation
kl.
M T‘
w
c (
.g 1
g r r
m
a
<
Phosphaeecence
F
S. )-—-5—
Vibrational
___ 1 1 1 L Relaxation

 

 

 

 

 

 

Figure 3.1. Photochemical processes in fluorescence

spectroscopy.

obtain information on dynamic protein crystallization behavior on the
nanometer length and nanosecond time scales. The structural and

spectroscopic properties of hen egg white lysozyme (HEL) are also reviewed.

Fluorescence and Anisotropy Processes

The initial event in the fluorescence process is the electronic excitation
of a fluorophore caused by the absorption of a photon. Following this event, a
relaxation occurs back to the ground state through spontaneous emission and
other nonradiative pathways. The photon absorption event occurs on the time
scale of femtoseconds. It is too rapid to permit the observation of the
dynamics occurring with protein interactions. Fluorescence, however, occurs
on time scales ranging from picoseconds to hundreds of nanoseconds. Because
of the slower time scales, it is possible to follow the dynamics of protein
interactions. The process of fluorescence is illustramd in Figure 3. 1, where So

43

and S, are the ground singlet state and exciwd singlet state, respectively, and
no and n, are the populations in these states. In the absence of nonradiative
relaxation pathways, the rate of depopulation of level S, is given by,

21:- (3.1)
d, AM.

where A10 is the Einstein coeficient for spontaneous emission. The intrinsic
fluorescence lifetime, 13, and the intrinsic fluorescence rate constant, kg, of

the excited state, $1, is related to the Einstein coeficient by,

tn = kl = -1— (3.2)

However, the processes of internal conversion, intersystem crossing and a
number of excitation quenching mechanisms contribute to a decrease in the
actual observed fluorescence lifetime.

These nonradiative processes can be useful in characterizing the efi'ects
of the probe microenvironment in biophysical systems. The rate constant for
internal conversion, kic, depends upon the dissipation of excitation energy
through solvent collisions or internal vibrations. Intersystem crossing at a
rate of kis, occurs when the electron converts fi'om the excited singlet state,
81, to the excited triplet state, T1. Phosphorescence fi'om T1 to So can then
occur with extremely long lifetimes. However, phosphorescence is rarely
observed under the conditions used in biological studies because of the
competition by internal conversion or quenching. Quenching processes result
fi'om collisions or energy transfer interactions with other molecular species in
solution. In the case of collisional quenching, difl'usion of quenchers results in
a bimolecular deoexcitation reaction with a rate constant, kq(Q). Together,

44

these processes influence the total depopulation rate, kp, from energy level 51
to define the observed fluorescence lifetime, ‘tp,

 

tr = —1— = l (3.3)
k, k, +lcin +k, +k,(Q)

The total rate for the depopulation of state SI, is given by,
£131. = -1; (3.4)
d! r”:
Solving this difi'erential equation gives the expression for the time
dependent population of 8,,
n, (t) = n, (0) exp(-r/ 7,.) (3.5)

where n1(0) is the initial population of 81. For an infinitely short excitation
pulse, the intensity of light emitted at time, t, is proportional to the rate of
depopulation from 81 and the fraction of depopulation of S1 due to

fluorescence, op,

I..(t)~=¢.%=(n.(0)/r.)cxp(-r/r.) we)

where,
W” = fir/7r 63-”

In the case where a mixture of fluorescent components is present in the
sample, the time dependent fluorescence intensity following an impulse

excitation is given by [73],

I..(r) = ZAmXM-t/n) (38>

45

  
 

1+1 LaserExcitation ’

Hi

 

Fluorescence
Emission

Figure 3.2. Photoselection in fluorescence anisotropy. The
arrows in the box represent the absorption dipole moments of
the fluorescent probes. Bold arrows indicate that absorption
occurs.

where p is the total number of components, Ag, the pre-exponential factor, is
proportional to the concentration of component k and If is its fluorescence
lifetime.

The rotational motions of the fluorophores in solution can be detected
by using a linearly polarized excitation source as shown in Figure 3.2 [47].
Through a process of photoselection, a population of fluorescent probes with
their absorption dipole moments oriented in the direction of polarization is
preferentially excited. The probability of photon absorption is proportional to
cos2 0, where 0 is the angle between the absorption dipole moment and the
axis of polarization. Because of the anisotropic orientations of the excited
probes, the orientation of the fluorescence emission will also be anisotropic.
The time dependent vertically, Iw(t), and horizontally, Ivh(t), polarized
emission intensifies from a vertically polarized excitation source defines the

fluorescence anisotropy [78],

1110‘

ml

Wh

[0U

Wht

med
3nd

46

I (t) - I (t)
R = g . ___m_ 3.9
‘0 I..(:)+2I..(r) ‘ )
The numerator of this expression is the difference decay. The denominator
represents the total fluorescence, Int“), and is the fluorescence seen in the
absence of polarization efi'ects. For an angle 5 between the absorption and the

emission dipole moments, the initial anisotropy is given by,

r, =(3cos2 g-1)/5 (3.10)

Thus, the maximum value of the anisotropy is 2/5 while the minimum is -1/5.
For molecules acted on by the randomizing forces in solution, the orientation
of the molecules eventually become isotropic. At long times, the difi'erence
between Iw(t) and Ivh(t) disappears so that the anisotropy approaches zero.

The rotational difl'usion experienced by a protein is reflected in the
motion of the attached fluorescence probe. For a spherical particle, the
rotational difi'usion is described by the equation,

iwliafllwmv’wwm) (3.11)

where W(0,¢.t) is the time dependent probability of a particular orientation
and Drot is the rotational diffusion coefficient [76]. Dmt is related to the
rotational fiiction coeficient, fret, by,

k
on, 7.1:???) (3.12)
re: Ii

where k; is Boltzman’s constant, T is the absolute temperature, V. is the
hydrodynamic volume of a non-interacting sphere and n is the viscosity of the

medium. From the initial distribution of the orientations of the excited probes

and the fluorescence decay, the fluorescence anisotropy is given by,

47

R(t) = r0 exp(-t/p) (3.13)

where p is the rotational correlation time defined by,

p=__1 =l’131 (3.14)
on", 1,2"

The rotational correlation time is a measure of the time required for the
randomization of the orientational anisotropy. For a spherical particle with a
rigidly attached fluorescence probe, the anisotropy is given by an exponential
decay. The multicomponent anisotropic decay is similar to the case of
multicomponent fluorescence decay,

R(t) = i B, cxp(-t/p,) (3. 15)

1.1

where Bi is the fractional contribution of the component i.

Experimental Determination of Fluorescence Parameters
The experimental apparatus for performing time-resolved fluorescence
measurements is illustrated in Figure 3.3. A vertically polarized light pulse
originating from a laser, impinges upon the sample causing the absorption of
photons. As the excited fluorophores relax back to the ground state, the time
dependent fluorescence emission is detected. The dye laser system consists of
a mode-locked Nd:YAG laser and a synchronously pumped, cavity dumped
dye laser. The output fi-om the dye laser is frequency doubled and passed
through a polarization rotator and a vertically oriented polarizer before
encountering the sample.
The fluorescence emission is collected through collimating lenses, a
rotatable emission polarizer and then a depolarizer before entering the
monochromator. A reversed mode time-correlated single photon counting

apparatus is used to collect the data [79]. This instrument uses a time to

 

    

 

 

—>

Diglal Data Acmisltion and Analysis

Figure 3.3. Time-resolved fluorescence and anisotropy
instrumentation.

amplitude converter which outputs a voltage that is proportional to the time
delay between the excitation signal and a detected fluorescence emission
signal. The reversed timing mode uses the emission photon signal as the
START input. The excitation signal is delayed by a specified time interval
and is used as the STOP input. A multichannel analyzer increments the
count in the channel corresponding to the elapsed time. Over the course of
the measurement, a histogram representing the fluorescence decay as a
function of time is constructed.

The analysis of time-resolved fluorescence data involves fitting the
fluorescence decay to a sum of exponential components by taking into account
the finite pulse shape of the excitation source. When a pulse with a finite
duration is used for excitation, the experimentally observed fluorescence
decay profile, lobs(t), is a convolution of the excitation pulse, L(t), with the

intrinsic fluorescence response, Imt(t),

49

1,,,,(:) = [gm-snout. (3.16)

Im(s), must be extracted from the convoluted fluorescence profile usually
using a least squares fitting procedure [80-83]. From equation 3.8, this

expression may be written as,

 

7t

133(‘)=i;L(s)§A.exp[-fl)dv (3.17)

In this procedure values of Ag and ti are varied until the reduced sum of

squares,

2: 1 fipam’ldcar
x (Iv-1... of (3.13)

is minimized. lob”, law and 0‘2 are the observed intensity, calculated

 

intensity and variance, respectively, for the discrete time channel i and N is
the total number of channels.

R(t) is also distorted by the excitation pulse profile, but R(t) cannot be
directly fit to the observed decay. Instead, the r,- and p 5 values are found by
numerically fitting the experimentally measured vertically, luck, and
horizontally, Ivh,obs, polarized emission using previously determined
parameters for 1m [83, 84]. From equation 3.9, the total fluorescence decay,
1m“), and the anisotropy decay, R(t), are related to the nondistorted emission

curves by,
1,,(t) = 161,011+ 2R(t)] (3.19s)
I..(:)=xz..(:)[1-R(:)] (3191»)

Convolution with the instrument response function, L(t), gives

1mg) = low ”mm (3.20s)

50

1,,,,,(:) = Eur-3)],,(s)ds (3.201».

From equations 3.8, 3.15 and 3.20, these expressions can be rewritten as,

1",..(t) = i£{F"(t) + 2: ]: L(s)Cu exp[- (t; 3)}11} (3.21s)

l-l

 

 

1,“,(t) = l: {P‘ (r) - 2L: L(s)Cu cxp[-('9-s)}1r} (3.21b)

l-l

 

where,
Ft ' r (t " S)
(t) = In L(s)A, exp -— (3.228)
K 71
-r
9,, =[L+.L) (3.22b)
7:: pi
and C, = 14.8, (3.22s).

Suitable computer programs using an iterative least-squares

deconvolution procedure have been developed to fit the experimentally

observed It“ parameters [80, 81]. These values are then used to
simultaneously fit the Ivvfib. and Ivh,obs curves [83]. The Marquardt-
Levenburg algorithm is used to minimize the x2 values for the fluorescence
decay curves by adjusting the fluorescence parameters and for parameters
taking into account the scattered light and time shift of the excitation pulse
[85] .

Applications of Fluorescence

Fluorescence spectroscopy has become a useful tool for the
investigation of macromolecular structure, dynamics and interactions in
solutions. Properties of protein bound fluorescent probes have been measured
and information gained on the structure, conformation and interactions of

proteins in numerous studies using conventional steady-state and time-

51

resolved fluorescence methods [67, 68, 74]. For example, solution studies on
immunoglobins have investigated antigen-antibody binding by measuring the
quenching of ligands, immunoglobin flexibility by measuring the fluorescence
anisotropy of bound fluorophores, and intermolecular distances using energy
transfer. Studies of muscle proteins used fluorescence anisotropy to detect the
flexibility of myosin and used energy transfer to determine the effect of
calcium on muscle contraction. Other areas where the use of fluorescence is
widespread has been in the study of lipid micelles [68, 86] and polymer
dynamics [71]. Fluorescence spectroscopy has become established as a
powerful tool for the experimental investigation of a wide variety of the
physical properties of molecules in solution.

Only recently has fluorescence spectroscopy been used to investigate
the crystallization behavior of proteins [87-89]. J ullien and coworkers studied
protein interactions in the crystallization of ribonuclease A by monitoring the
steady-state fluorescence anisotropy. The measured anisotropy was found to
increase as the protein concentration increased. Rotational correlation times
were calculated assuming that the lifetime remained constant. The efl'ects of
precipitating agents on crystallization were interpreted in terms of the virial

coeficient, a,

p’ = p(1+ aC) (3.23)
where p’ and p are the measured effective and infinite dilution values of the
rotational correlation times, and C is the protein concentration. The virial
coeficient was found to increase sharply under conditions that were favorable
for protein crystallization.

In further studies with time-resolved fluorescence, a maximum entropy
data analysis scheme was used to calculate a rotational correlation time

52

 

Table 3. 1. Amino sci? sequence (ff hen egg white lysozyme.

4O THRGINALATHRASNARGASNTl-RASPGLYSERTHRASP
53 TYRGLYIIEIEUGLNILEASNISERARGTRPTRPCYSASV
66 ASPGLYARGMPROGLYSERARGASNLEUCYSASNILE
79 PROCYSSERALALHJLEUSERSERASPIIETHRALASER
92 VALASNCYSALALYS LYS ILE VAL SERASP GLYAS‘IGLY
105 METASNALATRPVALALATRPARGASNARGCYSLYSGLY
118 'I'l-IRASPVALGINALATRPIIBARGGLYCYSARGIEU

 

distribution [90]. In the presence of high ammonium sulfate concentrations, a
bimodal distribution was observed. The rotational correlation time of the
aggregate peak varied between two and three times that of the monomer
peak. This aggregate peak appeared to be a stable intermediate in the
crystallization process and is possibly a symmetrical dimer of the
ribonuclease. Although light scattering methods have been far more
extensively used to study protein crystallization, these results represent only
the beginnings for the use of fluorescence techniques in investigations of
protein crystallization. Clearly, fluorescence methods have not yet been fully
exploited for the study of protein crystallization.

Fluorescence of HEL

HEL has been the subject of a majority of the previous research done
on protein crystallization and is also one of the better characterized proteins
[91]. To enable comparison with previous results this protein was chosen as
the model system in this current work. Lysozyme was first discovered by
Alexander Fleming because of a cold [92]. A drop from Fleming's nose had
fallen onto an agar plate resulting in the clearance of the microbial colonies.
The ability of the substance to lyse bacterial cells led to the enzyme’s name. It
accomplishes this lytic action by hydrolyzing the B-(1-4)-glycosidic linkage of

53

 

Figure 3.4. HEL d-carbon atoms showing the main polypeptide
chain (from reference [91]).

the tetra-sacharides found in bacterial cell walls. Lysozyme is found in the
tissues and secretions of animals and plants, but is the most plentiful in egg
whites.

HEL is a relatively small protein with a molecular weight of 14,300
and consists of 129 amino acid residues. The amino acid sequence of HEL is
shown in table 3.1. There are 17 basic residues and 9 acidic residues in HEL.
The isoionic point of is 11.1 and at pH 4.6 it carries a charge of +10 [38, 39].
HEL was the first enzyme structure that was determined using X-ray
crystallography [93]. The alpha carbon backbone is illustrated in Figure 3.4.
The overall shape of the protein molecule can be can be approximated as a
prolate spheroid with dimension of about 4.5 X 3.0 nm. A substrate binding
cleft separates the molecule into two lobes [30]. The larger lobe (residues 5-36
and 98-129) consists primarily of a—helices while the smaller lobe (residues
4094) has a B-sheet structure.

54

 

Table 3.2. Tryptophan fluorescence parameters for 0. 1% HEL.

 

 

Lifetimes A1 A; A3 11 :2 r3
2 Corrponents 0.27 0.73 3.28 0.76

Vos. et. al. 0.25 0.75 3.23 1.28

3 carponents 0.16 0.49 0.35 3.30 1.00 0.26
Vos. et. a1. 0.02 0.56 0.42 6.25 2.18 0.70
Anilotropy B1 33 p, 92

1 Carponant 0.21 3.08

Vos. et. a1. 0.22 3.80

2 Couponents 0.20 0.06 3.48 0.10

 

The intrinsic fluorescence of HEL has been previously investigated.
There are a total of six tryptophans in the protein. However, fi'om steady-
state fluorescence measurements, it was found that 80 % of the fluorescence
intensity comes from Trp-62 and/or Trp-108 [94]. There also appears to be
energy transfer from Trp-108 to Trp-62. The time-resolved fluorescence
lifetimes of HEL have been measured by Vos, et. al [95] and are seen in
Table 3.2. Measurements of the fluorescence anisotropy indicated a single
rotational correlation time component of 3.8 ns. This value is too low to
describe the overall rotational motion of HEL and may be a result of internal
motions in the protein.

To determine whether crystallization conditions have an influence on
the intrinsic fluorescence behavior, we have measured the efi'ects of sodium
chloride concentrations in HEL solutions. The time-correlated single photon
counting apparatus was used as described earlier. An excitation wavelength
of 300 nm fi'om the frequency doubled output of an R6G dye was used and the
emission collected at a wavelength of 340 nm. The total fluorescence lifetimes

were fit to a three component model. The fluorescence lifetimes and

55

 

9‘

u
a
1

 

(M)
a
-1- O
.
O
9
u o
a
U"
0
O
O

 

W Llellinu
e 'o o .
- L
Rotationd Correlation Time (as)
d N
O

 

 

 

 

1 0
0.6
A A A A
0': I I I I " I ‘ I I I 0'0 I ‘9‘ I ‘2 I ’9‘ I '1
0.0 1.0 2.0 3.0 4.0 0.0 0.0 7.0 0.0 0.0 1.0 2.0 3.0 4.0 6.0 0.0 7.0 0.0
M 90":

Figure 3.5. Effect of NaCl concentrations on the tryptophan a)
fluorescence lifetimes and b) rotational correlation times of 2% HEL
solutions.

rotational correlation times of 0.1% HEL in 0 % sodium chloride are shown in
table 3.2. The two longest lifetimes agree with the two component fits
obtained by Vos, et. al. However, we also observed a shorter lifetime
component. As seen in Figure 3.5a, the fluorescence lifetimes of 2 % HEL
solutions are not significantly afi'ected by the sodium chloride concentration.
It appears that a two component fit to the anisotropy decay is able to
separate the long and short contributions that do not appear in a one
component fit. The rotational correlation times of the tryptophan residues in
HEL are shown in Figure 3.5b. Because there is little efi'ect of the changes in
the solution conditions on the rotational correlation times, the intrinsic
fluorescence of HEL does not appear to be suitable for the measurement of
crystallization conditions. There are other practical difficulties in using
intrinsic fluorescence for monitoring protein crystallization as well. The high
concentration of protein present in the sample causes complete absorption of

the excitation beam leading to an inner filtering efi'ect. The wavelength of

56

excitation source causes photobleaching and denaturation of the protein if the
intensity is too strong. Attenuating the power of the beam results in
decreased signal. Furthermore, the relatively short lifetimes of tryptophan
present measurement dificulties.

To solve these problems we must turn to the use of extrinsic probes. To
begin, we investigate the effect of the binding of anionic ligands on the
crystallographic structure of HEL. From there, two different classes of
fluorescence probes are applied to the problems of protein crystallization. A
covalently bound probe is first used to demonstrate that the overall rotational
transport properties of HEL provide information on the crystallization
conditions. However, the labeling procedure used consumes valuable protein
material and is also not amenable to routine use. An alternative technique
using non-covalently bound fluorescent probes is demonstrated to be a
practical way to optimize and dynamically monitor crystallization conditions.
With this novel technique, the chemical effects of various precipitants on the
physical behavior of the protein are investigated. Applications to the
screening of protein crystallization conditions are discussed.

Chapter 4

The Effects of Co-Crystallization with Orange Ii on
the Structure of Lysozyme:

Abstract

To investigate the effects of organic anionic ligands on protein
crystallization, the structure of hen egg-white lysozyme (HEL) co-crystallized
with orange 11 was determined at 2.1 A resolution. This structure was
compared with a previously determined HEL structure from a crystal without
orange II. Orange II was not found in a specific location and did not
significantly perturb the structure of the protein itself. However, difl'erences
in the solvent shell and the crystallization behavior were evident. It is
possible that these differences are due to increased hydrophobic interactions
fi-om weakly associated orange II.

Introduction

The nucleation and subsequent growth of protein crystals results hour
the association of the proteins through a combination of electrostatic, Van
Der Waals, hydrodynamic, hydrogen bonding and hydrophobic interactions
[96]. These interactions are manipulated by altering solution conditions to
facilitate the assembly of protein molecules into nucleation centers which
eventually grow into macroscopic crystals. This process is usually achieved by
increasing the concentration of an appropriate crystallization agent thereby

driving the solution into a state of increasing supersaturation where

 

‘ Submitted to the Journal ofCrystal Growth.
57

58
nucleation and subsequent crystal growth can occur. The precipitating agents
are responsible for changing the salvation properties of the protein leading to
the increased protein-protein bonds which must result if crystals are to form.
However, the nature of these interactions and their roles in nucleation are
not well understood.

Previous investigations have examined the role of ions on the
crystallization behavior of hen egg-white lysozyme (HEL). Interactions with
anions are known to affect the solubility of HEL according to the reverse
order of the lyotropic series [97]. HEL readily crystallizes out of solutions
containing sodium chloride, but ammonium sulfate is considered to be an
unsuitable crystallization agent. It has also been suggested that a matrix
coprecipitation and co-crystallization reaction with organic ligands could
improve the crystallization process [41]. Such ligands could participate in
crystallization in two ways. First, the ligands could act as conformational
tighteners which decrease the conformational mobility of proteins. Secondly,
these ligands may participate in the crystallization process by generating
hydrophobic interactions between ligands to form a matrix. This process was
termed matrix coprecipitation.

We further investigate the role of organic ions in protein association
and crystallization by determining the X-ray crystallographic structure of
HEL co-crystallized with orange II. Orange II is an anionic organic ligand
with a hydrophobic moiety as illustrated in Figure 4.1. The effects of
orange II on the crystallization and precipitation behavior in the presence of
N aCl are examined. A comparison between the structures of the HEL
crystallized in the presence of orange 11 (OHEL) is made with HEL
crystallized in the absence of orange II (1HEL). The results do not indicate
significant differences in the structure of the protein itself. However,

59
03'

N

l
N

H...

Figm'e 4.1 Structure of Orange II.

difi'erences in the solvent structure were observed. These difl‘erences suggest
that orange 11 provides additional interactions between the proteins.

Material and Methods

Three times crystallized and lyophilized HEL was obtained fiom Sigma
and orange II was obtained from Aldrich. All solutions were made with
10 mM sodium acetate bufi'er at pH 4.6. The orange II was purified by
recrystallization from a water/ 1-propanol solution. The HEL was dissolved in
the bufi'er and filtered through a 0.45 um filter. In the crystallization trials,
HEL was co-crystallized with orange II using NaCl as a precipitant in
hanging-drop vapor difi'usion experiments. 10 [.11 drops containing HEL and
orange 11 and 5 ul of the reservoir solution were equilibrated against a 1 ml
reservoir of the limiting NaCl concentration. The limiting N aCl
concentrations in the reservoir were 0, 2, 3 and 4%. For the initial
concentration of 2% HEL, initial orange II concentrations were 0.2, 0.4, 0.6,
0.8, 1.0 and 1.2 mM. Crystallographic quality crystals were obtained from
initial orange II concentrations of 0.8 mM with a limiting NaCl concentration

60

 

Table 4.1. Summary of x-ray difi'raction and refinement statistics for
orange II/lysozyme (OHEL) and lysozyme (1HEL, from [98]).

 

 

 

 

 

 

 

 

OHEL 1Ha__

Cell Constants:
a.b (A) 79.1 79.1
c (A) 33.1 37.9
Unique Reflections 7.097 10,276
Resolution limit (A) 2.1 1.7
R-value 0.165 0.152
Deviation. Bonds (A) 0.018 0.019

. Deviation, Angle (Degree) 3.3 2.4

 

 

of 3%. A crystal with approximate dimensions of 1.0 mm x 0.45 mm was used
for the collection of X-ray data.

Three-dimensional X-ray diffraction data were collected at room
temperature with a Siemans Xentronics area detector and graphite
monochromated Cu K01 radiation radiation generated by a Rigaku RU200
X-ray generator operating at 7.5 kW. The crystal-detector distance was
13.0 cm, with a detector swing angle at 50°, and a scan range of 02° per
frame. Each fi'ame was collected for 200 s, with difi'raction extending to
2.08A. The XENGEN [99] suite of programs was used for intensity data
reduction. A total of 12,679 reflections were measured, of which 7,097 were
unique. A summary of the statistics for the data set is shown in Table 4.1.

Patterson rotational/translation molecular replacement methods were
used to solve the phase problem and the structure of OHEL. The atomic
coordinates of HEL, stripped of solvent, fi'om the Brookhaven Protein Data
Bank file 1LYZ were employed as a search model for HEL/orange II. The
rotational/translational search was performed using X-PLOR [100] on data
between 7.0-2.8 A resolution and iF l >2o( I Fl ). Rigid body refinement of the

61

 

Table 4.2. Co—crystallization of HEL with orange II. Values of [NaCl] are the
concentrations in the reservoir and values of [Orange II] are the initial
concentrations in the hanging dr0p. Xn indicates the presence of crystals
where n is the number of crystals, ppt indicates precipitate and + indicates
relatively many. Qualitative descriptions are given in the parenthesis
indicating small (sm), large (1g) and irregular (irr) crystals.

 

 

 

 

[N000 [Or-090 Ill (ml!)
(96) 0.2 0.4 0.0 0.0 1 1.2
0 Clear Clear ppt ppt+ ppt+ ppt+
2 Clear Clear X3 (irr) ppt+ ppt+ X+ (am)
3 Clear Clear X3 (irr) X2 (lg) X (lg) X+ (am)
4 X+ (sm) X3 (irr) X+ X (irr) X (in) X+ (sm)

 

 

 

P43212 solution reduced the crystallographic residual from 0.48 to 0.28.
Refinement was carried out using the restrained least-squares method with
the program PROFFT [101].

After 89 cycles of refinement the residual was reduced to 0.165 for data
with IFI >2o( I F l ) between 4.50 and 2.10 A resolution (6753 reflections). The
solvent sites were chosen only if the highest density persisted in the electron
density map throughout the final stages of refinement. 107 water molecules
were included in the final model (OHEL). Inspection of the electron density
map of the HEL/orange II did not reveal any regions where the orange II
could be tightly bound.

62

 

Figure 4.2. Structures of a) OHEL co-crystallized with orange 11
and b) 1HEL (fi'om Reference [98]) showing the protein and
associated solvent atoms.

Results

Eflects on Crystallization

The addition of orange 11 to HEL solutions was observed to afi'ect the
conditions under which crystals grow. Results of the crystallization trials are
shown in Table 4.2. In general, the addition of orange 11 appears to decrease
the concentration of NaCl required for the formation of crystals. Orange II
itself, at initial concentrations of 0.6 to 1.2 mM (final concentrations
approximately 1.8 to 3.6 mM), acts as an effective precipitant. However, only
amorphous precipitates were formed in the presence of orange II alone. The
crystallization of HEL with NaCl does not appear to be significantly altered
at initial orange 11 concentrations below 0.6 mM (final concentration
approximately 1.8 mM). As the N aCl concentration increases from 2 to 4 %,
crystal growth occurs. The crystals that grew were of the familiar tetragonal
morphology and were colored by the orange II. The optimal concentration for
the co-crystallization of HEL with orange II was in the range of 3 % NaCl and
initial orange 11 concentrations of 0.8 to 1.0 mM for an initial HEL
concentration of 2 %.

Comparison of the Structure of OHEL with 1HEL

The structure of OHEL is compared with HEL crystallized fi'om NaCl
alone (1HEL). The structure used for comparison was determined by Wilson,
et. al. [98] and is indexed as 1HEL in the Brookhaven Protein Data Bank.
The 1HEL crystals were grown fi'om an initial drop containing 10 ill of 2 %
HEL in 200 mM sodium acetate, pH 4.4, and 5 pl of a 4 % NaCl reservoir
solution. OHEL is isomorphous with 1HEL possessing identical cell
dimensions of a = b = 79.1 A and a slightly smaller cell dimension of
c =37.9 A The number of unique reflections obtained were less in the case of

OH}

in F
deli
fit a

Ct311‘
dhlt

refit

“Tan

HEL

 

 

 

 

Figure 4.3. a) Average root mean square difi‘erence between the
residues of OHEL and 1HEL. The models were overlaid by a
least-squares procedure minimizing the rms difference between
the backbone atoms. b) Thermal factors for OHEL and 1HEL.

OHEL as compared to 1HEL and is reflected in the resolution of the
structures.

The structures of OHEL and 1HEL are shown with the solvent atoms
in Figure 4.2. The protein structures of OHEL and 1HEL are similar. RMS
deviations between the backbones atoms were minimized by a least-squares
fit and calculated to be 0.614 A. As seen in Figure 4.3, these difl'erences also
correspond to regions where the thermal factors are greatest. The largest
differences are in the ARC side-chains which lie on the solvent exposed
surfaces of HEL. A maximum thermal factor of 30 A2 was used in the
refinement of OHEL and accounts for the differences in the average thermal
factors for each residue. The structure of HEL grown in the presence of
orangeII does not appear to be significantly different fiom the structure of
HEL grown fi'om NaCl only.

65

In contrast, the distribution of the solvent molecules between the two
structures appears to be significantly difi'erent. A thorough search of the
difference electron-density in the vicinity of the protein did not reveal any
large continuous regions indicating specific binding of orange II. From this
result, it appears that orange 11 is not strongly bound at specific locations to
HEL in the crystal. However, it is possible that orange II may be bound at
partial occupancy. There are significantly fewer solvent molecules in the
structure of OHEL. A total of 107 water molecules were placed in the electron
density surrounding OHEL, compared to 185 water molecules surrounding
1HEL. Of the 185 waters observed in 1HEL, 88 had thermal factors greater
than 50A2. It is possible that many of the water molecules in 1HEL were
observed because of the greater number of reflections used in the refinement.

In their comparison of crystal structures of T4 lysozyme at low,
medium and high ionic strengths, Matthews, et. al. [102] found that the
number of solvent molecules increased from the low, to medium to high ionic
strength crystal structures. Their observations suggested that some of the
solvent molecules present in the structure were actually bound ions at partial
occupancy. In the structure of OHEL, some of the solvent molecules in the
structures of HEL could also be bound chloride or orange II ions at partial
occupancy. The decreased number of solvent molecules found in OHEL as
compared to 1HEL may be due to the decreased ionic strength of the
conditions used to grow OHEL crystals. From this assertion, it is likely that
there are fewer ions bound to OHEL than to 1HEL.

Discussion
Insight into the crystallization mechanisms of proteins may be gained
by examining the structural results together with previous results on the

efft

01'8

spet
exp}
in
thlo
0H1

inve
T4 1]
Show

Siren

inbibi

66

effects of precipitants on HEL crystallization. Although the addition of
orange II to HEL solutions does afi‘ect the aggregation and crystallization
behavior of HEL in solution, co-crystallization with orange II does not appear
to alter the structural properties of the HEL molecule itself. The difi‘erences
in the protein structure between 1HEL and OHEL lie in regions where the
thermal factors are also high. These differences may be attributed to the
same factors leading to large thermal factors including static and dynamic
disorder.

In the model propose by Conroy and Lovrien an initial tightening of the
protein conformation by ligand binding is followed by a coprecipitation and
co-crystallization process where the co-crystallizing ligands participate in a
matrix stabilizing the crystal structure [41]. Orange II was not found to be
specifically bound to HEL in the crystal. However, chloride ions also do not
explicitly appear in the structure of 1HEL [93]. Because there is no
significant difference in the protein structures with orange II and in sodium
chloride only, conformational tightening does not appear to be occurring with
OHEL.

Our results appear to be in accordance with previous structural
investigations on the effect of solvent environments. The X-ray structures of
T4 lysozyme under conditions of high, medium and low salt concentrations
showed that the salt bridges in the protein are not affected by the ionic
strength [102]. Difi‘erences were observed primarily in the solvent shell.
Similar results are seen in other proteins such as bovine pancreatic trypsin
inhibitor where the crystal structures were grown in difi'erent potassium
phosphate concentrations [103]. A comparison of the structures of HEL in the
tetragonal form and in the trigonal form obtained fiom 0.23 M sodium nitrate
showed that differences were limited to regions of intermolecular contact in

67
the crystal [104]. Furthermore, structural difl'erences in the native and low
humidity forms of HEL were also found primarily in the solvent content
[105].

However, it is evident fi'om the crystallization trials and the difference
in the distribution of solvent molecules around the HEL molecule that
orange 11 does have an effect on the crystallization process. Orange II is an
eficient precipitating agent, causing decreases in solubility at concentrations
in the range of 2 mM. The crystallization trials show that orange II by itself
does not lead to the nucleation of crystals and only results in the formation of
amorphous precipitate. By taking into account the chemical interactions of
orange II and HEL, further insight into the mechanism of HEL
crystallization may be obtained.

At pH 4.6, HEL is known to highly charged with approximately +10
protons [38, 39]. Because of this property, anions are likely to interact with
the positively charged groups on the protein. The effect of ion pairing on the
crystallization of HEL was explained in terms of the polarizability of the ions
‘ as described by Pearson [106]. In this scheme, “soft” ions are more polarizable
with a large size and low ionic charge, whereas “hard” ions are small and
highly charged. The ability of various anions in decreasing the solubility of
HEL can be related to their association constants with the positively charged
residues.

It is likely that the role of orange 11 in the precipitation of HEL is
related to the mechanism by which the “soft” inorganic anions cause protein-
protein interactions. In precipitation reactions, Conroy and Lovrien found
that close to one molecule of organic anion is bound for each cationic charge
on the HEL [41]. Orange II could bind through specific ionic interactions
between the sulfonate group and the positively charged residues of HEL. The

68

aromatic residues could then facilitate protein-protein interactions through
hydrophobic interactions. Through these hydrophobic interactions,
polymerization between HEL molecules would result in the large scale
precipitation of the protein from the solution. Orange II would then
simultaneously neutralize the charges on HEL eliminating the repulsive
electrostatic forces and provide contact points for interprotein interactions
mediated by the hydrophobic moiety.

However, such contact may not be suitable for crystallization. Indeed,
for the crystallization of membrane proteins, hydrophobic contacts are
explicitly avoided by using detergents [107]. The protein-protein interactions
resulting from the molecular contacts of orange 11 are likely to be disordered
since hydrophobic interactions are not in general directional. Multiple
numbers of orange II bound to HEL would serve to randomly bind other
similarly hydrophobically shielded HEL molecules, resulting in amorphous
aggregation. The presence of sodium chloride appears to engender other
interactions which lead to nucleation.

From fluorescence anisotropy studies, it was found that concentrations
of sodium chloride which increases the rotational correlation times to
intermediate values are the most favorable for HEL crystallization (Chapters
5 to 7). These conditions cause HEL to participate in protein-protein
interactions but still allow suficient mobility so that precipitation does not
occur. Under optimal crystallization conditions, it is likely that although the
proteins are able to interact with one another through a diminishing of the
repulsive forces, there is enough mobility that the protein may reorient to
form the specific interactions leading to nucleation. The interactions caused
by orange 11 alone may not engender the favorable reorientation required for
nucleation. The decrease in the amount of NaCl required to grow crystals in

69
the presence of orange 11 may indicate additional interactions imposed by
orange 11.

The absence of any definite location in the crystallographic structure
for either orange II or sodium chloride suggest that the role of anions in the
crystallization of HEL is not that of a specifically bound ligand which
participates directly in forming crystal contacts. Rather, their role appears to
be more difi'use. It is possible that the anions serve to stabilize the structure
of the crystal. This lends support to a general concept of matrix c0-
crystallization. However, orange II in particular does not appear to be
favorably involved in this process and may actually increase the disorder in
the crystal by contributing non-directional hydrophobic interactions. The
sodium chloride appears to alleviate these contributions. Thus, the balance
between non-specific hydrophobic interactions and more specific ionic

interactions appears to be important in the crystallization of HEL.

Chapter 5

Time-Resolved Fluorescence and Anisotropy of
Covalently Coupled PBA for Monitoring the
Crystallization Conditions of Lysozyme:

Abstract

Time-resolved fluorescence and anisotropy measurements of trace
amounts of l-pyrenebutyric acid labeled hen egg-white lysozyme (PBA-HEL)
were used to characterize hen egg-white lysozyme (HEL) crthallization
conditions. The efi‘ects of sodium chloride and protein concentrations on the
fluorescence lifetimes and rotational correlation times of the labeled protein
were examined. These results were compared with the effects of the salts
ammonium acetate and ammonium sulfate. Addition of protein precipitants
caused increases in the rotational correlation times which were attributed to
a combination of steric, hydrodynamic, general electrostatic and specific ionic
interactions. This decrease in the rotational mobility of HEL appears to be a
necessary but not sufficient condition to allow the formation of specific
interactions leading to crystallization. The results demonstrated that
fluorescence measurements are effective in characterizing and monitoring

protein crystallization processes prior to the appearance of macroscopic
crystals.

 

' Submitted to the Journal ofCrystal Growth.
70

71

introduction

To expedite the screening and optimization of protein crystal growth
conditions, advanced methods are required that are able to monitor protein
interactions during nucleation and crystal growth in supersaturated
solutions. Through the measurement of the microenvironmental properties of
the protein and other solution constituents, spectroscopic techniques provide
a means by which intermolecular interactions in solution can be monitored
prior to the appearance of macroscopic crystals or precipitates. Information
on the physical chemical processes involved in the protein-protein and
protein-solvent interactions leading to crystallization may be obtained.

Steady-state fluorescence, time-resolved fluorescence and fluorescence
anisotropy represent powerful optical spectroscopic techniques for monitoring
the dynamics of macromolecular interactions in solution [66-68, 73],
Fluorescence techniques rely on the spontaneous emission of light by excited
state probe molecules which are sensitive to the local environment of the
probe. Specific information on the microenvironment 0f the fluorescent probe,
either he in solution or coupled to a macromolecule, can be obtained from
changes in the peak intensities and wavelengths in the steady-state spectra
[7 2]. Furthermore, measurements of the rotational transport properties of the
fluorophores, obtained from fluorescence depolarization techniques, are
highly sensitive to molecular scale interactions [108, 109].

Time-resolved techniques are able to directly separate and quantify the
relevant fluorescence parameters that contribute to the steady-state emission
parameters [70]. Values of the decay lifetimes are obtained that provide
information on the probe distribution and the nature of the local
microenvironments. Similarly, the time dependent anisotropy measurements

result in the direct quantitation of rotational correlation times [108]. The use

72

of time-resolved fluorescence methods to find the relationships between the
microscopic interactions of proteins and their crystallization behavior should
result in a more directed and rational approach for obtaining high quality
protein crystals.

J ullien and coworkers previously studied protein interactions in the
crystallization of ribonuclease A by monitoring the fluorescence anisotropy of
a covalently bound fluorophore [87 -89]. The efi'ects of precipitating agents on
crystallization were interpreted in terms of the solution non-ideality which
increased sharply under conditions that were favorable for protein
crystallization. Their subsequent studies using time-resolved methods have
shown that species with longer rotational correlation times are present in
conditions of high salt concentrations [90]. This species was postulated to be a
dimer of ribonuclease. Such results have demonstrated the applicability of
fluorescence techniques to the investigation of protein crystallization.

In this study, we measure the time-resolved fluorescence of
l-pyrenebutyric acid (PBA, Figure 5. 1) covalently coupled to hen egg-white
lysozyme (HEL) to probe the interactions involved in the crystallization
process. The fluorescence lifetime of PBA is known to be dependent on
microenvironmental parameters such as the polarity and accessibility of the
solvent [1 10]. Rotational correlation times ranging from a few nanoseconds to
microseconds may be measured in order to monitor the intermolecular
association of proteins in undersaturated and supersaturated solutions [11 1].
We compare the effects of the salts sodium chloride (NaCl), ammonium
acetate (NAc) and ammonium sulfate (NS) on the rotational correlation times
and fluorescence lifetimes of HEL solutions containing trace amounts of PBA-
HEL. These effects are, in turn, compared to the crystallization behavior of
HEL in the presence of these various precipitants.

73

 

Figure 5.1. The structure of l-pyrene butyric acid (PBA).

Experimental Methods

Labeling of HEL with PBA

For the labeling of HEL with PBA, succinimidyl l-pyrenebutryic acid
(SPBA) was obtained from Molecular Probes, Inc., and 3X crystallized HEL
was obtained from Sigma. 220 mg of HEL was dissolved in 22 ml of sodium
borate bufl'er at pH 8.5 and filtered through a 0.45 pm filter. 11 mg of SPBA
was dissolved in 200 pl of dimethyl formamide and then slowly added to the
HEL solution while stirring to form a cloudy suspension. The reaction
mixture was then stirred for 2 hr at 23° C, after which 2.5 ml of 1.5 M
hydroxyl amine at pH 8.3 was added to quench the reaction. After 30 min.,
the reaction mixture was then passed through a 0.45 um microfilter. Removal
of the unreacted SPBA was accomplished by passing the solution through a
G-25 desalting column and eluted with 20mM MES bufi‘er at pH 6.5.

The fractions containing protein, as determined by measuring the
absorbance at 280 nm, were collected and applied to a carboxymethyl-
sepharose CL-6B cation exchange column equilibrated to pH 6.5 with 20 mM
MES bufi'er. The mixture of unlabeled and labeled HEL were separated by
elution with a 0 to 1M NaCl gradient with 10 ml fractions taken. The

74

absorbance at 280 nm and 341 nm was measured to determine the respective
amounts of protein and PBA in each fraction. The fractions determined to
contain singly labeled PBA were collected. Final desalting was accomplished
by ultrafiltration through a 10,000 MW cutofi' filter and equilibrated by
washing three times with 50 mM sodium acetate bufl'er at pH 4.6.

Sample Preparation

All solutions were prepared in 50 mM sodium acetate buffer at pH 4.6
unless otherwise noted. All percent concentrations are expressed as w/v.
Stock HEL solutions of 20% were prepared by dissolving the solids in bufl'er.
The HEL solution was then washed three times with buffer using
ultrafiltration (10,000 MW cutoff). The concentration was measured by
serially diluting the solution 1000 times and measuring the
spectrophotometric absorbance at 280 nm using A1” = 26.4 [112]. Stock
solutions of 20% NaCl, 40% NS and 20% NAc were prepared in bufl'er using
reagent grade materials. Stock PBA-HEL solutions of 0.2 % w/v were
prepared and diluted ten times to obtain a concentration of 0.02% PBA-HEL
in the samples. Appropriate amounts of the stock solutions and buffer were

mixed together for the samples used in the fluorescence measurements.

Fluorescence Measurements

Steady-state fluorescence measurements were performed using a SPEX
Fluorolog spectrofluorimeter. For the time-resolved measurements, a
picosecond dye laser system was used as the excitation source and the
emission decay data collected using the time-correlated single-photon
counting (TCSPC) method [113]. A full description of the TCSPC apparatus
has been previously reported [79]. For our measurements, the output from
the dye LDS 698 was fi'equency doubled and passed through a polarization

75

rotator and a vertically oriented polarizer before impinging upon the sample.
Samples were excited with a wavelength of 350 nm and a pulse repetition
rate of 760 KHz. The fluorescence emission at 400 nm was collected through
collimating lenses, a rotatable emission polarizer and then a depolarizer
before entering the monochromator. 4096 channels were used where each
channel corresponded to a time interval of 0.197 ns.

All measurements were started within approximately 10 minutes after
mixing of the stock solutions and were performed at 23° C. During the time-
resolved measurements, the emission polarizer was alternately rotated fi'om
a vertical to a horizontal orientation every 120 s to average the efi'ects fi'om
fluctuations in the excitation intensity. The vertical and horizontal emission
decay profiles were summed until approximately greater than 10,000 counts
appeared in the peak channel for a total collection time of about 20 min. for
each sample. The instrument response ftmction fi'om the excitation pulse was
collected before each sample by measuring light fi'om a scattering solution
and was used for subsequent data analysis.

Data Analysis

The analysis of time-resolved fluorescence data involves fitting the
fluorescence decay to a sum of exponential components by taking into account
the finite pulse shape of the excitation source. The time-dependent
fluorescence, Itot(t), from an initial excited state population, decays
exponentially with characteristic lifetimes, ti [73],

I..(:) = fiend-rm) (5.1)

it!

where i represents a single fluorescence component and p is the number of
components. These fluorescence lifetimes are sensitive to the local

microenvironment of the probe including quenching effects. When a pulse

76

with a finite duration is used for excitation, the experimentally observed

fluorescence decay profile, lob.(t), is a convolution of the instrument response
function, L(t), with the intrinsic fluorescence response, Imt(t). lads) must be
extracted fi'om the convoluted fluorescence profile using a least squares
fitting procedure [80-83]

Excitation of a population of fluorescence molecules with vertically
polarized light preferentially excites the probes which are in a proper
orientation thereby inducing fluorescence anisotropy. The induced
fluorescence anisotropy decays to a randomly oriented distribution of
fluorescing species. This time-dependent induced fluorescence anisotropy is
defined by,

I -I I - "
=_W__n.=i= , - , .
Rm 1,, +21... I... gay“) VA) (5 2)

where Ivv and Iv h are the vertically and horizontally oriented polarized
emission intensities, respectively, for a vertically polarized excitation source.
It“ is the time-dependent total fluorescence intensity as before and Idif is the
difference fluorescence intensity.

The decay rate of R(t) depends on both the intrinsic properties of the
probe molecule and on the interaction between the probe and its local
environment [108]. Generally, R(t) can contain up to five exponential
components where j represents one decay component, q is the number of
components and Bj and pj are the initial anisotropies and rotational
correlation times of each component, respectively. R(t) is also distorted by the
excitation pulse profile, but R(t) can not be directly fit to the observed decay.
Instead, the B,- and p5 values are found by numerically fitting the
experimentally measured vertically and horizontally polarized emission using
previously determined parameters for Itot [83, 84].

77

Results

Chromatography and PAGE of PBA-Lye
For the ion exchange chromatography of the PBA-HEL reaction, the

. protein concentration was measured by monitoring the absorbance at 280 nm
while the PBA concentration was monitored at 341 nm. Three protein peaks
were eluted in the order A, B and C. Peak A showed no absorbance at 341 nm
and thus contained unlabeled HEL. Peak B showed approximately half the
relative absorbance at 341 nm as peak C. This suggests that peak B
contained singly labeled PBA-HEL while peak C contained doubly labeled
PBA-lysoyzme.

It is known that the succinimidyl group reacts with the he base form
of aliphatic amines to form stable carboxamides [114]. On HEL, there are 6 9-
amino groups of lysine and the N -terminal amine. At the labeling conditions
used (pH 8.5), the N-terminal amine is the most reactive site since the pKa is
7 .8-8.0 [115]. The pKa values of the lysine residues are all greater than 10.0
and are less reactive [115]. Thus, it is likely that the N-terminal amine is the
singly labeled species in peak B.

Further analysis of samples fi'om the ion-exchange chromatography
was performed using polyacrylamide gel electrophoresis (PAGE). Samples
corresponding to peaks A, B and C each resulted in a single band on the gel.
The band corresponding to the unlabeled HEL showed the greatest mobility
followed by the bands corresponding to peaks B and C. Fits to the logarithm
of the relative mobility show a linear relationship with respect to the
polyacrylamide concentration. All three fits give identical slopes within error
but with different intercepts projected to 0% polyacrylamide. These results
show that the unlabeled, and the apparently singly labeled and doubly
labeled HEL differ in net charge and not size. This result is expected since

78

 

 

 

       

 

 

 

1500 zo'oo 2500 3000
Channel it

o 5'00 1600

Figure 5.2. Time-dependent fluorescence intensity decays of fi-ee
PBA at 23°C in 50 mM sodium borate buffer at pH 8.5. Also
shown is the fit through the total fluorescence decay data. Ivv
and Iva are virtually indistinguishable because of the fast
rotational rate of the relatively small PBA. Each channel
represents a time interval of 0.197 ns.

the reaction of SPBA to an amine will neutralize the charge. All subsequent
experiments described use the apparently singly labeled PBA-HEL fi'om peak

B as the trace fluorescence probe.

Fluorescence Measurements of PBA-HEL

Steady state peak intensities occur at emission wavelengths near- 380
and 400 nm with a shoulder occurring at 417 nm. The emission fi'om PBA-
HEL shows a slight 2 nm red shift as compared to unconjugated PBA but the
shape of the spectra remains essentially identical. As seen in Figures 5.2 and
5.3, the time-resolved decay of the total fluorescence of he PBA decays at a
greater rate than the PBA-HEL. The fluorescence decay of free PBA could be
fit by a single exponential term with a fluorescence lifetime of 103 ns.

cons
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79

 

10‘.

Counts

10’.

 

 

 

 

‘6 '—' I I I V I ‘ I I .‘ I
0 500 1000 1500 2000 2500 3000
Channel it

 

Figure 5.3. Time-dependent fluorescence intensity decays of
0.02% PBA-HEL at 23°C in 50 mM sodium acetate buffer at pH
4.6. The fits are shown as the solid lines through the data points.
The difference in Ivv and Iv H is due to the fluorescence
anisotropy of the conjugated PBA. Each channel represents a
time interval of 0.197 ns.

As seen in Figure 5.3, the total fluorescence decay of PBA-HEL is
considerably more complex. Three exponential terms were required to
adequately describe this decay. At a PBA-HEL concentration of 0.02 %, there
is one long lifetime component of 151 ns, a medium lifetime of 69 ns and a
short lifetime of 6 ns. Because of the long lifetime of PBA, the long and
medium lifetime components can be attributed to the fluorescence fi'om the
conjugated PBA.

The increase in the value of the long lifetime component of the
conjugated PBA as compared to free PBA is likely to result fi'om either
solvent polarity efl'ects near the protein surface or decreased accessibility to
collisional quenchers, such as oxygen. The medium lifetime component is
most likely due to heterogeneity in the microenvironment surrounding the

conjugated PBA. The origin of the short lifetime component is not clear, but is

80

possibly attributable to fluorescence fi'om other sample constituents. Further
results will focus on the efi'ects of precipitants on the long component of the
fluorescence decay.

Previous investigations have estimated the dimensions of HEL,
assuming a prolate ellipsoid shape, to be 5.5 nm and 3.3 run along the major
and minor axis, respectively [116]. Two rotational correlation time
components were required to fit the experimental data. The long rotational
correlation time of 16.2 ns fi'om a 0.02% PBA-HEL solution agrees well with
the expected results for the overall rotation of HEL. This rotational
correlation time corresponds to a spherical rotor diameter of 5.0 nm [108]. A
short rotational correlation time of 0. 13 us was also present and most likely
represents segmental motions of the protein or PBA. For applications to
protein crystallization, we are primarily interested in the overall interactions
of HEL rather than local conformational changes. Thus, we will examine the
effects of the crystallization conditions on the long rotational correlation
times.

Efl'ects of NaCl

The efi'ects of N aCl on the long component of the fluorescence lifetimes
of 2 and 4% HEL are shown in Figure 5.4a. An increase in the fluorescence
lifetimes is seen as the NaCl concentration increases, with a slightly greater
increase in the case of 4% HEL than with the 2% HEL. The effects of NaCl on
the long component rotational correlation times of 2 and 4% HEL solutions
are shown in Figure 5.4b. In this case, the increase in the rotational
correlation times of the 4% HEL solutions are significantly greater than the

corresponding increase of the 2% solutions.

 

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g 155 E 20 U
3 §
150 vvvvvvvvvvvvvvvvvvvv .l 10 vvvvvvvvvvvvvvvvvvvv
0 2 4 6 8 10 0 2 4 C I 10
96 NaCl 96 NaCl

Figure 5.4. Dependence of the a) fluorescence lifetimes of and b)
rotational correlation times of PBA-HEL on NaCl concentrations
at 2% ( El ) and 4% ( O ) HEL. The X and ppt symbols represents
crystallization or precipitation, respectively. The + symbols
represent the relative amounts formed to show increasing
supersaturation.

Under conditions of lower NaCl concentration where no crystals form,
the fluorescence lifetimes and rotational correlation times show relatively low
Values. In the regime where conditions are optimal for producing high quality
crystals, the fluorescence lifetimes increase to intermediate values of about
162 to 168 ns while the rotational correlation times increase to a range of 30
to 60 ns. The crystals which formed appeared to be of the familiar tetragonal
morphology and exhibited the expected crystallization behavior at the
conditions used [8, 36]. Although it did not appear that the presence of PBA-
HEL at 0.02 % significantly interfered with the crystallization process, a
thOrough examination on the kinetic effects of fluorescence additives is
V"am-ranted in further investigations.
At a N aCl concentration of 8% and greater, rapid aggregation leads to
the eventual formation of needle shaped crystals. The presence of large
Q“llounts of visible particles at 8 % NaCl interferes with the fluorescence

 

 

 

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0 02 04 or as 1 12
(ionic Strength)“

Figure 5.5. Efi’ects of the ionic strength of NaCl on the rotational
correlation times of PBA-HEL at 2% (El ) and 4% (O ) HEL.

measurements due to multiple scattering and result in depressed values for
the largest rotational correlation time. Nonetheless, the increasing trend in
the rotational correlation time is clear. '

Figure 5.5 emphasizes the electrostatic effects of added NaCl by
showing the rotational correlation times of PBA-HEL at 2 and 4% HEL as a
function of the square root of the ionic strength. The square root of the ionic
strength is a more physically meaningful measure of electrostatic efi'ects
since it is proportional to the Debye screening length. It is interesting to note
that the rotational correlation times increase slowly as the ionic strength
increases in undersaturated solution, but shows an increased slope as the
solution becomes supersaturated. The greater rate of increase at 4% HEL
indicates that the effect of ionic strength is more pronounced at higher
protein concentrations.

The effects of HEL concentration at fixed concentrations of 2 and 5%
NaCl on the fluorescence lifetimes and rotational correlation times are seen

in Figure 5.6. With 2% NaCl, crystals do not appear at HEL concentrations

83

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Figure 5.6. Dependence of the a) fluorescence lifetimes and b)
rotational correlation times of PBA-HEL on HEL concentrations
at 2% (D ) and 5% ( O ) NaCl. See Figure 5.4 for an explanation
of the X and ppt symbols.

between 1 and 8%. Solutions containing 5% N aCl are more favorable for
crystal growth with the optimal concentrations of HEL lying between 2 and
6%. Rapid nucleation occurs at 8% HEL and 5% NaCl. The fluorescence
lifetimes reach a plateau near 167 ns for the 5% NaCl solutions and near
160 ns for the 2% NaCl solutions. It is also seen that as the HEL
concentration is increased, greater increases in the rotational correlation

times are observed in the presence of 5% NaCl than with 2% NaCl.

Efiects of Ammonium Acetate and Ammonium Sulfate

To determine the effects of different salts on the crystallization and
fluorescence behavior, the effects of NAc and NS are compared with those of
NaCl. In Figure 5.7a, the effects of NS, NAc and NaCl on the fluorescence
and crystallization behavior of PBA-HEL in 4% HEL solutions are shown.
The fluorescence lifetimes of PBA-HEL in NS solutions show a larger

increase as the NS concentration is increased as compared to either the NaCl

 

 

 

 

 

 

 

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[Salt] (M) [Salli (M)

Figure 5.7. Dependence of the a) fluorescence lifetimes and b)
rotational correlation times of PBA-HEL on salt concentrations

at 4% HEL. The (O ), (A) and (U) represent solutions
containing N aCl, NAc and NS, respectively.

or NAc solutions. The greater increase in the fluorescence lifetimes seen in
the presence of NS indicates that the interactions of the conjugated PBA are
qualitatively different than the interactions experienced with NaCl and NAc.
With NAc, the fluorescence lifetimes show a small increase at the lowest
concentration but remain essentially constant as the concentration of NAc
increases.

From the relationship of the rotational correlation times to N aCl, NAc
and NS concentrations seen in figure 5.7b, ionic effects are observed to cause
an increase in the rotational correlation times and thus reflect greater
interactions between HEL molecules. The rotational correlation times of
PBA-HEL increase as the NS concentration increases and are similar to the
values with NaCl at the same molar concentrations. Increases in the NAc
concentration also cause increases in the rotational correlation times with

crystallization occurring at values greater than 30 ns.

A A A A l A A A n L AAAAAAAAA

 

 

 

 

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(ionic Strength)“

Figure 5.8. Effects of the ionic strength with NaCl (0 ), NAc
(A) and NS (D) on the rotational correlation times of PBA-
HEL at 4% HEL.

To further examine the electrostatic effects of salts on the fluorescence
and crystallization behavior, Figure 5.8 shows the rotational correlation
times of 4% HEL in N 901, NAc and NS solutions plotted against the square
root of the ionic strength. In all three cases, there appears to be a inflection in
the slope of the rotational correlation time as the ionic strength increases.
However, with NS the change in the slope occurs at a higher ionic strength
than with NaCl and NAc. From the different degrees of increase in the
rotational correlation times due to N aCl, NAc and NS as a function of ionic
strength, it is clear that electrostatic screening is not the only operative efl'ect
on the molecular interactions.

It is also clear that these interactions are related to the efi'ectiveness of
difi'erent concentrations of precipitants on the outcome of the crystallization.
This is seen with NaCl and NAc where intermediate values of the rotational
correlation times are conducive to the formation of crystals. Conditions which
show low values of the rotational correlation times do not exhibit strong
enough interactions for crystallization to occur. Conditions which show

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86

rotational correlation times that are too large lead to the rapid aggregation of
HEL to form small, intergrown and needle-like crystals. In the case of NS,

large increases in the rotational correlation times result in the formation of

an amorphous gel.

Discussion

The time-resolved fluorescence of PBA-HEL appears to be a sensitive
method for measuring the molecular interactions which lead to the
crystallization of HEL. Fluorescence lifetimes provide information on the
polarity and solvent accessibility of the conjugated PBA due to changes in the
solution constituents. It is unclear whether the differences in the fluorescence
lifetimes are due to intramolecular or intermolecular interactions induced by
the salt. However, changes in the measured rotational correlation times
appear to provide direct information on the intermolecular interactions of
HEL under crystallization conditions. In particular, the rotational correlation
times have been shown to measure the influence of precipitants on the
rotational mobility of HEL.

It is apparent that both the concentrations of N aCl and HEL together
influence the crystallization and rotational behavior. The results suggest that
increases in the rotational correlation times due to the presence of solution
additives are a necessary but not sufficient indication that nucleation will
occur. This increase in the rotational correlation time may be attributed to a
combination of the difl'erent types of interactions which together influence the
crystallization behavior. Increases in the viscosity of the solvent due to the
addition of precipitants are taken into account in the rotational correlation
times [108]. These changes in the bulk viscosity are the result of interactions

in the PBA-HEL microenvironment and should also influence the

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87

crystallization behavior. However, because of the large increases in the
rotational correlation times, they can not be attributed to changes in the
viscosity alone [117].

A possible explanation for the observed increases in the rotational
correlation time is that aggregates of various sizes are formed and remain
stable during the time scale of the measurements. Another possibility is that
transient interactions occur between the protein molecules and lead to
increased fiictional resistance. Bishop, et. al. used light scattering to examine
the nature of the changes in the translational difi‘usion coeficients of HEL
[56]. The results from those investigations suggested that the decrease in the
measured diffusion rates are not due to the formation of discrete isolated
aggregates but rather, are due to an increase in the friction factor of the
proteins. We observed no direct evidence that distinct populations of
aggregates are formed although the possible is not excluded.

The types of interactions between proteins include general electrostatic
effects caused by increasing salt concentrations, volume exclusion and
hydrodynamic coupling effects from increasing protein concentrations.
Although conditions which are conducive for crystallization lead to increasing
rotational correlation times, the absolute value of the rotational correlation
times do not by themselves indicate whether crystallization will occur. For
example, at constant HEL concentrations, rapid aggregation occurs with a
rotational correlation time of 62 ns with 4% HEL, while at 2% HEL
precipitation occurs at a rotational correlation time of only 38 ns. Increasing
the HEL concentration will increase the probability of protein-protein
interactions through steric and hydrodynamic coupling resulting in decreased
mobility. Increasing salt concentrations should then further influence the
degree of these interactions through ionic effects.

88

The efi'ects of salts on protein association may be classified according to
three types of interactions [118]. These are 1) general electrostatic effects,
which include ionic screening effects and double-layer interactions,
2) lyotropic salt effects, involved in the salting out of hydrophobic proteins
and 3) site-specific ion bonding. Because HEL has a positive charge of about
+10 protons at pH 4.6 [39], general and site-specific electrostatic effects are
expected to play an important role in the interactions of HEL.

Increasing the salt concentrations results in a shielding of the
repulsive electrostatic forces [24]. At higher salt concentrations Van Der
Waals attractive forces dominate and nucleation may occur. The specific
nature of the anion is known to play an important role in the crystallization
process. Riés-Kautt and Ducruix determined that the efi'ectiveness of ions in
decreasing the solubility of HEL follows the order C1' > CHsOO' > 8042' [37].
This efi‘ect was explained in terms of the relative ability of difl‘erent anions to
participate in ion pairing with the positively charged protein.

Thus, both general electrostatic and site-specific ion binding efi‘ects
may be important processes in the crystallization of HEL. The increase in the
rotational correlation times at different ionic strengths appear to indicate the
efl'ectiveness of the difi'erent salts for inducing interactions that lead to
crystallization. This retardation of the rotational mobility may allow the
formation of specific ionic interactions by NaCl and NAc but not with NS. For
HEL, salts that cause an increase in the rotational correlation times at lower
ionic strengths appear to be more effective agents for crystallization. A
sharper increase in the rotational correlation times is also observed in these
salt solutions as the solution becomes supersaturated. Further investigations
are required to determine whether this is a general phenomenon.

89

The ability to measure the nature and magnitudes of the molecular
interactions between protein molecules under crystallization conditions
should result in a more directed approach in producing high quality crystals

for X-ray crystallography. These methods appear to be able to dynamically
monitor the supersaturation levels in situ and would be useful in the
optimization of precipitant and protein concentrations. The ability to
characterize the molecular interactions in a particular protein system
operating under supersaturated conditions is useful in directing the choice of
precipitants. It is important to emphasize that these interactions are evident
with fluorescence methods before the appearance of macroscopic crystals.
Further work is necessary to establish the detailed protocols for the
application of fluorescence spectroscopy to the screening of conditions.

However, it is clear that fluorescence spectroscopy holds promise as a

valuable aid in the crystallization of proteins.

Chapter 6

Time-Resolved Fluorescence and Anisotropy of
Non-Covalently Bound ANS for Monitoring the
Crystallization Conditions of Lysozyme:

Abstract

Time-resolved fluorescence measurements and anisotropy
measurements of the non-covalently bound probe, 1-anilino-8-naphthalene
sulfonic acid (ANS), is demonstrated to be a practical in situ method to
monitor the solution conditions of hen egg-white lysozyme (HEL). The
sensitivity of ANS to the microenvironment of the protein is useful in
isolating the fluorescence behavior of the bound fraction. Sodium chloride and
ammonium sulfate were found to cause increased binding of ANS to HEL
resulting in increased fluorescence intensities. This technique was used to
map the response of the total fluorescence and rotational correlation times of
ANS to the influence of salt and protein concentrations. ANS fluorescence
was then applied to dynamically monitor the progress of protein

cI')rstallization in both batch and vapor difi'usion experiments.

Introduction
Since the realization that conventional methods for the production of
Protein crystals were inadequate, there has been a rapid development of new
screening and optimization strategies. However, these methods primarily rely
on the visual inspection of crystallization trials. Because of the long time

\

1‘ Submitted to the Journal of Crystal Growth.
90

91

periods required to establish solubility relationships for a particular protein-
precipitant combination and the insufficient information gained on the
molecular processes, this optimization process may be dificult. Methods that
could dynamically measure the effects of various precipitants on the
interactions of proteins in supersaturated conditions would be helpful in
improving the efficiency. Such methods could be used to delineate suitable
conditions from which protein nucleation and crystal growth would occur.
Furthermore, crystallization conditions could be dynamically monitored to
provide for the active control of protein and precipitant concentrations [1 19].

Previously, we had used a covalently bound probe, 1-pyrenebutyric acid
(PBA), to determine the effects of protein crystallization conditions on the
fluorescence and anisotropy behavior of hen egg-white lysozyme (HEL)
(Chapter 5). Time-resolved methods were used to directly quantify the
fluorescence lifetime and rotational correlation times in the presence of
precipitating agents. Increases in the rotational correlation times were
observed with increasing protein and precipitant concentrations. This
decrease in the rotational mobility of the covalently labeled protein was
attributed to protein-protein interactions caused by the precipitants. It was
shown that such techniques could be used to monitor the solution conditions
leading to nucleation and crystallization.

In this work, we investigate a novel application of fluorescence
spectroscopic techniques which holds promise for the practical optimization of
protein crystallization conditions. Non-covalently bound fluorescence
molecules which are able to dynamically monitor the protein-protein and
protein-solvent interactions are used. The use of a non-covalently bound
probe eliminates the difficulties encountered in labeling procedures. Such
dimculties include the consumption of limited protein material and the need

92

NH soa-
O 0

Figure 6.1. Structure of ANS.

to separate the fi'ee probes from the protein coupled probes. Because the non-
covalently bound probe is directly added to the solution, no extra protein
material is used. Interfernece from free probe molecules is also eliminated by
exploiting the properties of fluorescent probes that are sensitive to the local
solvent environment. Only the probes which are bound to the protein display
significant amounts of fluorescence emission.

1-anilino-8-naphthalene sulfonic acid (ANS, Figure 6.1) was chosen as
the non-covalently bound fluorescence probe for this work. This probe has
been extensively used in studies of protein folding [120], protein ligand
binding [121, 122] and lipid dynamics [123]. In aqueous solutions, ANS
displays a weak green emission, but bound to proteins or lipid membranes, an
intense blue emission is observed [123-125]. These properties are used to map
the response of the time-resolved fluorescence and anisotropy parameters of
ANS to varying concentrations of sodium chloride (N aCl) and ammonium
sulfate (NS) in HEL solutions. It is also demonstrated using both batch and
vapor diffusion experiments that the time evolution of the crystallization

trials may be dynamically monitored.

93

Experimental

Solution Preparation
All solutions were prepared in 50 mM sodium acetate buffer at pH 4.6

unless otherwise noted. Three times crystallized HEL was obtained from
Sigma. Stock HEL solutions of 10% were prepared by dissolving the solids in
buffer. After a 0.45 um pore filtration, the lysozyme solution was washed
three times with buffer using an ultrafiltration cell (10,000 MW cutofl).
Protein concentrations were measured by the spectrophotometric absorbance
of a serially diulted solution at 280 nm with A195 = 26.4 [112]. ANS was
obtained fi'om Eastman Kodak and was used without further purification. A
10’3 M solution of ANS was prepared as the stock solution. This was diluted
ten times for a final concentration of 10'4 M ANS in the samples. 3.45 M
(20 %) NaCl and 3 M NS were also used as stock solutions. The samples were
prepared by adding, in order, the appropriate amounts of HEL, buffer, ANS
and precipitant with thorough mixing after each addition.

Fluorescence Measurements

Steady-state fluorescence measurements were performed using a SPEX
Fluorolog spectrofluorimeter. A picosecond dye laser system was used as the
excitation source for the time resolved measurements. The emission decay
data was collected using the time-correlated single-photon counting method
[113]. More detailed descriptions of the laser system [79] and the
measurement procedure (Chapter 3) have previously been reported. Samples
were excited with a wavelength of 350 nm and the time-resolved fluorescence
decays were collected at 480 run through a 370 nm cut-off filter and
monochromator. A total of 4096 channels was used to record the decay. Each
channel corresponded to a time interval of 0.040ns.

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The measurements were started within approximately ten minutes
after mixing of the stock solutions except for the time-courses of the batch
and vapor difi'usion experiments. All measurements were performed at 23° C.
For the determination of salt effects, 100 pl samples were prepared in 96 well
culture plates. A micro-capacity quartz cuvette was used to hold
approximately 70 pl of each sample.

For the batch time course experiment, a thin walled glass capillary
tube, sealed at the ends with Parafilm, was used to contain the sample. A
sitting drop vapor diffusion experiment was also performed by placing a 15 pl
drop in a quartz cup. This cup was attached to one corner of a 4 ml capacity
quartz cuvette with silicon grease. 1 ml of limiting salt solution was placed in
the bottom of the cuvette which was then sealed with a Teflon stopper. In
these time course experiments, the laser was directed in a region of the
solution that was devoid of crystals. This was easily performed visually
because of the intense emission from the crystals.

During the time-resolved measurements, the emission polarizer was
alternately rotated from a vertical to a horizontal orientation every 50 s to
average the effects from fluctuations in the excitation intensity. The
instrument response function from the excitation pulse was collected before
each sample by measuring light from a scattering solution and was used for
subsequent data analysis.

The data analysis procedure was described in detail previously
(Chapter 3). Briefly, the time-dependent fluorescence, Itot(t), from an initial
excited state population, may be fit to a sum of exponential terms with
characteristic lifetimes, ti, and pre-exponential factors, Ai, where i represents
a single fluorescence component [7 3]. The time-dependent induced

fluorescence anisotropy is defined by,

R(t) = —W—-— = -I-— = :8]. exp(-r/pj) (6.1)

where IW and Ivh are the vertically and horizontally oriented polarized
emission intensities, respectively, for a vertically polarized excitation source.
It“ is the time-dependent total fluorescence intensity as before and Idif is the
difference fluorescence intensity. The anisotropic decay is also described by a
sum of exponential decays where j represents one decay component and q is
the number of components. Bj and p j are the initial anisotropies and
rotational correlation times of each component, respectively. The Bj and p5
values are found by numerically fitting the experimentally measured
vertically and horizontally polarized emission using the determined
parameters for Ito); [83, 84]. In a mixture of different fluorescent species, each
component of the anisotropic decay can be associated with one or several

separate components of the total fluorescence decay.
Results

Response of ANS Fluorescence to Solution Conditions

In buffer alone, the steady-state fluorescence intensity from ANS is
negligible compared to the intensity observed in the presence of HEL.
Further increases in the steady state fluorescence intensity of ANS is
observed as the concentration of NaCl is increased. A corresponding blue shift
in the fluorescence spectra from approximately 490 nm to 480 nm is also
observed. To further investigate the cause of this fluorescence enhancement
in the presence of HEL and the increase as salt concentrations increase, the
time-resolved fluorescence decays are examined.

An example of the total time-resolved fluorescence decay is shown in

Figure 6.2 where the emission from ANS in a 3.6% lysozyme solution is

In

96

 

Counts

 

 

 

 

Channei (0.040 ns/ch)

Figure 6.2. Time resolved fluorescence decay curves for 10'4 M
ANS in 3.6 % HEL.

measured. Four exponential components were required to adequately fit the

total fluorescence decay. The fluorescence lifetimes of these components are

denoted 1:1 to 14 in order of decreasing lifetime, with associated pre-
exponential factors A1 to A4. For all of the samples, the total fluorescence
decay is found to be due to the combined contributions of two short lifetime
components of approximately 0.2 ns and 1.0 ns and to two longer lifetime
components of approximately 5 and 17 ns.

We examined the efi‘ects of increasing concentrations of NaCl and HEL
on the fluorescence lifetimes and pre-exponential factors of ANS. Only a
slight increase in the lifetimes of the fluorescence components was observed
as the concentration of NaCl increases. There also appeared to be no
significant effect from increasing concentrations of HEL. However, as shown
in Figure 6.3, we observed that the pre-exponential factors of the two longer
lifetime components (A1 and A2) increase while those of the two shorter

lifetime components (A3 and A4) decrease with increasing concentrations of

NaCl. From these results, we can conclude that the increase in the steady-

97

 

 

 

om .................... HIP-0'50
a 0 '
g I . e E 35
=8 0.15 C “
‘E e a . :7,
<3 I L
_ o ~0.40 g
2 0.10 o : §
. o , _
eoes
g 1:) 0 .
e a : 3’
2 0.05 O U L030 8,
.: D D : §-
“4 CI 1 3.
o'm I ' ' ' I fl ' I I ' ‘ f I ' ' ' I ' ' ' I ' ' ' 9'25
0 02 0.4 0.0 05 1 12

(NaCl Ionic Strength)"2

Figure 6.3. Response of the fi'actional pre-exponential factors A1
(0 ), A2 (O ), A3 (Cl) and A4 (I) on NaCl concentrations for
3.6 % HEL.

state fluorescence intensity is due to increases in the relative contributions
from A1 and A2.

Because the fractional contributions from both long lifetime
components increased concomitantly, it is likely that these components arise
from the same or related fluorescent species. From previous investigations
using ANS, it has been found that protein bound ANS displays lifetimes of
approximately 15 ns [123]. It is likely that the longer lifetime contributions
are due to lysozyme bound ANS and that the shorter lifetime components
originate from unbound ANS. Because the objective of this study is to map
the response of the fluorescence parameters to the crystallization conditions
on HEL, we examine the effects of salt on the bound form of ANS.

Figure 6.4 shows the effects of the ionic strength of NaCl and HEL
concentrations on the combined fractional contributions of the long lifetime
forms (A1+A2, denoted FA12) along with the crystallization results. As the

NaCl and HEL concentrations become favorable for nucleation and

98

 

 

 

 

 

050 ........................ w .....................
a l b mo
0.40 )- 010 0
X6 0
x“ X“. o b 8
o 0 CI 1 O
0.30 X X» )- 03
0 D x t N 0
N 2 .. D
.- 0 . o
‘ 8 D x xc xc I E U
“- 020 D 0 ° . 020 CI 0 o
0 A: o
A
2 xct
0.10 - 0.10
0'00 '''''''''''''''''''' ’ o‘m ''''''''''''''''''
o 02 0.4 0.0 0.9 1 12 ° 0-5 l :I: 2
(NaCl Ionic Strength)"2 ("5 '°"'° 3mm)

Figure 6.4. Response of the combined fi'actional contributions fiom
A1 and A2 (FA12) of HEL associated ANS to the ionic strength of
NaCl (a) and NS (b). For a), symbols represent 1.0 (A), 2.0 ( O ),
3.6 ( Cl) and 5.0 % ( O ) HEL. For b), symbols represent 2.1 ( <> ),
3.6 ( Cl) and 4.3 % ( O ) HEL. X indicates the formation of
crystals, XC indicates crystalline spherulites and ppt indicates
precipitation. The 1» symbols represent relative amounts formed.

subsequent crystallization, the amount of HEL bound ANS is observed to
increase. This correlation is stronger at 3.6 and 5% HEL than at the lower
protein concentrations. An increase in the slopes appears to occur near the
concentration of NaCl which causes saturation. N aCl concentrations greater
than approximately 1 M result in the formation of amorphous precipitate
which eventually transform into crystalline spherulites. Under such
conditions of immediate precipitation, the presence of large visible particles
interferes with the fluorescence measurements. At the lower concentrations
of HEL, only crystalline spherulites are formed at high NaCl concentrations.
Figure 6.4b shows the effects of the ionic strength of ammonium
sulfate (NS) on the bound fraction of ANS in HEL solutions. NS is known to
be a salt that is not amenable for the crystallization of HEL [8]. Although the

amount of bound ANS increases as the HEL and NS concentrations increase,

99

no crystallization is observed under these conditions. At high concentrations
of NS and HEL, a precipitate forms which gradually transforms into a gel.
Again, there appears to be a break in the slopes as the square root of the ionic
strength increases. However, in the case of NS, this break appears well below
the solubility limit. The change in slope also appears to occur at lower NS

concentrations as the HEL concentration increases.

Response of the Rotational Correlation Times to Solution Conditions

The parallel and perpendicular components of the polarized emission
decay of ANS in 3.6% HEL solution are shown in Figure 6.2. From the fits to
a sum of exponential components, the rotational correlation times from each
component are denoted p1, p2, p3, ..., in order of decreasing magnitude with
the corresponding initial anisotropies denoted B1, B2, B3, The rotational
correlation times which resulted from the one component fit appeared to
describe the overall rotational motions of HEL and showed a strong
dependence on the particular solution conditions. Although one component
fits were adequate to describe the decays at higher HEL and NaCl
concentrations, the initial portion of the decays were not well fit at lower
protein concentrations.

The use of two components in the anisotropy decay was judged to
provide the most physically meaningful and consistently good fits for the
data. The two component fits consisted of a short decay component, p2, on the
order of 1.5 ns and a longer component, p1, that exhibited a strong
dependence on the solution conditions. This component most likely originates
from the bound fraction of ANS. For the two component fits, the pi
component was associated with the two longer fluorescence lifetime

components in the calculations. This procedure has been shown to provide the

100

most physically meaningful fits for fluorescence from multiple emitting
species [126]. The p2 component was associated with all four total
fluorescence decay components. The p1 component appeared homogenous and
could not be resolved into additional components representing monomers,
dimers or higher aggregates.

Three component fits, with the two longest components associated with
the fluorescence from the bound form, resulted in an additional short
component on the order of 0.1 ns. The use of three components did not
significantly improve the quality of the ,fits as judged visually and by the
reduced sum of squares. One, two and three component fits all yielded similar
values for p 1. These results suggest that the p1 component represents the
overall rotational motion of ANS bound HEL.

In the absence of salt, the measured long rotational correlation times
agrees well with that expected from the overall rotation of HEL in solution.
The measured p1 value of 14.8 ns in a 1 % HEL solution corresponds to a
rotating sphere with a diameter of 4.8 nm [127]. Using the covalently bound
fluorescent probe PBA, a value of 16.2 ns was determined for PBA-HEL.
These values agree well with the dimensions of HEL, which can be
approximated as a prolate ellipsoid measuring 5.5 nm and 3.3 nm along the
major and minor axis, respectively [116]. The effect of N aCl on the measured
values for p1 with ANS also agree well with those measured with PBA-HEL,
providing furhter support that ANS is rigidly bound to HEL.

101

 

 

 

 

 

 

 

l e e e l 1111111 l ....... l n n a ‘m . . e n l ..............
w ‘ : 4 b N‘ o r
70 :10 >
w )-
w X+++ B t
O O .
A U A
g 50 XO-b X“ a w o D ,
- - O D
"9 Ci]: m 0 40 c
30 o o , 0 D
A’ l U 0
g g o A xc I . D 0 O l
20 20?
‘0 1 w ' ' r *w w T ' ' ' I ' ' r 1 ' ' r I ' ' ' r ' ' ' ' r ' ' ' ' I ' ' ' ' 1 ' w—' '
0 0.2 0.4 0.6 0.8 1 1.2 0 0.5 1 1.5 2
. . trz
(NaCl ionic Strength)"2 (NS lDl‘iiC Strength)

Figure 6.5. Response of the long rotational correlation times (9 1)
of HEL associated ANS to the ionic strength of NaCl (8) and NS
(b). For a), symbols represent 1.0 ( A), 2.0 ( O ), 3.6 ( U) and
5.0 % ( O) HEL. For b), symbols represent 2.1 (O ), 3.6 ( Cl)
and 4.3 % (O) HEL. See Figure 6.4 for explanations of the
other symbols.

The effects of NaCl on the p1 values of HEL bound ANS are shown in
Figure 6.5a. An increase in p1 is observed as the NaCl and HEL
concentrations increase. As plotted against the square root of the ionic
strength, three regimes in the p1 values are seen. At low ionic strengths, the
rate of increase in p1 is relatively slow and remains below 30 ns. At
intermediate ionic strengths, the p1 values show an increased slope similar to
the increase observed with the FA12 values. This increase is particularly
evident at HEL concentrations greater than 2 %. In this region of
intermediate ionic strengths, optimal N aCl concentrations for nucleation are
seen if the p1 values are in the range of approximately 30 to 60 us. As the
ionic strength of NaCl is further increased, immediate amorphous
precipitation results. Measurements that were performed on these highly

scattering solutions gave inconsistent results. Presumably, the rotational

102

correlation times would continue to increase since macroscopic particles are
observed visually.

Values for the short rotational correlation times remain at
approximately 1.5 ns and showed no significant changes for all N aCl and
HEL concentrations. However, the initial anisotropy of the short rotational

correlation time (B2) did show a decrease as the ionic strength increased. The
initial anisotropy of the long rotational correlation times (B1) remains nearly
constant at an approximate value of 0.21 for all NaCl and HEL
concentrations.

The effects of NS on the p1 values of HEL bound ANS is shown in
Figure 6.5b. Similar effects of the ionic strength are seen with NS as with
NaCl except that NS did not result in crystallization. The p1 values in NS
solutions are seen to be strongly dependent on both the ionic strength and
HEL concentrations. Changes in the slopes of p1 also showed increases as the
ionic strength increased. As with N aCl, the short rotational correlation time
did not vary greatly from 1.5 ns. The values obtained for 31 did not appear to
change significantly from values between 0.20 to 0.24. Again, the B2 values

for ANS in NS solutions decreased as the NS concentration increased.

Monitoring the Progress of Batch Crystallization

The fluorescence parameters of ANS in HEL solutions were measured
during the progress of a batch crystallization experiment to demonstrate that
the crystallization conditions due to changes in HEL concentration could be
dynamically monitored. Changes in the NaCl concentration are expected to be
small [128]. Initial concentrations are 4.2 % HEL with 5 % NaCl. Crystals
first became clearly visible at approximately 20 hrs at which point the

103

 

 

EVVY

[HEL] (%)
[HEL] (°/.)
D
(so) '0

 

 

 

‘
l
O
n
a “ IQWIQ' ' "

 

 

020409090100120 020405090100120
Time (hr) TING (hf)

Figure 6.6. Monitoring the batch crystallization of HEL. The
(O ) symbols represents HEL concentrations from A281
measurements of diluted aliquots taken at the indicated times.

The ( Cl) symbols are the FA12 values in a) and the p1 values in
b) from in situ fluorescence measurements.

concentration of HEL began to decrease. The crystals appeared to be of the
familiar tetragonal morphology.

In Figure 6.6a, the FA12 values of ANS is shown together with the
spectrophotometrically determined protein concentration. After nucleation,
there appears to be an initial fast decrease in the HEL concentration at about
20 to 30 hrs, followed by a slower decrease up to 104 hrs until the solution
reached equilibrium at 0.8% HEL. There appears to be a good correlation
between the relative amounts of bound ANS with the HEL concentration as
the solution becomes depleted. However, the fraction of ANS bound appears

to decrease at a faster rate than the HEL concentration in the slow portion of
the crystallization. In this experiment, the decrease in the values of FA12 are

due primarily to the relative increase in the values of A4 whereas A3 remains

nearly constant and A1 and A2 decrease.

104

A similar decreasing trend of the p1 values is seen in Figure 6.6b as the
crystallization progressed. There is again good agreement with the time
profile of the measured HEL concentration. However, from 30 to 104 hrs, the
rotational correlation time continues to decrease at a faster rate than the
HEL concentration. The p2 values remained constant to about 60 hrs and
then began to sharply decrease as the initial anisotropy of this component
increases. This behavior is most likely a result of the low concentrations of
protein remaining in solution.

At the end of the crystallization, the laser was directed onto a single
crystal. Irradiation of the crystal revealed that ANS had been incorporated
into the crystal as seen by the intense blue emission. The total fluorescence
fits resulted in a FA12 value of 0.33 with lifetimes of 12.0, 5.6, 1.4 and
0.11 ns. The longest lifetime component is considerably shorter than that in
solution. Fitting of the anisotropic decay resulted in a long rotational
correlation time that tended to infinitely large values (>1000 ns). The fits
yielded a limiting anisotropy of 0.38 for the long rotational correlation time
and 0.14 for the initial anisotropy of the 0.96 ns short rotational correlation
time component. As expected, the rotational motion of bound ANS in the
crystals is highly constrained.

Monitoring of Vapor Diffusion Crystallization

To determine the response of the fluorescence parameters under
conditions where both the protein concentration and NaCl concentrations
dynamically change, a vapor diffusion experiment was performed. In this
case, the volume of the sitting drop used was too small to collect aliquots of
the protein solution. Initially, the 15 pl sitting drop contained 4 % HEL and
3 % NaCl. This solution was equilibrated against a 6% NaCl reservoir.

105

 

 

 

 

 

 

 

 

om AJ_1_A nnnnn I nnnnnnnnn l tttttttt m‘ A LA I A a n l n n A l xxxxxxx 1 nnnnnnnn ’
i a ’ 1 b O :
M“ o ’ 553 o o f
: m ; sol 0 E
ooze ~ 3 o :
o 1 b
— l 0 ° . ’3 ‘5‘: F
“- j 09 a. ‘0] o f
023-1 0 0 g
2 O t 1 o b
1 w o P : t
028-1 )- 30‘ :-
‘ O l I? I
l’ . : :
0'24 """""""""""""""""" a 17"‘I"'T"1I"‘I'"Tfif'h
o 50 100 150 o 20 40 so so 100 120 140
Tints (hr) Time (hr)

Figure 6.7. Monitoring the progress of a HEL vapor diffusion
crystallization trial using ANS fluorescence with a) FA12 and b)

Pl-

Figure 6.7 shows the time profile of the FA12 and the p1 values. As the
volume of the sitting drop solution decreased, the solution became
supersaturated resulting in the formation of two tetragonal crystals at
approximately 70 hrs. A concomitant increase in the bound fraction is
observed. Upon crystallization, both the bound fraction and long rotational
correlation time follow the decrease in the supersaturation as the crystals
grow. The values of the fraction of ANS and the rotational correlation time

decrease to near the initial values.

Discussion

Generally, ANS displays substantially increased fluorescence
intensities in more nonpolar and viscous solvent microenvironments. It is
known that the binding of ANS to proteins causes a substantial increase in
the steady-state fluorescence intensity [123]. This behavior has been
commonly interpreted to be the result of binding to hydrophobic regions in
the protein. However, in the case of chymotrypsin, the crystallographic

106

structure showed that ANS is bound in a polar region and participates in an
alternating charge array [121, 122]. The observed fluorescence enhancement
was attributed to the ordering of the polar solvent molecules near the binding
site. Furthermore, it has been demonstrated with apomyoglobin that the
fluorescence behavior of bound ANS is mainly determined by the restrictions
of the probe microenvironment [125].

Free ANS in water exhibits a lifetime of approximately 0.25 ns [129]
and corresponds to the shortest lifetime, 14, measured in this study. The two
longest lifetime components, 11 and 12, are likely to arise fi'om protein bound
ANS. The origin of two separate lifetime components may be due to either
static or dynamic heterogeneity. There may be different classes of distinct
binding sites on HEL corresponding to static heterogeneity, each with
different solvent microenvironments affecting the fluorescence lifetime.
Alternatively, one class of binding sites may exist which exhibits dynamic
heterogeneity due to conformational fluctuations of the protein or the excited
state kinetics of ANS.

Kowaser and coworkers have descibed the photophysical behavior of
ANS with the sequential formation of two excited states [130]. Absorption of
light first leads to a fluorescent non-planar excited state that displays little
sensitivity to solvent polarity. Subsequent conversion to the solvent sensitive
charge transfer excited state is then controlled by the local solvent mobility.
This two state process suggests that that the presence of the two long
component fluorescence lifetimes is due to a single class of bound ANS
displaying photochemical heterogeneity. However, further physical
characterization is required to completely resolve this issue. Regardless of

whether the heterogeneity is static or dynamic, the longer lifetime

107

components do appear to arise fi'om rigidly bound ANS as evidenced by the
corresponding rotational correlation times.

The physical interpretation of the t3 component is less clear. This
lifetime component is intermediate between that of free ANS in the bulk
solution and those that are rigidly bound. A possible explanation is that the
fraction of ANS corresponding to this fluorescence component may be weakly
associated to HEL. This weak association may correspond to the localization
of ANS in the bound solvent that is near the vicinity of the protein. The value
of the short p2 component at higher lysozyme concentrations is too long to be
attributed to free ANS, which is expected to be on the order of 150 ps. At low
HEL concentrations, the value of p2 does approach the expected value and
may reflect a increase in the mobility of the solvent surrounding HEL.
However, this explanation for the origin of the t3 component is highly
tentative and warrants further investigation.

Previous studies have investigated the binding of other organic anions
such as orange II to lysozyme and their influence on lysozyme precipitation
and crystallization [41]. Precipitation and equilibrium binding studies
performed by Colvin found that the binding of methyl orange to HEL is
cooperative and was attributed to interacting hydration effects [131].
According to this model, an inhomogenous electrostatic field about the
positive HEL molecule orients the water dipoles in the vicinity of the surface
and hinders initial absorption of the anion. At increased concentrations of the
anion, an increased probability of Coulomb interactions enables the initial
absorption of the anion. This event leads to a decrease in the inhomogenous
field further allowing the adsorption of other anions.

From the effects of NaCl and NS on the pre-exponential factors of the

HEL bound ANS component, it is apparent that increasing salt

108

concentrations and HEL concentrations lead to increased amounts of bound
ANS. This cooperative behavior suggests that a similar mechanism to that of
methyl orange adsorption may occur as the sodium chloride and ammonium
sulfate concentrations increase. Binding of the choride and sulfate ions may
disrupt the inhomogenous field surrounding the HEL molecules thereby
increasing the binding of ANS.

The enhanced binding of ANS at higher salt concentrations is also
observed to correspond to increases in the pi times. Decreases in both the
rotational and translational mobility of proteins under crystallization
conditions is well known [57, 88-90]. Increases in the rotational correlation
time appear to be the due to increased intermolecular interactions between
the HEL molecules (Chapter 5). Binding of anions could provide a mechanism
for the observed increase in the long rotational correlation times. Anions
bound to specific sites would decrease the net charge on each HEL molecule
thereby decreasing the repulsive electrostatic interactions and allowing closer
contact. This increased degree of contact between the HEL molecules would
result in the decreased mobility of the protein. Although it is clear that the
HEL molecules are interacting to a greater degree under crystallization
conditions, the precise nature of these interactions and any aggregates that
result are at present not well defined.

The time required for nucleation and the number of crystals eventually
formed are related to the degree of supersaturation caused by NaCl [128].
There appears to be a strong relationship between the degree of
supersaturation, the amount of bound ANS and the rotational correlation
time of the HEL associated probe. The nucleation process appears to be
influenced by the rotational mobility of HEL in supersaturated solutions. It is
likely that the bound anions participate directly in this nucleation process.

109

The binding of the chloride ions could serve to decrease the mobility of the
HEL molecules in solution and enable the specific protein-protein
interactions that lead to nucleation.

The results indicate that the applications of non-covalently bound
fluorescence probe techniques to the screening and optimization of protein
crystallization conditions as well as to the further study of protein
crystallization phenomena are diverse. Precipitants that lead to increases in
the rotational correlation time and that produce nuclei, such as sodium
chloride with HEL, would appear to warrant further optimization of
conditions. Plots such as Figures 6.4a and 6.5a, would prove useful in rapidly
delineating the optimal protein and precipitant concentrations required to
achieve nucleation and subsequent crystal growth. Salts, such as ammonium
sulfate, that show increases in the rotational correlation time without
subsequent nucleation would not merit further investigation. Further
comparisons between different salts will be treated in a subsequent
publication (Chapter 7 ).

As seen in the batch and vapor diffusion experiments, dynamic
monitoring of supersaturation has been demonstrated. This technique could
be extended to the direct control of crystallization conditions for the
optimization of protein crystal growth. Not only are fluorescence techniques
able to monitor the bulk kinetics of protein crystallization, but are also able
to monitor the spatial properties of the crystal growth solution. With the use
of other fluorophores and extensions of the experimental apparatus, it may be
possible to directly and simultaneously monitor parameters such as protein
and precipitant concentration, temperature and pH. Fluorescence probe
techniques appear to ofl‘er an extensive potential for improvements in protein
crystal growth methodology.

Chapter 7

The Effects of Precipitants on the Time-Resolved
Fluorescence and Anisotropy of ANS for
Characterizing Lysozyme Crystallization:

Abstract

The spectroscopic behavior of a non-covalently bound fluorescent probe
1-anilino-8-naphthalene sulfonic acid (ANS) was measured to determine the
effects of various precipitants and protein concentration on the crystallization
of hen egg-white lysozyme (HEL). Increasing concentrations of precipitants
and protein caused increases in the binding of ANS and the rotational
correlation times. The various precipitants were found to exhibit differing
effects on the fluorescence behavior. The results suggest that HEL nucleation
involves a two stage process where bound anions cause increased protein
interactions followed by the formation of specific protein-protein bonds. The
implications of these findings for improving the efficiency screening of

crystallization conditions are discussed.

introduction

The fundamental problems involved in finding protein crystallization
conditions are the limitations of the amount of protein material available and
the effort involved to screen the possible conditions. Consequently, a more
efficient search for protein crystallization conditions depends on reducing the
number of experimental trials and the time involved in each trial. Various

 

‘ Submitted to the Journal of Crystal Growth.
110

111
strategies including factorial [34, 50] and sparse matrix methods [132] have
been developed to improve the efficiency of this screening process. All of these
strategies rely on the judicial choice of screening conditions.

A more complete understanding of the factors involved in the protein
crystallization process would be helpful in guiding the choice of precipitants
during crystallization trials. The current approach of such investigations has
largely been phenomenological. Typically, a correlation between a measurable
property of the solution such as the translational diffusion [55], the
polydispersity [54], or the growth kinetics of protein aggregates [8] is sought
which will provide a clear indication of whether or not the solution will
engender crystallization. Although these physical phenomenon are likely to
be related to the protein crystallization process, the underlying chemical
mechanisms are not well understood.

There have been previous investigations on the nature of the chemical
interactions involved in protein crystallization. Because of its ease of
crystallization, the protein most encountered in protein crystallization
studies is hen egg-white lysozyme (HEL). Reis-Kautt and Ducruix have
studied the effects of salts on the crystallization of HEL [37, 97]. Their
findings indicate that ion pairing occurs between the protein and the anions
in solution. Pusey and coworkers have further investigated the binding of 01'
ions [133]. The desolubilization of the protein was found to coincide with the
saturation of possible binding sites on HEL. As nucleation and crystallization
occurred, fewer 01' ions were bound. These studies demonstrated that the
interactions occurring between the protein and salt precipitants are crucial
aspects of crystallization.

We had previously demonstrated that the probe 1-anilino-8-
naphthalene sulfonate could be used to dynamically monitor the protein-

112
protein and protein-solvent interactions of HEL under crystallization
conditions (Chapter 6). The increase in the fluorescence intensity of ANS was
found to be due to the extent of binding to HEL. Closely related to this
increased binding of ANS and the crystallization behavior of HEL are the
decreased rotational mobility of the protein. In the current work, we compare
the effects of various crystallizing and noncrystallizing precipitants on the
time-resolved fluorescence decay and rotational correlation times. The effects
of the salts sodium thiocyanate (N aSCN ), sodium chloride (N aCl), ammonium
acetate (NAc), sodium phosphate (NaP) and ammonium sulfate (NS) on the
fluorescence behavior of ANS in HEL solutions are investigated. We also
determine the effects of HEL concentration in the presence of these various
salts. The findings provide further information on the mechanisms of protein
crystallization and the relation to measurements of physical transport
properties. The implications of these results to the application of fluorescence
techniques for the screening of protein crystallization conditions is also

investigated.
Experimental

Solution Preparation

All solutions were prepared in 50 mM sodium acetate bufi‘er at pH 4.6
unless otherwise noted. Three times crystallized HEL was obtained fi'om
Sigma. Stock HEL solutions of 10% were prepared by dissolving the solids in
buffer and passing through a 0.45 pm pore filter. The HEL solution was then
washed three times with buffer using an ultrafiltration cell (10,000 MW
cutoff). The protein concentrations were measured by using the
spectrophotometric absorbance at 280 nm with A195 = 26.4 [112]. ANS was
obtained from Eastman Kodak and was used without further purification. A

113
10'3 M solution of ANS was prepared as the stock fluorescence probe solution.
This was diluted ten times for a final concentration of 10'4 M ANS in the
samples. Stock solutions of NaSCN, N aCl, NAc, NaP and NS were prepared
and added to the samples. The samples were prepared by adding, in order,
the appropriate amounts of HEL, buffer, ANS and precipitant with mixing
after each addition.

Fluorescence Measurements

The steady-state and time-resolved fluorescence measurements and
the data analysis were previously described in detail (Chapters 3, 5 and 6,
[79]). For the time-resolved measurements, emission decay data were
collected using the time-correlated single-photon counting method [113].
Samples were excited with a wavelength of 350 nm and the time-resolved
fluorescence decays were collected at 480 nm. A total of 4096 channels was
used to record the decay with each channel corresponding to a time interval
of 0.040ns.

The measurements were started within approximately ten minutes
after mixing of the stock solutions. All measurements were performed at
23° C. For the determination of salt effects, 100 pl samples were prepared in
96 well culture plates. A micro-capacity black quartz cuvette was used to hold
approximately 70 p1 of each sample. The instrument response function from
the excitation pulse was collected before each sample by measuring light from
a scattering solution and was used for subsequent data analysis.

The time-dependent fluorescence, Itot(t), from an initial excited state
population, was fit to a sum of exponential terms with characteristic
lifetimes, ti, and pre-exponential factors, Ai, where i represents a single

fluorescence component [7 3]. A least squares fitting procedure was used to

1 14
deconvolute the observed fluorescence decays from the instrument response
function [80-83].
The time-dependent induced fluorescence anisotropy is defined by,

R(t)=-£——=—=ZB exp(— t/pj) (7.1)

where IW and Ivh are the vertically and horizontally oriented polarized
emission intensities, respectively, for a vertically polarized excitation source.
Ian is the time-dependent total fluorescence intensity as before and Idif is the
difl'erence fluorescence intensity. The anisotropic decay is also described by a
sum of exponential decays wherej represents one decay component and q is
the total number of components. BJ- and pi are the initial anisotropies and
rotational correlation times of each component, respectively. The Bj and pi
values are found by numerically fitting the experimentally measured
vertically and horizontally polarized emission using previously determined

parameters for It“ [83, 84].

Results

Fluorescence Properties of ANS in HEL solutions

The total fluorescence decays of all the samples are multiexponential,
requiring four exponential components to adequately fit the data. The
fluorescence lifetimes are denoted 11 to 1:4 in order of decreasing magnitude.
In a 3.6% HEL solution, the lifetimes were found to be 16.6, 5.4, 1.0 and
0.2 ns. The corresponding fractional pre-exponential factors, denoted A1 to
A4, are 0.04, 0.11, 0.39 and 0.46. Previously, we had assigned the fluorescence
lifetime components to fractions of the ANS that are located in different
microenvironments in the solution (Chapter 6). 11 and 1:2 likely originate fi'om
ANS molecules which are bound to HEL, while 14 is the lifetime of ANS in the

115

bulk solution. The origin of 13 was less clear but may to be due to ANS which

is associated with solvent surrounding HEL. Thus, the sum of the pre-

exponential factors A1 and A2 represent the relative amount of ANS that is
bound to the HEL (denoted FA12) whereas A3 and A 4 represent the
remaining fluorescence from species that are either fi'ee in solution or weakly

associated with HEL.
The IW and Iv), profiles that compose the anisotropic decays were fit

using a two rotational correlation time component model as previously
described (Chapter 6). The two rotational correlation times are denoted p1
and p2 with corresponding pre-exponential factors B1 and B2. In this model,
p1 represents the overall rotational correlation of HEL and is thus associated
with the bound lifetime components of ANS (11 and 12). This component could
not be further decomposed into subcomponents representing monomers and
higher aggregates. p1 was found to be yield similar values under different
methods of analysis. p2 was associated with all four components of the total
lifetime decay. Because we are primarily interested in the interactions of
HEL, the value of p1 under various crystallization conditions is of the most

interest.

Comparison of Salt Efl'ects at 3.6 % HEL

The effects of increasing concentrations of NaSCN, NaCl, NAc, NaP
and NS on the crystallization and fluorescence behavior were compared at
3.6 % HEL. NaSCN, NaCl and NAc (at pH 7.7 and 6.4) were found to
engender the crystallization of HEL. The 3 M stock NAc solutions exhibited a
pH of 7.7. Further adjustments of the pH to 6.4 and 4.6 were made by the
addition of acetic acid. Samples using the NAc solutions that were adjusted to
pH 4.6 did not produce crystals. NaP was found to be a poor crystallization

116
agent, at first producing a gel with ensuing disordered crystal growth fi'om
the gel. Only gel was formed fi'om the NS solutions. Although the presence of
10'4 M ANS did not appear to greatly afi‘ect the solubility or crystal
morphology of HEL, further study of these effects may be warranted.

The fluorescence lifetimes of ANS as a function of the square root of
the ionic strength of the salts did not show appreciable trends. The long
lifetime component, n, was found to range from 16 to 18 ns, while 12 varies
between 5.5 and 6.5 ns. 13 was found to vary between 1.0 and 1.4 ns and t4
between 0.1 and 0.2 ns. Although these fluctuations may appear to show
slight trends as the concentrations of the salts are increased, they are most
likely not significant. Hence, the various microenvironments of ANS do not
appear to significantly change in character as the concentrations of salt
increases.

In contrast, as seen in Figure 7.1a, the combined fractional pre-
exponential contributions (Ari-A2, denoted FA12) from the components of
bound ANS show a strong dependence on the ionic strength of the salts. The
different salts appear to influence these values to differing degrees. The
behavior of the pH 6.4 NAc solutions appear to be anomalous and are
examined in further detail below. For the other salts, the FA12 values show
increases with increasing ionic strength. In the case of NaSCN and NaCl,
further increases in FA12 are seen as the supersaturation of the solution
increases. In the NaP and NS solutions, this increase in the slope of FA12 is
observed before saturation is reached. To compensate for the combined
increases in A1 and A2, A3 and A4 decrease as the concentration of salt
increases.

The effects of the pH of NAc solutions on the FA12 values of ANS are

shown in Figure 7.2a. No significant changes were observed in the

117

 

 

 

 

 

 

 

0‘01 . r . . l . . 1 . l r . L . l r . . 3 w‘ a . 1 . l .............. ’
a El ’ 1 b D X++0 O
0.35 o 70-: X+ E.
D o 3 0 r
030 A X++ 00-: E-
XC A X+ L : X++ X+ O t
N xcv r ‘5‘ 50~ x Ch 0 h-
(" 025 xcv q“ o L 5 1 C" E
u. x "' .‘ A)“ L
v‘7 at 0 F °- “’1 xcxg BAX g o ;
020 V A 0 ° ° 0 ° 903 ‘0 o '-
v o x x X+ X+ ? i )9 D O :
0.15 L 1 v A :
. 20 v .
, (I v ;
b
0-19 them” ......... ’ to ................... ‘
F 05 i 15 :2 0 05 1 1.5 2
. . 1’2
(Salt Ionic Strength) "2 (Salt Ionic Strength)

Figure 7.1. Effects of the ionic strength of NS ( O ), NaP ( Cl),
pH 4.6 NAc(<>), NaCl (A) and NaSCN(V) salts on the

a) FA12 and b) p1 fluorescence parameters and crystallization
behavior of 3.6% HEL solutions. X indicates the formation of
crystals and XC indicates crystalline clusters. The + symbols
represent relative amounts formed.

fluorescence lifetimes. The greatest changes in FA12 are seen at pH 7 .7,
where no acetic acid was added. Concurrent decreases are seen in the values
of A3 and A4. At pH 4.6, the FA 12 contributions decrease as the concentration
of NAc increases. The changes of the fluorescence contributions at pH 6.4
appears to be intermediate between those at pH 4.6 and 7.7.

The effects of the ionic strengths of the precipitants on the long
rotational correlation time of AN S (p1) are shown in Figure 7.1b. The p1 times
show a strong dependence on the particular salt present and the
concentrations of the salts. For NaSCN, NaCl and pH 6.4 NAc, the pi times
rapidly increase as supersaturation occurs. Greater values for p1 also
correspond to increased amounts of crystalline material. For these salts with
3.6 % HEL, it appears that a threshold p1 value of approximately 30 ns
indicates that nucleation will occur. For NaP and NS, which both form gels at

high salt concentrations, large increases in p1 are observed well before

118

o.‘o'A44A+lAAJA1AJAJJAAJL ‘m AAA;1AAAA1AAAAl#AAJ

 

 

 

 

 

 

 

a X“ E 1 b o '
”5 x x50 r mi ox.“ L
030 O oX+++ _ .4 »
o < ’
0 ; L
“025 ’ 1; '°, )5» 0x. .
" x x x I c i 0 ’
o . I- v 1 P
E 20 D D D D D 0 x0. : a:- ”a x‘o 0x. )-
? . r
0.15 L ,
0 o E ‘ x0 DX [
0.10 0 o o 3 do: 00 B 0x T
0.05 i + 00 B .
: 20 ~
0'00 vvvvvvvvvvvvvvvvv ’ I f v . v v - ' . ' v ' ' 1 ‘ I ' 'fi '
6 05 1 15 :2 o 05 1 1.5 2
. . V2
(NAc lomc Strength)“ (NAc lomc Strength)

Figure 7 .2. Efl‘ects of the ionic strengths on the a) FA12 and b) p1

fluorescence parameters and crystallization behavior of
3.6% HEL solutions at pH 7.7 ( O ), 6.4 (U) and 4.6 (O ). See
Figure 7 . 1 for an explanation of the other symbols.

saturation is reached. The values of p1 at saturation (not shown) are much
greater with N aP and NS than with the crystallizing salts.

It is interesting to note that the values of p1 appear to follow similar
trends, with three distinct regions. These values initially fall on a shallow
slope as the square root of the ionic strength increases. At higher ionic
strengths, an intermediate region displaying a more rapid increase in p; is
observed. A third region, at high salt concentrations which results in
immediate precipitation, is also observed. The values of p1 in this region could
not be accurately determined because of excessive light scattering and
settling of the particles, but are presumably greater than in the intermediate
region.

The values for the p2 at 3.6% HEL only show a slight decrease as the
ionic strengths of the different salts decrease (not shown). p2 remains in the
range of 1.7 to 1.2 ns throughout the range of conditions measured. However,
the initial anisotropies corresponding to p; and p2 showed greater salt effects.

119

 

 

 

[HEL] (96) [HEL] (%)

Figure 7.3. Effects of HEL concentrations on the a) FA12 and the

b) m fluorescence parameters and crystallization behavior of

0.86 ionic strength NS ( O ), NaP ( D ), pH6.4 NAc ( O ),
NaCl ( A ), NaSCN ( V) and 0.86M concentration NS ( 0)
solutions. See Figure 7.1 for an explanation of the other symbols.

Decreases observed in 32 as the ionic strength increased reflect the behavior
of A3 and A4. The values of 32 appeared to be dependent on the fraction of
ANS that is bound to HEL.

The effect of pH on p1 in NAc solutions is seen in Figure 7 .2b. The p1
values at pH 4.6, 6.4 and 7.7 increase as the concentration of NAc increases.
NAc appears to show the least effect at pH 6.4 and shows the greatest rate of
increase at pH 4.6. Only a slight decrease in p2 is observed at pH 7 .7 and 6.4.

However, significant decreases in 92. that are concomitant with the increase
in m, were observed at pH 4.6. The B2 values also appears to be reflect the
amount of ANS bound to HEL.

Efl‘ects of HEL Concentration
To determine the effects of HEL concentration on the crystallization

behavior, the fluorescence of ANS solutions were measured at an ionic

strength of 0.86 M for NS (molar concentration 0.29 M), NaP, NAc at pH 6.4,

120

N aCl and NaSCN. The effects of HEL concentration in the presence of 0.86 M
NS was also determined. At these salt concentrations, only the solutions
containing NaSCN and NaCl produced crystals. In the N aSCN solutions,
concentrations of HEL above 0.6 % were not used because of immediate
precipitation with subsequent crystal growth from the precipitate. The NaP
solutions at 6% HEL also produced a precipitate which subsequently gelled.

As in the case with the precipitants, there also appears to be little
dependence of the fluorescence lifetimes on the HEL concentration.
Figure 7.3a shows that the values of FA12 are observed to increase as a
function of the HEL concentration with the extent of increase depending on
the particular salt present. These values appear to approach a limiting value,
which depends on the particular precipitant, as the concentration of HEL
increases above about 3%. In contrast to the effects of increasing salt
concentration, A3 appears to increase as the concentration of HEL
approaches 3% and remains near a value of about 0.3 from 3.0 to 8.0 % HEL.

Figure 7.3b shows the efi'ects of HEL concentration on the p1 times of
ANS in the presence of the different salts. The greatest effect is seen in the
solutions containing NaSCN, with large increases in p1 observed under small
increases in the HEL concentration. All the NaSCN solutions eventually
yielded crystals but precipitation with subsequent crystallization occurred
within minutes in the solutions displaying p1 greater than 25 ns. The rate of
increase in the p1 values for the NaCl solutions also appeared to increase at a
greater rate than the non-crystallizing precipitants. The p1 values for all the
non-crystallizing mediums appeared to increase at a similar rate as a
function of the HEL concentration. The p2 values did not reveal any
significant trends and remained between 1 and 1.7 ns for all the solutions
except with NaSCN. The values of oz for NaSCN remained at 0.1 to 0.2 us for

121

all conditions measured. This low value of p2 for NaSCN appears to be due to

the lower protein concentrations.

Discussion

All of the salts except for NAc at pH 4.6 appear to induce some degree
of increased ANS binding to HEL. This behavior is likely to be due to a
repartitioning of the ANS into the different microenvironments of the protein
itself, the solvent surrounding the protein and the bulk solvent (Chapter 6).
Although it is commonly assumed that the mechanism of ANS binding to
proteins is that of hydrophobic interactions, charge effects are likely to be
important as well [121, 122]. The increased degree of ANS binding may be a
result of cooperative efi'ects of specific ion binding or alternatively, increased
hydrophobic effects due to solvent ordering by the salts. Hydrophobic effects
appear to be minimal since NaSCN, which is a chaotropic salt, causes the
greatest degree of binding at the lowest concentrations. Because of the
positive charges on HEL, anions are expected to interact strongly with HEL
[38, 39]. However, structural studies of HEL bound ANS would prove to be
helpful in further elucidating the mechanisms of ANS binding.

The rotational correlation times are related to the mobility of the ANS
in these various environments. We had shown previously that the p1 times
are consistent with the overall rotational mobility of HEL (Chapter 6).
Increases in p1 may be attributed to restricted mobility due to increasing
protein-protein interactions. The short rotational correlation time is less well
defined. It is likely to be a composite of the librational motions of the bound
ANS, weakly associated ANS and free ANS. Although it may be possible to
further separate the components of the short rotational correlation time, for
the purposes of monitoring protein crystallization conditions, there does not

appear to be significant advantages in doing so. It also does not appear

122
feasible to further decompose the long rotational correlation times.
Nevertheless, the long rotational correlation time does appear to represent
tightly bound ANS and reflects the efl'ects of crystallization agents on the
interactions of HEL.
The interactions of anions with HEL are known to play an important
role in the crystallization process. According to the results of Reis and

Ducruix, the effectiveness of various anions in decreasing the solubility of

HEL follows the reverse order SCN' > C1“ > MO ~ HzPO4' > 8042' [37, 97].
Cations showed similar but smaller effects. This phenomena was attributed
to ion pairing between the anions and the positively charged groups on HEL.
The results presented here are similar. At constant HEL concentrations, the
concentration of salt at the solubility limit increases in the order NaSCN,
NaCl, N aAc, NaP and NS. However, increased binding of ANS and increases
in the p1 times in the presence of NaP appear at lower salt concentrations
than with NaCl or NAc.

The different processes involved in causing the increased anion
binding, increased rotational correlation times and the crystallization of HEL
as the salt and protein concentrations increases appear to be related. For all
salt conditions except for NAc at pH 4.6 and 6.4, increases in the ANS
binding correspond to increases in the rotational correlation times. The
binding of anions to HEL is expected to alter the surface properties of the
protein by neutralizing the local charges. This decrease in charge would
subsequently decrease the repulsive electrostatic forces between the proteins
in solution. The decrease in the repulsive electrostatic forces would be
expected to enable a greater degree of interaction between the HEL molecules
and lead to decreased rotational mobility (Chapter 5 and 6). Because of the
different effects between the salts, it appears that specific interactions

123
between the protein and the anions are more important than general
electrostatic efl‘ects.

Furthermore, the effect of the protein concentrations appear to be
mediated by the presence of precipitants. At low salt concentrations, few
anions are likely to be bound on the surface of HEL. Under such conditions,
weak interactions occur at all protein concentration. At intermediate salt
concentrations, increased anion binding allows greater interactions at higher
protein concentrations but are decreased at lower protein concentrations. At
higher salt concentrations and in the presence of strong precipitants such as
SCN', the surface potential of the protein is expected to be completely
neutralized by anion binding. Under such conditions, the aggregation appears
to be non-specific since the immediate formation of amorphous precipitate is
observed.

The effects of NAc at the different pH’s appear to be anomalous. This
behavior may be explained by considering the solution as a mixture of the two
different agents acetic acid and ammonium acetate. At pH 7.7, where only the
acetate and ammonium ions are present, the binding of ANS and the
rotational correlation times appear to follow the same trends as the other
salts. Increasing the concentration of acetic acid to decrease the pH has the
effect of decreasing the binding of ANS to HEL. Because the other salts all
cause increased binding at pH 4.6, it appears that this decreased binding of
ANS can be attributed to the presence of acetic acid in the lower pH
solutions. N onpolar interactions with the acetic acid in the bulk solution may
result in the additional solvation of the ANS. However, the rotational
correlation times of the bound fraction does show increases as the NAc

concentration increases without the formation of crystals.

124

Previous investigations have suggested that HEL nucleation occurs
through the addition of monomer units to growing protein aggregates [14].
However, there appears to be additional processes occurring in the nucleation
of HEL. At 3.6% HEL, the rotational correlation times are seen to increase
with all of the salts, including those that do not lead to crystallization. This
increased degree of association between the proteins appears to enable
additional protein-protein reactions leading to nucleation. This nucleation
step appears to be mediated by a specific chemical reaction since sulfate and
phosphate ions do not produce nuclei under these conditions but do lead to
decreased rotational mobilities. It is interesting to compare the precipitation
and gelation caused by NS to the phenomena at very high NaCl
concentrations, where amorphous aggregates initially form and subsequently
nucleate into large numbers of disordered crystals. In the case of NS, the
amorphous aggregate appears to follow a separate pathway to the formation
of a gel.

The precise nature of these additional nucleation reactions is not clear,
but salts that do not lead to crystallization do not appear to participate
effectively. Although NS is commonly used as an example of a salt which only
induces amorphous aggregation with HEL, tetragonal crystals have been
obtained by using ion-exchanged protein [134]. Using mass spectroscopy,
preferential non-covalent binding was observed with H2804 and H3PO4, but
not for AcOH and HCl. These results suggest that non-specific bridging of
HEL molecules by sulfate and phosphate ions occurs at lower pH. In aqueous
solution, chloride ions have been shown to bind to HEL but are released upon
subsequent crystallization [133]. There is also prior evidence that HEL
nucleation is kinetically, and not transport, limited [135, 136].

125

These findings, together with our results showing the increasing
rotational correlation times in the presence of non-crystallizing agents,
suggest that the release of the bound anions is a crucial step in the nucleation
process. Under optimal conditions, protein crystallization appears to
composed of two processes. The first process involves the binding of anions
allowing increased association between the protein molecules. This decrease
in the rotational mobility would permit the formation of specific protein-
protein interactions leading to nucleation and the subsequent release of the
bound anions. Additives such as NS, NaP and AcOH appear to inhibit this
second nucleation step.

From these results, a strategy for screening protein crystallization
conditions may be developed. It is apparent that the chemical effects of
precipitants are crucial to the nucleation and crystallization of HEL. These
chemical effects manifest themselves in the physical interactions indicated by
the fluorescence and other physical techniques. By measuring the effects of
different salts on the binding and rotational motions of fluorescence probes,
the interactions of the proteins may be determined and used to more
rationally and efficiently choose proper conditions. Increases in the rotational
correlation time appear to be a neccessary but not sufficient condition for
optimal nucleation and crystal growth.

Once suitable precipitants have been found, the fluorescence methods
may be used to map the response of ion binding and rotational correlation
times to the precipitant and protein concentrations (Chapter 6). These
techniques were also shown to be useful for dynamically monitoring protein
crystallization conditions. Used in conjunction with current screening and
visual monitoring techniques, fluorescence techniques appear to be a

practical method for elucidating the chemical effects responsible for protein

126
crystallization. Other protein-precipitant systems are currently being
investigated to determine the generality of these methods and to further
understand the mechanisms of protein nucleation and crystal growth.

Chapter 8

Summary and Conclusions
Conclusions

The goal of this work was to deve10p techniques that will improve the
efficiency of finding optimal protein crystallization conditions. Toward this
end, time resolved fluorescence and anisotropy measurements were
demonstrated to be a useful technique for monitoring the protein-protein and
protein-solvent interactions leading to crystallization. Previously, research
along this line had focused on finding a simple diagnostic based on
translational difl'usion or kinetic measurements to determine whether
solution conditions would engender crystallization or amorphous
precipitation. Our findings, together with other research, indicate that this
strategy is insufficient to explain and predict crystallization behavior. Thus,
the application of physical monitoring techniques is incomplete.

To exploit the potential of physical monitoring techniques, a greater
understanding of the effects of the solution conditions on the mechanisms of
nucleation and crystal growth is required. The chemical interactions of
precipitants with proteins and the solvent are ultimately responsible for the
events leading to crystallization. These precipitants alter the surface
properties of the protein and the solvent resulting in protein-protein and
protein-solvent interactions. It is this perturbation in the protein interactions
which may be monitored with physical methods to guide the choice of suitable
conditions.

The ability to monitor the physical interactions of proteins in
conjunction with knowledge of the chemical mechanisms of crystallization

will result in the most efficient strategy for finding optimal conditions.
127

Although such monitoring techniques most likely will not supplant the
information gained from macroscopic observations, they will enhance the
information gained from the crystallization trials. We have investigated the
mechanisms of hen egg-white lysozyme (HEL) crystallization and
demonstrated the utility of fluorescence methods for protein crystallization.

128

The following conclusions were reached:

1) The crystallographic structure of HEL co-crystallized with the

2)

3)

organic ion orange 11 showed that the ligand was not bound in a
specific location on the protein. The structure of the protein itself
was not significantly perturbed by the presence of orange 11.
However, the decrease in the solvent shell indicates that increase
hydrophobic interactions resulted from the presence of orange II.
These hydrophobic interactions were not considered favorable for

crystallization.

Time-resolved fluorescence and anisotropy measurements of 1-
pyrene butryic acid covalently labeled to HEL (PBA-HEL) is useful
as a trace fluorescence probe in monitoring the effects of salt
precipitants on protein-protein interactions. It was demonstrated
that increases in the rotational correlation times of PBA-HEL were
able to indicate increases in the protein interactions which are

necessary for crystallization.

A non-covalently bound probe, 1-anilino-8-naphthalene sulfonate
(ANS), was shown to be a more practical method for monitoring
protein crystallization conditions. The salts were also found to
cause cooperative binding of ANS to HEL resulting in increased

129
fluorescence intensity. The polarity sensitive behavior of ANS was
used to eliminate interference fiom unbound species. This system
was used to map the increases in the binding and rotational
correlation times to the influence of salt and protein concentrations.
It was demonstrated that this technique could be used to
dynamically monitor protein crystallization conditions in both batch

and vapor difi‘usion experiments in a practical manner.

4) Investigations on the effects of various salts on the fluorescence and
anisotropy behavior of the AN S/HEL system were able to provide
information on the mechanisms of HEL crystallization. HEL
crystallization likely involves a two step process. In this model,
binding of the anions acts to reduce the repulsive interactions
between the positively charged groups of HEL. For nucleation to
occur, specific protein-protein bonds must form. It is likely that the
formation of these bonds requires a decrease in the orientational
mobility of the HEL molecules and involves a release of the bound
anions. The implications of these findings for improving the

screening of crystallization conditions were discussed.

From these findings, it appears that the specific interactions between the
HEL and the anions is the central phenomenon involved in nucleation and
crystallization. These interactions are mediated by the particular chemical
properties of the bound anions. As observed with the fluorescence techniques,
the binding of these anions cause increased interactions between the protein
and leads to a decrease in the rotational mobility. Subsequent nucleation and
crystallization depends on the ability of these bound anions to participate
during the formation of crystalline contacts between HEL molecules. To

130
determine whether these findings are generally applicable to the
crystallization of other proteins and to develop screening and optimization
methods incorporating these results, firrther work is required.

Recommendations for Further Research

In regards to the crystallization of HEL, further studies which were
beyond the scope of the current work may provide useful information on the
crystallization process. A more thorough study of the effects of fluorescence
probes and other ligands on the crystallization behavior is recommended.
Such studies may be classified as investigations on the effects of
contaminants on protein crystallization. More detailed investigations on the
effects of various concentrations of ANS on the crystallization behavior is
recommended to define the perturbations introduced with the use of a
fluorescence probe. It is also recommended that the structure of the ANS-
HEL conjugate be determined. Structural knowledge of the binding
properties of ANS would enhance the interpretation of the fluorescence
behavior.

Preliminary investigations have shown that PBA-HEL crystallizes
under vastly different conditions than the native form and requires the
addition of a detergent and decreased temperatures. More detailed
investigations on the crystallization behavior would provide information on
the perturbations imposed by the large hydrophobic moiety. It would also
prove to be interesting to determine the crystallographic structure of PBA-
HEL. Through the structure determination, the specific location and
stereochemistry of the PBA group could be identified. Furthermore, it is
likely that the interactions of the PBA with detergents could be
characterized. This system could provide a useful model system for the
crystallization of other hydrophobic proteins.

131

To generalize the application of fluorescence techniques to the
crystallization of different proteins, the spectroscopic behavior of other
protein/probe systems should be investigated. These systems should include
proteins with properties difi‘erent from HEL. Such proteins may be classified
according to surface properties including acidic, basic or hydrophobic
characteristics and according to the size and conformational heterogeneity.
Alternatively, difi'erent proteins may be chosen according to the types of
conditions and precipitants which lead to crystallization. A suitable candidate
for further experiments is a-chymotrypsin. The structure of the
AN Slat-chymotrypsin complex has been determined crystallographically and
would be helpful in interpreting the results of the fluorescence experiments.
The use of other probes could be useful for investigating other probe-protein
interactions and may be required for proteins that do not bind ANS.

Improvements in the fluorescence instrumentation are recommended
to increase the speed and accuracy of the measurements. These
improvements are required for fluorescence spectroscopy to become a routine
tool for use by crystallographers. To increase the accuracy of the time
anisotropy measurements, an intensity integrator is recommended to monitor
intensity fluctuations in the laser excitation source. A laser power integrator
which monitors the laser intensity during the measurement of each emission
polarizer orientation has been designed and constructed, but has not yet been
implemented. The relative intensity of each decay can then be normalized to
the excitation power. An electronically controlled polarizer rotator would
facilitate the measurement of rotational correlation times. This apparatus
would be useful in the automatic monitoring and control of solution

conditions during time-course experiments.

132

To decrease the cost of the instrumentation for routine applications,
the use of the frequency modulation techniques should be investigated as an
alternative to the time-correlated single photon counting technique. The
frequency modulation technique involves the use of a sinusoidally varying
excitation source as opposed to the pulsed excitation source currently used.
The relative cost and benefits should be examined for each technique.
Alternatively, the fluorescence measurements could be performed in steady-
state mode. However, resolution of the different decay components would be
lost.

After the improvements in the instrumentation and the
characterization of other protein/probe systems have been completed, the
development of a general crystallization strategy is warranted. It is unlikely
that current protocols for previously uncrystallized protein based on the
visual observation of crystallization trials will be completely supplanted.
However, the incorporation of the fluorescence probe technique into current
screening and optimization procedures should be defined to achieve
maximum effectiveness. Such procedures would likely involve the proper
selection of probes based on the particular properties of the protein and the
subsequent characterization of the effects of various precipitants on the
protein interactions. Although it is in its infancy, the application of
fluorescence techniques to protein crystallization problems shows significant

promise.

APPENDIX A

Tabulated Data for Chapter 5

Appendices A, B and C contain the fluorescence and
anisotropy parameters from the least squares deconvolution fits
of the intensity decays. Total fluorescence parameters are listed
first followed by the anisotropy parameters. The first column
lists the conditions of each sample, M is the molarity, IS is the
ionic strength and sqrt(I S) is the square root of the ionic
strength. For the fit parameters, chisqr is the reduced sum of
squares for the fit, Scott and Shift are the scatter and shift
parameters for the instrument response function and Offset is
the zero offset value. For the total fluorescence fits, A1, A2, A3,
..., are the pre-exponential factors and T1, T2, T3, ..., are the
fluorescence lifetimes. For the anisotropic fits. B1, B2, B3, ..., are
the pre-exponential factors and R1, R2, R3, ..., are the rotational
correlation times. Also included with the total fluorescence data
are the visual observations made on the solution denoted as obs.
Please refer to the text for the other symbols and abbreviations.

133

134

Total Fluorescence: Set 2, Series 2B. 2% HEL vs. [NaCl]

 

 

 

%NaCl sqrt(|S) chisqr Scatt Shift Otiset Gas
0.00 0.000 0.000 0.000 1.615 0.000 -0.032 0.000
2.00 0.342 0.342 0.585 1.713 0.000 -0.019 0.000
4.00 0.684 0.684 0.827 1.826 0.000 0.004 0.000
5.00 0.856 0.856 0.925 1.411 0.000 -0.036 0.000 X
6.00 1.027 1.027 1.013 1.838 0.000 -0.016 0.000 X.-
8.00 1.369 1.369 1.170 1.744 0.000 -0.019 0.000 PPT+

%NaCl A1 Sum
0.00 0.678 0.1 16 0.206 139.8
2.00 0.641 0.152 0.207 110.4
4.00 0.616 0.146 0.238 105.7
5.00 0.609 0.165 0.227 107.6
6.00 0.616 0.161 0.223 91.6
8.00 0.630 0.156 0.214 90.2

%NaCl
0.00 151.4 57.5 2.6
2.00 156.0 65.7 2.6
4.00 159.3 64.9 2.1
5.00 162.1 69.4 2.6
6.00 164.2 70.4 2.4
8.00 167.1 67.4 2.4

135

Total Fluorescence: Set 2, Series 2A. 4% HEL vs. [NaCl]

 

 

 

%NaCI sqrt(|S) chigr Scatt Shift Ottset Gas
0.00 0.000 0.000 0.000 1.907 0.000 0033 0.000
2.00 0.342 0.342 0.585 1.770 0.000 -0.002 0.000
4.00 0.684 0.684 0.827 1.590 0.000 -0.006 0.000 X+
5.00 0.856 0.856 0.925 1.645 0.000 -0.040 0.000 X+
6.00 1.027 1.027 1.013 1.679 0.000 ~0.009 0.000 X++
8.00 1.369 1.369 1.170 1.647 0.000 -0.027 0.000 PPT-H-

%NaCi A1 Sum
0.00 0.551 0.1 15 0.334 125.7
2.00 0.538 0.128 0.334 132.9
4.00 0.525 0.139 0.335 120.7
5.00 0.523 0.147 0.331 120.9
6.00 0.533 0.144 0.323 152.2
8.00 0.532 0.146 0.323 140.4

%NaCi T1
0.00 151.4 54.3 2.3
2.00 156.1 59.1 2.4
4.00 162.1 63.5 2.3
5.00 166.1 67.5 2.8
6.00 167.1 67.1 2.5
8.00 169.3 68.6 2.7

136
Total Fluorescence: Set 2, Series 3D. 2% NaCl vs. [HEL]

 

 

 

% gs chisqr Scaft Shift Offset (11s
1.00 1.418 0.000 0.045 0.000
2.00 1 .595 0.000 -0.027 0.000
4.00 2.142 0.000 0.019 0.000
6.00 1.757 0.000 0053 0.000
8.00 2.245 0.000 -0.031 0.000

16.03 Sum
1.00 0.692 0.151 0.158 98.1
2.00 0.621 0.138 0.242 99.6
4.00 0.508 0.126 0.366 1 16.2
6.00 0.439 0.1 14 0.447 147.8
8.00 0.384 0.101 0.515 167.9

“I. Lys T1
1 .00 152.8 65.5 2.6
2.00 154.2 62.2 2.6
4.00 156.7 59.8 2.5
6.00 157.7 55.2 2.6
8.00 158.2 50.8 2.5

137

Total Fluorescence: Set 2, Series BC. 5% NaCl vs. [HEL]

 

 

 

96 Lys chisqr Scatt Shift Offset (115

1.00 1.489 0.000 0.000 0.000
2.00 1.41 1 0.000 -0.036 0.000 X
4.00 1.645 0.000 -0.040 0.000 X+
6.00 1.969 0.000 -0.046 0.000 X+++
8.00 2.214 0.000 -0.040 0.000 PPT+

LL” Sum
1 .00 0.722 0.152 0.126 93.8
2.00 0.609 0.165 0.227 107.6
4.00 0.523 O. 147 0.331 120.9
6.00 0.437 0.1 15 0.448 11 1.7
8.00 0.385 0.102 0.513 113.3

% Lys
1.00 156.2 66.7 3.4
2.00 162.1 69.4 2.6
4.00 166.1 67 .5 2.8
6.00 166.2 59.2 2.6
8.00 166.3 53.3 2.5

138
Total Fluorescence: Set 2, Series C. 4% HEL vs. [NAc]

 

 

 

%NAc M IS sqrt(|S) chisqr Scatt Shift Offset Gas
0.00 0.000 0.000 0.000 1.186 0.000 -0.037 0.000
2.00 0.244 0.244 0.494 1.314 0.000 0.017 0.000
4.00 0.488 0.488 0.698 1.384 0.000 -0.008 0.000
6.00 0.731 0.731 0.855 1.782 0.000 0.004 0.000
8.00 0.975 0.975 0.988 1.594 0.000 -0.091 0.000
10.00 1.219 1.219 1.104 1.766 0.000 0.006 0.000 X+
12.00 1.463 1.463 1.209 1.613 0.000 -0.079 0.000 X++

%NAc A2 Sum
0.00 0.559 0.1 18 0.324 21.8
2.00 0.537 0.129 0.334 47.4
4.00 0.509 0.137 0.354 68.1
6.00 0.500 0.138 0.362 92.1
8.00 0.499 0.144 0.357 111.1
10.00 0.465 0.1 53 0.382 96.2
12.00 0.475 0.143 0.381 70.8

%NAc T1 T2
0.00 153.1 24.4 2.2
2.00 159.7 50.7 3.9
4.00 159.4 46.0 4.0
6.00 160.7 52.0 4.2
8.00 161.0 52.6 4.8
10.00 160.6 50.4 4.7
12.00 158.4 48.5 4.7

139
Total Fluorescence: Set 2, Series 1K. 4% HEL vs. [NS]

 

 

 

°/.NS M IS sqrt(|S) chisqr Scatt Shift Offset Gas
0.00 0.000 0.000 0.000 1.753 0.000 -0.038 0.000
4.00 0.303 0.908 0.953 2.042 0.000 -0.010 0.000
8.00 0.605 1.816 1.348 1.810 0.000 -0.002 0.000
12.00 0.908 2.724 1.651 1.800 0.000 0.010 0.000
16.00 1.211 3.633 1.906 1.736 0.000 0.003 0.000 PPT
%NS A3 Sum
0.00 0.574 0.1 10 0.317 133.9
4.00 0.520 0.141 0.339 1 14.4
8.00 0.521 0.144 0.336 104.8
12.00 0.508 0.144 0.349 108.8
16.00 0.519 0.130 0.351 117.7
%NS T3
0.00 151.6 54.2 2.3
4.00 163.6 61.6 2.5
8.00 166.5 62.4 2.5
12.00 171.3 66.4 2.4
16.00 174.2 61.8 2.5

140
Fluorescence Anisotropy: Set 2, Series 23. 2% HEL vs. [NaCl]

 

 

%NaCl M iS sqrt(|S) chisqr Scatt Shift Offset
0.00 0.000 0.000 0.000 1.325 0.000 0.032 0.000
2.00 0.342 0.342 0.585 1.380 0.000 -0.019 0.000
4.00 0.684 0.684 0.627 1.448 0.000 0.003 0.000
5.00 0.856 0.856 0.925 1.238 0.000 -0.037 0.000
6.00 1.027 1.027 1.013 1.481 0.000 -0.016 0.000
8.00 1.369 1.369 1.170 1.418 0.000 -0.019 0.000

%NaCl 81 82 Sum Rt R2
0.00 0.127 0.073 0.199 17.508 0.940
2.00 0.131 0.088 0.219 21.820 0.549
4.00 0.133 0.097 0.230 25.366 0.404
5.00 0.131 0.091 0.222 28.396 0.810
6.00 0.128 0.081 0.210 32.738 0.794
8.00 0.099 0.098 0.197 38.239 0.498

141
Fluorescence Anisotropy: Set 2, Series 23. 4% HEL vs. [NaCl]

 

 

%NaCf M IS sqrt(|S) chisqr Scatt Shift Offset
0.00 0.000 0.000 0.000 1.473 0.000 -0.032 0.000
2.00 0.342 0.342 0.585 1.440 0.000 -0.002 0.000
4.00 0.684 0.684 0.827 1.377 0.000 -0.006 0.000
5.00 0.856 0.856 0.925 1.389 0.000 -0.041 0.000
6.00 1.027 1.027 1.013 1.415 0.000 -0.01 1 0.000
8.00 1.369 1.369 1.170 1.399 0.000 -0.028 0.000

%NaCl 81 82 Sum Rt 82
0.00 0.137 0.113 0.250 16.749 0.564
2.00 0.138 0.139 0.277 25.622 0.561
4.00 0.131 0.129 0.260 37.621 0.741
5.00 0.123 0.105 0.228 49.526 1.837
6.00 0.120 0.097 0.217 57.288 1 .736
8.00 0.121 0.145 0.266 61.549 0.781

142
Fluorescence Anisotropy: Set 2, Series 3D. 2% NaCl vs. [HEL]

 

 

SGHB. chisqr Scatt Shift Offset
1.00 1.219 0.000 -0.045 0.000
2.00 1.317 0.000 -0.028 0.000
4.00 1.656 0.000 0.019 0.000
6.00 1.445 0.000 -0.054 0.000
8.00 1.760 0.000 -0.033 0.000
10.00 1.631 0.000 -0.051 0.000
%HEL 81 Sum Fit 82
1.00 0.135 0.065 0.200 18.955 0.570
2.00 0.136 0.089 0.225 20.744 0.522
4.00 0.137 0.121 0.258 27.210 0.807
6.00 0.138 0.148 0.286 35.057 1.123
8.00 0.138 0.157 0.294 44.222 1.325
10.00 0.130 0.158 0.288 56.686 1.700

143
Fluorescence Anisotropy: Set 2, Series 30. 5% NaCl vs. [HEL]

 

 

_%_H_EL chisqr Scatt Shift Offset
1.00 1.261 0.000 0.000 0.000
2.00 1 .238 0.000 -0.037 0.000
4.00 1.389 0.000 -0.041 0.000
6.00 1 .620 0.000 -0.050 0.000
8.00 1 .728 0.000 -0.044 0.000
10.00 2.4T! 0.000 -0.038 0.000
% HEL 81 82 Sum R1
1.00 0.128 0.051 0.180 22.417 0.788
2.00 0.131 0.091 0.222 28.396 0.810
4.00 0.123 0.105 0.228 49.526 1 .837
6.00 0.120 0.138 0.257 87.921 2.072
8.00 0.116 0.177 0.293 111.954 1.584
10.00 0.1 12 0.217 0.329 127.075 1.574

144
Fluorescence Anisotropy: Set 2, Series C. 4%HEL vs. [NAc]

 

 

%NAc M IS sqrt(|S) chisqr Scatt Shift Offset
0.00 0.000 0.000 0.000 1.1 14 0.000 —0.036 0.000
2.00 0.244 0.244 0.494 1 .1 67 0.000 0.017 0.000
4.00 0.488 0.488 0.698 1 .217 0.000 -0.008 0.000
6.00 0.731 0.731 0.855 1 .355 0.000 0.004 0.000
8.00 0.975 0.975 0.988 1.330 0.000 -0.091 0.000
10.00 1.219 1.219 1.104 1.413 0.000 0.006 0.000
12.00 1.463 1.463 1.209 1.352 0.000 -0.079 0.000
%NAc 81 82 R1 R2
0.00 0.150 0.144 0.294 18.539 0.436
2.00 0.1 33 0.160 0.293 27.007 0.591
4.00 0.135 0.163 0.298 29.958 0.577
6.00 0.104 0.151 0.255 34.430 0.531
8.00 0.125 0.150 0.275 39.621 0.715
10.00 0.122 0.188 0.310 47.156 0.540
12.00 0.1 16 0.173 0.289 51.426 0.722

145
Fluorescence Anisotropy: Set 2, Series 1K. 4%HEL vs. [NS]

 

 

%NS M IS sqrt(|S) chisqr Scatt Shift Offset
0.00 0.000 0.000 0.000 1.428 0.000 -0.038 0.000
4.00 0.303 0.908 0.953 1.591 0.000 -0.010 0.000
8.00 0.605 1.816 1.348 1.491 0.000 -0.002 0.000

12.00 0.908 2.724 1.651 1.470 0.000 0.008 0.000
16.00 1.211 3.633 1.906 1.460 0.000 0.000 0.000

%NS 81 Sum 81 82
0.00 0.141 0.099 0.240 17.291 0.612
4.00 0.137 0.100 0.237 28.986 0.847
8.00 0.130 0.087 0.217 38.239 1 .713

12.00 0.1 18 0.079 0.198 60.458 4.739
16.00 0.109 0.076 0.184 96.454 7.503

APPENDIX B

Tabulated Data for Chapter 6

See Appendix A for an explanation of the header
abbreviations and symbols.

146

147

Total Fluorescence: Set 3, Series 21. 1%HEL vs. NaCl

 

 

 

%N8CI M IS Sqls chisqr Scatt Shift 011391 (In
0.00 0.000 0.000 0.000 1.985 0.000 0.006 2.897
2.00 0.345 0.345 0.587 1.507 0.000 0.004 2.665
6.00 1.034 1.034 1.017 1.437 0.000 0.008 0.851
8.00 1.379 1.379 1.174 1.506 0.000 0.009 2.977 xc
°/oNaC| A1 A2 A3 A1 +A2 Sum
0.00 0.017 0.056 0.324 0.603 0.073 1885
2.00 0.036 0.089 0.227 0.648 0.125 1 1 13
6.00 0.046 0.099 0.224 0.631 0.145 1054
8.00 0.052 0.1 07 0.242 0.599 0.159 817
%NaCl T1 T2 T3
0.00 17.030 5.192 0.946 0.183
2.00 17.513 5.839 1.071 0.180
6.00 17.752 6.128 1.124 0.184
8.00 17.549 5.847 1.042 0.165

Total Fluorescence: Set 3, Series SB. 2%HEL vs. NaCl

148

 

 

 

%NaCl M IS 8qu chisqr Scatt Shift Offset Gas
0.00 0.000 0.000 0.000 1.726 0.000 0.005 3.521
2.00 0.345 0.345 0.587 1.553 0.000 0.007 2.095
4.00 0.690 0.690 0.830 1.423 0.000 0.01 1 1 .647
6.00 1.034 1.034 1.017 1.440 0.000 0.007 0.440 )C
7.00 1.207 1.207 1.099 1.277 0.000 0.013 1 .005 )C
%NaC| A1 A2 A3 A1+A2 Sum
0.00 0.024 0.071 0.378 0.527 0.095 1495
2.00 0.039 0.103 0.291 0.568 0.142 964
4.00 0.052 0.120 0.284 0.544 0.171 831
6.00 0.068 0.133 0.265 0.534 0.201 730
7.00 0.080 0.136 0.263 0.521 0.216 578
%NaCI T1 T2 T3
0.00 16.961 5.146 0.918 0.147
2.00 17.199 5.621 1.014 0.161
4.00 17.244 5.744 1.013 0.145
6.00 17.731 6.176 1.148 0.164
7.00 17.344 5.729 0.998 0.1 1 6

149

Total Fluorescence: Set 3, Series 2G. 3.6%NaCl vs. NaCl

 

 

 

%NaCI M IS Sqis chisqr Scatt Shift Offset (115
0.00 0.000 0.000 0.000 1.306 0.000 -0.007 6.403
1.00 0.172 0.172 0.415 1.468 0.000 0.007 1.837
2.00 0.345 0.345 0.587 1.326 0.000 0.002 0.252
3.00 0.517 0.517 0.719 1.293 0.000 0.01 1 1.480
4.00 0.690 0.690 0.830 1.404 0.000 0.013 -0.484 X
5.00 0.862 0.862 0.928 1.208 0.000 0.023 -1.344 X+
6.00 1.034 1.034 1.017 1.159 0.000 0.032 -0.211 X++
%NaCI A1 A2 A3 A1+Ag Sum
0.00 0.036 0.105 0.394 0.465 0.141 962.18
1.00 0.051 0.141 0.342 0.467 0.192 834.49
2.00 0.064 0.1 56 0.321 0.460 0.219 658.13
3.00 0.077 0.168 0.305 0.451 0.245 570.29
4.00 0.087 0.174 0.288 0.451 0.261 571 .72
5.00 0.107 0.184 0.285 0.424 0.291 399.98
6.00 0.121 0.196 0.269 0.414 0.318 419.87
%NaCI T1 T2 T3
0.00 16.600 5.420 1.035 0.189
1.00 17.085 5.738 1.079 0.163
2.00 17.323 6.024 1.188 0.185
3.00 17.336 6.042 1.196 0.170
4.00 17.426 6.040 1.202 0.157
5.00 17.460 6.029 1.148 0.140
6.00 17.918 6.531 1.330 0.169

150
Total Fluorescence: Set 3, Series 3A. 5%HEL vs. NaCl

 

 

 

%NaCi M IS Sqis chisqr Scatt Shift Offset ms
0.00 0.000 0.000 0.000 1.472 0.000 0.010 -1.020
2.00 0.345 0.345 0.587 1.305 0.000 0.008 -0.245
3.00 0.517 0.517 0.719 1.554 0.000 -0.025 -2.004 X
4.00 0.690 0.690 0.830 1.197 0.000 0.006 0.591 X++
5.00 0.862 0.862 0.928 1.278 0.000 0.009 0.527 X+++
6.00 1.034 1.034 1.017 1.149 0.000 0.007 0.748 XC
%NaCI A1 A2 A3 A1+A2 Sum
0.00 0.037 0.1 13 0.386 0.464 0.150 1 166
2.00 0.071 0.169 0.323 0.437 0.240 689
3.00 0.092 0.188 0.301 0.419 0.280 496
4.00 0.108 0.205 0.284 0.404 0.313 508
5.00 0.120 0.202 0.274 0.404 0.322 413
6.00 0.134 0.213 0.269 0.384 0.347 412
%NaCl T1 T2 T3
0.00 16.456 5.245 0.962 0.124
2.00 16.875 5.714 1.100 0.131
3.00 17.253 6.173 1.393 0.215
4.00 17.346 5.994 1.219 0.156
5.00 17.497 6.077 1.187 0.114
6.00 17.860 6.279 1.198 0.1 11

151

Total Fluorescence: Set 3, Series 1E. 2.1%HEL vs. NS

 

 

 

%NS Sgls chisrm Scatt Shift
0.00 0.000 0.000 0.000 1.501 0.000 0.009
4.00 0.303 0.908 0.953 1.387 0.000 0.019
8.00 0.605 1.816 1.348 1.314 0.000 0.001
12.00 0.908 2.724 1.651 1.540 0.000 0.009
14.00 1.060 3.179 1.783 1.425 0.000 0.015
16.00 1.21 1 3.633 1.906 1.371 0.000 0.007
%NS A3 A4 A1+A2 Sum
0.00 0.033 0.088 0.380 0.500 0.120 1362
4.00 0.052 0.1 17 0.266 0.564 0.170 968
8.00 0.072 0.1 39 0.267 0.522 0.21 1 729
12.00 0.075 0.136 0.261 0.528 0.211 741
14.00 0.125 0.159 0.235 0.482 0.283 565
16.00 0.177 0.21 1 0.226 0.386 0.388 462
%NS T3 T4 Offset
0.00 17.229 5.529 0.990 0.167 2.178
4.00 17.636 5.776 1.017 0.152 9.647
8.00 17.772 6.040 1.082 0.145 4.863
12.00 17.381 5.786 0.989 0.133 -6.135
14.00 17.078 5.625 0.894 0.066 -3.796
16.00 17.241 6.230 1.079 0.1 10 -4.881

152
Total Fluorescence: Set 3, Series 3H. 3.6% HEL vs. NS

 

 

 

%NS M IS Sqls ChISfi Scatt Shift Offset Gas
0.00 0.000 0.000 0.000 1.306 0.000 -0.007 6.403
1.98 0.150 0.450 0.671 1.312 0.000 0.001 2.256
3.96 0.300 0.900 0.949 1.270 0.000 0.016 1.683
7.92 0.600 1.800 1.342 1.255 0.000 0.010 0.548
1 1.88 0.900 2.700 1.643 1.272 0.000 0.011 0.103
13.86 1.050 3.150 1.775 1.184 0.000 0.016 0.876
15.84 1 .200 3.600 1.897 1.226 0.000 0.013 0.758
%NS A1 A1+A2 Sum
0.00 0.036 0.105 0.394 0.465 0.141 962
1.98 0.062 0.145 0.302 0.491 0.208 778
3.96 0.067 0.157 0.304 0.472 0.224 760
7.92 0.090 0.175 0.296 0.439 0.265 565
1 1 .88 0.136 0.200 0.264 0.400 0.336 462
1 3.86 0.155 0.208 0.252 0.385 0.363 340
1 5.84 0.186 0.214 0.226 0.374 0.400 406
%NS T1
0.00 16.600 5.420 1.035 0.189
1.98 17.800 6.165 1.248 0.202
3.96 17.732 6.016 1.117 0.160
7.92 17.745 6.121 1.125 0.148
11.88 17.810 6.524 1.276 0.153
13.86 17.771 6.566 1.239 0.112
15.84 17.689 6.492 1.162 0.085

153
Total Fluorescence: Set 3, Series 1D. 4.3% HEL vs. NS

 

 

 

%NS M IS 5qu chisqr Scatt Shift Offset (In
0.00 0.000 0.000 0.000 1.475 0.000 0.002 4.337
4.00 0.303 0.908 0.953 1.400 0.000 0.008 -0.389
8.00 0.605 1.816 1.348 1.172 0.000 0.013 6.330
12.00 0.908 2.724 1.651 1.240 0.000 0.002 5.642
14.00 1.060 3.179 1.783 1.171 0.000 -0.005 3.658
16.00 1.21 1 3.633 1.906 1.166 0.000 -0.006 3.734 PPT
%NS A2 A3 A4 A1+A2 Sum
0.00 0.042 0.116 0.391 0.451 0.159 1017
4.00 0.087 0.171 0.287 0.455 0.258 499
8.00 0.125 0.196 0.274 0.406 0.321 506
12.00 0.152 0.206 0.235 0.408 0.358 371
14.00 0.192 0.229 0.235 0.344 0.421 309
16.00 0.219 0.251 0.215 0.314 0.471 302
%NS T2 T3 T4
0.00 16.868 5.504 1.013 0.144
4.00 17.632 5.980 1.142 0.138
8.00 17.742 6.373 1.287 0.170
12.00 17.895 6.467 1.198 0.102
14.00 17.833 6.714 1.315 0.116
16.00 18.205 7.172 1.518 0.153

154
Total Fluorescence: Set 3, Series 1T. Batch Time Course

 

 

Time (hr) A278 I-E. chisqr Scatt Shift Offset
0.25 0.222 4.213 1.196 0.000 0.003 14.291
4.50 0.228 4.326 1.159 0.000 -0.009 3.710
16.00 1.250 0.000 0.001 4.129
17.00 0.192 3.643 1.201 0.000 0.001 0.330
21.00 0.162 3.074 1.217 0.000 0.011 2.393
32.00 0.084 1.594 1.178 0.000 -0.011 4.278
66.00 0.055 1.044 1.261 0.000 -0.009 3.395
90.00 0.045 0.854 1.644 0.000 ~0.014 -1.870
105.00 0.041 0.778 1.261 0.000 -0.042 4.249
Crystal at 105hr 1.220 0.000 -0.002 0.561
Time (hr) A1 A1 +A2 Sum
0.25 0.125 0.198 0.260 0.417 0.323 481
4.50 0.1 15 0.184 0.238 0.463 0.299 653
16.00 0.126 0.199 0.261 0.414 . 0.325 463
17.00 0.133 0.209 0.268 0.390 0.342 355
21.00 0.1 19 0.189 0.258 0.434 0.308 493
32.00 0.095 0.156 0.259 0.490 0.251 563
66.00 0.081 0.139 0.251 0.529 0.220 654
90.00 0.076 0.129 0.241 0.555 0.205 978
105.00 0.062 0.124 0.219 0.595 0.186 678
XTAL105 0.106 0.227 0.317 0.350 0.333 574

155

 

(Continued...)

Time (hr) T1 T2 T3 T4
0.25 17.844 6.191 1.161 0.105
4.50 17.835 6.639 1.478 0.179
16.00 18.086 6.578 1.343 0.158
17.00 17.889 6.491 1.393 0.190
21.00 17.711 6.096 1.171 0.136
32.00 18.124 6.393 1.237 0.180
66.00 18.010 6.161 1.124 0.161
90.00 17.771 5.918 1.062 0.165
105.00 18.891 6.889 1.365 0.213
XTAL105 12.029 5.634 1.468 0.111

156
Total Fluorescence: Set 3, Series 4T. Vapor Difiusion Time Course

 

Time (hr) chisqr Scatt Shift Offset
0.25 1.265 0.000 0.01 1 1.958
5.00 1.282 0.000 0.003 1.736
9.00 1 .356 0.000 0.006 1.702

22.00 1 .257 0.000 0.004 0.440
27.00 1 .279 0.000 -0.003 1.346
47.00 1.296 0.000 0.010 0.034
57.00 1 .349 0.000 0.002 -0.279
70.50 1 .302 0.000 0.002 1.890
73.25 1.245 0.000 -0.008 -0.178
77.50 1 .206 0.000 0.010 0.739
82.25 1 .292 0.000 -0.006 -0.766
84.50 1.203 0.000 -0.014 0.223
91.50 1.177 0.000 -0.011 1.396
101.00 1.142 0.000 -0.011 1.158
101.00 1.239 0.000 -0.012 1.754
120.00 1.130 0.000 -0.013 8.014
144.00 1.288 0.000 0.002 1.942

157

 

(Continued. . .)
Time (hr) A1 A3 A4 FA12 Sum
0.25 0.078 0.170 0.298 0.455 0.248 692
5.00 0.087 0.180 0.301 0.433 0.267 643
9.00 0.087 0.181 0.298 0.434 0.268 525
22.00 0.097 0.194 0.288 0.421 0.291 416
27.00 0.099 0.1 95 0.285 0.421 0.294 573
47.00 0.104 0.200 0.268 0.428 0.304 489
57.00 0.107 0.201 0.277 0.416 0.307 482
70.50 0.122 0.218 0.277 0.382 0.341 476
73.25 0.1 18 0.21 1 0.276 0.395 0.329 475
77.50 0.1 19 0.208 0.277 0.395 0.328 537
82.25 0.116 0.197 0.276 0.411 0.313 466
84.50 0.1 12 0.188 0.274 0.426 0.300 474
91 .50 0.102 0.171 0.268 0.460 0.272 493
101.00 0.112 0.171 0.244 0.473 0.283 434
101.00 0.109 0.171 0.256 0.464 0.280 459
120.00 0.105 0.160 0.234 0.500 0.265 518
144.00 0.095 0.157 0.228 0.520 0.252 594

158

 

(Continued. . .)
Time (hr) T1 T2 T3 T4
0.25 17.717 6.323 1.287 0.178
5.00 17.573 6.202 1.245 0.164
9.00 17.558 6.227 1.253 0.160
22.00 17.683 6.388 1.316 0.168
27.00 17.604 6.300 1.324 0.167
47.00 17.670 6.120 1.146 0.102
57 .00 17.723 6.410 1.291 0.127
70.50 17.892 6.631 1.380 0.161
73.25 17.671 6.175 1.186 0.127
77.50 17.670 6.298 1.298 0.167
82.25 17.797 6.454 1.296 0.160
84.50 17.840 6.426 1.292 0.180
91 .50 17.903 6.514 1.303 0.183
101.00 18.213 6.771 1.355 0.177
101.00 18.062 6.440 1.184 0.165
120.00 18.078 6.691 1.250 0.174
144.00 17.905 6.639 1.234 0.147

159

Fluorescence Anisotropy: Set 3, Series 21. 1%HEL vs. N 1101

 

 

%NaCl M IS Sqls chisqr Scatt Shift Offset
0.00 0.000 0.000 0.000 1.850 0.000 0.005 0.000
2.00 0.345 0.345 0.587 1.495 0.000 0.003 0.000
6.00 1.034 1.034 1.017 1.394 0.000 0.006 0.000
8.00 1 .379 1 .379 1.174 1.401 0.000 0.007 0.000
%NaCl 81 82 F81 Sum 81 82
0.00 0.166 0.154 0.520 0.320 14.805 1.61 1
2.00 0.198 0.137 0.591 0.335 22.398 1.480
6.00 0.194 0.140 0.581 0.334 24.554 1.467
8.00 0.196 0.141 0.582 0.337 26.075 1 .291

160

Fluorescence Anisotropy: Set 3, Series 38. 2%HEL vs. NaCl

 

 

96 M IS Sqls chisqr Scatt Shift Offset
0.00 0.000 0.000 0.000 1.634 0.000 0.004 0.000
2.00 0.345 0.345 0.587 1.419 0.000 0.006 0.000
4.00 0.690 0.690 0.830 1.332 0.000 0.010 0.000
6.00 1.034 1.034 1.017 1.366 0.000 0.006 0.000
7.00 1.207 1.207 1.099 1.241 0.000 0.012 0.000
% 81 82 F81 Sum 81 82
0.00 0.175 0.165 0.514 0.340 17.458 1.624
2.00 0.193 0.147 0.568 0.340 21.132 1.634
4.00 0.199 0.145 0.579 0.344 24.190 1.453
6.00 0.204 0.137 0.597 0.341 29.800 1.692
7.00 0.208 0.143 0.593 0.351 34.183 1.201

161
Fluorescence Anisotropy: Set 3, Series 26. 3.6%NaCl vs. NaCl

 

 

% M IS Sqls chisqr Scatt Shift Offset
0.00 0.000 0.000 0.000 1.345 0.000 -0.006 0.000
1.00 0.172 0.172 0.415 1.361 0.000 0.006 0.000
2.00 0.345 0.345 0.587 1.259 0.000 0.001 0.000
3.00 0.517 0.517 0.719 1.270 0.000 0.010 0.000
4.00 0.690 0.690 0.830 1.321 0.000 0.012 0.000
5.00 0.862 0.662 0.928 1.243 0.000 0.022 0.000
6.00 1.034 1.034 1.017 1.185 0.000 0.031 0.000
7.00 1 .207 1 .207 1.099 2.268 0.000 -0.022 0.000
°/. 81 82 F81 Sum 81
0.00 0.186 0.166 0.529 0.353 18.478 1.661
1.00 0.206 0.155 0.571 0.361 21.846 1.416
2.00 0.207 0.146 0. 587 0.353 25.357 1 .517
3.00 0.207 0.145 0.569 0.352 31.718 1.558
4.00 0.212 0.142 0.596 0.354 35.950 1.472
5.00 0.212 0.135 0.61 1 0.347 40.800 1.299
6.00 0.211 0.130 0.618 0.341 50.505 1.514
7.00 0.1 13 0.095 0.544 0.208 51 .294 0.807

162

Fluorescence Anisotropy: Set 3, Series 3A. 5%HEL vs. NaCl

 

 

%NaCI M IS Sqls chisqr Scatt Shift Offset
0.00 0.000 0.000 0.000 1.341 0.000 0.009 0.000
2.00 0.345 0.345 0.587 1.276 0.000 0.007 0.000
3.00 0.517 0.517 0.719 1.471 0.000 -0.026 0.000
4.00 0.690 0.690 0.830 1.190 0.000 0.004 0.000
5.00 0.862 0.862 0.928 1.206 0.000 0.009 0.000
6.00 1.034 1.034 1.017 1.155 0.000 0.005 0.000
7.00 1.207 1.207 1.099 1.524 0.000 -0.017 0.000
%NaCl 81 82 F81 Sum 81 82
0.00 0.199 0.173 0.535 0.371 18.812 1.375
2.00 0.208 0.149 0.583 0.357 29.554 1.392
3.00 0.221 0.148 0.600 0.369 32.662 1.354
4.00 0.209 0.133 0.612 0.342 47.862 1.419
5.00 0.211 0.130 0.616 0.341 56.841 1.440
6.00 0.220 0.1 29 0.630 0. 350 69.822 1 .307
7.00 0.098 0.143 0.406 0.241 86.007 0.176

163

Fluorescence Anisotropy: Set 3, Series 1E. 2.1%HEL vs. NS

 

 

%NS IS Sqls chisqr Scatt Shift Offset
0.00 0.000 0.000 0.000 1.572 0.000 0.009 0.000
4.00 0.303 0.906 0.953 1.655 0.000 0.018 0.000
8.00 0.605 1.816 1.348 1.547 0.000 -0.001 0.000
12.00 0.908 2.724 1.651 1.689 0.000 0.007 0.000
14.00 1.060 3.179 1.783 1.624 0.000 0.014 0.000
16.00 1.21 1 3.633 1.906 1.497 0.000 0.006 0.000
%NS 82 F81 Sum 81
0.00 0.191 0.185 0.507 0.376 20.676 1 .894
4.00 0.216 0.161 0.573 0.376 25.184 1.387
8.00 0.221 0.160 0.580 0.380 26.378 1.058
12.00 0.227 0.159 0.589 0.385 29.576 1.193
14.00 0.231 0.136 0.630 0.367 39.359 0.935
16.00 0.218 0.123 0.639 0.341 50.493 1.057

164

Fluorescence Anisotropy: Set 3, Series 33. 3.6% HEL vs. NS

 

 

%NS M IS Sqls chisqr Scatt Shift Offset
0.00 0.000 0.000 0.000 1.345 0.000 -0.008 0.000
1.98 0.150 0.450 0.671 1.285 0.000 0.000 0.000
3.96 0.300 0.900 0.949 1.253 0.000 0.015 0.000
7.92 0.600 1.600 1.342 1.241 0.000 0.009 0.000
11.86 0.900 2.700 1.643 1.215 0.000 0.010 0.000
13.86 1.050 3.150 1.775 1.173 0.000 0.015 0.000
15.84 1.200 3.600 1.897 1.206 0.000 0.012 0.000
17.62 1.350 4.050 2.012 1.364 0.000 .001 1 0.000
%NS 81 82 F81 Sum 81 82
0.00 0.166 0.166 0.529 0.353 18.478 1 .681
1.96 0.21 1 0.162 0.566 0.372 26.651 1.551
3.96 0.205 0.152 0.574 0.357 29.906 1 .375
7.92 0.220 0.148 0.598 0.366 35.339 1 .377
1 1.86 0.224 0.135 0.625 0.359 47.010 1.465
13.86 0.224 0.125 0.642 0.346 54.694 1.315
15.84 0.217 0.105 0.673 0.322 76.715 1 .405
17.82 0.029 0.290 0.092 0.319 73.337 0.001

165

Fluorescence Anisotropy: Set 3, Series 1D. 4.3% HEL vs. NS

 

 

%NS IS Sgls chisqr Scatt Shift Offset
0.00 0.000 0.000 0.000 1.551 0.000 0.001 0.000
4.00 0.303 0.908 0.953 1.546 0.000 0.007 0.000
8.00 0.605 1.816 1.346 1.275 0.000 0.015 0.000
12.00 0.906 2.724 1.651 1.259 0.000 0.001 0.000
14.00 1.060 3.179 1.783 1.269 0.000 -0.007 0.000
16.00 1.211 3.633 1.906 1.182 0.000 -0.007 0.000
%NS 82 Sum
0.00 0.219 0.193 0.532 0.412 20.499 1 .419
4.00 0.230 0.1 58 0.592 0. 386 36.473 1 .348
8.00 0.234 0.140 0.625 0.374 46.504 1 .725
12.00 0.234 0.126 0.646 0.362 57.302 1.308
14.00 0.236 0.120 0.663 0.356 70.866 1.205
16.00 0.204 0.095 0.682 0.299 96.775 1 .353

166
Fluorescence Anisotropy: Set 3, Series 1T. Batch Time Course

 

 

105

Time A276 i-E. chisqr Scatt Shift Offset
0.25 0.222 4.213 1.340 0.000 0.002 0.000
4.50 0.228 4.326 1.352 0.000 -0.01 1 0.000
16.00 1.256 0.000 -0.002 0.000
17.00 0.192 3.643 1.532 0.000 0.000 0.000
21 .00 0.162 3.074 1.364 0.000 0.009 0.000
32.00 0.064 1.594 1.249 0.000 -0.012 0.000
66.00 0.055 1.044 1.384 0.000 -0.010 0.000
90.00 0.045 0.854 2.017 0.000 ~0.015 0.000
105.00 0.041 0.778 3.449 0.000 -0.028 0.000
Crystal-105 1.330 0.000 -0.004 0.000

Time 81 82 T1 T2

0.25 0.243 0.147 0.623 0.391 54.656 1 .171
4.50 0.241 0.158 0.604 0.398 53.532 1 .289
16.00 0.233 0.140 0.624 0.373 55.643 1 .518
17.00 0.238 0.154 0.608 0.392 52.099 1.231
21 .00 0.230 0.149 0.606 0.379 46.472 1 .092
32.00 0.219 0.153 0.589 0.372 33.596 1 .505
66.00 0.212 0.158 0.574 0.370 27.974 1 .212
90.00 0.219 0.166 0.541 0.405 21.539 0.745
105.00 0.260 0.413 0.404 0.694 15.667 0.149
Crystal- 0.379 0.250 0.603 0.628 >1 OE3 1 .673

167

Fluorescence Anisotropy: Set 3, Series 4T. Vapor Difl‘usion Time
Course

Time 4hr) chisqr Scatt Shift Offset
0.25 1.238 0.000 0.010 0.000
5.00 1.240 0.000 0.002 0.000
9.00 1.267 0.000 0.006 0.000

22.00 1 .203 0.000 0.003 0.000
27.00 1 .219 0.000 -0.003 0.000
47.00 1.21 1 0.000 0.010 0.000
57.00 1.234 0.000 0.001 0.000
70.50 1.237 0.000 0.001 0.000
73.25 1.221 0.000 -0.009 0.000
77.50 1.227 0.000 -0.01 1 0.000
82.25 1.212 0.000 -0.007 0.000
84.50 1.225 0.000 -0.015 0.000
91 .50 1.156 0.000 -0.012 0.000
101.00 1.140 0.000 -0.012 0.000
101.00 1.222 0.000 -0.013 0.000
120.00 1.146 0.000 -0.014 0.000
144.00 1.262 0.000 0.001 0.000

168

 

(Continued. . .)

Time (hr) 81 82 F81 Sum 81 82
0.25 0.191 0.130 0. 595 0.322 29.753 1 .412
5.00 0.187 0.128 0.594 0.315 36.854 1.530
9.00 0.177 0.120 0.595 0.297 34.735 1 .554
22.00 0.180 0.1 17 0.607 0.297 42.454 1.555
27.00 0.170 0.109 0.610 0.279 35.414 1.328
47.00 0.183 0.1 13 0.618 0.296 47.937 1 .209
57.00 0.188 0.1 16 0.618 0.304 53.336 1.525
70.50 0.198 0.122 0.619 0.320 59.008 1 .530
73.25 0.181 0.1 14 0.613 0.295 52.487 1.395
77.50 0.189 0.1 19 0.615 0.308 50.927 1 .428
82.25 0.165 0.099 0.626 0.264 35.373 1 .312
84.50 0.195 0.128 0.604 0.323 41.550 1.262
91 .50 0.181 0.1 17 0.607 0.299 34.837 1.556
101.00 0.175 0.1 13 0.608 0.288 35.690 1.375
101.00 0.184 0.123 0.599 0.307 35.006 1.221
120.00 0.175 0.120 0.593 0.295 34.130 1.346
144.00 0.168 0.122 0.579 0.291 39.252 1 .389

APPENDIX C

Tabulated Data for Chapter 7

See Appendix A for an explanation of the header
abbreviations and symbols.

169

170

Total Fluorescence: Set 3, Series 2A. 3.6%HEL vs. NaSCN

 

 

 

%NaSCN M IS Sqls chisqr Scatt Shift Offset as
0.00 0.000 0.000 0.000 1.306 0.000 -0.007 6.403
0.20 0.025 0.025 0.158 1.416 0.000 0.01 1 7.822
0.41 0.050 0.050 0.224 1.410 0.000 0.017 7.71 1
0.61 0.075 0.075 0.274 1.545 0.000 0.009 -2.816
0.81 0.100 0.100 0.316 1.401 0.000 0.013 2.071 X
1.01 0.125 0.125 0.354 1.336 0.000 0.015 1.285 XD
1.22 0.150 0.150 0.387 1.389 0.000 0.010 1.332 )C
1.22 0.150 0.150 0.387 1.340 0.000 0.012 1.792 )C
%NaSCN A1 A2 A3 A4 A1+A2 Sum
0.00 0.036 0.105 0.394 0.465 0.141 962
0.20 0.044 0.126 0.366 0.464 0.171 964
0.41 0.051 0.140 0.345 0.464 0.191 1035
0.61 0.058 0.160 0.336 0.446 0.218 1093
0.81 0.061 0.171 0.311 0.457 0.232 612
1.01 0.071 0.183 0.296 0.450 0.254 580
1.22 0.074 0.191 0.292 0.442 0.266 674
1.22 0.079 0.192 0.292 0.438 0.270 701
%NaSCN T1 T2 T3 T4
0.00 16.600 5.420 1.035 0.189
0.20 15.940 5.390 1.034 0.167
0.41 15.812 5.513 1.034 0.139
0.61 16.050 5.787 1.104 0.156
0.81 16.571 6.118 1.211 0.174
1.01 16.496 6.109 1.183 0.146
1.22 16.679 6.255 1.267 0.173
1.22 16.604 6.257 1.237 0.150

See Appendix C.

171

Total Fluorescence: Set 3, Series 2G. 3.6%HEL vs. NaCl

Total Fluorescence: Set 3, Series 36. 3.6%HEL vs. NAc pH6.4

 

 

 

%NAc M IS Sqls chisqr Scatt Offset Gas
0.00 0.000 0.000 0.000 1.306 0.000 0.007 6.403
2.31 0.300 0.300 0.548 1.356 0.000 0.012 1.202
4.63 0.600 0.600 0.775 1.462 0.000 0.008 1.235
9.25 1.200 1.200 1.095 1.491 0.000 0.01 1 1.276 X
11.56 1.500 1.500 1.225 1.476 0.000 -0.003 1.100 X
13.88 1.800 1.800 1.342 1.474 0.000 0.013 1.708 X+
18.50 2.400 2.400 1.549 1.578 0.000 0.007 1.164 X+
23.13 3.000 3.000 1.732 1.452 0.000 0.01 1 1.729 X-H-
%NAc A1 A2 A1+A2 Sum
0.00 0.036 0.105 0.394 0.465 0.141 962
2.31 0.044 0.127 0.333 0.497 0.170 865
4.63 0.050 0.137 0.317 0.497 0.186 872
9.25 0.054 0.140 0.302 0.504 0.194 640
1 1.56 0.055 0.144 0.297 0.504 0.198 864
13.88 0.053 0.136 0.291 0.520 0.189 856
18.50 0.053 0.138 0.295 0.514 0.191 932
23.13 0.049 0.130 0.297 0.525 0.179 993
%NAc T1 T2
0.00 16.600 5.420 1.035 0.189
2.31 16.791 5.673 1.032 0.140
4.63 17.006 5.877 1.097 0.148
9.25 16.878 5.864 1.1 1 1 0.145
1 1.56 17.081 6.160 1.269 0.200
13.68 16.579 5.617 1.030 0.114
18.50 16.485 5.759 1.125 0.138
23.13 15.765 5.173 1.010 0.125

Total Fluorescence: Set 3, Series 28. 3.6%HEL vs. NaP

172

 

 

 

‘itNaP Sqls chisqr Scatt Shift Offset (be
0.00 0.000 0.000 0.000 1.702 0.000 0.013 2.333
3.60 0.300 0.300 0.548 1.360 0.000 0.014 -0. 134
7.20 0.600 0.600 0.775 1.323 0.000 0.01 1 1.847
10.80 0.900 0.900 0.949 1.240 0.000 0.016 0.584
14.40 1.200 1.200 1.095 1.196 0.000 0.010 0.937
18.00 1.500 1.500 1.225 1.144 0.000 0.010 0.249 PPT
%NaP A3 A4 A1+A2 Sum
0.00 0.034 0.105 0.391 0.470 0.139 1 157
3.60 0.067 0.1 52 0.323 0.458 0.219 669
7.20 0.096 0.173 0.295 0.436 0.269 620
10.80 0.131 0.197 0.278 0.395 0.328 457
14.40 0.173 0.207 0.235 0.365 0.380 321
18.00 0.235 0.227 0.204 0.334 0.462 253
%NaP T3 T4
0.00 17.033 5.609 1.017 0.159
3.60 17.260 6.004 1.102 0.146
7.20 17.777 6.421 1.213 0.143
10.80 17.949 6.445 1.163 0.111
14.40 18.017 6.530 1.180 0.079
18.00 18.315 6.996 1.352 0.088

Total Fluorescence: Set 3, Series 3H. 3.6%HEL vs. NS

See Appendix C.

173

Total Fluorescence: Set 3, Series 3E. 3.6% HEL vs. NAc, pH 4.6

 

 

 

%NS M IS Sqls chisqr Scatt Shift Offset Gas
0.00 0.000 0.000 0.000 1.306 0.000 -0.007 6.403
3.08 0.400 0.400 0.632 1.526 0.000 0.010 0.765
6.17 0.800 0.600 0.894 1.634 0.000 0.007 1 .195
9.25 1 .200 1 .200 1.095 1.859 0.000 0.000 0.551
12.33 1.600 1.600 1.265 1.777 0.000 0.002 1.701
15.42 2.000 2.000 1.414 1.923 0.000 0.016 0.723
%NS A1 A2 A3 A4 A1+A2 Sum
0.00 0.036 0.105 0.394 0.465 0.141 962
3.08 0.030 0.101 0.351 0.518 0.130 1235
6.17 0.026 0.096 0.342 0.536 0.122 1208
9.25 0.020 0.092 0.354 0.534 0.1 12 1462
12.33 0.016 0.091 0.378 0.515 0.107 1716
15.42 0.012 0.081 0.342 0.565 0.093 2734
%NS T1 T2 T3 T4
0.00 16.600 5.420 1.035 0.189
3.08 16.538 4.962 0.990 0.153
6.17 15.721 4.569 0.964 0.158
9.25 15.072 4.121 0.660 0.157
12.33 13.757 3.391 0.682 0.082
15.42 13.520 3.287 0.654 0.050

174
Total Fluorescence: Set 3, Series 2F. 3.6% HEL vs. NAc, pH 7.7

%NAc M IS 8qu chisqr Scatt Shift Offset (be

0.00 0.000 0.000 0.000 1.304 0.000 -0.007 0.005

4.63 0.600 0.600 0.775 1.389 0.000 0.005 0.712

6.94 0.900 0.900 0.949 1.318 0.000 0.009 -2.782

9.25 1.200 1.200 1.095 1.345 0.000 0.016 -1.190

11.56 1.500 1.500 1.225 1.347 0.000 0.002 -3.478 X
13.88 1.800 1.800 1.342 1.312 0.000 0.006 -2.074 X+
16.19 2.100 2.100 1.449 1.302 0.000 0.008 -1.436 X++
18.50 2.400 2.400 1.549 1.223 0.000 0.016 0.743 X+++

 

%NAc A1 A2 A3 A4 A1+A2 Sum
0.00 0.036 0.105 0.394 0.465 0.141 962
4.63 0.069 0.172 0.300 0.459 0.241 663
6.94 0.061 0.185 0.287 0.447 0.266 630
9.25 0.095 0.197 0.271 0.436 0.292 519
1 1 .56 0.1 10 0.206 0.253 0.430 0.316 469
13.88 0.126 0.215 0.242 0.417 0.341 423
16.19 0.132 0.213 0.243 0.413 0.345 384
16.50 0.124 0.188 0.197 0.492 0.311 571
%NAc T1 T2 T3 T4

 

0.00 16.600 5.420 1.035 0.189
4.63 17.251 6.323 1.165 0.174
6.94 17.171 6.214 1.105 0.143
9.25 17.306 6.401 1.119 0.134
11.56 17.261 6.407 1.168 0.134
13.88 17.150 6.423 1.173 0.132
16.19 17.099 6.316 1.070 0.098
18.50 17.186 6.508 1.131 0.074

175

Total Fluorescence: Set 3, Series 4B. 0.862 IS NaSCN vs. HEL

 

 

 

we. M IS Sqls chisqr Scatt Shift Offset Che
0.30 0.000 0.000 0.014 2.360 0.000 0.000 1.631 )C
0.40 0.000 0.000 0.017 2.463 0.000 -0.002 2.130 )C
0.45 0.000 0.000 0.016 2.383 0.000 0.005 1.595 xc
0.48 0.000 0.000 0.018 1.882 0.000 -0.003 1.147 XC
0.50 0.000 0.000 0.019 1.948 0.000 -0.001 2.847 XC
0.60 0.000 0.000 0.020 2.031 0.000 0.066 1.855 )C
%HEL A1 A2 A3 A1 +A2 Sum
0. 30 0.009 0.027 0.1 16 0.848 0.036 3642
0.40 0.012 0.031 0.121 0.636 0.043 2616
0.45 0.012 0.041 0.158 0.789 0.053 2770
0.48 0.021 0.047 0.143 0.790 0.067 2561
0.50 0.022 0.056 0.143 0.778 0.078 2027
0.60 0.023 0.058 0.250 0.669 0.081 1222
%HEL T1 T2 T3
0.30 16.350 5.020 0.792 0.199
0.40 16.435 5.196 0.847 0.198
0.45 16.081 4.776 0.781 0.186
0.48 15.960 5.338 0.868 0.194
0.50 16.003 5.573 0.928 0.191
0.60 14.915 4.595 0.541 0.122

176
Total Fluorescence: Set 3, Series 4A. 0.862 IS NAc pH 6.4 vs. HEL

 

 

 

%HB. chisqr Scatt Shift Offset Gas
1.00 1.592 0.000 0.004 1.766
2.00 1 .299 0.000 0.005 2.951
3.00 1.347 0.000 0.014 0.806 X
4.00 1.262 0.000 0.007 1.013 X+
5.00 1.166 0.000 0.014 0.392 X++
6.00 1.192 0.000 0.010 0.052 X++
%HEL A1 A2 A1+A2
1.00 0.036 0.089 0.232 0.643 0.125 1193
2.00 0.066 0.135 0.275 0.525 0.200 716
3.00 0.089 0.169 0.288 0.455 0.258 641
4.00 0.1 12 0.193 0.280 0.415 0.306 552
5.00 0.123 0.207 0.282 0.388 0.330 518
6.00 0.139 0.225 0.278 0.358 0.364 509
°/.HEL T1 T2
1.00 17.342 5.809 1.050 0.177
2.00 17.388 5.817 1.066 0.157
3.00 17.701 6.137 1.152 0.143
4.00 17.697 6.326 1.290 0.165
5.00 17.798 6.373 1.277 0.140
6.00 17.983 6.61 1 1.391 0.155

177
Total Fluorescence: Set 3, Series 4F. 0.862 IS NaP vs. HEL

%HE. chisqr Scatt Shift Offset as
1.00 1.763 0.000 0.001 -0.923
2.00 1.373 0.000 0.005 1.385
3.00 1.435 0.000 0.012 -0.186
4.00 1 .397 0.000 0.004 -0.571
5.00 1.360 0.000 0.016 0.902
6.00 1.262 0.000 0.010 0.173
7.00 1.359 0.000 0.010 -0.151

 

%HE.. A1 A2 A3 A4 A1 +A2 Sum
1.00 0.021 0.071 0.232 0.677 0.091 1630
2.00 0.033 0.098 0.290 0.57 9 0.131 656
3.00 0.047 0.131 0.309 0.513 0.178 828
4.00 0.058 0.152 0.309 0.482 0.209 710
5.00 0.063 0.161 0.310 0.466 0.223 716
6.00 0.073 0.180 0.303 0.444 0.253 567
7.00 0.075 0.175 0.300 0.450 0.250 572

%HEL T1 T2 T3 T4

 

1.00 15.942 5.222 0.966 0.177
2.00 16.449 5.460 0.968 0.155
3.00 16.785 5.760 1.058 0.151
4.00 16.920 5.870 1.121 0.152
5.00 16.915 5.809 1.100 0.125
6.00 17.176 6.071 1.232 0.146
7.00 16.790 5.673 1.050 0.087

Total Fluorescence: Set 3, Series 4G. 0.862 IS NS vs. HEL

178

 

 

 

lei-lg chisqr Scatt Shift Offset Gas
1.00 1.316 0.000 0.004 2.001
2.00 1.242 0.000 0.01 1 0.986
3.00 1.135 0.000 0.010 2.084
4.00 1 .274 0.000 0.013 0.874
5.00 1.176 0.000 0.018 1.076
6.00 1.159 0.000 -0.001 -1.235 PPT
%HEL A1 A2 A3 A4 A1 +A2 Sum
1.00 0.062 0.102 0.252 0.584 0.164 819
2.00 0.101 0.155 0.282 0.462 0.256 513
3.00 0.127 0.182 0.274 0.418 0.309 394
4.00 0.133 0.185 0.257 0.425 0.317 412
5.00 0.154 0.198 0.234 0.415 0.351 322
6.00 0.177 0.221 0.249 0.353 0.398 357
1.8% Tt T2 T3 T4
1.00 17.232 6.1 15 1.084 0.169
2.00 ‘ 17.635 6.289 1.131 0.153
3.00 17.904 6.538 1.209 0.127
4.00 18.047 6.579 1.220 0.098
5.00 18.004 6.452 1.221 0.088
6.00 17.799 6.257 1.158 0.086

179
Total Fluorescence: Set 3, Series 1F. 0.862 M NS vs. HEL

%HE. chisqr Scatt Shift 011891 (b
1.08 1.489 0.000 0.01 1 -6.597
2.1 5 1 .282 0.000 0.001 -1.760
4.30 1.637 0.000 0.012 -12.128
6.45 1 .539 0.000 0.013 -8.922
8.60 1.231 0.000 0.016 0.869
10.75 1 .129 0.000 0.018 -0.024

 

%HEL A1 A2 A3 A4 A1 +A2 Sum
1.08 0.058 0.107 0.217 0.619 0.165 799
2.15 0.1 13 0.180 0.274 0.433 0.293 543
4.30 0.164 0.202 0.242 0.392 0.366 469
6.45 0.187 0.221 0.225 0.367 0.408 412
8.60 0.188 0.218 0.215 0.380 0.405 380
10.75 0.199 0.221 0.184 0.396 0.420 293
°/oHEL T1 T2 T3 T4

 

1.08 17.264 5.634 0.915 0.103
2.15 17.619 6.127 1.074 0.130
4.30 17.179 5.803 1.074 0.098
6.45 17.517 6.011 1.106 0.085
8.60 17.981 6.752 1 .306 0.087
10.75 18.017 6.616 1.333 0.086

 

180
Fluorescence Anisotropy: Set 3, Series 2A. 3.6%HEL vs. NaSCN

 

 

WSCN M IS Sqls chisqr Scatt Shift 011891
0.00 0.000 0.000 0.000 1.345 0.000 -0.008 0.000
0.20 0.025 0.025 0.158 1.427 0.000 0.010 0.000
0.41 0.050 0.050 0.224 1.396 0.000 0.016 0.000
0.61 0.075 0.075 0.274 1.604 0.000 0.008 0.000
0.81 0.100 0.100 0.316 1.321 0.000 0.011 0.000
1.01 0.125 0.125 0.354 1.299 0.000 0.014 0.000
1.22 0.150 0.150 0.387 1.345 0.000 0.009 0.000
1.22 0.150 0.150 0.387 1.305 0.000 0.01 1 0.000
1.42 0.175 0.175 0.418 1.579 0.000 -0.018 0.000
°/oNaSCN B1 B2 F81 Sum 81
0.00 0.186 0.166 0.529 0.353 18.478 1 .681
0.20 0.205 0.159 0.564 0.363 17.406 1.307
0.41 0.202 0.1 55 0.566 0.357 20.400 1 .317
0.61 0.205 0.151 0.576 0.356 23.452 1.327
0.81 0.206 0.145 0.587 0.351 27.298 1 .492
1.01 0.204 0.136 0.599 0.340 38.448 1.536
1.22 0.196 0.133 0.595 0.328 40.236 1.61 1
1.22 0.203 0.134 0.602 0.336 47.198 1.614
1.42 0.053 0.049 0. 520 0.101 85.712 0.782

181
Fluorescence Anisotropy: Set 3, Series 2G. 3.6%HEL vs. N aCl

See Appendix C.

Fluorescence Anisotropy: Set 3, Series 36. 3.6%HEL vs. NAc pH6.4

 

 

%NAc M IS Sqls chisqr Scstt Shift Offset
2.31 0.300 0.300 0.548 1.345 0.000 0.01 1 0.000
4.63 0.600 0.600 0.775 1.290 0.000 0.007 0.000
9.25 1.200 1.200 1.095 1.341 0.000 0.010 0.000
1 1.56 1.500 1.500 1.225 1.818 0.000 -0.004 0.000
13.88 1.800 1.800 1.342 1.317 0.000 0.012 0.000
18.50 2.400 2.400 1.549 1.417 0.000 0.006 0.000
23.13 3.000 3.000 1.732 1.344 0.000 0.010 0.000
%NAc 81 82 Sum 81 Q
2.31 0.21 1 0.170 0.554 0.380 25.464 1.441
4.63 0.210 0.1 58 0.571 0.369 30.206 1 .483
9.25 0.209 0.154 0.575 0.363 36.792 1 .439
11.56 0.217 0.164 0.569 0.381 36.249 1.173
13.88 0.217 0.157 0.581 0.374 50.754 1.291
18.50 0.216 0.156 0.581 0.372 64.310 1.340
23.13 0.213 0.157 0.576 0.369 75.894 1.190

182

Fluorescence Anisotropy: Set 3, Series 2B. 3.6%HEL vs. NaP

 

 

%NaP IS Sqls chisqr Scatt Shift Offset
0.00 0.000 0.000 0.000 1.507 0.000 0.012 0.000
3.60 0.300 0.300 0.546 1.272 0.000 0.013 0.000
7.20 0.600 0.600 0.775 1.268 0.000 0.010 0.000
10.80 0.900 0.900 0.949 1 . 174 0.000 0.015 0.000
14.40 1.200 1.200 1.095 1.193 0.000 0.009 0.000
18.00 1.500 1.500 1.225 1.180 0.000 0.009 0.000
%NaP 82 Sum 81
0.00 0.182 0.169 0.519 0.351 19.081 1.549
3.60 0.210 0.156 0.574 0.366 29.006 1 .387
7.20 0.214 0.142 0.601 0.356 38.235 1.512
10.60 0.220 0.126 0.632 0.349 50.545 1.410
14.40 0.225 0.1 16 0.660 0.341 73.687 1 .262
18.00 0.232 0.101 0.698 0.333 122.637 1.377

183
Total Fluorescence: Set 3, Series 3H. 3.6%HEL vs. NS

See Appendix C.
Fluorescence Anisotropy: Set 3, Series 3E. 3.6% HEL vs. NAc, pH 4.6

%NAc M IS Sqls chisqr Scatt Shift Offset
0.00 0.000 0.000 0.000 1.345 0.000 -0.008 0.000
3.08 0.400 0.400 0.632 1.479 0.000 0.009 0.000
6.17 0.600 0.600 0.894 1.531 0.000 0.005 0.000
9.25 1 .200 1 .200 1.095 1.652 0.000 -0.001 0.000
12.33 1.600 1.600 1.265 1.598 0.000 0.001 0.000
15.42 2.000 2.000 1.414 1.703 0.000 0.015 0.000

%NAc 81 82 F81 Sum 81 82
0.00 0.166 0.166 0.529 0.353 18.478 1.681
3.06 0.194 0.166 0.538 0.360 24.574 1.419
6.17 0.196 0.160 0.550 0.357 29.456 1.315
9.25 0.180 0.160 0.530 0.340 40.825 1.034
12.33 0.173 0.181 0.489 0.354 68.633 0.525
15.42 0.156 0.191 0.449 0.347 117.354 0.415

184
Fluorescence Anisotropy: Set 3, Series 2F. 3.6% HEL vs. NAc, pH 7.7

%NAc M IS Sqls chisqr Scatt Shift Offset
4.63 0.600 0.600 0.775 1.345 0.000 0.003 0.000
6.94 0.900 0.900 0.949 1.296 0.000 0.008 0.000
9.25 1.200 1.200 1.095 1.308 0.000 0.015 0.000
11.56 1.500 1.500 1.225 1.316 0.000 0.001 0.000
13.88 1.800 1.800 1.342 1.253 0.000 0.004 0.000
16.19 2.100 2.100 1.449 1.271 0.000 0.007 0.000
18.50 2.400 2.400 1.549 1.221 0.000 0.015 0.000

%NAc 81 82 F81 Sum 81 82
4.63 0.206 0.145 0.567 0.350 27.693 1 .562
6.94 0.212 0.143 0.597 0.355 32.608 1.416
9.25 0.220 0.137 0.617 0.357 40.689 1.386
1 1 .56 0.228 0.132 0.633 0.360 47.360 1.246
13.88 0.222 0.125 0.641 0.347 61.159 1.369
16.19 0.234 0.124 0.654 0.357 71.357 1.1 14
16.50 0.216 0.112 0.659 0.326 104.531 1.241

185
Fluorescence Anisotropy: Set 3, Series 48. 0.862 IS NaSCN vs. HEL

%HEL chisqr Scatt Shift Offset
0.30 2.064 0.000 0.000 0.000
0.40 2.177 0.000 -0.002 0.000
0.45 2.181 0.000 0.005 0.000
0.48 2.005 0.000 -0.003 0.000
0.50 2.004 0.000 -0.002 0.000
0.60 1 .693 0.000 0.066 0.000

%HEL BI 82 F81 Sum 81 82
0.30 0.232 0.247 0.485 0.479 10.223 0.097
0.40 0.234 0.264 0.470 0.499 10.990 0.094
0.45 0.218 0.231 0.486 0.449 13.508 0.117
0.48 0.205 0.246 0.454 0.451 28.673 0.117
0.50 0.184 0.198 0.481 0.382 41.612 0.188
0.60 0.184 0.237 0.437 0.421 53.485 0.106

186

Fluorescence Anisotropy: Set 3, Series 4A. 0.862 IS NAc pH 6.4 vs.
HEL

%HEL chisqr Scatt Shift 011391
1.00 1.521 0.000 0.003 0.000
2.00 1 .290 0.000 0.004 0.000
3.00 1.240 0.000 0.013 0.000
4.00 1.221 0.000 0.006 0.000
5.00 1 . 192 0.000 0.013 0.000
6.00 1 . 193 0.000 0.009 0.000

%HEL B1 82 F81 Sum 81 F12
1.00 0.193 0.142 0.577 0.334 21.072 1.321
2.00 0.207 0.147 0.584 0.354 29.691 1 .343
3.00 0.213 0.145 0.595 0.358 37.625 1 .421
4.00 0.219 0.139 0.612 0.358 49.827 1.473
5.00 0.218 0.133 0.622 0.351 58.61 1 1.583
6.00 0.221 0.125 0.638 0. 346 77.391 1 .624

187
Fluorescence Anisotropy: Set 3, Series 4F. 0.862 IS NaP vs. HEL

%HEL chisqr Scatt Shifl 011381
1.00 1 .756 0.000 0.000 0.000
2.00 1 .326 0.000 0.003 0.000
3.00 1.344 0.000 0.01 1 0.000
4.00 1 .336 0.000 0.003 0.000
5.00 1.271 0.000 0.017 0.000
6.00 1 .254 0.000 0.008 0.000
7.00 1 .269 0.000 0.009 0.000

%HEL 81 82 F81 Sum F11 82
1.00 0.193 0.145 0.571 0.338 19.597 1.001
2.00 0.202 0.150 0.573 0.352 25.384 1.319
3.00 0.209 0.157 0.571 0.366 31.027 1.455
4.00 0.215 0.155 0.581 0.371 35.172 1.480
5.00 0.214 0.156 0.578 0.369 40.1 13 1.385
6.00 0.215 0.154 0.583 0.368 47.857 1 .593
7.00 0.212 0.154 0.57 8 0.366 50.568 1.432

Fluorescence Anisotropy: Set 3, Series 4G. 0.862 IS NS vs. HEL

188

 

 

%HEL chisqr Scatt Shift Offset
1.00 1.350 0.000 0.003 0.000
2.00 1.214 0.000 0.010 0.000
3.00 1.176 0.000 0.009 0.000
4.00 1.194 0.000 0.012 0.000
5.00 1.135 0.000 0.017 0.000
6.00 1.165 0.000 -0.002 0.000

°/.HE. 81 F81 Sum Rt
1.00 0.214 0.147 0.594 0.361 32.208 1.581
2.00 0.224 0.142 0.611 0.366 36.582 1.332
3.00 0.227 0.135 0.627 0.362 45.954 1.263
4.00 0.224 0.131 0.631 0.354 52.328 1.358
5.00 0.232 0.125 0.650 0.356 66.988 1.204
6.00 0.229 0.113 0.670 0.341 70.235 1.173

189
Fluorescence Anisotropy: Set 3, Series 1F. 0.862 M NS vs. HEL

%HEL chisqr Scatt Shift 011991
1.08 2.331 0.000 0.010 0.000
2.15 1 .502 0.000 0.000 0.000
4.30 2.089 0.000 0.01 1 0.000
6.45 1 .696 0.000 0.012 0.000
8.60 1.212 0.000 0.015 0.000
10.75 1.156 0.000 0.017 0.000

%H8. 81 82 F81 Sum 81 82
1.08 0.218 0.1 56 0.583 0.373 26.287 1 .000
2.15 0.228 0.145 0.61 1 0.373 38.891 1.219
4.30 0.237 0.127 0.651 0.364 48.489 1.050
6.45 0.245 0.1 19 0.674 0.364 72.591 1.038
8.60 0.248 0.121 0.671 0.369 1 15.258 1 .195
1 0.75 0.250 0.1 16 0.683 0.366 237.034 1 .241

10.
11.

12.
13.
14.
15.
16.
17.

18.
19.

20.

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HGI 8N STRTE UNIV.

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