PICOSECOND SPECTROSCOPIC STUDIES OF EQUILIBRIUM
STRUCTURAL FLUCTUATIONS OF NATIVE AND
PARTIALLY UNFOLDED STATES OF ZNII -SUBSTITUTED
AND METAL-FREE CYTOCHROMES C
By
Jagnyaseni Tripathy

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Physics
2011

ABSTRACT
PICOSECOND SPECTROSCOPIC STUDIES OF EQUILIBRIUM
STRUCTURAL FLUCTUATIONS OF NATIVE AND
PARTIALLY UNFOLDED STATES OF ZNII -SUBSTITUTED
AND METAL-FREE CYTOCHROMES C
By
Jagnyaseni Tripathy

Picosecond time-resolved fluorescence spectroscopy was employed to characterize the equilibrium and non-equilibrium protein structural fluctuations in ZnII substituted (ZnCytc) and metal-free (fbCytc) cytochromes c using dynamic fluorescence Stokes shift (FSS) and fluorescence anisotropy (FA) measurements. The intrinsic porphyrin chromophore is used as the probe for the structural fluctuations of the
surrounding protein and solvent. The FSS experiments examine how the time scales
detected from the dynamic solvation of a chromoprotein report changes in the character of motion. ZnCytc and fbCytc serve as limited, single-chromophore models for
photosynthetic reaction center and light-harvesting proteins. The dynamic solvation
of redox and light-harvesting chromophores in photosynthesis plays an important
role in the quantum efficiency of electron transfer and energy transfer performed by
these systems, respectively.
The FSS response function of fbCytc in water is biexponential over the 100-ps–
50-ns regime and the two time constants are 1.4 ns and 9.1 ns. ZnCytc under similar
solution conditions shows a biexponential FSS response but with time constants of
0.2 ns and 1.5 ns. The two correlation times from the FSS response function correspond to motions of the hydrophobic core and the solvent-contact layer, respectively.

Both FSS correlation times were lengthened and the solvation reorganization energy
was reduced from 43 cm 1 to 33 cm 1 in the presence of 50 % (v/v) glycerol. A
Brownian diffusion model with thermally activated barrier crossings on the proteinfolding energy landscape is used to interpret these results. The conclusion is that the
mean-squared deviations of the fluctuations exhibited by fbCytc are perhaps a factor
of ten larger than those in ZnCytc, which is consistent with the suggestion that fbCytc
assumes a dynamic, partially unfolded structure with some of the characteristics of
a molten globule.
The nature of the motion associated with the unfolding reaction coordinate was
then studied in ZnCytc using the FA response of the ZnII –porphyrin probe as guanidinium ion (Gdm+ ) is added to the solution. An unfolding transition-state-like intermediate is formed at ⇠1.0 M Gdm+ , well below the unfolding transition concentration
at ⇠2.0 M. The intermediate is characterized by an enhanced angular fluctuation of
the porphyrin compared to the native and the denatured structures. The correlation
time for internal angular motion returned by the FA response for the 1.0 M intermediate is similar to those observed for the FSS response of fbCytc, which suggests that
the axial ligands for the ZnII porphyrin have been lost.
The FSS response was then obtained as ZnCytc is titrated with Gdm+ using the
same data sets as the FA studies. The FSS results show that even at the lowest concentrations of Gdm+ , the native fold is destabilized so that the optical excitation of
the ZnII porphyrin chromophore perturbs the motions of the surrounding protein
and solvent so that they depart from the linear-response regime. This conclusion
is supported by the observation of an unusual bidirectional FSS response. This action of Gdm+ appears to saturate well prior to the formation of the 1-M intermediate
structure noted in the FA studies. The main implication of these results is that structural changes in the hydration layer surrounding the folded protein are the origin of
the dynamical changes reported in the FSS response in the presence of Gdm+ .

To my parents and in laws

iv

ACKNOWLEDGMENTS

The research presented in this dissertation could not have been performed without the help and support of many other individuals who has been there for me all
these years. First and foremost, I would like to thank my advisor, Professor Warren
Beck for providing me the opportunity to be a part of his research group. Without
his invaluable guidance, mentorship and endless support, I would never be in a position to present this thesis. I am especially thankful to my committee members, Prof.
Lisa Lapidus, Prof. Stuart Tessmer, Prof. C. W. Lai, Prof. Filomena Nunes and Prof.
Lynmarie Posey for their valuable time and input.
I thank Professor Gary Blanchard and Dr. Sanela Lampa-Pastirk for their patience
and instruction. They taught me almost everything I know about how to perform
picosecond spectroscopy. I thank Dr. Kevin Dillman for his help. I also owe big
thanks to my fellow graduate students Michael Bishop and Jenny Jo Mueller. Their
curiosity and questions have led me to a better understanding of my own work. I
have been fortunate to work with several talented undergraduate students, and I
particularly wish to acknowledge Kenneth Barnes, Ryan Hendericks and Steven Miller.
I wish to thank Navneet and all my Indian friends at Michigan State University for
helping me to get through the difficult times and making my stay homely.
I also owe large thanks to my family for their endless support and love throughout
my education and for encouraging me to pursue my dreams and aspirations.
Finally I convey special acknowledgement to the Department of Physics at Michigan State University for a Teaching Assistantship (2005–2009), to the National Science Foundation Biomolecular Systems Cluster/Molecular Biophysics program for
stipend support under grants MCB-009120 and MCB-0520002 for their financial support. Additional support for instrumentation was provided by the Michigan Struc-

v

tural Biology Center at Michigan State University, which is supported by the Michigan
Life Sciences Corridor.

vi

TABLE OF CONTENTS

LIST OF TABLES

ix

LIST OF FIGURES

x

LIST OF ABBREVIATIONS

xii

1 Introduction

1

1.1 Reaction Centers and Light-Harvesting Proteins . . . . . . . . . . . . . . . .

2

1.1.1 Reaction Centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.1.2 Light-Harvesting Proteins . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.2 Dynamic Solvation in Liquids and Proteins . . . . . . . . . . . . . . . . . . .

7

1.3 ZnII -substituted Cytochrome c . . . . . . . . . . . . . . . . . . . . . . . . . .

11

1.4 Aims and Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . .

14

2 Fluctuations in fbCytc from the Fluorescence Stokes Shift Response

17

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

2.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

2.2.1 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

2.2.2 Absorption and Fluorescence Spectroscopy . . . . . . . . . . . . . .

22

2.2.3 Picosecond Time-resolved Fluorescence Spectroscopy . . . . . . .

22

2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

2.3.1 Absorption and Fluorescence Emission Spectra . . . . . . . . . . . .

23

2.3.2 Picosecond Time-resolved Fluorescence Spectroscopy . . . . . . .

29

2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

2.4.1 Solvent-Response Functions in Liquids and Proteins . . . . . . . . .

37

2.4.2 Activated Barrier-Crossing Model for Protein Fluctuations . . . . .

41

2.4.3 Comparison of the Solvation Response in fbCytc and ZnCytc . . .

45

3 Picosecond Fluorescence Anisotropy Decays from ZnCytc in the Presence
of Gdm+

50

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

3.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

3.2.1 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

3.2.2 Absorption and Fluorescence Spectroscopy . . . . . . . . . . . . . .

54

3.2.3 Time-Resolved Fluorescence Measurements . . . . . . . . . . . . . .

54

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

3.3.1 Absorption and Fluorescence Emission Spectra . . . . . . . . . . . .

56

3.3.2 Picosecond Fluorescence Anisotropy Decays . . . . . . . . . . . . .

67

vii

3.3.3 Wobbling-in-Cone Mechanical Model . . . . . . . . . . . . . . . . . .

76

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

4 Fluorescence Stokes Shift Response Functions from ZnCytc in the Presence
of Gdm+

89

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

4.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

4.2.1 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

4.2.2 Absorption and Fluorescence Spectroscopy . . . . . . . . . . . . . .

93

4.2.3 Time-Resolved Fluorescence Measurements . . . . . . . . . . . . . .

93

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

4.3.1 Absorption and Fluorescence Emission Spectra . . . . . . . . . . . .

94

4.3.2 Picosecond Time-Resolved Fluorescence Spectroscopy . . . . . . .

98

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5 Conclusion

122

5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.2 Comparison to Other Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.3 Conclusions and Next Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
BIBLIOGRAPHY

128

viii

LIST OF TABLES

2.1 Lognormal and Gaussian lineshape models for the 0–0 peak in the absorption (A) and fluorescence (F ) spectra from fbCytc in water and in
50% (v/v) glycerol (see Figures 2.1 and 2.2) and estimates for the solvation reorganization energy ( ). . . . . . . . . . . . . . . . . . . . . . . . . . .

26

2.2 Model parameters for the time evolution of the time-resolved fluorescence spectrum observed in water and 50% glycerol in metal-free (fbCytc) and ZnII -substituted (ZnCytc) cytochrome c at 22 C

. . . . . . . .

36

3.1 Absorption (Q) and fluorescence (F ) lognormal lineshape parameters for
the unfolding transition of ZnCytc in the presence of Gdm+ . . . . . . . .

64

3.2 Thermodynamic parameters for the equilibrium unfolding transition for
ZnCytc and the transition midpoints. . . . . . . . . . . . . . . . . . . . . . .

65

3.3 Fluorescence anisotropy decay parameters for ZnCytc in the presence
of Gdm+ at 22 C.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

3.4 Wobbling-in-cone model parameters and the apparent hydrodynamic radius, Rh , for ZnCytc in the presence of Gdm+ at 22 C. . . . . . . . . . . .

80

4.1 Lognormal lineshape parameters for the 0–1 vibronic feature of the
time-resolved fluorescence spectra from ZnCytc in water at 22 C. . . . . 101
4.2 Lognormal lineshape parameters for the 0–1 vibronic feature of the
time-resolved fluorescence spectra from ZnCytc in 2.0 M Gdm+ at 22 C. 105
4.3 Model parameters for the time evolution of the Fluorescence Stokes
shift for ZnCytc in the presence of Gdm+ at 22 C. . . . . . . . . . . . . . . 108

ix

LIST OF FIGURES

1.1 Structure of the Rhodopseudomonas viridis reaction center (1PRC.pdb). .

4

1.2 Energy levels and generalized solvent coordinate to describe solvation
in molecular liquids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Structure of ferricytochrome c from horse heart (1hrc.pdb).

. . . . . . .

8
12

2.1 Continuous-wave absorption and fluorescence emission spectra from
metal-free cytochrome c (fbCytc) in water. . . . . . . . . . . . . . . . . . . .

24

2.2 Continuous-wave absorption and fluorescence emission spectra from
fbCytc in 50% (v/v) glycerol.

. . . . . . . . . . . . . . . . . . . . . . . . . . .

25

2.3 Time-resolved fluorescence dipole strength spectra from fbcytc in water. 31
2.4 Time evolution of the mean frequency of the 0–1 fluorescence transition, h⌫0–1 i, from fbCytc in water. . . . . . . . . . . . . . . . . . . . . . . . .

32

50% (v/v) glycerol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

2.5 Time-resolved fluorescence dipole strength spectra from fbcytc in
2.6 Time evolution of the mean frequency of the 0–1 fluorescence transi-

tion, h⌫0–1 i, from fbCytc in 50% (v/v) glycerol. . . . . . . . . . . . . . . . .

35

barrier-crossing events.

43

2.7 Model for equilibrium structural fluctuations in a protein involving

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1 Q-band region of the absorption and fluorescence spectra from ZnCytc
in water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

3.2 Fluorescence spectra from ZnCytc in water and over a range of Gdm+
concentrations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

3.3 Gdm+ fluorescence titration curves for ZnCytc. . . . . . . . . . . . . . . . .
3.4 Gdm+ absorption titration curves for ZnCytc. . . . . . . . . . . . . . . . . .
3.5 Simulation of the fluorescence spectral changes that accompany Gdm+

61

unfolding of ZnCytc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

62

3.6 Gdm+ concentration dependence of the ratio of the fluorescence intensity of the 0–1 and 0–0 vibronic peaks in ZnCytc. . . . . . . . . . . . . . . .

66

3.7 Polarized fluorescence emission transients from ZnCytc in water. . . . .

68

3.8 Single-wavelength and integrated dichroism-free fluorescence intensity
transients from ZnCytc in water. . . . . . . . . . . . . . . . . . . . . . . . . .

70

3.9 Integrated fluorescence anisotropy transients for the 0–1 band from ZnCytc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

3.10 Anisotropy decay amplitudes of ZnCytc at 22 C and pH 7.0. . . . . . . .

73

3.11 Anisotropy decay correlation time constants of ZnCytc at 22 C and pH 7.0. 74

x

3.12 Gdm+ concentration dependence of r0 , the total anisotropy amplitude
of ZnCytc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

3.13 Wobbling-in-cone model for fluorescence depolarization arising from
protein dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

3.14 Anisotropy decay correlation times of ZnCytc from the wobbling-in-cone
mechanical model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

3.15 Gdm+ concentration dependence in ZnCytc for S, the anisotropic order
parameter, and ✓c , the cone angle. . . . . . . . . . . . . . . . . . . . . . . . .
3.16 Gdm+ concentration dependence in ZnCytc for the effective hydrody-

82

namic radius, Rh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

4.1 Q-band region of the absorption and fluorescence spectra from ZnCytc
in water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

4.2 Gdm+ fluorescence titration curves for ZnCytc. . . . . . . . . . . . . . . . .

97

4.3 Time-resolved fluorescence dipole strength spectra from ZnCytc in water.100
4.4 Time evolution of the mean frequency of the 0–1 fluorescence emission,
h⌫01 i, from ZnCytc in water. . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4.5 Time-resolved fluorescence dipole strength spectra from ZnCytc in

2.0 M Gdm+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.6 Time evolution of the mean frequency of the 0–1 fluorescence emission,
h⌫01 i, from ZnCytc over a range of Gdm+ concentrations. . . . . . . . . . 107

4.7 Fluorescence Stokes shift time constants for ZnCytc as a function of the

Gdm+ concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.8 Fluorescence Stokes shift amplitudes for ZnCytc as a function of the
Gdm+ concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.9 Viscosity of aqueous solutions of guanidinium hydrochloride at room
temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.10 Gdm+ concentration dependence in ZnCytc of the total fluorescence
Stokes shift amplitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.11 Gdm+ concentration dependence of ⌧int , the correlation time for internal motion, and ✓c , the wobbling cone angle, from the picosecond
anisotropy decays from ZnCytc. . . . . . . . . . . . . . . . . . . . . . . . . . 118

xi

LIST OF ABBREVIATIONS

BChl, bacteriochlorophyll
BPheL , bacteriopheophytin electron acceptor
FA, fluorescence anisotropy
FSS, fluorescence Stokes shift
fbCytc, metal-free (or free-base) cytochrome c
FeCytc, FeIII cytochrome c
fwhm, full width at half maximum
K, lysene
Mb, myoglobin
P, primary electron donor in the photosynthetic reaction center
Qa , primary quinone electron acceptor
Qb , secondary quinone electron acceptor
TCSPC, time-correlated single photon counting
ZnCytc, ZnII -substituted cytochrome c
ZnTMPyP, ZnII meso-tetrakis(N-methylpyridyl)porphyrin
ZnTPP, ZnII tetraphenylporphyrin

xii

CHAPTER 1
Introduction

Summary
This dissertation presents a time-resolved picosecond spectroscopic study of the dynamic fluorescence Stokes shift (FSS) and fluorescence anisotropy (FA) response functions of ZnII -substituted cytochrome c (ZnCytc). ZnCytc was a chosen as a limited
model for a single-chlorophyll-containing protein system with some of the features
of a photosynthetic light-harvesting or reaction-center protein. The goal of this work
was to determine how the equilibrium structural fluctuations of the protein and solvent are sensed by the intrinsic ZnII porphyrin in ZnCytc. The significance of this
question relates to the longstanding issue of how the protein structure controls the
directionality and quantum efficiency of electron-transfer reactions in reaction centers and the directionality and yield of energy transport in light-harvesting proteins.
The results establish for the first time a connection between the correlation time
scales in the FSS and FA response functions to those for diffusive motion on the
protein-folding energy landscape.

1

1.1 Reaction Centers and Light-Harvesting Proteins
Photosynthesis is one of most important yet complex processes found in plants, certain bacteria and algae in which light is converted into chemical energy. Photons
are initially absorbed by light-harvesting or antenna proteins. The absorbed energy
is rapidly (<100 ps) and efficiently transferred to a photosynthetic reaction center,
where the photon’s energy is trapped and drives transmembrane electron-transfer
reactions. The result is storage of energy as a transmembrane electrochemical gradient. This stored energy is used by other membrane proteins to drive the synthesis of ATP and to make reducing agents that are used in the chemical reactions
of the organism. The processes of absorption, transfer and trapping of excitation
energy as well as electron transfer in photosynthesis are highly directional and quantum efficient. The high efficiency likely arises from the microscopic details of the
chromophore–chromophore interactions that are organized within the well-defined
chromophore–protein structures of the light-harvesting units and reaction centers.1

1.1.1 Reaction Centers
Figure 1.1 shows the X-ray crystal structure for the reaction center from a purple
photosynthetic bacterium called Rhodopseudomonas viridis in two different representations.2 The original crystal structure was described by Deisenhofer et al.3, 4
and consists of four subunits as shown in Figure 1.1.

The ribbon structure of

the chromophore–protein complex shows the cytochrome c subunit attached to the
periplasmic side of the lipid-bilayer membrane in green with the heme centers embeded in it. The two symmetrical subunits of the reaction center, L and M, are shown
labelled by their components in the stick representation; these are shown as the
magenta and purple units in the ribbon structure. Each of these two units L and
M contain a bacteriochlorophyll (BChl) molecule and together make up the primary

2

electron donor (P), an additional bacteriochlorophyll molecule, a bacteriopheophytin
(BPh) molecule, and a quinone (QA or QB ). Note that the structure of the bacterial reaction center is structurally comparable to the photosystem reaction center although
little structural homology is observed.5
The primary electron donor P is often called the “special pair” because it consists
of a pair of strongly coupled BChl molecules. Absorption of a photon by P, either
directly or via long-distance energy transfer from a light-harvesting protein, initiates
the electron-transfer process across the membrane.6 The initial charge separation
occurs in ⇠3 ps resulting in a ground-state radical cation–anion pair, P+ and BPh- .
An electron is subsequently transferred to a quinone molecule QA in ⇠200 ps and
later to a second quinone QB in ⇠100 µs. This charge separation process is repeated
but prior to the second charge separation event, P+ must be reduced by a nearby
cytochrome c2 , as shown in Figure 1.1.
The electron-transfer processes in a photosynthetic reaction center are highly
directional. Though the molecular-orbital overlap between the participating chromophores is the major factor that determines the rate of electron transfer, small
changes in the surrounding structure can also impact the electron tranfer rates; slight
differences in binding of the cofactors to the protein and in the surrounding protein
environment has been shown to enhance the rate of electron transfer.7 It has long
been proposed that the forward electron-transfer reaction is favored over the back
reaction due to the reorganizational, protein conformational changes that occur during the formation of the charge-separated intermediates.8
The structural origin of the quantum efficiency of natural photosynthetic
electron-transfer processes in reaction-center protein complexes has been heavily
discussed.3, 4, 9–14

Over the last twenty years, covalently linked donor–acceptor

supramolecular assemblies15–18 have been synthesized with the intention of emulating some of the photochemical properties of natural photosynthetic reaction cen-

3

Figure 1.1. Structure of the Rhodopseudomonas viridis reaction center (1PRC.pdb), as
shown in a ribbon representation on the left and a stick representation for the chromophores on the right. The ribbon diagram shows: the L and M subunits in magenta
and purple, respectively, the cytochrome c subunit in green shown at the top over
the L and M subunits, and the H subunit is shown in green at the bottom of the complex. The stick diagram shows the chromophores in the L, M and the cytochrome c
subunits: the primary electron donor, P, the monomeric bacteriochlorophylls (BChl),
the bacteriopheophytins (BPh), and the quinones QA and QB . A non-heme Fe ion is
shown between the L and M subunits as a red sphere. For interpretation of the references to color in this and all other figures, the reader is referred to the electronic
version of this dissertation.

4

ters. Long-lived charge-separations with relatively high quantum yields have been
achieved,19–21 and some impressive progress has been made in connecting lightharvesting arrays22–24 to charge-separation units to make artificial reaction centers
that reproduce the essential features of bacterial photosynthesis.25, 26 The artificial
systems, however, do not yet match the quantum efficiency of the natural photosynthetic reaction center even though the same or similar redox-active chromophores
have been employed in a wide range of constructs.
The unusually long lifetimes for the charge-separated states in the reaction center
are likely to arise from two aspects of the dynamics of the protein medium that
surrounds the redox-active chromophores:
• Protein-derived vibrational motions in the 100-cm 1 regime27 are coupled to
the forward primary and secondary electron-transfer reactions in the purplebacterial reaction center so that they occur in a nearly activationless manner.28
• Formation of the charge-separated intermediates is followed by a solvation-like
reorganization of the reaction-center protein that dissipates the energy of the
transition state by displacing modes that are not directly along the reaction
coordinate.29
Thus, it will be important in future work to determine the timescales and structures associated with the solvation of the excited-state and charged chromophores
involved in the energy-transfer and electron-transfer reactions in order to understand
better how solvation plays a role in these processes.

1.1.2 Light-Harvesting Proteins
Light-harvesting proteins are the chromophore–protein systems that act as the
medium through which light energy is transferred to a photosynthetic reaction center.30, 31 The overall antenna for an organism contains several light-harvesting pro-

5

teins in a multisubunit complex that is arranged structurally in the membrane so that
the excitation energy is funneled towards a centrally located reaction center.31–34
Light-harvesting proteins are in general relatively small molecular weight (6–30 kDa)
polypeptides. The chromophores are highly ordered and typically arranged in clusters. As an example, the X-ray crystal structure of the light-harvesting system LH2
in purple bacteria consists of a cylinder of nine paired transmembrane ↵-helical protein subunits that carries nine pairs of overlapping BChl a (B850) molecules; the
overall complex exhibits a nine-fold symmetry.35 The LH1 complex that surrounds
the purple-bacterial reaction center has a ring-like structure similar to that of LH2
but contains sixteen subunits and carries 32 BChl a molecules.
Energy-transfer processes in light-harvesting complexes have been extensively
studied using picosecond and femtosecond spectroscopy.1, 36, 37 It takes less than
100 ps overall for the excitation energy absorbed by a light-harvesting protein subunit to be transferred and trapped by a reaction center,1 but the energy transfer time
scale between a given pair of chromophores is typically 200 fs or less. For example,
the Fleming38, 39 and Wasielewski40 groups have observed energy-transfer processes
between chlorophyll molecules on the 200 fs time scale in the light-harvesting complexes of photosystem I (LHCI) and photosystem II (LHCII). Bradforth et al.41 found
a biphasic fluorescence anisotropy response in the purple bacterial light-harvesting
system LHI with time constants of 110 and 400 fs; the components are attributed
to the energy transfer between BChl a molecules. Jimenez et al.42 found a biexponential fluorescence depolarization response from B850 in the purple bacterial LH2
complex, with the time constants of 50–90 and 400–500 fs.
The energy-transfer steps in light-harvesting complexes are radiationless processes mediated by dipolar interactions between adjacent chromophores. For weakly
coupled chromophores, the excitation-energy is transferred through an inductive resonance mechanism that involves an incoherent hopping (F¨rster) mechanism. When
o

6

the electronic interactions between the excited singlet states of the chromophore
are very strong, however, the energy-transfer process is said to be coherent and involves excited-state wavefunctions that are delocalized over more than just one chromophore.43, 44 Fluctuations of the surrounding protein structure results in randomization of the ordering of the energy level in a given dimer or larger chromophore
cluster, and localization of the initially coherent excited state onto a single chromophore is the result. Beck and coworkers have suggested that localization can play
an important role in directing energy towards the reaction center.45, 46

1.2 Dynamic Solvation in Liquids and Proteins
Proteins undergo a wide range of motions on very short time scales.47, 48 The protein
dynamics that underly the functional motions that control energy-transfer pathways
and electron-transfer rates in photosynthesis are probably the short-ranged fluctuations that accompany propagation on the protein-folding energy landscape near the
native minimum.47–50 The individual energy-transfer steps in light-harvesting proteins are known to occur on the 20 fs–10 ps time scale or longer.1 The time scale
for solvation-like reorganizational dynamics and vibrational equilibration in these
proteins are comparable to the energy-transfer time scales.
One approach at determining the relevant time scales in a chromoprotein is the
method of dynamic solvation, which has been very widely used to study dynamics in liquids.51–54 When a chromophore in solution is optically excited, the excited
state of the molecule has a significantly different charge distribution compared to the
ground state. This causes the excited state molecule typically to have a larger permanent dipole moment. The reorientational response of the surrounding solvent to
the change in charge distribution or dipole moment of the chromophore between the
ground and excited states is called dynamic solvation. Figure 1.2 shows how the sol-

7

Energy

S1

t

hn

S0

Solvation Coordinate
Figure 1.2. Energy levels and generalized solvent coordinate to describe solvation
in molecular liquids. The potential energies of the ground and first-excited singlet
states of a probe molecule (yellow circles), S0 and S1 , respectively, are shown with
respect to a generalized solvation coordinate. After formation of the excited state,
the surrounding solvent molecules (blue ovals) reorient so as to return to equilibrium
with respect to the excited state’s generally larger dipole moment (arrows). The resulting stabilization of the probe/solvent system makes the excited-to-ground-state
energy gap decrease. The solvation process can be detected in terms of the shift of
the time-resolved emission spectrum to lower energy as the solvation reorganization
process proceeds. Adapted from reference 51.

8

vent’s reorganizational response results in a dynamic Stokes shift, a time-dependent
shift of the molecule’s emission spectrum to the red. The solvent response is often
described by a normalized response function,51
S⌫ (t) =

⌫(t)
⌫(0)

⌫(1)
⌫(1)

(1.1)

where ⌫(t) is the mean frequency of emission at time t. In this dissertation, experimentally measured S⌫ (t) responses are called fluorescence Stokes shift (FSS) response functions.
The molecular character involved in the FSS response function is usually discussed in terms of the fluctuations of the local electric field that arise from the random motions of the solvent dipoles or charges around the probe chromophore. In
the time domain, the probe’s ground-to-excited state transition frequency ! = 2⇡ ⌫
exhibits fluctuations due to the motions of the surrounding solvent. These fluctuations are characterized by a energy-gap time-correlation function,
M(t) =

h !(0) !(t)i
h( !)2 i

(1.2)

which describes the associated loss of memory over time of the instantaneous transition frequency !(0) that was present initially at some reference time t = 0. At high
temperatures and in the linear-response regime, where the fluctuation–dissipation
relation holds, M(t) is equal to the solvent-response function S⌫ (t).54–56 The requirement for the linear-response regime is generally met in most probe/solvent systems because the optical excitation of the probe results only in a small change in the
probe’s dipole moment and accordingly presents a small perturbation to the motions
and structure of the solvent.57, 58
The instantaneous normal-mode theory of liquids51, 59, 60 provides some suggestions about the time scale and character of the solvation response in liquids. Three
regions of solvation response have been identified in molecular dynamics simulations of liquids: an inertial or ballistic, free-rotor motion regime in the short-time
9

limit (⇠100 fs or so), an intermediate-time regime in which oscillatory motions are
observed, and then a long-time (>500 fs) regime in which the oscillatory motions are
damped out and diffusive, random motions predominate. The ordering of these time
scales effectively describes the onset of intermolecular forces; in the inertial regime,
the molecules move independently, whereas the intermediate and long-time scales
are associated with coherent and incoherent motions, respectively, under the action
of the intermolecular forces. From the molecular dynamics trajectories, the instantaneous normal-mode theory projects the motions associated with these solvation
time regimes into a spectrum of intermolecular frequencies that primarily involves
hindered translational and hindered rotational (librational) motions.51 Fleming and
coworkers61, 62 confirmed experimentally that the solvent response function of small
molecular solvents is bimodal in character, with perhaps 50% of the solvation response of water61 and acetonitrile63 on the <100 fs time scale identified as an inertial response with a Gaussian shape, whereas the subsequent diffusive, exponential
solvent response occurs on a slower (<1 ps) time scale.
The dynamics of folded proteins are arguably more like those of liquids than
of crystalline solids, where long-range order is permanently organized, especially
because internal diffusion of small molecules occurs in proteins.64 The structural
fluctuations occur over a wide range of time scales in proteins and are especially temperature dependent. In some landmark investigations, Frauenfelder et al. used the
reaction rate of the photochemical dissociation of carbon monoxide from myoglobin
to probe the underlying conformational timescales.47, 48 The results suggested that
proteins share a number of the structural and dynamical properties in common with
glasses. It was found that protein conformational changes do not exhibit exponential
time dependences or Arrhenius-type temperature dependences. These observations
suggested that the protein motions involve sampling a rough energy landscape with
a hierarchy of barrier heights.

10

1.3 ZnII -substituted Cytochrome c
Applying the dynamic solvation approach directly to a characterization of protein
fluctuations in photosynthetic reaction centers and light-harvesting proteins is not
presently feasible owing to the presence typically of a large number of chromophores
with overlapping spectra. In order to learn about the relevant time scales for protein
motion in photosynthesis, then, we will need to use a model system that mimics
aspects of how the chromophores are contained in a photosynthetic protein but has
just a single chromophore.
McLendon and coworkers65 and Pierce and Boxer66 have investigated the solvation of extrinsic chromophore as probes for the dynamics in heme proteins. The
time scale for the FSS response function obtained with various probes in these experiments was in the range of picoseconds to nanoseconds. The solvation time scales
were strongly dependent on the probe used and also depended on the character of
the bulk solvent. The use of extrinsic probe in these experiments added complexity
to the experiments because their interaction with the heme binding site was not well
understood. An ideal system for the measurement of solvation dynamics in a protein
would employ an intrinsic probe chromophore tightly held in the binding pocket with
a well defined structure.
In the late 1990’s, the research group of Warren Beck began some studies at Vanderbilt University on bacteriochlorophyll-containing systems using the approach suggested by Boxer and coworkers, who synthetically modified bacteriochlorophyll a so
that it could be installed into the heme-binding pocket in hemoglobin.68 Subsequently, after moving to Michigan State University, the Beck group chose to study
ZnII -substituted cytochrome c (ZnCytc) as the main target system for their protein
solvation studies. By replacing the native FeII ion with ZnII or by removing it entirely,
an intrinsic fluorophore with good photophysical properties comparable to those of
chlorophyll a is obtained.69–72
11

Figure 1.3. Structure of ferricytochrome c from horse heart (1hrc.pdb).67 The porphyrin, its thioether linkages from cysteine ligands C14 and C17, and the axial ligands to the metal ion, from the histidine and methionine residues H18 and M80,
respectively, are rendered as stick structures.

12

Figure 1.3 shows the X-ray crystal structure of horse-heart ferricytochrome c (FeCytc). 2D NMR studies have shown that the solution structure of ZnCytc is very similar to that of FeCytc,72, 73 and the structure of the ZnII -containing sites was not distinguishable from the FeIII -containing sites in Zn/Fe cocrystals of cytochrome c.74 The
porphyrin in cytochrome c is attached to the protein by the two cysteine residues,
C14 and C17, via thioether linkages, and the metal ion is axially ligated by the histidine and methionine residues, H18 and M80. Except for a small exposure of the
edge of the porphyrin to the external medium via a cleft on the protein surface that
constrains the porphyrin orthogonal to its plane, the porphyrin is largely confined to
the hydrophobic core of the protein. This structural organization of the porphyrin
in ZnCytc makes it well suited for the solvation dynamic studies. The porphyrin is
positioned well to serve as an intrinsic probe that senses the internal motions of the
protein, but owing to the slight exposure of the edges it is also capable of sensing
the motion in the solvent-contact layer of the protein.
The initial studies of dynamic solvation in ZnCytc were conducted in the Beck laboratory by Sanela Lampa-Pastirk.75 She characterized the time-resolved fluorescence
spectrum from ZnCytc over the 100-ps–25-ns timescale using the time-correlated,
single-photon counting approach.76–78 The findings from this work are extensively
reviewed and discussed in the following chapters, but the main points are as follows. Lampa-Pastirk found that the FSS response function from ZnCytc had two
exponential components with time constants of 200 ps and 1.5 ns in water. That
the slower of these two components was sensitive to the presence of added glycerol
in the surrounding solvent suggested an assignment to characteristic motions of the
solvent-contact layer of the protein. The faster of the two components was accordingly assigned to the hydrophobic core of the protein.76 When the excitation laser
was tuned to the Soret absorption band in the blue (420-nm) part of the spectrum,
however, an unprecedented bidirectional FSS response function was observed that

13

was terminated with a sustained blue shift that lasted throughout the fluorescence
timescale, out to >20 ns. This result was interpreted as showing that the protein had
absorbed the blue photon’s excess vibrational energy above the S1 state’s energy and
had been vibrationally excited over the activation barriers that separate the native
state from a partially unfolded state along the protein unfolding/refolding reaction
coordinate.78, 79

1.4 Aims and Summary of Results
The work by Lampa-Pastirk provides the primary motivation for the experiments discussed in this dissertation. Although the glycerol dependence in the FSS response of
ZnCytc provides the very first structural information in any protein solvation study,
it does not account for the different timescales in a manner that affords any structural insight about the types of motions that are detected. Further, that the FSS
response would depend so sensitively on the amount of excess vibrational energy
used to prepare the S1 state is unprecedented by any study in a molecular liquid, so
its bidirectional character is uniquely that from a protein. The following chapters
describe an effort to obtain chiefly a better structural picture for the motions that
contribute to the FSS response in ZnCytc. The following aims were addressed:
• Obtain the relationship between the time scales and the amplitudes of the equilibrium structural fluctuations that contribute to the FSS response in ZnCytc.
• Determine how motions associated with the unfolding reaction coordinate contribute to the FSS response in ZnCytc.
• Compare the timescales returned by the FSS response with the timescales detected in the fluorescence anisotropy (FA) response, which is a direct measure
of internal motion in ZnCytc.

14

Here is an overview of the experimental work described in the following chapters
of this dissertation:
In Chapter 2, we discuss the dynamic solvation response in fbCytc cytochrome
c using FSS measurements. This system was chosen as an analogue of a partially
unfolded form of ZnCytc or FeCytc. The time scales of the FSS response function for
fbCytc were determined to be 1.4 ns and 9.1 ns compared to the time scales obtained
for ZnCytc under similar solution conditions which are 250 ps and 1.45 ns, respectively. A comparison of the results from the ZnII -substituted and metal-free forms
of cytochrome c suggests that the mean-squared deviations of the structural fluctuations exhibited by fbCytc are ⇠10 times larger than that of ZnCytc. This is consistent
with the idea that loss of metal ion in fbCytc allows the native state to adopt a partially unfolded conformation with some of the characteristics of a molten globule.79
Unlike ZnCytc where only the slower of the two time components of FSS response
function shows a solvent viscosity dependence77 both components in fbCytc show a
lengthening on changing the solvent from water to a 50% (v/v) glycerol mixture. The
results establish a connection between the time scales and amplitudes of fluctuations
for motions along the energy surface. The results lead to a structural interpretation
of the motion using a model for Brownian diffusion with thermally activated barrier
crossings on the folding energy landscape.
In Chapter 3, the structural fluctuations that occur when ZnCytc is driven through
an unfolding transition in the presence of guanidinium ion concentration (Gdm+ ), a
chemical denaturant, is probed using the FA response. The mechanism of Gdm+ ’s
action involves an interaction with the hydration layer of water that surrounds and
stabilizes the native fold of the protein.80 The goal of this study was to establish
a relation between the protein dynamics detected by the FSS response and the thermodynamic stability of the protein. The fluorescence anisotropy gives a direct measure of the motions of the protein that immediate surround the ZnII porphyrin. The

15

results indicate that the unfolding transition is accompanied by the formation of intermediates at low denaturant concentrations that are characterized by porphyrin
motions of intermediate amplitude and angular range relative to those in the native
and unfolded states.
Chapter 4 discusses how the fluorescence Stokes shift (FSS) reports the changes in
protein dynamics that occur during the unfolding titration of ZnCytc with Gdm+ . The
results are compared to those obtained using the FA response. The results show that
the presence of Gdm+ destabilizes the native fold enough even at very low concentrations that the optical transition of the ZnII -porphyrin chromophore departs from the
linear-response regime; the FSS response changes from the monotonic response expected from a pure solvation response to a biphasic, blue/red response that reports
the transient production of a structure that is displaced significantly from the equlibrium structure present prior to the optical excitation. These observations strongly
implicate structural changes in the hydration layer as the origin of the dynamical
changes reported in the FSS response as the protein approaches the unfolded state.
The work described in this dissertation provides arguably the first direct studies of the relationship between the timescales of fluctuations and the amplitudes
of motions over the timescales that are relevant to understanding energy-transfer
processes in photosynthetic light-harvesting proteins. The results obtained suggest
strongly that the dynamics in the hydration layer play a dominant role in controlling the stability of a folded protein, so studies have already been initiated in the
Beck laboratory to employ fluorescent probes covalently mounted on the surface of
ZnCytc to measure directly how the hydration layer is affected as denaturants are
added. The next logical step is to perform analogous experiments on folded proteins
in situ in a membrane to understand how the membrane controls the dynamics in a
photosynthetic protein.

16

CHAPTER 2
Fluctuations in fbCytc from the
Fluorescence Stokes Shift Response

Summary
We used picosecond time-resolved fluorescence spectroscopy to characterize the fluorescence Stokes shift (FSS) response function of metal-free (or free-base, fbCytc)
cytochrome c under the solution conditions that favor the native states of ferricytochrome c (FeCytc) and ZnII -substituted cytochrome c (ZnCytc). The intrinsic
porphyrin chromophore serves in these experiments as a fluorescent probe of the
structural fluctuations of the surrounding protein and solvent. Demetalation of the
porphyrin destabilizes the folded structure of cytochrome c owing to the loss of the
axial metal–histidine and metal–methionine bonds. Thus, these experiments examine
how the timescales detected in a dynamic solvation experiment in a chromoprotein
report changes in the character of the motion. The FSS response function in fbCytc in
water and pH 7 is well described by a biexponential response over the 100-ps–50-ns
regime with time constants of 1.4 ns and 9.1 ns; under similar conditions, ZnCytc exhibits a biexponential FSS response with time constants of 250 ps and 1.5 ns.77 These

17

time constants correspond, respectively, to the correlation timescales for motions of
the hydrophobic core and the solvent-contact layer of the protein. Both of the time
constants observed in fbCytc are further lengthened upon addition of glycerol to the
external solvent so that a significant fraction of the protein dynamics is rendered
effectively static on the fluorescence timescale. The solvation reorganization energy,
the time-integrated Stokes shift of the fluorescence spectrum, is reduced by about
a third to 33 cm 1 in 50% glycerol from 43 cm 1 in water. These results are interpreted structurally using a model for Brownian diffusive motion with thermally activated barrier crossings on the protein-folding energy landscape. The results suggest
that the mean-squared deviations of the structural fluctuations exhibited by fbCytc
are nearly a factor of ten larger than those of ZnCytc. This conclusion is consistent
with the suggestion that fbCytc assumes a dynamic, partially unfolded structure with
the characteristics of a molten globule.

2.1 Introduction
The energy landscape paradigm accounts for the molecular dynamics of folded proteins in terms of a hierarchy of conformational states sorted by tiers of intervening
activation-energy barriers of increasing magnitude.47, 81, 82 On the single-molecule
level, a protein makes a diffusive search of the potential energy surface near the
native structure by hopping from minimum to minimum over the barriers that are
thermally accessible.83, 84 These motions correspond to what Frauenfelder calls equilibrium fluctuations.47 Similar dynamics are expected to accompany the folding of a
protein as it descends the funnel-shaped Gibbs free-energy gradient and approaches
the native structure,85 but the details of the motions that a protein makes as it
searches for the native structure or when the structure is displaced from that at

18

equilibrium by a perturbation deserve additional experimental and theoretical attention.
In recent work from this laboratory, we showed how ZnII -substituted cytochrome
c (ZnCytc) can be driven from the native fold to a series of partially unfolded structures by the intramolecular vibrational excitation generated by the radiationless decay of the intrinsic ZnII -porphyrin chromophore.78, 79 When the 0–0 vibronic transition in the Q absorption band is pumped, so that the S1 electronic state is prepared
with very little excess vibrational energy, the time-resolved fluorescence spectrum
exhibits a conventional, unidirectional dynamic fluorescence Stokes shift (FSS) response51, 54 to the red with two characteristic timescales, 250 ps and 1.45 ns. This response is assigned in analogy to that in polar liquids to a polar solvation response of
the surrounding protein to the ground-to-excited-state change in the ZnII -porphyrin’s
dipole moment. The two timescales were assigned to motions of the hydrophobic
core and solvent-contact layers of the protein, respectively, because addition of glycerol to the external solvent medium slowed only the latter component. When the
excitation wavelength was set at 420 nm in the Soret band, so that that the S1 state is
prepared with ⇠7000-cm 1 excess vibrational energy, the ZnII –porphyrin in ZnCytc
exhibits an unusual bidirectional FSS response that directly reports a change in the
surrounding protein structure. The time-resolved fluorescence spectrum shifts initially to the red with a 125-ps time constant; after the 180-ps delay point, however,
the spectrum begins a slower, biexponential shift to the blue that persists to the end
of the fluorescence timescale (>12 ns). The blue-shifted fluorescence spectrum is
assigned to a partially unfolded state of the protein that transiently resembles that
of the molten-globule state observed under acid conditions;86, 87 the heat-denatured
state of ZnCytc also exhibits a blue-shifted fluorescence spectrum.88
Subsequent work79 showed that the continuous-wave fluorescence spectrum
from ZnCytc reports the activation-enthalpy thresholds to at least three partially

19

unfolded states in terms of step-like transitions of the solvation reorganization energy,89 the time-integrated Stokes shift of the fluorescence spectrum. The corresponding barriers in metal-free (or free-base, fbCytc) cytochrome c occur at relatively
low enthalpies, perhaps one-third of those in ZnCytc. This finding shows that the axial metal–histidine (H18) and metal–methionine (M80) bonds in cytochrome c play an
important structural role (see Figure 1.3). Under the solution conditions that favor
the native state of ferricytochrome c (FeCytc) or ZnCytc, it is likely that fbCytc exists as a partially unfolded, molten-globule-like structure that retains a well-defined
hydrophobic core like that of ZnCytc.79
In this chapter, we discuss the FSS response obtained from fbCytc with the excitation laser tuned close to the 0–0 vibronic transition. This work allows a direct
comparison to the previously reported FSS response observed in the native state of
ZnCytc.77 These experiments provide a unique opportunity to determine how the
timescales detected in a dynamic solvation experiment in a chromoprotein report
changes arising from a structural perturbation. The results show that the two exponential time constants observed in the FSS from fbCytc are lengthened by almost
a factor of ten from those of ZnCytc and that both components are sensitive to the
presence of glycerol in the external solvent medium. By applying a model for the
structural fluctuations that arise from Brownian diffusion on the protein-folding energy landscape,90 we infer that the increased polar solvation timescales observed
in fbCytc correspond to significantly enhanced fluctuation amplitudes compared to
those in ZnCytc under similar solvent conditions.

20

2.2 Experimental
2.2.1 Sample Preparation
The procedure established by Vanderkooi and coworkers69, 91 was used to prepare
fbCytc using horse-heart ferricytochrome c (FeCytc, Sigma) as the starting material.
The free-base porphyrin is obtained in situ using liquid anhydrous hydrogen fluoride
(HF) as the demetalating agent. The reaction of FeCytc with HF was run on a homebuilt gas-handling system that employs tubing, valves, and reaction vessels all made
of Teflon. The extent of the demetalation reaction was monitored spectrophotometrically using the vibronic structure of the Q -band region of the absorption spectrum.
The fbCytc product was worked up using methods adapted from those employed by
Winkler and coworkers92 and Kosti´ and coworkers.93 After desalting, the protein
c
was isolated by cation-exchange chromatography first on a Whatman CM-52 column
and optionally then on a Mono-S 4.6/100 PE FPLC column (GE Healthcare Life Sciences). Fractions corresponding to fbCytc were combined and then were equilibrated
with a 25 mM sodium phosphate buffer solution at pH 7.0 by repeated concentration
using an Millipore YM10 ultrafilter and dilution with the buffer solution. After a final
ultrafiltration step, the product was analyzed on a Superdex 75 FPLC gel-filtration
column (GE Healthcare Life Sciences). This procedure yields fbCytc free of the low
molecular-weight polypeptide contaminants that are typically observed directly from
the HF demetalation reaction. The concentrated fbCytc solution obtained from the final ultrafiltration step was divided into small aliquots and then flash-frozen in liquid
nitrogen. The frozen samples were stored in a -85 C freezer for up to a year.
For use in fluorescence spectroscopy, one of the frozen samples was thawed and
then diluted with 25 mM phosphate buffer solution at pH 7.0 or with a glycerol-buffer
solution mixture (50% glycerol by volume). The final protein solution was then passed
through a 0.22 µM microfilter to remove any large debris. The sample’s concentration

21

was then adjusted by adding additional diluent solution so that the absorption at the
peak of the Qy absorption band for a path length of 1.0 cm ranged from 0.1–0.2. The
sample was held in quartz cuvettes with the headspace purged with dry nitrogen gas
prior to an experiment.

2.2.2 Absorption and Fluorescence Spectroscopy
Absorption spectra were acquired with a Hitachi U-2000 spectrophotometer (2-nm
band pass). Fluorescence spectra were obtained with a home-built spectrofluorimeter79 consisting of an Jobin-Yvon AH10 100-W tungsten-halogen light source, a JobinYvon H10 excitation monochromator (4-nm bandpass), an Acton Research SP-150
emission spectrograph (2-nm bandpass), and a Jobin-Yvon Symphony charge-coupled
device (CCD) detector. The CCD detector employs a liquid nitrogen cooled, backilluminated, 2000 ⇥ 800 pixel silicon detector chip (EEV corporation). The sample cuvette was held in a Quantum Northwest TLC50F Peltier-effect temperature controller.
As presented as a function of wavenumber, the fluorescence intensities are multiplied
by the square of the wavelength in order to compensate for the fixed (in wavelength
units) spectral bandpass of the emission spectrograph.94 The absorption and fluorescence instruments were controlled by LabVIEW (National Instruments) programs.

2.2.3 Picosecond Time-resolved Fluorescence Spectroscopy
Single-wavelength fluorescence transients were acquired with a time-correlated, single photon counting (TCSPC) system operated in the reverse triggered mode. This instrument was described in detail in an earlier contribution.76 Excitation pulses were
obtained from a synchronously pumped, cavity-dumped rhodamine-6G dye laser (Coherent 702-1), which was pumped by the 532-nm second-harmonic output of a modelocked NdIII -YAG laser (Coherent Antares 76-S). The cavity dumper on the dye laser

22

was operated at 4 MHz, so the excitation interpulse period was 250 ns. The zerobackground autocorrelation width of the excitation pulses was 5 ps, as measured
using an Inrad 5-14A autocorrelator. The fluorescence emission was collected at
90 from the excitation laser beam and was analyzed by a calcite polarizer set to
the magic angle with respect to the plane of the excitation laser so that dichroismfree transients were acquired. The emission was then detected using a double subtractive monochromator (CVI CM112) and a microchannel-plate photomultiplier tube
(Hamamatsu R3809U-51), the output of which was analyzed using a NIM-based TCSPC setup as previously described. The instrument-response function obtained with
a dilute scattering solution at the sample position had a width (fwhm) of approximately 100 ps in these experiments. A LabVIEW (National Instruments) program controlled the emission monochromator and the photon-counting hardware so that a set
of single-wavelength fluorescence transients over a range of emission wavelengths
across the fluorescence spectrum could be automatically acquired. The sample was
held in a water-cooled mount, which was maintained at 22 C with a Neslab 221 water
circulator.

2.3 Results
2.3.1 Absorption and Fluorescence Emission Spectra
Figures 2.1 and 2.2 show the absorption (A(⌫)) and fluorescence (F (⌫)) spectra obtained at 22 C from fbCytc at pH 7.0 in water and 50% (v/v) glycerol, respectively.
The spectra are plotted with respect to wavenumber ⌫ as relative dipole strengths,
AD (⌫) = A(⌫)/⌫ and FD (⌫) = F (⌫)/⌫ 3 , respectively.94–96 The plotted region shows
the Q band, which consists of a pair of partially resolved vibronic bands from the x
and y polarized transition-dipole moments in the plane of the ZnII porphyrin. The
fluorescence spectrum’s 0–0 and 0–1 peaks exhibit an approximate mirror-symmetry
23

Relative Dipole Strength
Relative Dipole Strength

0-1
0-1
0-0
0-0
0-1
1-0
0
0

0
0
15600
15600

14000
14000

16000
16000

18000
18000

15900
15900

16200
16200

20000
20000

16500
16500

Frequency (cm-1)
Frequency (cm-1)
Figure 2.1. Top panel: Continuous-wave absorption (dashed) and fluorescence emission (solid) spectra from metal-free cytochrome c (fbCytc) in water at 22 C and pH 7,
plotted as relative dipole strengths, A(⌫)/⌫ and F (⌫)/⌫ 3 , respectively. The fluorescence spectrum was obtained with the excitation light source tuned to 16130 cm 1

(620 nm). Bottom panel: Detailed view of the 0–0 region, with the data points shown
superimposed with log-normal line shapes (see Table 1 for the fit parameters).

24

0-1

Relative Dipole Strength

0-0
0-1

0
14000

0
15600

16000

18000

15900

16200

20000

16500

Frequency (cm-1)
Figure 2.2. Top panel: Continuous-wave absorption (dashed) and fluorescence emission (solid) spectra from fbCytc in 50% (v/v) glycerol at 22 C and pH 7, plotted as
relative dipole strengths, A(⌫)/⌫ and F (⌫)/⌫ 3 , respectively. The fluorescence spectrum was obtained with the excitation light source tuned to 16130 cm 1 (620 nm).

Bottom panel: Detailed view of the 0–0 region, with the data points shown superimposed with log-normal line shapes (see Table 2.1 for the fit parameters).

25

Table 2.1. Lognormal and Gaussian lineshape models for the 0–0 peak in the absorption (A) and fluorescence (F ) spectra from fbCytc in water and in 50% (v/v) glycerol
(see Figures 2.1 and 2.2) and estimates for the solvation reorganization energy ( ).
Water

50% (v/v) Glycerol
Lognormal
Gaussian

Parametera

Lognormal

⌫0–0, A
⌫0–0, A
⇢0–0, A

16198 cm 1
426 cm 1
1.13

16199 cm 1
408 cm 1
—

16194 cm 1
396 cm 1
1.22

16201 cm 1
370 cm 1
—

⌫0–0, F
⌫0–0, F
⇢0–0, F

16122 cm 1
476 cm 1
1.22

16133 cm 1
465 cm 1
—

16144 cm 1
396 cm 1
1.22

16135 cm 1
337 cm 1
—

38 cm 1

43 cm 1

25 cm 1

33 cm 1

Gaussian

a See Equation 2.1 and the text.

26

with respect to the two lowest wavenumber features, the 0–0 and 0–1 peaks from
the Qy transition. The relative scaling of the absorption and fluorescence spectra in
Figures 2.1 and 2.2 was set so that the 0–0 peaks have the same intensities.
In order to determine the changes in spectral lineshape and position that are
induced by the change of solvent from water to 50% glycerol, we fit the the 0–0
peaks of the absorption and fluorescence dipole-strength spectra to Gaussian and
lognormal97 lineshapes. The lower panels of Figures 2.1 and 2.2 show the lognormal
lineshapes superimposed on an expanded view of the 0–0 peaks. The fit parameters
listed in Table 2.1 include the center frequencies (⌫0–0 ), the widths (fwhm,

⌫0–0 )

and for the log-normal lineshapes, the asymmetry (or skew) parameter, ⇢0–0 . Estimates for the solvation reorganization energy, , were then obtained as one-half the
difference between the center frequencies of the absorption (A) and fluorescence (F )
0–0 peaks,
= (⌫0–0, A

⌫0–0, F )/2.

(2.1)

Using the ⌫0–0 parameters from the fitted lognormal lineshapes, this equation returns values for

of 38 cm 1 in water and 25 cm 1 in 50% glycerol. These estimates

are valid if the ground-state and excited-state potential-energy surfaces are harmonic
and have the same normal-mode frequencies,98, 99 which is the case if the absorption
and fluorescence spectra exhibit an exact mirror symmetry with respect to frequency.
An additional formal requirement for the applicability of Equation 2.1 is that the vibronic lineshapes are Gaussians.100 The estimates for

are somewhat larger in both

solvents if Gaussian lineshapes are used to fit the 0–0 peaks (43 cm 1 and 33 cm 1 ,
respectively). Still, these peak-shift estimates for

should be regarded as lower lim-

its. Because the 0–0 peaks are only partially resolved, it is not possible to apply
rigorously the equation for

introduced by Fleming and coworkers,100
R1

d⌫ ⌫ [ a (⌫)
f (⌫)]
R
= 01
,
0 d⌫ [ a (⌫) + f (⌫)]
27

(2.2)

which integrates over the absorption ( a ) and fluorescence ( f ) spectra and avoids
assumptions about the lineshapes. When applied to the spectra shown in Figures 2.1
and 2.2, Equation 2.2 obtains estimates for

that are about a factor of two larger

than those listed in Table 2.1. This scaling of estimates for

using Equations 2.1

and 2.2 is similar to that obtained by Fleming and coworkers for eosin in water and
for lysozyme labelled with eosin.100
The reduction by at least a third of the solvation reorganization energy for fbCytc that accompanies the change from water to 50% glycerol (see Table 2.1) is too
large to be explained only by the change in solvent. Using a dielectric continuum
treatment of the solvent surrounding a probe chromophore, the Lippert-Mataga equation94, 101, 102 relates the solvation reorganization energy to the dielectric constant,
✏0 , and the index of refraction, n, in a given solvent mixture:
#
2 "
µeg
✏0 1
n2 1
=
.
hca3 2✏0 + 1 2n2 + 1
The first term in this equation depends on the probe; it indicates that

(2.3)
depends on

the ground-to-excited-state change in the probe’s dipole moment, µeg , and the radius
of the surrounding spherical solvent cavity, a. If these parameters are held constant,
is reduced only by about ten percent by changing the parameters in the bracketed
expression from those for water (✏0 = 80.37, n = 1.3326) to those for 50 % (v/v)
(or 56 % (w/w)) glycerol/water (✏0 = 64, n = 1.4063) at 25 C.103, 104 This estimate
would be appropriate if the porphyrin chromophore in fbCytc is fully solvated by
the external solvent, but it is probable that the porphyrin is almost fully solvated by
the surrounding protein structure; Table 2.1 shows that the fluorescence spectrum
is only shifted a few cm 1 to the blue by the change from water to 50% glycerol. In
contrast, the fluorescence spectrum from ZnCytc shifts 50 cm 1 to the blue when
water is replaced by 50% glycerol. Such a shift is consistent with the partial exposure
to the external solvent of the edge of the porphyrin macrocycle that is indicated by
the FeCytc crystal structure (see Figure 1.3). The change in solvent to 50% glycerol
28

has no effect, however, on

for ZnCytc; the same value,

= 145 cm 1 , is observed

in water and in 50% glycerol.77

2.3.2 Picosecond Time-resolved Fluorescence Spectroscopy
Since the dielectric properties of the external solvent account only for a small fraction
of the reduction of the solvation reorganization energy, , that accompanies changing
the solvent from water to 50% glycerol, it is likely that the average timescale for the
solvation response of the protein in fbCytc is lengthened enough in the presence
of 50% glycerol so that some of the motions are slowed enough that they do not
contribute to

. These conclusions are supported by the measurements of the FSS

response function that are described next.
Time-resolved fluorescence spectra from fbCytc in water and in 50% glycerol
were obtained as slices from a time–wavelength–intensity (dipole-strength) surface
FD (⌫, t) that spanned the 0–50-ns by 13500–16000-cm 1 region. The excitation laser
was fixed at 16130 cm 1 , which is near to the wavenumber of the 0–0 transition in
water and 50% glycerol, respectively (see Figures 2.1 and 2.2). The surface was acquired as a set of single-wavelength transients spaced by 5.0 nm (⇠130 cm 1 at
620 nm), the bandpass of the emission monochromator. The emission tuning range
spans the 0–1 peak and continues nearly to the maximum of the 0–0 peak. Owing
to the 5-nm bandpass of the emission monochromator and the relatively small value
for , we were unable to work further to the red than the maximum of the 0–0 peak
because of interference from scattering from the excitation laser. Because the transients were recorded over the 0–50-ns delay range, a span of 25 times the fluorescence lifetime under the chosen sample conditions, the time–wavelength–intensity
surface was constructed by normalizing the integral of each transient to the fluorescence dipole strength observed in the continuous-wave spectrum at the emission
wavenumber of the transient. The transients were then used directly, without de29

convolution of the instrument-response function, and they were truncated so that
the first data point employed in further analysis was that of the 100-ps delay, a full
instrument-response width after the center of the excitation pulse.
Figure 2.3 shows a set of time-resolved fluorescence dipole-strength spectra from
fbCytc in water at 22 C. The spectra were obtained as slices from the FD (⌫, t) time–
wavelength–intensity surface at four delay times t. Fitted lognormal lineshapes are
shown superimposed on the data points. As the time delay increases, the spectra decay in intensity and the wavenumber of the peak maximum shifts to lower frequency.
The time evolution of the mean fluorescence dipole strength for the 0–1 peak, h⌫(t)i,
was obtained by integrating over the time-resolved spectrum at a given time t:
R ⌫2
⌫ d⌫ ⌫ FD (⌫, t)
h⌫(t)i = R 1
.
(2.4)
⌫2
⌫1 d⌫ FD (⌫, t)

The h⌫(t)i response is used without normalization in the following as a direct measure of the FSS response function (Equation 2.5) over the 100-ps–50-ns regime. This
practice avoids the need to estimate the mean fluorescence emission frequencies at
zero time and at infinite time (see also the discussion on this issue in ref. 105). The
response shown in Figure 2.4 is well described by a biexponential decay function.
The limits for the integral, ⌫1 = 14000 cm 1 and ⌫2 = 15500 cm 1 , were selected so
that the range of integration spanned the 0–1 peak but avoided the onset of the 0–0
peak. The calculated h⌫(t)i response is essentially invariant with different choices of
⌫1 and ⌫2 , but the fitted t = 1 asymptote varies over a few wavenumbers depending
on how far the integration extends over the congested region between the 0–1 and
0–0 peaks. In the previous work on ZnCytc,77 h⌫(t)i was determined from the time
evolution of the fluorescence 0–0 transition frequency, which was obtained from a
fitted vibronic progression for the 0–0 and 0–1 peaks. The use of the mean-frequency
calculation in the present work allows us to obtain a robust measurement of the FSS
response function despite the smaller solvation reorganization energy and the poorer
signal/noise ratio of the fbCytc data sets. A similar approach was used previously by
30

2.0 ns

Relative Dipole Strength

5.0 ns
9.0 ns
13.0 ns

0
14000

14500

15000
Frequency (cm-1)

15500

Figure 2.3. Time-resolved fluorescence dipole strength spectra from fbcytc in water
at 22 C at four time delays. The displayed spectral region corresponds to the 0–1
peak. The spectra are superimposed with fitted lognormal line shapes.

31

Mean Frequency (cm-1)

14700

14680

14660
0

10000

20000

30000

40000

Time (ps)
Figure 2.4. Time evolution of the mean emission frequency of the 0–1 fluorescence
transition, h⌫0–1 i, from fbCytc in water at 22 C. The data points are superimposed
on a fitted double-exponential model. The fit parameters are listed in Table 2.2.

32

Toptygin et al. in their study of dynamic solvation in single-tryptophan mutants of
IIAGlc protein.106
The addition of glycerol to the fbCytc solution results in a significant slowing
of the FSS response function. Two exponential components are observed, just as in
water, but the total shift to the red is smaller than observed in water (see Figures 2.5
and 2.6). The time constants observed in 50% glycerol, 3.18 ns and 13.71 ns, are
lengthened significantly compared to those observed in water, 1.37 ns and 9.06 ns,
respectively (see Table 2.2). The reduction of

indicated by the continuous-wave

spectra (Figure 2.2) and by the h⌫(t)i response (Figure 2.6) further requires that a
portion of the motion observed in water is rendered effectively static relative to the
fluorescence timescale in 50% glycerol.
Table 2.2 also lists the parameters that describe the FSS response function observed previously from ZnCytc under similar conditions.77 Both of the time constants observed in ZnCytc are almost ten times shorter than those of fbCytc. Note
that only the slower of the two components observed from ZnCytc is affected significantly by the addition of glycerol to the external solvent medium (see Table 2.2). That
the solvation reorganization energy for ZnCytc in water is the same as that in 50%
glycerol77 supports the conclusion that the addition of glycerol primarily acts on the
FSS response by damping the motions of groups in the solvent-contact layer of the
protein; the studies by Vincent et al.107 suggest that this frictional action of glycerol
involves changes of the structure and dynamics of water molecules in the hydration
layer. The results observed here with fbCytc evidence a similar structural order of
assignment for the two timescales in the FSS response but with an even larger effect
of the solvent friction than observed with ZnCytc.

33

5.30 ns

Relative Dipole Strength

8.65 ns
14.2 ns
20.0 ns

0
14000

14500

15000

15500

Frequency (cm-1)
Figure 2.5.

Time-resolved fluorescence dipole strength spectra from fbcytc in

50% (v/v) glycerol at 22 C at four time delays. The displayed spectral region corresponds to the 0–1 peak. The spectra are superimposed with fitted lognormal line
shapes.

34

Mean Frequency (cm-1)

14650

14640

14630

14620

0

10000

20000

30000

40000

Time (ps)
Figure 2.6. Time evolution of the mean emission frequency of the 0–1 fluorescence
transition, h⌫0–1 i, from fbCytc in 50% (v/v) glycerol at 22 C. The data points are

superimposed on a fitted double-exponential model. The fit parameters are listed in
Table 2.2.

35

Table 2.2. Model parameters for the time evolution of the time-resolved fluorescence spectrum observed in water and 50% glycerol in metal-free (fbCytc) and
ZnII -substituted (ZnCytc) cytochrome c at 22 C
Protein

Solvent

A1 , cm 1

⌧1 , ns

A2 , cm 1

⌧2 , ns

fbCytca

water
50% glycerol

13.9
18.4

1.37
3.18

36.5
11.4

9.06
13.7

ZnCytcb

water
50% glycerol

70
60

0.250
0.260

100
90

1.450
2.200

⌫1 , cm 1
14663
14621
16940
17000

t/⌧1 + A e t/⌧2 + ⌫ , see Equation 2.4 and the text.
a h⌫
1
0–1 (t)i = A1 e
2
b From reference 16; h⌫
(t)i = A1 e t/⌧1 + A2 e t/⌧2 + ⌫1 , from a fitted vi0–0

bronic progression over the 0–0 and 0–1 region of the fluorescence spectrum.

36

2.4 Discussion
The main finding is that the FSS response function measured for fbCytc over the
100-ps–50-ns timescale is significantly slower than that of ZnCytc under the solution
conditions that favor the native folded state. The motions that are sensed by the intrinsic porphyrin chromophore in this timescale regime are predominantly from fluctuations of the surrounding protein structure. In the following, we review the current
thinking about the origin of the FSS response in chromoproteins that supports this
assignment, and then we consider how the correlation timescales observed in the FSS
response function of fbCytc and ZnCytc can be interpreted structurally in terms of
Brownian diffusive motion on the protein-folding energy landscape. The effect of external solvent friction is included by incorporating an Arrhenius expression relating
the barrier heights that divide the minima on the energy landscape to the correlation
timescales for the fluctuations. Overall, the analysis supports the conclusion that
the slowing of the FSS response function in fbCytc arises from an increase in the
mean-square displacements of the core and surface fluctuations compared to those
in ZnCytc. These conclusions are consistent with the suggestion that the equilibrium
structure of fbCytc is a partially unfolded, molten-globule-like state.

2.4.1 Solvent-Response Functions in Liquids and Proteins
The FSS or solvent-response function, S⌫ (t),51, 54, 89, 108 describes the reorganizational response triggered in a condensed phase medium by the ground-to-excitedstate change in the probe’s dipole moment that accompanies its optically driven absorption transition. It is usually defined in terms of the time evolution of the mean
frequency of the time-resolved fluorescence spectrum, h⌫(t)i, as
S⌫ (t) =

h⌫(t)i
h⌫(0)i

37

h⌫(1)i
.
h⌫(1)i

(2.5)

In polar liquids, most of the properties of S⌫ (t) observed experimentally can be
calculated by treating the liquid medium as a dielectric continuum.54, 102 Here the
optical transition of the probe is treated as applying a step-function change in the
electric field that is sensed by the surrounding solvent molecules. In the simplest
picture, given the parameters from a description of the liquid’s frequency dependent
dielectric response, ✏(!), using a single Debye dispersion,
✏(!) = ✏1 +

✏0 ✏1
,
1
i!⌧D

(2.6)

the calculated solvation response is a single exponential function with a time constant
⌧F =

2✏1 + ✏c
2✏0 + ✏c

!

⌧D .

(2.7)

In these equations, ✏1 and ✏0 are the infinite-frequency and zero-frequency (static)
dielectric constants and ⌧D is the dielectric (Debye) relaxation time. The parameter
✏c is the dielectric constant of the cavity in the solvent medium that surrounds the
probe chromophore; it can be calculated knowing the structure of the probe and the
polarizability of the solvent medium. Because usually ✏0

✏1 and ✏0

✏c , the sol-

vation time constant ⌧F is equal to the longitudinal relaxation time constant54, 62, 102
⌧L = (✏1 /✏0 )⌧D .

(2.8)

This result indicates that ⌧F ⌧ ⌧D .62 In polar solvents, ⌧F is predominantly determined by the timescale for rotational diffusion. At very short timescales, hindered
rotations (librations)62 and inertial (free-rotor) motions59, 61, 63, 109–111 make major
contributions to the solvent-response function.
The molecular character of S⌫ (t) is usually discussed in terms of the fluctuations
of the local electric field that arise from the random motions of the solvent dipoles
around the probe chromophore. In the time domain, the probe’s ground-to-excited
state transition frequency ! = 2⇡ ⌫ exhibits fluctuations
!(t) = h!i
38

!(t)

(2.9)

from that averaged over time or averaged instantaneously over the ensemble. The
fluctuations are characterized by a time-correlation function,
M(t) =

h !(0) !(t)i
,
h( !)2 i

(2.10)

which describes the associated loss of memory over time of the instantaneous transition frequency !(0) that was present initially at some reference time t = 0. At high
temperatures and in the linear-response regime, where the fluctuation–dissipation
relation holds, M(t) is equal to the solvent-response function S⌫ (t).54–56 The requirement for the linear-response regime is generally met in most probe/solvent
systems because the optical excitation of the probe results only in a small change
in the probe’s dipole moment and accordingly presents a small perturbation to the
motions and structure of the solvent.57, 58

Note that the three-pulse stimulated

photon-echo peak shift (3PEPS) response is usually taken as being a direct measure
of M(t).55, 56 In several systems, however, the 3PEPS response includes components
from intramolecular nonradiative electronic state dynamics in addition to those arising from solvation dynamics.46, 108, 112 Given knowledge of M(t), or of the spectral
density, ⇢(!), which is obtained as its Fourier transform, it is possible to calculate all
of the spectroscopic observables for the probe/solvent system. For example, the solvation reorganization energy, , is equivalent to the mean frequency of the spectral
density,56, 89
=

Z1
0

d! ! ⇢(!).

(2.11)

The studies of dynamic solvation in small proteins using transient holeburning, time-resolved fluorescence, or stimulated photon-echo methods have targeted
predominantly the <100-ps regime that is readily probed by femtosecond spectroscopy.46, 113–120 Even when sensed by electronic probes located in the interior
of a protein, the motions of water molecules in the bulk or in the hydration layer
surrounding proteins still make dominant contributions to the detected response
39

function and especially at short times (<1 ps).100, 121 Because the effective dielectric
constant in the interior of a protein is small,122 the electric-field fluctuations sensed
by the probe from water molecules in the surroundings are poorly screened by the
protein medium. In liquid water, M(t) decays according to two phases, the inertial
(<100 fs, Gaussian) and diffusive reorientational (<1 ps, exponential) responses.61 In
a number of studies, components in the FSS response with time constants as long as
100 ps have been assigned to motions of water molecules as they exchange between
sites on the surface of proteins and the hydration layer.115–117, 123–125 In contrast,
Nilsson and Halle58 argued that the FSS response cannot sense these water motions
because the exchange reactions would not be accompanied by a modulation of the
local electric field; replacement of a bound water molecule with a free water molecule
from the bulk would occur in a concerted fashion. Using the results from molecular
dynamics (MD) simulations that featured calculations of the dielectric response of
the protein and surrounding solvent at each step in the trajectory, they concluded
instead that the motions of water molecules in the hydration layer are only somewhat slowed from those in the bulk solvent, with <1.5-ps correlation times being
characteristic. Slower correlation times in the response function were assigned only
to the motions of protein-derived groups as the timescales increase into the >10ps range and longer.58 These conclusions are strongly supported by the recent MD
simulations of Toptygin et al., but these authors add the interesting observation that
their calculated response functions poorly reproduce the experimentally observed
FSS timescales when protein motions are predominantly involved.105
There have been only a few observations of protein-derived motions using dynamic solvation methods in the >100-ps regime of time featured in the present work
because the probe has usually been located in a binding site that is adjacent to or
on the solvent-contact surface, where the electric-field fluctuations are dominantly
those from the external water molecules. The very first picosecond time-resolved flu-

40

orescence investigations of dynamic solvation in small proteins, in the McLendon65
and Boxer66 laboratories, accessed ps–ns motions in apomyoglobin using extrinsic
solvatochromic probes in the heme-binding site. Vincent et al.107 used the single
tryptophan residue in cytidine monophosphate kinase from Escherichia coli as a fluorescent probe in studies of the FSS response of the protein over the 100-ps–ns regime.
Toptygin et al. subsequently characterized the solvation response over the 100-ps–
10-ns regime in single-tryptophan-containing mutants of the IIAGlc protein106 and in
the B1 domain fragment (GB1) of Streptococcus protein G.126
Previously76, 77 in the Beck group we chose to characterize the FSS response of
ZnII -substituted cytochrome c (ZnCytc) because the intrinsic porphyrin could be exploited as a fluorescent probe that senses both internal and surface motions of the
protein owing to its central position in the structure and its span to the solventcontact surface via a cleft that mediates its physiological role in electron transfer
(see Figure 1.3). The present study of fbCytc extends the work on ZnCytc by showing
that the timescales assigned to the hydrophobic core and surface-contact layers are
both lengthened in fbCytc and that no new timescales are detected. In contrast to
the work on GB1 noted above,126 the FSS response functions in both ZnCytc and fbCytc are well described by the sum of exponential components. This finding suggests
that what is observed in fbCytc and ZnCytc are well isolated characteristic timescales
for discrete protein motions. This point is significant especially because fbCytc is
a partially unfolded structure under the equilibrium solution conditions used in the
present experiments.

2.4.2 Activated Barrier-Crossing Model for Protein Fluctuations
While it would be obviously desirable eventually to compare the present FSS results
with a full MD simulation of the time evolution of the dielectric response, as has been
done for the protein G system mentioned above,105, 118, 126–128 the long timescales
41

we observed experimentally for fbCytc would necessitate the calculation of especially
long MD trajectories to obtain convergence of the calculated time-correlation functions for the structural fluctuations. An additional critical problem is that the fbCytc
system does not have a well defined starting structure. In order to discuss further the
structural implications of the lengthened FSS timescales detected in fbCytc, we apply
in the following a model for the fluctuation timescales that would arise from diffusive motion on the protein-folding energy landscape. The goal of this analysis is to
provide a reasonable framework for an interpretation of both the change in timescale
that arises upon demetalation of ZnCytc to obtain fbCytc and also the effect of the
change in solvent friction that occurs upon addition of glycerol.
Figure 2.7 describes qualitatively how the ground-to-excited-state energy gap for
an electronic probe responds to a fluctuation of the structure of a protein. As the
structure samples the energy landscape, it periodically passes over barriers in moving from one local free-energy minimum to the next. The presence of barriers can be
inferred from the sensitivity of the correlation times to the external solvent friction
or to internal (steric) friction129, 130 and/or from their temperature dependence.131
If the displacement of the structure for a given motion results in a change of the local
electric field at the position of the probe, the ground- and excited-state energy levels fluctuate synchronously; the energy gap between them is modulated because the
dipole moment and polarizability of the probe are different in the two states.132 The
coupling strength h( !)2 i term in the energy-gap time-correlation function, M(t)
(Equation 2.10), relates how strongly the energy gap fluctuates in response to the
motion of the protein and its surrounding solvent. In analogy to the rotational motions sensed in FSS experiments on the ps timescale in polar liquids, the motions that
would primarily be sensed in the FSS response in proteins in the >100-ps regime are
librational (hindered rotational or torsional) in character.

42

A

E
S1

eg
eg

S0
i

j

B
i

Q1
‡

j
Q2
Figure 2.7.

Model for equilibrium structural fluctuations in a protein involving

barrier-crossing events: (a) Fluctuation with correlation time ⌧ of the ground-toexcited-state energy gap !eg for an electronic probe coupled to motion of the protein
between two structures at minima in the energy landscape, i and j; (b) Contour representation of the energy landscape with respect to two structural coordinates Q1
and Q2 , showing minima for the structures i and j and a transition-state barrier, ‡,
between them.

43

In the theory discussed by Garc´ and Hummer90 for a protein making diffusive
ıa
motions with respect to its configurational coordinates, the resulting structural fluctuations are treated in terms of the stochastic displacements and velocities x(t) and
⇣(t) for a Brownian particle,
x(t) =

Zt
0

⇣(t 0 ) dt 0 + x(0).

(2.12)

If x(t) and ⇣(t) are uncorrelated, the mean-square displacement for an ensemble of
proteins is given by
hx 2 (t)i =

Zt
0

dt 0

Z t0
0

dt 00 h⇣(t 0 )⇣(t 00 )i.

(2.13)

For Brownian motion, the derivative of the mean-square displacement with respect to
time returns a diffusion constant D expressed in terms of C(t), the time-correlation
function for the velocity ⇣(t),
Zt
Zt
d
2 (t)i = 2
0 h⇣(t 0 )⇣(0)i = 2
dt
dt 0 C(t 0 ) = 2D.
hx
dt
0
0

(2.14)

This result has the important implication that Brownian motion is characterized by
a linear relationship between the propagation time and the mean-square displacement,133
hx 2 (t)i = 2Dt.

(2.15)

The sub-diffusion and super-diffusion regimes associated with motion impeded
by traps or with longer range jumps over barriers, respectively, exhibit sublinear
(hx 2 (t)i / t n<1 ) or superlinear (hx 2 (t)i / t n>1 ) dependences on time.90
The correlation timescale ⌧ for a fluctuation can then be expressed by an Arrhenius expression,
⌧ = ⌧0 exp( G‡ /RT ),
so that the correlation time increases as the barrier height

(2.16)
G‡ increases. For Brow-

nian diffusion, the transition-state structure at the peak of the barrier would be accessed at a characteristic timescale, ⌧0 , defined by the diffusion constant D and the
44

mean-squared displacement, hx 2 (⌧0 )i,
⌧0 = hx 2 (⌧0 )i / 2D.

(2.17)

This result shows that the correlation timescale ⌧ is linearly proportional to the
mean-square displacement for the fluctuation. The diffusion constant D would be
expected to be inversely proportional to the friction f ,134
D = kB T /f

(2.18)

so an increase of friction would result in a lengthening of the correlation time. If the
associated structural change for a fluctuation involves regions of the protein that are
damped by the external solvent, as is observed for fbCytc and ZnCytc, ⌧0 would be
lengthened as the solvent friction increases.85, 129, 130, 135 If the solvent conditions
are kept constant, however, a lengthening of the correlation time for a particular fluctuation would be consistent with an increase in the amplitude of the associated motion. Given that the barrier heights for motion on the energy landscape are likely to
be strongly coupled to the conformational state, it should be clear that Equation 2.17
provides only a rule-of-thumb for qualitative use in the interpretation of correlation
timescales. Nevertheless, it is fully consistent with the observations made by Webb
and coworkers using fluorescence correlation spectroscopy of fluctuations associated
with conformational changes in apomyoglobin on the µs timescale.136

2.4.3 Comparison of the Solvation Response in fbCytc and ZnCytc
The FSS response from fbCytc and ZnCytc with the excitation laser tuned to the 0–0
vibronic transition in the Q band consists of monotonic biexponential shifts of the
time-resolved fluorescence to lower energy. Because the observed shifts are relatively
small, a few hundred cm 1 at most, the change in the porphyrin’s dipole moment is
relatively small, perhaps a few Debye, and because the porphyrin chromophore is
45

relatively large, it is reasonable to assume that the linear-response regime is applicable. Note that in addition to the polar solvation response to the optical transition,
there is also a nonnegligible nonpolar solvation response in ZnCytc that arises from
the biphasic photodissociation of the axial ligands to the ZnII ion, the histidine (H18)
and methionine (M80) side chains. We consider this a nonpolar response because
the size of the probe effectively increases as it throws off the axial ligands. The
timescales associated with the response of the protein and the external solvent to
the ligand photochemistry are apparently uncorrelated with the timescales for the
FSS response.76, 77 As discussed in the Introduction, however, with excitation of ZnCytc into the Soret-band region of the absorption spectrum, the protein is launched
along an unfolding trajectory along a pathway that successively populates at least
three partially unfolded states. A similar unfolding process is apparently triggered
in fbCytc at much lower excess vibrational excitations.78, 79 The assumption of linear response in the interpretation of the FSS response is obviously not valid if the
laser excitation is tuned above the unfolding activation thresholds. In the present
work, the excitation laser was tuned close to the 0–0 transition precisely to avoid this
issue and to avoid adding a vibrational relaxation component to the observed FSS
response. The time constants returned by the FSS response functions can then be
considered the correlation times for two analogous classes of structural fluctuations
in fbCytc and ZnCytc.
The model outlined above for the fluctuation timescales detected in the FSS response suggests a simple structural picture for the change in protein dynamics
caused by demetalation of ZnCytc to form fbCytc. The observed correlation times
are almost an order of magnitude longer in fbCytc than in ZnCytc, and there is no
evidence that the components observed in ZnCytc are present but strongly attenuated in fbCytc. These results are consistent either with a significant increase in
the structural amplitudes of the fluctuations of the hydrophobic core and solvent-

46

contact regions or a significant increase in the height of the associated barriers. The
former conclusion is obviously favored because the loss of the axial-ligand–metal interactions would, if anything, lower the barriers for motions of the folded protein
orthogonal to the plane of the porphyrin (see Figure 1.3).
The molecular dynamics (MD) simulations obtained for horse-heart FeCytc by
Garc´ and Hummer90 include fluctuations that are associated with transitions beıa
tween local minima on the 100-ps timescale. The most active (largest mean-squared
displacements) region of the structure in the MD trajectories is the region spanning
amino-acid residues 36–61, which bridges the loops on the left and right-hand sides
of the protein (as shown in Figure 1.3) that project the axial ligands (the side chains
of H18 and M80, respectively) towards the metal ion. The latter region is associated
with especially rapid hydrogen-exchange rates in the work by Englander and coworkers.137
The FSS responses observed in ZnCytc and fbCytc are well described by exponential components rather than by stretched exponentials or distributions of exponential
components, which might be expected from a rough energy landscape characterized
by a range of barrier heights.138 Thus, the response in ZnCytc and fbCytc might
be considered sparse; only two classes of motion are coupled significantly to the
⇡

⇡⇤ transition of the intrinsic porphyrin in ZnCytc or fbCytc on the fluorescence

timescale. It is likely that the motions that are detected in the FSS response are
highly correlated motions: only the motions that result in coherent electric field fluctuations at the probe will have nonzero coupling strengths. Of course, groups in
motion near to the probe would be expected to be more strongly coupled, but the
low dielectric constant of the protein medium permits the motion of even distant
charges or dipoles to be sensed. Noisy, uncorrelated motions will project incoherent
electric field fluctuations that are cancelled or attenuated when superimposed at the
probe. The present results imply further that the fluorescence lifetime of the probe

47

limits the detected response to a fairly narrow range of timescales. The mean-square
displacements for the ps–ns motions we have detected in ZnCytc and fbCytc are probably fairly short-range in character, so they are likely to be associated with hindered
torsional motions of the side chains of amino acids or of the polypeptide backbone.
Future studies of the barrier heights associated with these correlation times through
variation of the temperature, as in the work by Bhattacharyya and coworkers,131 may
provide some additional guidance for assignments of the character of motion.
Lastly, the conclusion that the fluctuations detected on the fluorescence timescale
in fbCytc exhibit much larger mean-squared displacements than those in ZnCytc
should be considered in the context of the dynamics for unfolding reactions.
Barrier-crossing processes associated with diffusive motion along a generalized onedimensional protein-folding reaction coordinate have been treated with transitionstate theory expressions that are similar in form to that of Equation 2.16.85, 139–141
The two correlation times observed in our fluorescence experiments probably arise
from fluctuations along distinct structural coordinates near the native minimum
of the energy landscape, and an association of either motion with the unfolding/refolding reaction coordinate requires additional information. As mentioned
above, we observed previously that the enthalpies of activation for the partial unfolding transitions in fbCytc are about one-third of those measured in ZnCytc under
the same solution conditions. The products of these unfolding reactions probably
correspond to intermediates that are populated late along the folding pathway of
FeCytc,79 and the transition-state structures are likely to be found at small displacements from the native structure along coordinates that are perturbed by demetalation. It is accordingly reasonable to suggest that the short-range, metal-dependent
fluctuations of the native structure observed in the FSS response function of fbCytc
and ZnCytc are among those that promote the formation of the unfolding transition

48

states under denaturing conditions and lead to longer-range unfolding/refolding motions on the µs–ms timescale.142

49

CHAPTER 3
Picosecond Fluorescence Anisotropy
Decays from ZnCytc in the Presence of
Gdm+

Summary
This chapter begins a discussion of how the addition of guanidinium ions (Gdm+ ) to
the surrounding solution alters the fluctuation timescales and amplitudes in ZnCytc
as the protein is denatured. The overall goal of this work is to determine the nature of the motions that are associated with the unfolding reaction coordinate and to
learn how the thermodynamic stability of the protein correlates with the amplitude
and character of the structural fluctuations. Using the fluorescence anisotropy (FA)
response function, we probe directly the structural fluctuations of the protein that
induce reorientational motions of the enclosed ZnII porphryin. The unfolding transition in the presence of Gdm+ is reported in terms of an increased cone angle for the
porphyrin’s angular fluctuations. Additionally, an unfolding intermediate with both
an increased cone angle and an lengthened correlation time is formed at 1 M, well

50

prior to the unfolding transition at 2 M. This intermediate has some of the structural
aspects of an unfolding transition state.

3.1 Introduction
The thermodynamic stability of folded proteins is routinely determined by equilibrium titrations with denaturants, such as guanidinium ion or urea.80, 143 Many proteins exhibit a cooperative transition between the native and denatured states at a
certain critical denaturant concentration. The unfolding transition is conveniently
monitored using far-UV circular dichroism spectroscopy to probe the secondary
structural composition of the protein. Alternatively, the transition can often be characterized using the fluorescence of an intrinsic or extrinsic probe chromophore. The
latter approach permits one additionally to apply time-resolved fluorescence spectroscopy to characterize the protein dynamics that are associated with the unfolding
reaction coordinate.
In some recent work,77 we showed how the dynamic fluorescence Stokes shift
(FSS) response51, 54 of the intrinsic porphyrin chromophore can be used to characterize fluctuations of the structure of ZnII -substituted cytochrome c in the native
state. When the 0–0 vibronic transition in the Q absorption band is pumped, so
that the S1 electronic state is prepared with very little excess vibrational energy, the
time-resolved fluorescence spectrum exhibits a conventional, unidirectional FSS response51, 54 to the red with two characteristic timescales, 250 ps and 1.45 ns. This response is assigned in analogy to that in polar liquids to a polar solvation response of
the surrounding protein to the ground-to-excited-state change in the ZnII -porphyrin’s
dipole moment. The two timescales were assigned to motions of the hydrophobic
core and solvent-contact layers of the protein, respectively, because addition of glycerol to the external solvent medium slowed only the latter component. Subsequently

51

we showed that the correlation timescales obtained from the exponential time constants in the FSS response function in metal-free (or free-base) cytochrome c (fbCytc)
were determined to be almost ten times longer than those of ZnCytc.144 By applying
a model for the Brownian diffusive motion90 and thermally activated barrier crossing events83, 84 that are associated with structural fluctuations on the protein-folding
energy landscape,47, 81, 82 we inferred that the increased polar solvation timescales
observed in fbCytc correspond to significantly enhanced fluctuation amplitudes compared to those in ZnCytc under similar solvent conditions. This conclusion is consistent with the suggestion we made previously79 that fbCytc assumes a dynamic,
partially unfolded structure with some of the characteristics of a molten globule owing to the loss of the stabilizing influence of the two axial metal–ligand interactions
in the native ferricytochrome c structure.
In this contribution, we begin a discussion of how the addition of guanidinium
ions (Gdm+ ) alters the fluctuation timescales and amplitudes in ZnCytc as the protein is denatured. The overall goal of this work is to determine the nature of the
motions that are associated with the unfolding reaction coordinate and to learn how
the thermodynamic stability of the protein correlates with the amplitude and character of the structural fluctuations. Our approach will be to compare the correlation
timescales detected by the porphyrin chromophore for the fluctuations of ZnCytc
in the presence and absence of Gdm+ using two methods: the FSS response, as discussed above, and the fluorescence anisotropy (FA) response. While the FSS response
detects the motions of the protein structure indirectly using the fluctuating local
electric field sensed by the chromophore, the FA response senses the motions of the
porphyrin directly using the decay of the alignment of the photoselected ensemble
that was initially prepared by a plane-polarized excitation laser pulse. Given that the
protein structure prepares a tight-fitting cavity for the porphyrin (see Figure 1.3), the
FA response primarily reports the structural fluctuations of the protein that induce

52

reorientational motions of the porphryin. Of course, on a longer timescale than those
associated with internal motions of the protein, the FA response will also include a
decay component associated with rotational diffusion of the entire solvated protein.
The present contribution focuses on the FA response in ZnCytc as a function of
the Gdm+ concentration and compares directly the motions of the protein in the native and denatured states. The internal rotational diffusion timescale, 700–1150 ps,
is comparable to that determined previously for the motions of the hydrophobic core
using the FSS response. The results also show that a partially unfolded structure is
populated in the presence of Gdm+ prior to the denaturation transition. The intermediate is distinctive in being characterized by equilibrium fluctuations with enhanced
mean squared deviations relative to those in the native and denatured structures, so
it possesses some of the properties of a transition-state structure.

3.2 Experimental
3.2.1 Sample Preparation
ZnCytc was prepared from horse-heart ferricytochrome c (FeCytc) from Sigma using the procedure developed by Vanderkooi and coworkers.69, 91 The metal free
cytochrome c product of the demetalation reaction of FeCytc in liquid anhydrous HF
was reconstituted with ZnII using a 10-fold molar excess of zinc acetate. The ZnCytc
product was worked up using methods based on those employed by Winkler and
coworkers92 and Kosti´ and coworkers.93 The final concentrated ZnCytc solution
c
obtained after repeated ultrafiltration steps using a Millipore YM10 ultrafilter was
divided into small aliquots and flash-frozen in liquid nitrogen for later use.
On the day of a fluorescence experiment, frozen samples were thawed and then
diluted with a range of Gdm+ concentrations in a 25 mM phosphate buffer solution at
pH 7.0. The resulting protein solution was then allowed to settle for an hour before
53

it was filtered through a 0.22 µM microfilter to remove any large debris. The final
concentration of the sample was then adjusted by adding additional diluent solution
to obtain an absorption of 0.1–0.2 at the peak of the 0–0 absorption band for a path
length of 1.0 cm. The sample was held in quartz cuvettes and the headspace was
purged with dry nitrogen gas prior to an experiment.

3.2.2 Absorption and Fluorescence Spectroscopy
Absorption spectra were acquired with a Hitachi U-2000 spectrophotometer (2-nm
band pass). Fluorescence spectra were obtained with a home-built spectrofluorimeter79 consisting of a Jobin-Yvon AH10 100-W tungsten-halogen light source, a JobinYvon H10 excitation monochromator (4-nm bandpass), an Acton Research SP-150
emission spectrograph (2-nm bandpass), and a Jobin-Yvon Symphony charge-coupled
device (CCD) detector. The CCD detector employs a liquid nitrogen cooled, backilluminated, 2000 ⇥ 800 pixel silicon detector chip (EEV corporation). The sample cuvette was held in a Quantum Northwest TLC50F Peltier-effect temperature controller.
As presented as a function of wavenumber, the fluorescence intensities are multiplied
by the square of the wavelength in order to compensate for the fixed (in wavelength
units) spectral bandpass of the emission spectrograph.94 The absorption and fluorescence instruments were controlled by LabVIEW (National Instruments) programs.

3.2.3 Time-Resolved Fluorescence Measurements
The time-resolved experiments described in chapter 2 were performed using a Lformat photon counting system with only one detector. Single-wavelength fluorescence transients for the FA experiments discussed in this chapter and the FSS response in the following chapter were acquired using a T-format time-correlated single photon counting (TCSPC) instrument. Excitation pulses were obtained from a

54

synchronously pumped cavity-dumped dye laser (Coherent 702-2). The dye laser was
pumped by a passively mode-locked, diode-pumped NdIII :YVO4 laser (Spectra-Physics
Vanguard); it produced 13 ps pulses with an average power of 2.5 W at 355 nm and
532 nm and a repetition rate of 80 MHz. The dye laser produced 5 ps pulses over the
583–585 nm tuning range using either the Rhodamine-6G or Pyromethine 567 dyes.
The repetition rate on the dye laser was adjusted to 4 MHz using the cavity dumping
electronics (Gooch & Housego).
In the detection system, the vertically polarized excitation pulse from the dye
laser was divided into two parts. One part of the pulse was fed to a reference photodiode (Becker & Hickl PHD-400-N), and the other part was directed to the sample.
The fluorescence emission was collected using a Cassegranian reflective microscope
objective (40⇥ magnification). The collected emission was then split by a polarizing cube beam splitter into two orthogonal polarization components with planes of
polarization parallel (0 ) and perpendicular (90 ) to that of the vertically polarized
excitation pulse. The two components were detected simultaneously with microchannel plate photomultiplier tubes (MCP-PMT, Hamamatsu R3809U-50) after selection
of the emission wavelength by subtractive double monochromators (Spectral products, CM-112). Emission transients were recorded with a two-channel TCSPC system
(Becker & Hickl SPC-132). The instrument-response width was 65 ps. LabVIEW (National Instruments) programs were used to control the data-acquisition hardware and
monochromators so that a set of single-wavelength fluorescence transients could be
automatically acquired over a range of emission wavelengths. The sample was held
in a water-cooled mount that was regulated at 22 C using a Neslab RTE-110 water
circulating bath.

55

3.3 Results
3.3.1 Absorption and Fluorescence Emission Spectra
Figure 3.1 shows the Q-band region of the absorption and fluorescence emission
spectra obtained from ZnCytc in water at 22 C and pH 7.0. The spectra are plotted
as relative dipole strengths, A(⌫)/⌫ and F (⌫)/⌫ 3 , respectively, as a function of the
wavenumber, ⌫. The 0–0 and 0–1 peaks of the fluorescence spectrum exhibit a near
mirror-symmetry with respect to the 0–0 and 0–1 peaks of the absorption spectrum.
An estimate for the lower limit for the solvation reorganization energy,

= 55 ±

10 cm 1 , was then obtained using the shift of the wavenumber of the fluorescence
spectrum’s 0–0 peak, ⌫0–0, F , from that of the absorption spectrum, ⌫0–0, A :100, 144
= (⌫0–0, A

⌫0–0, F )/2

(3.1)

The peak maxima for the absorption and fluorescence 0–0 peaks were found using
Mathematica peak-finding routines and the smoothed first-derivative spectra.
In some of the previous work on ZnCytc from this laboratory,77, 78 the metal-free
product (fbCytc) of the demetalation of FeCytc in liquid anhydrous HF and the ZnCytc
product obtained after ZnII reconstitution were worked up using Sephadex G-75 gelfiltration chromatography, as described by Vanderkooi and coworkers.91 The value
for

obtained with these preparations was typically 145 cm 1 . In subsequent work79

and in the present work, we worked up the fbCytc and ZnCytc products using ionexchange chromatography using the approach used by Winkler and coworkers and
Kosti´ and coworkers.92, 93 These preparations exhibit absorption and fluorescence
c
spectra with narrower vibronic lineshapes; the reader should compare Figure 3.1 in
this paper with the similar figure in reference 78. The smaller value for

obtained

with the ion-exchange procedure arises primarily from the narrower lineshapes, and
we find that it is consistent from preparation to preparation.

56

Relative Dipole Strength

675

650

Wavelength ￿nm￿

625

600

575

550

525

0-1

0-1
0-0

0
15 000

16 000

17 000

Frequency ￿cm￿1 ￿

18 000

19 000

Figure 3.1. Q-band region of the absorption and fluorescence spectra from ZnCytc
in water at 22 C and pH 7.0. The spectra are plotted as relative dipole strengths,
A(⌫)/⌫ (dashed line) and F (⌫)/⌫ 3 (solid line), respectively. The spectra are scaled
such that the 0–0 peaks have the same relative intensity.

57

As Gdm+ is added to ZnCytc solutions, the fluorescence spectrum exhibits two
types of changes that report the denaturation of the protein structure (see Figure 3.2).
The first is a shift to the blue according to a two-state cooperative transition with a
midpoint Gdm+ concentration of ⇠2.0 M. Figures 3.3 and 3.4 show the Gdm+ titration
curves from ZnCytc obtained by plotting separately the trends of the peak wavenumbers for the 0–0 and 0–1 fluorescence and absorption transitions, respectively, as a
function of the Gdm+ concentration. The model curves used in Figures 3.3 and 3.4
assume an equilibrium between the unfolded (U) and native (N) states, here stated as
a folding reaction:
U

Keq

N

(3.2)

The Gibbs free energy of folding can be then expressed as
GFold =

1

RT ln

fu

fu

!

=

H O

2
GFold + m [Gdm+ ]

where fu represents the fraction of unfolded proteins in the ensemble,

(3.3)
H O

2
GFold relates

the Gibbs free energy of folding in pure water, and m relates the change in Gibbs
free energy that occurs with the addition of Gdm+ to the solution. Solving for fu , we
obtain

2

0

B
6
fu = 41 + exp @

13 1
H2 O
+
GFold + m [Gdm ] C7
RT

A5

(3.4)

The titration curves, fu as a function of Gdm+ concentration, were calculated from
the observed 0–0 and 0–1 peak wavenumbers using a series of simulated spectra
(see Figure 3.5) determined as the linear combination of the experimental spectra observed in the native (fu = 0) and unfolded (fu = 1) states, respectively. The lineshape
parameters (center frequency, !0 , width,

, and asymmetry, ⇢, see Table 3.1) for the

native and unfolded states were determined by fitting a lognormal lineshape97 to the
experimental spectra at 0.0 M and 5.0 M Gdm+ . As shown in Figures 3.3 and 3.4,
Equation 3.4 serves as a good fitting model for the experimental data and does a
58

good job of describing the blue shift of both vibronic peaks in absorption as well as
emission spectra of ZnCytc as Gdm+ is added to the protein solution. At the midpoint (fu = 0.5) of these transitions, the two states are at equilibrium ( GFold = 0);
from Equation 3.3, we then obtain
H O

2
GFold =

m [Gdm+ ]1/2 =

m Cm

(3.5)

where Cm represents the denaturant concentration at the midpoint of the transition.
Table 3.2 lists the fit parameters obtained for the fluorescence and absorption
Gdm+ titration curves for ZnCytc shown in Figures 3.3 and 3.4. The averaged thermodynamic parameters for the fluorescence and absorption transitions are statistically
similar. While the transition midpoints for the 0–0 and 0–1 peaks of fluorescence are
within 0.1 M on the Gdm+ axis, the midpoint for the 0–0 peak of the Q band absorption occurs about 0.16 M later on the Gdm+ axis than that for the 0–1 peak. This
observation suggests that the ZnII –porphyrin in ZnCytc is somewhat strained in the
native state (vide infra); the response of the spectrum is somewhat inhomogeneous
with respect to the effect of Gdm+ in both ground and excited state. Bhuyan et al.
has shown that FeCytc in the presence of Gdm+145 has a

H O

2
GFold =

30.96 kJ/mol

using fluorescence intensity from the intrinsic tryptophan residue as a measure of
the folded state. On average, the fit parameters show that ZnCytc is significantly
less stable than FeCytc but perhaps more stable than the metal free cytochrome c
as evidenced from studies in urea induced unfolding;87, 146 the Gibbs free energy
of unfolding for ZnCytc is one-third that of FeCytc. The folded structure of ZnCytc
is less sensitive than FeCytc to Gdm+ , however, because the m value is significantly
smaller.145 This parameter largely controls the sharpness of the sigmoidal transition; the response is less abrupt in ZnCytc than FeCytc. These findings suggest that
the axial coordination of the metal ion in cytochrome c plays an important role in
controlling the stability of the native fold.

59

650

625

600

575

Relative Dipole Strength

675

Wavelength ￿nm￿

14 500

15 000

15 500

16 000

16 500

Frequency ￿cm￿1 ￿

17 000

17 500

Figure 3.2. Fluorescence spectra from ZnCytc at 22 C and pH 7.0 in water (solid line)
and in the presence of Gdm+ at 1 M (- - -), 2 M (– – –) and 3 M (— — —). The spectra
are plotted as relative dipole strengths, F (⌫)/⌫ 3 , and are normalized by the intensity
of the 0–0 peak.

60

1.0

￿

￿
￿

￿
￿

￿
￿

￿

￿
￿

0.8

Fraction Unfolded

￿
￿ ￿
￿

￿
￿

0.6

￿

0.4

￿
0.2
0.0 ￿ ￿
0

￿
￿

￿

1

￿
￿

￿

￿

2

3

￿Gdm￿ ￿ ￿M￿

4

5

Figure 3.3. Gdm+ fluorescence titration curves for ZnCytc at 22 C and pH 7.0. The
fraction of unfolded proteins in the ensemble determined from the wavenumber of
the peak maximum of the 0–0 and 0–1 peaks in the fluorescence spectrum is plotted
as a function of the Gdm+ concentration; the data points are superimposed upon separate models for a two-state unfolding transition (Equation 3.4). The thermodynamic
parameters for the unfolding transition are listed in Table 3.2.

61

1.0

￿
￿ ￿
￿ ￿
￿

Fraction Unfolded

0.8

0.6

￿
0.4

￿
￿

0.2
0.0 ￿ ￿
￿
0

￿
￿

￿
￿

1

￿

￿
￿

￿
￿

￿
￿

￿
￿

￿
￿

￿
￿

￿

￿

2

3

￿Gdm￿ ￿ ￿M￿

4

5

Figure 3.4. Gdm+ absorption titration curves for ZnCytc at 22 C and pH 7.0. The
fraction of unfolded proteins in the ensemble determined from the wavenumber of
the peak maximum of 0–0 and 0–1 peaks in the absorption spectrum is plotted as a
function of the Gdm+ concentration; the data points are superimposed upon separate models for a two-state unfolding transition (Equation 3.4). The thermodynamic
parameters for the unfolding transition are listed in Table 3.2.

62

Dipole Strength
0
16 500

16 750

17 000

Frequency ￿cm￿1 ￿

17 250

17 500

Figure 3.5. Simulation of the fluorescence spectral changes that accompany Gdm+
unfolding of ZnCytc. Fluorescence emission (dipole strength) spectra are shown for
the native state (0 M Gdm+ , black) and the unfolded state (5 M Gdm+ , red) and at
several states with fractional unfolding (0.1–0.9, blue curves). Table 3.1 lists the
lognormal lineshape parameters that were used to calculate the fractionally unfolded
spectra as linear combinations of native and unfolded spectra.

63

Table 3.1. Absorption (Q) and fluorescence (F ) lognormal lineshape
parametersa for the unfolding transition of ZnCytc in the presence of
Gdm+ .
!0 (cm 1 )
F0
F0
F0
F0
Q0
Q0
Q0
Q0

0,
0,
1,
1,

Nativeb
Unfoldedc
Native
Unfolded

0,
0,
1,
1,

Native
Unfolded
Native
Unfolded

(cm 1 )

⇢

17017.6
17065.9
15513.1
15580.2

220
265
437.8
478.9

1.2
1.2
1.2
1.2

17148.5
17227.6
18227.6
18336.9

268.4
349.5
413.7
441.7

1.1
1.1
1.1
1.1

a See the text.
b Native = 0 M Gdm+ .
c Unfolded = 5 M Gdm+ .

64

Table 3.2. Thermodynamic parameters for the equilibrium unfolding
transitiona for ZnCytc and the transition midpoints.
H O

2
GFold (kJ/mol)

F0 0
F0 1
b
Average
Q0 0
Q0 1
cAverage

m (kJ/mol/M)
6.32 ± 0.42
5.99 ± 0.25
6.16 ± 0.49

-11.31 ± 0.30
-10.16 ± 0.45
-10.74 ± 0.54
-10.60 ± 0.63
-10.36 ± 0.35
-10.48 ± 0.52

Cm (M)
1.79 ± 0.13
1.70 ± 0.10
1.75 ± 0.16

5.99 ± 0.34
5.38 ± 0.18
5.69 ± 0.15

a See Equation 3.4 and Figures 3.3 and 3.4.
b Average of the two fluorescence transitions.
c Average of the two absorption transitions.

65

1.77 ± 0.15
1.93 ± 0.09
1.85 ± 0.10

￿

1.24
￿

￿ ￿

F 01 ￿F 00

1.21
1.18

￿
￿

￿

￿

￿
￿

￿

￿

￿

￿

￿

1.15

￿
￿

1.12
0

1

2

3

￿Gdm ￿ ￿M￿

4

5

￿

Figure 3.6. Dependence on the Gdm+ concentration of the ratio of the intensity of
the 0–1 and 0–0 vibronic peaks in the fluorescence spectrum from ZnCytc at 22 C
and pH 7.0.

66

The second change in the fluorescence spectrum that accompanies the denaturation reaction in the presence of Gdm+ is a decrease in the ratio of the intensity
of the 0–1 and 0–0 peaks, F01 /F00 (see Figure 3.6). The overall decreasing trend is
broken by a positive peak at 2.5 M, and the ratio oscillates over the 3.5–5.0 M Gdm+
range. As discussed previously,76, 79 the F01 /F00 ratio is sensitive to the dissociation
and rebinding of axial ligands to the ZnII ion; the ratio increases as the M80 and H18
ligands dissociate in the S1 excited state. The trends in the F01 /F00 ratio suggest
that the protein structure reorganizes as Gdm+ is added so that alternate ligands are
accessible to the ZnII ion.79

3.3.2 Picosecond Fluorescence Anisotropy Decays
FA transients from ZnCytc as a function of the Gdm+ concentration were acquired
with the excitation laser tuned to the wavenumber of the 0–0 transition (see Figure 3.1) and with emission wavelengths scanned fully across the 0–1 peak. The parallel (Ik ) and perpendicularly (I? ) polarized fluorescence transients were acquired
simultaneously, and the FA transient was computed directly as
r (t) =

Ik (t)

I? (t)

Ik (t) + 2I? (t)

(3.6)

The FA transients were fit to a biexponential model
r (t) = A1 e t/⌧1 + A2 e t/⌧2

(3.7)

As will be discussed in the following section, the shorter of the two anisotropy
timescales corresponds essentially to motion of the ZnII -porphyrin’s transition dipole
moment with respect to the protein, whereas the longer timescale is associated with
rotational diffusion of the entire protein.
In order to assess whether the 0–1 peak is homogeneous with respect to the FA
decays, we compared single-wavelength FA transients from ZnCytc in water detected
67

Figure 3.7. Polarized fluorescence emission transients from ZnCytc in water at 22 C.
The parallel and perpendicular transients obtained from: (a) Single-wavelength transients recorded at 640 nm, at the peak of the 0–1 vibronic band. (b) Integral of
single-wavelength transients across the 0–1 vibronic band (14750–16700 cm 1 ). The
spikes in the polarized emission transients arise from the timing electronics of the
detection system. The insets for (a) and (b) show the anisotropy transients computed
from the intensity transients using Equation 3.6 superimposed on a fitted biexponential decay defined by Equation 3.7. The model parameters for the fitted transients are:
(a) A1 = 0.041, ⌧1 = 685.02 ps, A2 = 0.306, ⌧2 = 10.63 ns, and (b) A1 = 0.041, ⌧1 =
686.0 ps, A2 = 0.285, and ⌧2 = 10.64 ns.

68

at the peak maximum with those obtained by integrating over the entire width of
the band. Figure 3.7 shows that the single-wavelength and integrated FA transients
are described by indistinguishable biexponential models but that the integrated transients have significantly higher signal/noise ratios. In the following analysis, we employ the integrated FA transients exclusively.
The dichroism-free intensity of fluorescence emission was computed from the
polarized transients as
I(t) = Ik (t) + 2I? (t)

(3.8)

Figure 3.8 compares the single-wavelength and integrated intensity transients. Both
are well described by biexponential models with comparable intensities for the two
components. The average fluorescence lifetime for the ZnII –porphyrin in ZnCytc
is 3.98 ns; Vanderkooi et al. has previously measured an average lifetime of ⇠3.2
ns.

The biexponential decay of fluorescence intensity in ZnCytc was noted pre-

viously by Vanderkooi;91 the two lifetimes probably arise from distinct instantaneous conformations of the ZnII –porphyrin. A similar biexponentiality is noted for
ZnII tetraphenylporphyrin (ZnTPP) and tetrakis (N -methyl-4-pyridyl) porphyrin ZnII
(ZnTMPyP).147, 148 Thus, the results noted here for ZnCytc do not necessarily arise
from a spectral or protein conformational heterogeneity.
Figure 3.9 shows a set of FA transients from ZnCytc over a range of Gdm+ concentrations. As was observed in the absence of Gdm+ (see Figure 3.7), a biexponential
model (Equation 3.7) provides an excellent description of all the decays. Table 3.3
lists the model parameters for all the Gdm+ concentrations studied. Plots of the fit
parameters (see Figures 3.10–3.12) show that significant changes in the anisotropy
decays are observed at Gdm+ concentrations prior to the unfolding transition. Figure 3.10 shows that the amplitude A1 that scales the component with the shorter
time constant, ⌧1 , increases as Gdm+ is added. In contrast, the amplitude A2 for
the slower component with the time constant ⌧2 decreases as the concentration of
69

104 Counts

6
5
4

Intensity

3
2
1
0

105 Counts

6
5
4

Intensity

3
2
1
0
0

2000

4000

6000

8000

Time ps
Figure 3.8.

Comparison of single-wavelength (top) and integrated (bottom)

dichroism-free fluorescence intensity transients from ZnCytc in water at 22 C calculated from the polarized fluorescence transients as Ik + 2I? . The single-wavelength
transient was recorded at 640 nm, the peak of the 0–1 band. The integrated transient is the sum of the single-wavelength transients recorded at ten wavelengths
across the 0–1 vibronic band. The data points in the two transients are each superimposed on a biexponential decay model. The model parameters for the singlewavelength transient are: I1 =34563.5±175, ⌧1 = 1025.9±8.2 ps, I2 = 36429.8±203.7,
⌧2 = 4852.3 ± 21 ps.

The model parameters for the integrated transient are:

I1 =369290 ± 1688, ⌧1 = 1041.2 ± 7 ps, I2 = 352295 ± 1960, ⌧2 = 4668 ± 19 ps.

70

Figure 3.9. Integrated fluorescence anisotropy transients for the 0–1 band from ZnCytc at 22 C and pH 7.0 as a function of the Gdm+ concentration. The data points are
superimposed on a biexponential model defined by Equation 3.7. The fit parameters
are listed in Table 3.3.

71

Table 3.3. Fluorescence anisotropy decay parameters for ZnCytc in the
presence of Gdm+ at 22 C.
Gdm+ (M)

A1 a

⌧1 (ps)

A2

⌧2 (ns)

0.00
0.25
0.50
1.00
1.50
2.00
3.00
4.00
5.00

0.048 ± 0.01
0.034 ± 0.005
0.04 ± 0.002
0.101 ± 0.019
0.10 ± 0.035
0.082 ± 0.029
0.095 ± 0.004
0.101 ± 0.033
0.105 ± 0.026

780 ± 94
723 ± 141
860 ± 24
1157 ± 32
925 ± 157
776 ± 164
844 ± 114
857 ± 225
707 ± 158

0.278 ± 0.01
0.225 ± 0.029
0.229 ± 0.006
0.242 ± 0.022
0.220 ± 0.011
0.198 ± 0.021
0.195 ± 0.003
0.208 ± 0.021
0.209 ± 0.006

10.47 ± 0.16
9.06 ± 0.53
8.21 ± 0.30
8.51 ± 0.62
7.14 ± 0.84
5.78 ± 0.21
7.33 ± 0.89
6.18 ± 0.46
6.81 ± 0.56

a See Equation 3.7.

72

0.28
0.26

A2

0.24
0.22
0.20
0.18

0.13
0.11

A1

0.09
0.07
0.05
0.03
0

1

2

Gdm

3

4

5

M

Figure 3.10. Anisotropy decay amplitudes (see Equation 3.7 and Table 3.3) for ZnCytc
at 22 C and pH 7.0 as a function of the Gdm+ concentration.

73

Figure 3.11. Anisotropy decay correlation time constants for ZnCytc at 22 C and
pH 7.0 as a function of the Gdm+ concentration. The model parameters are listed in
Table 3.3. These time constants are related to the time constants in the mechanical
model via Equation 3.13 and 3.14.

74

￿

0.34

￿

￿

0.32

r0

￿

￿

0.30

￿
￿

0.28

￿
0.26

￿

0

1

2

3

￿Gdm ￿ ￿M￿

4

5

￿

Figure 3.12. Gdm+ concentration dependence of r0 , the total anisotropy amplitude
(see Equation 3.7 and Table 3.3) at time t=0, for ZnCytc at 22 C and pH 7.

75

Gdm+ increases. Both curves show inflections in the 0.25 M and 1.0 M regions. Both
amplitudes are more or less constant after the unfolding transition at 2.0 M Gdm+ ;
A1 is more or less constant after ⇠1.0 M if we consider the error bars. A similar
trend is indicated by Figure 3.11, which shows that the time constants ⌧1 and ⌧2 are
essentially constant at Gdm+ concentrations above 2.0 M. Well prior to the unfolding
transition, however, ⌧1 exhibits a broad peak, and ⌧2 exhibits an inflection centered
at 1 M Gdm+ . Figure 3.12 shows that the initial (t = 0) anisotropy amplitude r0
also exhibits a peak in the 1 M region that is superimposed on a generally increasing
trend. Note that r0 is significantly less than 0.4 in water and that an abrupt decrease in the 0–0.5 M Gdm+ region is observed; these observations imply that there
is a fast depolarization on the <100-ps timescale that arises from electronic state
degeneracy112 and that the presence of Gdm+ even at very low concentrations has
an effect on the electronic properties of the ZnII porphyrin. Thus, even prior to the
application of a mechanical model for the fluctuations that gives rise to the faster of
the two anisotropy decay components, these results suggest that one or more partially unfolded structures are populated at Gdm+ concentrations below the unfolding
transition.

3.3.3 Wobbling-in-Cone Mechanical Model
A mechanical model that describes the internal motion of the transition dipole moment of the ZnII –porphryin in ZnCytc with respect to the overall protein structure
is the wobbling-in-cone (WIC) model (see Figure 3.13) introduced by Kinosita et al.
to describe the anisotropy decay of a fluorescent probe in lipid membranes.149, 150
This model has been used extensively to treat internal motion of a probe in proteins.151–153 The WIC model describes how the diffusive tilting motion of the transition dipole moment of a probe around its center exhibits a limiting cone angle
with respect to the frame of a tumbling protein to which the probe is bound. This
76

Z
N

m

q
q
qc
qc
Y
X
Figure 3.13. Wobbling-in-cone model for fluorescence depolarization arising from
protein dynamics. The probe’s transition dipole moment µ diffuses within a cone of
half angle ✓c with respect to the normal vector, N, which is carried by the protein’s
frame. Adapted from reference 149.

77

model can be reasonably applied to ZnCytc because the porphyrin is linked to the
polypeptide backbone by the two cysteine residues C14 and C17 at one corner of the
macrocycle, and the axial ligands to the ZnII ion from the histidine and methionine
residues H18 and M80 and the cleft in the native structure constrain the porphyrin
orthogonally to its plane (see Figure 1.3).
Using the notation of reference 149, the total anisotropy, r (t), of the system can
be expressed as the product of the anisotropy due to the motion of the probe, rp (t),
and that due to the overall rotation of the protein, rr (t), as
r (t) = rp (t) ⇥ rr (t)

(3.9)

The WIC model assumes that the internal and tumbling motions are mechanically
independent. If the internal motions are constrained by a structural limitation, the
resulting anisotropy decay is described by,94, 154
r (t) = r0 [(1

S 2 ) e t/⌧int + S 2 ] e t/⌧rot

(3.10)

where ⌧int and ⌧rot are the correlation time scales for the internal and tumbling
motions and S is a generalized order parameter that can be expressed in terms of
the ensemble average of the second Legendre polynomial,
S = hP2 (cos ✓)i

(3.11)

where ✓ is the angle between the instantaneous transition dipole-moment vector,
µ, and the normal vector, N, along the symmetry axis of the protein molecule (see
Figure 3.13). In terms of the cone angle, ✓c , that describes the structural constraint,
S is determined as
S = 1 cos ✓c (cos ✓c + 1)
2

(3.12)

The fit parameters obtained from the phenomenological biexponential models for
the experimental anisotropy decays (see Equation 3.7) can be used to calculate the
78

parameters in Equation 3.10 as follows. The internal and tumbling correlation times
are determined by
⌧int = (1/⌧1

1/⌧2 ) 1

⌧rot = ⌧2

(3.13)
(3.14)

Thus, the slower of the two anisotropy decay time constants corresponds directly to
the tumbling timescale, and the internal timescale is obtained as the harmonic mean
of the two experimental time constants. The relation for the square of the order
parameter is obtained from the amplitudes of the anisotropy decay components as
S 2 = A2 /r0 = A2 /(A1 + A2 )

(3.15)

Table 3.4 lists the model parameters we obtained from the fitted ZnCytc anisotropy
decays in the presence of Gdm+ .
Figure 3.14 shows the dependence of the correlation times for internal motion
and overall tumbling on the Gdm+ concentration. The correlation time constants ⌧int
and ⌧rot are almost an order of magnitude different in time scale (see Table 3.4).
Except for a peak centered at 1.0 M Gdm+ , the ⌧int plot is essentially constant at
⇠900 ps. In contrast, the ⌧rot plot shows a generally decreasing trend from 10 ns to
6 ns over the 0–5 M Gdm+ range.
The peak in the ⌧int plot (see Figure 3.14) suggests that an intermediate structure
is formed in the presence of 1.0 M Gdm+ , well prior to the global unfolding transition at ⇠2.0 M. Figure 3.15 shows that the trends exhibited by the cone angle, ✓c , or
the order parameter, S, has two inflection points over the 0.25–2.0 M Gdm+ range.
The main transition correlates with the 1.0 M feature in the ⌧int plot; ✓c abruptly
increases from 17 to 27 , and S decreases from 0.92 to 0.83. At Gdm+ concentrations above 1.0 M, both parameters are more or less constant, if the 95 % confidence
intervals are considered; only a small decrease in S and a small increase in ✓c accompany the unfolding transition at 2 M. These results suggest that the protein assumes
79

Table 3.4. Wobbling-in-cone model parametersa and the apparent hydrodynamic radius, Rh , for ZnCytc in the presence of Gdm+ at 22 C.
Gdm+ (M)

⌧int (ps)

⌧rot (ns)

S

0.00
0.25
0.50
1.00
1.50
2.00
3.00
4.00
5.00

844 ± 111
790 ± 171
960 ± 17.4
1341 ± 58
1071 ± 219
900 ± 218
954 ± 131
1002 ± 293
798 ± 205

10.47 ± 0.16
9.06 ± 0.53
8.21 ± 0.30
8.51 ± 0.62
7.14 ± 0.84
5.78 ± 0.21
7.33 ± 0.89
6.18 ± 0.46
6.81 ± 0.56

0.924 ± 0.01
0.933 ± 0.003
0.923 ± 0.003
0.839 ± 0.034
0.831 ± 0.054
0.843 ± 0.036
0.821 ± 0.003
0.821 ± 0.05
0.818 ± 0.037

a See Equation 3.12.

80

✓c
18.42
17.34
18.54
27.15
27.79
26.83
28.86
28.70
29.10

± 1.37
± 0.28
± 0.28
± 3.05
± 4.96
± 3.21
± 0.28
± 4.41
± 3.22

Rh (nm)
2.17
2.06
1.98
1.99
1.86
1.72
1.82
1.67
1.67

± 0.02
± 0.04
± 0.02
± 0.05
± 0.07
± 0.02
± 0.07
± 0.04
± 0.05

Figure 3.14. Anisotropy decay correlation times (Equation 3.13 and 3.14) for ZnCytc
at 22 C and pH 7.0 as a function of the Gdm+ concentration. The model parameters
are listed in Table 3.4.

81

Figure 3.15. Gdm+ concentration dependence for S, the anisotropic order parameter, and ✓c , the cone angle (see Equation 3.12), for ZnCytc at 22 C and pH 7. The
parameters are listed in Table 3.4.

82

a partially unfolded state at ⇠1.0 M Gdm+ that allows the ZnII porphyrin to exhibit
a significantly larger range of motion with respect to the protein than is observed in
the native state. It is interesting to note that the range of motion for the ZnII porphyrin does not increase as dramatically at the 2.0 M global unfolding transition even
though the change in the environment of the ZnII porphyrin makes a significant shift
during the unfolding transition.
The tumbling correlation time, ⌧rot , obtained from the ZnCytc anisotropy decays
as the longer of the two exponential time constants, can be used to determine an
estimate for the effective hydrodynamic radius, Rh , using a relation obtained from
the Stokes-Einstein-Debye Equation155
3
Rh =

3RT
⌧rot
4⇡ ⌘

(3.16)

Figure 3.16 shows that the calculated Rh decreases as the Gdm+ concentration increases. This finding is at odds with the expectation that Rh should increase owing
to the unfolding transition because a less compact structure should result and because the cone angle ✓c increases. Further, an increased Rh is observed for the
unfolded forms of several similar proteins.145, 156–158 Pielak and coworkers159 used
pulsed-field gradient NMR spectroscopy to determine that the effective Rh for FeCytc
˚
˚
expands from 18 A in the native state to 31 A in the acid (pH 2) denatured state. Thus,
it is probable that the reduced ⌧rot we observe in the unfolded state in the presence
of Gdm+ arises from the protein’s assumption of an elongated, non-spheroidal structure from which more than one rotational correlation time would be expected.160
If one of the rotational moments in the unfolded state exhibits a correlation time
that is significantly longer than the fluorescence timescale, its contribution to the
anisotropy decay would be attenuated relative to that of a shorter moment.
The trend of the effective Rh as a function of Gdm+ shown in Figure 3.16 includes
distinct inflections centered at 1.0 M and between 2.0–3.0 M that are statistically significant if the confidence intervals are considered. The 1 M inflection correlates with
83

￿
2.1

￿

Rh ￿nm￿

2.0

￿

￿

1.9

￿
￿

1.8

￿

1.7

￿
0

1

2

3

￿Gdm ￿ ￿M￿

￿

4

5

￿

Figure 3.16. Gdm+ concentration dependence for the effective hydrodynamic radius,
Rh , as calculated from the anisotropy decay time constant ⌧rot and Equation 3.16 for
ZnCytc at 22 C and pH 7. (See Table 3.4.)

84

the intermediate suggested by the increased ✓c and the increased internal correlation time ⌧int , so there is some global structural evidence for a change in overall
size for this intermediate. The 2.0–3.0 M inflection occurs as the ensemble finishes
the unfolding transition and accompanies the peak in the F01 /F00 vibronic structure
ratio that is asociated with a change in the axial coordination of the ZnII ion (see
Figure 3.6).

3.4 Discussion
The finding that the global unfolding transition of ZnCytc is preceeded during the
titration with Gdm+ by formation of an intermediate raises some important questions
about how it relates dynamically and structurally to the native and unfolded states. In
the following, we discuss how the internal correlation time and the order parameter
or cone angle returned from the picosecond fluorescence anisotropy decays suggest
that the intermediate has some of the properties of an unfolding transition state.
The anisotropy results show that an intermediate structure characterized by an
enhanced cone angle for the ZnII porphyrin is populated at 1 M Gdm+ , well below the
overall unfolding transition at 2 M Gdm+ (see Figure 3.15). The intermediate structure
exhibits a significantly longer internal correlation time than observed either in the
native state or in the unfolded state (see Figure 3.14). Despite the significant change
in correlation timescale, the intermediate is formed in the absence of a large change
in overall structure. The Gdm+ titrations do not evidence significant inflections of
either the absorption spectrum or fluorescence spectrum in the 1 M Gdm+ range
(see Figures 3.4 and 3.3), so the local environment of the ZnII porphyrin does not
change much on average as the intermediate is formed. Figure 3.16 shows that the
apparent hydrodynamic radius has an inflection in the Gdm+ range that accompanies
formation of the intermediate, but the rearrangement of the protein that produces

85

an asymmetric tumbling structure is smoothly associated with the overall unfolding
transition that is more or less complete at 3 M Gdm+ . Thus, the formation of the
intermediate at 1 M Gdm+ is primarily marked by changes in the fluctuations of the
protein structure that are reported by the correlation timescale and by the change in
the ZnII porphyrin’s range of motion.
The relationship between the correlation timescale for internal motion obtained
from the anisotropy decay, ⌧int , and the amplitude of the corresponding structural
fluctuation can be obtained in analogy to that discussed previously144 for fluctuations detected in the dynamic fluorescence Stokes shift (FSS) response. The internal
motions can be considered Brownian diffusive motions over the protein-folding energy landscape along an effective one-dimensional coordinate.90, 144 As averaged
over the ensemble of proteins in solution, the structural fluctuations that contribute
to the diffusive motion are characterized by the mean-square displacement, hx 2 (t)i,
and the propagation time, t, as
hx 2 (t)i = 2Dt

(3.17)

The diffusion constant, D, would be expected to be inversely proportional to the
internal or external solvent friction f
D = kB T /f

(3.18)

The correlation timescale, ⌧, for a fluctuation can then be expressed by an Arrhenius
equation as that for a thermally driven crossing of a local barrier of height
⌧ = ⌧0 exp( G‡ /RT )

G‡ ,
(3.19)

where ⌧0 is the characteristic timescale at which the transition-state structure at the
barrier is accessed:
⌧0 = hx 2 (⌧0 )i/2D
86

(3.20)

Thus, the correlation time ⌧ increases as as the barrier height,

G‡ , increases. Equa-

tion 3.20 indicates that the correlation timescale ⌧ is linearly proportional to the
mean-square displacement for the associated structural motion, the width of the
overall probability distribution.
In contrast, the cone angle is a measure of the range of motion for the ZnII porphyrin; it marks the probability distribution’s upper half-maximum point.149 The intermediate structure’s longer correlation timescale and enhanced cone angle is consistent, then, with a looser structure that makes longer range motions across the
energy landscape owing to the lowering of activation barriers, so it has some of the
properties of a transition state for unfolding. Such a structure can be populated thermally during a denaturant titration only if relatively low activation barriers along the
folding/unfolding coordinate divide it on both sides from the native and unfolded
states. Owing to the addition of Gdm+ during a titration, the Gibbs free energy of
the equilibrium ensemble decreases (see Equation 3.3) until the ensemble unfolds, at
Gdm+ concentrations above ⇠2 M. The usual assumption made in the interpretation
of a denaturant titration is that only two states, the native and unfolded states, contribute significantly to the ensemble at any Gdm+ concentration because either the
folding reaction or the unfolding reaction is spontaneous and goes to completion.
The results obtained in this paper show that this assumption is not valid for ZnCytc
and Gdm+ . At 1 M Gdm+ , the ensemble is poised so that the intermediate structure
is predominantly populated.
As the Gdm+ concencentration is increased further so that the ensemble increasingly populates the unfolded structure, the cone angle for the internal motions remains at the same level accessed by the intermediate at 1 M. That the mean-squared
amplitude for the fluctuations in the unfolded state decays from that of the intermediate back to the level of the native state (see Figure 3.14) is distinctive. These
observations suggest that the unfolded state is less condensed than the native state,

87

so the ZnII porphyrin’s motions are constrained less tightly than in the native state,
but that the activation barriers along the unfolding coordinate that limit the meansquared amplitudes of the fluctuation are nearly as large as they were in the native
state.
In closing, this study provides to our knowledge the first evidence from picosecond anisotropy decays using an intrinsic fluorescent probe for the formation of a
transition-state-like, partially unfolded structure during titration of a protein by a denaturant. That one or more intermediates are populated along the folding/unfolding
reaction coordinate of FeCytc has been discussed extensively in the work by Englander,161, 162 Roder,163 Rousseau,164–166 and their coworkers; a non-twostate folding
behavior was observed previously in the refolding of ferricytochrome c evidenced by
the circular dichroism (CD222) signal at around 1.3 M Gdm+ .167 Rate-limiting steps
along the folding pathway involve exchange of non-native histidine and water axial
ligands from the FeII porphryin complex in FeCytc to obtain finally the native state’s
methionine (M80) ligation.165 The change in the vibronic structure of the fluorescence spectrum that occurs during the Gdm+ unfolding of ZnCytc (see Figure 3.6)
evidences an release of axial ligands from those present in the native state. A suggestion for the intermediate populated at 1 M Gdm+ would be one in which both of
the native axial ligands have been released from the ZnII porphyrin, at least in its
⇡

⇡⇤ excited state. Such a structure would be expected to exhibit both an en-

hanced cone angle and a larger mean-squared deviation for the angular fluctuations;
the internal correlation time is comparable to that obtained from the FSS response of
fbCytc.144 In the native state of ZnCytc, the folded protein’s packing forces impose
a six-coordinate structure, whereas the unfolded structure would be very likely to assume a five-coordinate structure with a non-native axial ligand.76, 79 Either of these
two limiting structures might be expected to exhibit smaller fluctuation amplitudes
for the ZnII porphyrin than a deligated intermediate structure.

88

CHAPTER 4
Fluorescence Stokes Shift Response
Functions from ZnCytc in the Presence
of Gdm+

Summary
We report the changes in shift amplitude and correlation timescales from the dynamic fluorescence Stokes shift (FSS) response that occur during the unfolding titration of ZnII -substituted cytochrome c with guanidinium ion (Gdm+ ). The FSS response
functions are compared with the picosecond fluorescence anisotropy (FA) response
functions, which report how the fluctuations of the protein structure cause angular
motions of the intrinsic ZnII porphyrin macrocycle with respect to its equilibrium
orientation. The presence of Gdm+ , even at the lowest concentrations and well below the global denaturation limit, destabilizes the native fold and causes the optical
transition of the ZnII porphyrin to depart from the linear-response regime at Gdm+
concentrations well below those that prepare the transition-state-like partially unfolded intermediate that was detected using the FA response. These results strongly

89

implicate structural changes in the hydration layer as the origin of the dynamical
changes reported in the FSS response as the protein approaches the unfolded state.

4.1 Introduction
The structural fluctuations detected in small proteins using the dynamic fluorescence
Stokes shift (FSS) response function on the >100-ps timescale arise from diffusive,
barrier-crossing motions on the folding energy landscape.47, 81, 82 In recent work
from this laboratory, we have examined how the fluctuation correlation timescales of
ZnII -substituted cytochrome c (ZnCytc) change as the structure moves away from the
native fold towards perturbed, partially unfolded structures. Three different methods have been used to prepare the nonnative structures: intramolecular vibrational
excitation (IVE) via the radiationless decay and vibrational relaxation of the intrinsic
ZnII porphyrin chromophore,78, 79 structural modification via demetalation of the
porphyrin,144 and, most recently, by the addition of guanidinium ion, as was discussed in the previous chapter. These investigations are intended to apply the longstanding question from chemical dynamics of how the thermodynamic stability of a
folded protein relates to the motions and energetics along the reaction coordinate
for folding and unfolding.
Our finding that the correlation timescales obtained from the exponential time
constants in the FSS response function in metal-free (or free-base) cytochrome c (fbCytc) are almost ten times longer than those of ZnCytc shows directly that the FSS
response function is sensitive to protein motions that are pertinent to the stability of
a folded protein.144 Using a model for Brownian diffusive motion on the energy landscape associated with thermally activated barrier-crossing events,83, 84 we concluded
that the increased polar solvation timescales observed in fbCytc correspond to significantly enhanced fluctuation amplitudes compared to those in ZnCytc under similar

90

solvent conditions.144 Because fbCytc lacks the stabilizing influence of the two axial
metal–ligand interactions that are present in the native ferricytochrome c (FeCytc)
structure, it assumes a dynamic, partially unfolded structure with the characteristics
of a molten globule.79, 146
The addition of guanidinium ions (Gdm+ ) destabilizes the native fold of ZnCytc
externally by acting on the structure and dynamics of the hydration layer.80 In order
to learn how the dynamics of ZnCytc in the presence of Gdm+ compare with those of
the native state, we performed studies of the fluorescence anisotropy (FA) response
using the intrinsic ZnII -porphyrin as a probe. These studies were discussed in the
previous chapter. The FA response directly reports the structural fluctuations of the
protein that induce reorientational motions of the probe from the initial alignment
of the photoselected ensemble of probe molecules that was prepared by a planepolarized excitation laser pulse. The results show that a partially unfolded ZnCytc
structure is populated in the presence of 1.0 M Gdm+ , well prior to the denaturation
transition at 2.0 M Gdm+ . This intermediate is characterized by wobbling motions of
the porphyrin macrocycle that are significantly enhanced in mean-squared deviation
compared to the native and denatured structures. The correlation timescale obtained
from the FA response of the intermediate is comparable to that observed for fbCytc,
so it is possible that the intermediate is a structure in which both of the axial-ligand
interactions to the ZnII porphyrin have been lost. Such a structure would have some
of the characteristics of the transition state along the folding/unfolding reaction coordinate for FeCytc, where the axial-ligand exchange reactions are key rate-limiting
steps.161–166 The general picture that emerges from this work and the fbCytc study
is that the structural fluctuations increase in amplitude as the protein approaches
the equilibrium conditions that favor unfolding.
Using the same picosecond fluorescence data set used in the FA work, we now
report the FSS response that occurs during the titration of ZnCytc with Gdm+ . For

91

the first time to our knowledge, this work permits us to assess experimentally several aspects of the structural character of the protein fluctuation timescales that are
associated with the electric-field fluctuations measured by the FSS response. The results show that the presence of Gdm+ , even at the lowest concentrations and well
below the global denaturation limit, destabilizes the native fold enough that the optical transition of the ZnII -porphyrin chromophore departs from the linear-response
regime. This action of Gdm+ saturates well prior to the formation of the unfolding
intermediate that was detected using the FA response. These results strongly implicate structural changes in the hydration layer as the origin of the dynamical changes
reported in the FSS response as the protein approaches the unfolded state.

4.2 Experimental
4.2.1 Sample Preparation
ZnCytc was prepared using using horse-heart ferricytochrome c (FeCytc, Sigma) as
the starting material following the procedure established by Vanderkooi and coworkers.69, 91 The metal free product from the demetalation reaction of FeCytc was reconstituted with the metal ion in presence of 10-fold molar excess of zinc acetate.
The ZnCytc product was worked up following the methods adapted from the ones
employed by Winkler and coworkers92 and Kosti´ and coworkers.93 The final ZnCytc
c
solution was concentrated using repeated ultrafiltration steps through an Amicon
YM10 ultrafilter (Millipore). The concentrated ZnCytc solution was divided into small
aliquots and flash frozen in liquid nitrogen prior to storage at -85 C.
When required, a ZnCytc sample was prepared for use in a picosecond fluorescence experiment by diluting a thawed aliquot with a 25 mM phosphate buffer solution at pH 7.0 that also contained Gdm+ at concentrations ranging over the 0–5-M
range. After thorough mixing, the solution was allowed to settle for an hour before
92

it was passed through a 0.22 µM microfilter. The ZnCytc concentration was then
adjusted by adding additional buffer solution with the same Gdm+ concentration to
obtain an absorption between 0.1–0.2 at the peak of the absorption band for a path
length of 1.0 cm. The sample was held in a 1-cm quartz cuvette; the headspace was
purged with dry nitrogen gas prior to exposure to laser light.

4.2.2 Absorption and Fluorescence Spectroscopy
Absorption spectra were acquired with a Hitachi U-2000 spectrophotometer (2-nm
band pass). Fluorescence spectra were obtained with a home-built spectrofluorimeter79 consisting of an Jobin-Yvon AH10 100-W tungsten-halogen light source, a JobinYvon H10 excitation monochromator (4-nm bandpass), an Acton Research SP-150
emission spectrograph (2-nm bandpass), and a Jobin-Yvon Symphony charge-coupled
device (CCD) detector. The CCD detector employs a liquid nitrogen cooled, backilluminated, 2000 ⇥ 800 pixel silicon detector chip (EEV corporation). The sample cuvette was held in a Quantum Northwest TLC50F Peltier-effect temperature controller.
As presented as a function of wavenumber, the fluorescence intensities are multiplied
by the square of the wavelength in order to compensate for the fixed (in wavelength
units) spectral bandpass of the emission spectrograph.94 The absorption and fluorescence instruments were controlled by LabVIEW (National Instruments) programs.

4.2.3 Time-Resolved Fluorescence Measurements
Single-wavelength polarized fluorescence transients were recorded using a T-format
time-correlated single photon counting (TCSPC) instrument as described in chapter 2. The picosecond excitation pulses were obtained from a synchronously pumped
cavity-dumped dye laser (Coherent 702-2). The dye laser was pumped by a passively
mode-locked, diode-pumped NdIII –YVO4 laser (Spectra-Physics Vanguard), which pro-

93

duced 13-ps pulses with an average power of 2.5 W at a repetition rate of 80 MHz.
The dye laser produced 5-ps pulses over the 583–585 nm tuning range using either
the Rhodamine-6G or Pyromethine 567 dyes. The repetition rate on the dye laser was
adjusted to 4 MHz using Gooch & Housego cavity dumping electronics.
In the detection system, the vertically polarized excitation pulse from the dye
laser output was divided into two parts. One part of the pulse was fed to a reference photodiode (Becker & Hickl PHD-400-N), and the other part was directed to
the sample. The fluorescence emission was collected using a Cassegranian reflective
microscope objective (40⇥ magnification). The collected emission was then split by
a polarizing cube beam splitter into two orthogonal polarization components with
planes of polarization parallel (0 ) and perpendicular (90 ) to that of the vertically
polarized excitation pulse. The two components were detected simultaneously with
microchannel plate photomultiplier tubes (MCP-PMT, Hamamatsu R3809U-50) after
selection of the emission wavelength by subtractive double monochromators (Spectral products, CM-112). Emission transients were simultaneously recorded with a
two-channel TCSPC system (Becker & Hickl SPC-132). The instrument-response width
was 65 ps (fwhm). LabVIEW (National Instruments) programs were used to control the data-acquisition hardware and monochromators in order to acquire a set
of single-wavelength fluorescence transients automatically over a range of emission
wavelengths. The sample was held in a temperature-controlled mount that was regulated at 22 C using a Neslab RTE-110 water circulating bath.

4.3 Results
4.3.1 Absorption and Fluorescence Emission Spectra
Figure 4.1 shows the Q-band region of the absorption (A) and fluorescence (F) spectra from ZnCytc in water at 22 C and pH 7.0. The spectra are plotted as relative
94

dipole strengths, A(⌫)/⌫ and F (⌫)/⌫ 3 , respectively, as a function of wavenumber
⌫. The 0–0 and 0–1 vibronic peaks in the fluorescence spectrum exhibit a near
mirror-symmetry with respect to the corresponding vibronic peaks in the absorption spectrum. The 0–0 transition is approximately at the wavenumber where the
two spectra cross each other; with the excitation laser tuned to this wavenumber
in the picosecond dynamic solvation experiments, the S1 state is prepared without
any excess vibrational energy, so the FSS response should not exhibit a significant
component arising from vibrational relaxation.
The solvation reorganization energy,

, was estimated using the shift of the

wavenumber of the fluorescence spectrum’s 0–0 peak, ⌫0–0, F , from that of the absorption spectrum, ⌫0–0, A :100, 144
= (⌫0–0, A
The value of

⌫0–0, F )/2

(4.1)

obtained for ZnCytc in water in the present work is 55 ± 10 cm 1 . This

value is significantly smaller than reported in some of the previous work on ZnCytc
from this laboratory.77, 78 The observed value for

evidently depends on how the

samples are processed. When the metal-free product (fbCytc) of the demetalation of
FeCytc in liquid anhydrous HF and the ZnCytc product obtained after ZnII reconstitution are worked up using Sephadex G-75 gel-filtration chromatography, as described
by Vanderkooi and coworkers,91 the value for

obtained is larger, 145 cm 1 . In

our subsequent work,79 the fbCytc and ZnCytc products were worked up using ionexchange chromatography using the approach described by Winkler and coworkers
and by Kosti´ and coworkers.92, 93 These preparations exhibit absorption and fluc
orescence spectra with narrower vibronic lineshapes; the reader should compare
Figure 4.1 in this paper with the similar figure in reference 78. Note that the FSS
response from both types of ZnCytc samples exhibit nearly the same correlation
timescales and relative component amplitudes as first reported,76 so the larger value
of

from the older ZnCytc preparations probably arises from heterogeneity.
95

Relative Dipole Strength

675

650

Wavelength ￿nm￿

625

600

575

550

525

0-1

0-1
0-0

0
15 000

16 000

17 000

Frequency ￿cm￿1 ￿

18 000

19 000

Figure 4.1. Q-band region of the absorption and fluorescence spectra from ZnCytc
in water at 22 C and pH 7.0. The spectra are plotted as relative dipole strengths,
A(⌫)/⌫ (dashed curve) and F (⌫)/⌫ 3 (solid curve), respectively.

96

1.0

￿

￿
￿

￿
￿

￿
￿

￿

￿
￿

0.8

Fraction Unfolded

￿
￿ ￿
￿

￿
￿

0.6

￿

0.4

￿
0.2
0.0 ￿ ￿
0

￿
￿

￿

1

￿
￿

￿

￿

2

3

4

￿Gdm￿ ￿ ￿M￿

5

Figure 4.2. Gdm+ fluorescence titration curves for ZnCytc at 22 C and pH 7.0. The
fraction of unfolded proteins in the ensemble was determined from the wavenumber of the peak maximum of the 0–0 (dashed curve) and 0–1 peaks (solid curve)
in the fluorescence spectrum; the data points are superimposed upon separate
models for a two-state unfolding transition (Equation 4.2). The average thermodynamic parameters for the unfolding transition are:
m = 6.16±0.49 kJ/mol, and Cm = 1.75 ± 0.16 M.

97

H O

2
GFold =

10.74 ± 0.54 kJ/mol,

Addition of Gdm+ to ZnCytc solutions results in an apparent two-state denaturation response that results in a shift of the fluorescence and absorption maxima
to the blue. Figure 4.2 shows the unfolding transition in terms of the fraction of
unfolded proteins in the ensemble, fu , as determined from the experimentally observed 0–0 and 0–1 peak wavenumbers using the precedure discussed in the previous chapter. The transition is modeled using an equation derived from a two-state
native-to-unfolded equilibrium,
2
where

H O

0

B
6
fu = 41 + exp @

13 1
H2 O
GFold + m [Gdm+ ] C7
A5
RT

(4.2)

2
GFold relates the Gibbs free energy of folding in water, and m determines

the Gdm+ concentration dependence of the change in Gibbs free energy. The average
thermodynamic parameters obtained from the 0–0 and 0–1 fluorescence titration
curves of ZnCytc are:

H O

2
GFold =

10.74 ± 0.54 kJ/mol, m = 6.16 ± 0.49 kJ/mol, and

the midpoint of transition, Cm = 1.75±0.16 M. The absorption spectra exhibit similar
titration parameters, but note that the unfolding transition occurs at a slightly higher
Gdm+ concentration:

H O

2
GFold =

10.48 ± 0.52 kJ/mol, m = 5.69 ± 0.15 kJ/mol and

Cm = 1.85 ± 0.10 M. These results were interpreted previously as showing that the
folded structure in the ground electronic state, S0 , is more stable than the resonant
first-excited singlet state, S1 , owing to photodissociation of the axial ligands to the
metal ion in the excited state.76

4.3.2 Picosecond Time-Resolved Fluorescence Spectroscopy
Time-resolved fluorescence spectra from ZnCytc in water and a range of Gdm+
concentrations were acquired as slices from a time–wavelength–intensity dipolestrength surface, FD (⌫, t). The excitation laser was tuned in these experments to the
wavenumber of the 0–0 transition (see Figure 4.1). The dipole-strength surface was
acquired as a set of dichroism-free, single-wavelength transients spaced by 5.0 nm,
98

the bandpass of the emission monochromators, over the entire 0–1 band and nearly
to the peak of the 0–0 band. The intensity transients were computed from the simultaneously acquired parallel (Ik ) and perpendicular (I? ) polarized fluorescence transients as
I(t) = Ik (t) + 2I? (t)

(4.3)

The polarized transients in these data sets were used to calculate the anisotropy
decays that were discussed in the previous chapter. The dipole-strength surface
was constructed by normalizing the integral of each intensity transient to the dipole
strength observed in the continuous-wave fluorescence spectrum at the emission
wavenumber of the transient. The transients were used without deconvolution of
the instrument-response function, and they were truncated so that the first data
point used in further analysis was that of the 100-ps delay, almost a full instrument
response width from the center of the excitation pulse.
Figure 4.3 shows a set of time-resolved fluorescence dipole-strength spectra at
five time delays from ZnCytc in water at 22 C. The data points are shown superimposed with fitted lognormal lineshapes.97 As the delay time increases, the spectra
exhibit a decay in area (integrated dipole strength) as the excited-state population
decays, and the peak wavenumber shifts to lower frequency (see Table 4.1 for the
lineshape parameters).
The time evolution of the mean fluorescence dipole strength, h⌫(t)i, was obtained
by integrating over the time-resolved spectrum at a given time t to obtain the first
moment,

R ⌫2

⌫ d⌫ ⌫ FD (⌫, t)
h⌫(t)i = R 1
⌫2
⌫1 d⌫ FD (⌫, t)

(4.4)

The h⌫(t)i response is used here as a direct measure of the FSS response function
S⌫ (t) =

h⌫(t)i
h⌫(0)i

99

h⌫(1)i
.
h⌫(1)i

(4.5)

Relative Dipole Strength

￿ ￿
￿

￿
￿
￿
￿

￿

15 000

￿

￿

￿

￿

￿
￿
￿
￿
0 ￿

￿ ￿
￿

￿

￿
￿
￿ ￿ ￿ ￿
￿ ￿
￿
￿ ￿
￿ ￿ ￿
￿
￿ ￿ ￿￿
￿ ￿ ￿ ￿￿ ￿ ￿ ￿ ￿
￿ ￿
￿
￿ ￿
15 250

15 500

15 750

16 000

￿

￿
￿

￿
￿
￿
16 250

Frequency ￿cm￿1 ￿

￿
￿
￿
￿
16 500

￿
￿
￿
￿
￿

￿

￿
￿
￿

16 750

Figure 4.3. Time-resolved fluorescence dipole strength spectra from ZnCytc in water

•

at delay times of 100 ps ( ), 1 ns ( ), 2 ns (}), 5 ns (⇥), and 9 ns (⇧). The displayed
spectral region spans the 0–1 vibronic band and the onset of 0–0 band. The spectra are superimposed with lognormal lineshapes fitted over the 14900–16500 cm 1
region.

100

Table 4.1. Lognormal lineshape parametersa for the 0–1 vibronic
feature of the time-resolved fluorescence spectra from ZnCytc in
water at 22 C.
delay (ps)

A

⌫0 (cm 1 )

100
1000
2000
5000
9000

1139.11
729.52
452.16
209.72
98.34

15660.6
15644.1
15642.2
15639.6
15632.4

(cm 1 )
629.99
629.99
629.53
644.47
648.66

⇢
1.31
1.24
1.22
1.15
1.06

a Area (integrated dipole strength), A; center frequency, ⌫ ; width,
0

; asymmetry (skew), ⇢.

101

over the ps–ns regime without normalization105, 144 in order to avoid the need to
estimate the mean fluorescence emission frequencies at t = 0 and at t = 1. The
limits of the integration for the mean frequency determination with Equation 4.4, ⌫1
and ⌫2 , were chosen to enclose the 0–1 peak but to avoid the congested region at
the onset of the 0–0 peak. In some of the earlier work on the FSS response function
from ZnCytc from this laboratory,77 the FSS response was determined from the time
evolution of the 0–0 peak wavenumber, which was obtained from a fitted vibronic
progression for the 0–0 and 0–1 peaks. The first-moment approach was used in our
recent paper on the FSS response function of fbCytc144 where it was shown to be
robust even when the signal/noise ratio was not especially high.
The top panel of Figure 4.4 shows that the FSS response function from ZnCytc
in water is a monotonic decay to the red that is well described by a biexponential
function
h⌫0 1 (t)i = A1 e t/⌧1 + A2 e t/⌧2 + ⌫1

(4.6)

The time constants, ⌧1 = 135 ps and ⌧2 = 1.6 ns, and the relative magnitudes of the
corresponding amplitudes, A1 and A2 , are similar to those reported previously.77
The monotonic character of the FSS response function is consistent with its interpretation (vide infra) as a solvation time-correlation function arising from the dielectric
response of the protein and solvent medium around the ZnII porphyrin chromophore.
In contrast, the addition of even a small amount of Gdm+ to the ZnCytc solution
results in an unusual bidirectional response; the first and faster part is a shift to
the blue in all the Gdm+ concentrations studied. The bottom panel of Figure 4.4
shows the FSS response from ZnCytc in the presence of 0.25 M Gdm+ , the lowest
concentration we characterized. The blue shift has a time constant of ⌧1 = 819 ps,
which is more than four times longer than that of the fast phase of the red shift in
water. The red shifting component that completes the FSS response in 0.25 M Gdm+

102

!"#
&' $)'

&' $%'

12
'()*+),-."/-0" 3

&' $('

&' $$'
!

"!!!

#!!!

$!!!

%!!!

!$%&"#
&' $(!

&' $$!

&' $'!

&' $#!
!

"!!!

#!!!

$!!!

%!!!

*+,-. /0
4)56."/783
Figure 4.4. Time evolution of the mean frequency of the 0–1 fluorescence emission,
h⌫01 i, from ZnCytc in water (top) and in the presence of 0.25M Gdm+ (bottom) at

22 C. The data points are superimposed with fitted biexponential models. The fit
parameters are listed in Table 4.3.

103

Relative Dipole Strength

￿ ￿

￿
￿
￿
￿

￿ ￿
￿

￿
￿

￿

￿ ￿

￿
￿ ￿

￿
￿
￿
￿
￿
0

￿
￿ ￿ ￿
￿ ￿
￿ ￿ ￿
￿
￿
￿ ￿ ￿ ￿ ￿ ￿ ￿
￿ ￿ ￿ ￿
￿ ￿
15 000

15 250

15 500

￿
￿

￿
￿

￿
￿

￿

￿

￿
￿

￿
￿

￿

￿
￿

￿
￿ ￿ ￿ ￿ ￿ ￿
￿
￿
￿ ￿ ￿
￿ ￿
￿ ￿ ￿
￿ ￿ ￿ ￿ ￿ ￿
￿ ￿ ￿ ￿ ￿
15 750

16 000

16 250

Frequency ￿cm￿1 ￿

16 500

16 750

Figure 4.5. Time-resolved fluorescence dipole strength spectra from ZnCytc in 2.0 M

•

Gdm+ concentration at delay times 200 ps ( ), 500 ps ( ), 1.2 ns (}), 4 ns (⇥), and
8 ns (⇤). The displayed spectral region spans the 0–1 vibronic band till the onset of
the 0–0 band. The spectra are superimposed with lognormal lineshapes fitted over
the 14900–16500 cm 1 region.

104

Table 4.2. Lognormal lineshape parametersa for the 0–1 vibronic
feature of the time-resolved fluorescence spectra from ZnCytc in
2.0 M Gdm+ at 22 C.
delay (ps)

A

⌫0 (cm 1 )

200
500
1200
4000
8000

931.10
747.28
430.90
178.90
70.15

15672.1
15683.4
15678.9
15674.7
15657.1

(cm 1 )
589.99
609.99
589.94
589.42
588.55

⇢
1.31
1.31
1.31
1.31
1.30

a Area (integrated dipole strength), A; center frequency, ⌫ ;
0

width,

; asymmetry (skew), ⇢.

105

has a time constant of ⌧2 = 3.53 ns, which is about twice that of the ⌧2 = 1.6-ns time
constant in water.
The appearance of the initial blue shift in the presence of Gdm+ indicates that
rather than arising purely from solvation dynamics, the observed FSS response arises
from a prompt structural change in the ZnII porphyrin itself or its protein surroundings that is followed by a reorganizational relaxation of the surrounding protein
medium. The latter’s red-shifting direction of response would be formally a solvation
response, but its starting configuration would be significantly displaced from that of
the ground state porphyrin and the protein and solvent that was initially in equilibrium with it. We examined the time-resolved fluorescence spectra observed in the
presence of Gdm+ during the FSS response to see if the lineshapes evidence a structural change in the porphyrin. For example, Figure 4.5 shows a set of time-resolved
fluorescence dipole-strength spectra at five delays from ZnCytc in 2.0 M Gdm+ . As
shown in Table 4.2, the blue and red shifts of the FSS response are reported by the
trends in the peak wavenumber, ⌫0 , but the linewidths and asymmetry parameters,
and ⇢, respectively, are essentially constant with time. These results are consistent
with the interpretation that the FSS response arises from a structural response of the
surrounding protein medium rather than from a large change in structure of the ZnII
porphryin itself.
The trends of the amplitudes and time constants for the biphasic FSS response
from ZnCytc were characterized as a function of the Gdm+ concentration to probe
the changes in protein dynamics that accompany the unfolding transition. Figure 4.6
shows the FSS response functions for a range of Gdm+ concentrations. Each was
well fit by a biexponential model that includes a fast blue shift and a slower red
shift. The fit parameters for the entire series of Gdm+ concentrations we studied
are listed in Table 4.3; the indicated 95% confidence intervals were obtained from
a set of at least three repeated measurements. The trends in the fit parameters

106

Figure 4.6. Time evolution of the mean frequency of the 0–1 fluorescence emission,
h⌫01 i, from ZnCytc at Gdm+ concentrations of 1.0, 2.0, 3.0 and 5.0 M, at 22 C and

pH 7.0. The data points are superimposed on a biexponential model defined by
Equation 4.6. The fit parameters are listed in Table 4.3.

107

Table 4.3. Model parameters for the time evolution of the Fluorescence Stokes shifta for
ZnCytc in the presence of Gdm+ at 22 C.
Gdm+ (M)
0.00
0.25
0.50
1.00
1.50
2.00
3.00
4.00
5.00

A1
9.84 ± 1.69
21.05 ± 1.15
27.69 ± 3.94
26.46 ± 4.21
26.34 ± 1.47
27.51 ± 4.87
11.21 ± 1.15
29.64 ± 5.68
22.67 ± 4.68

⌧1 (ps)

A2

⌧2 (ns)

135 ± 36
819 ± 30
577 ± 144
695 ± 28
658 ± 49
575 ± 120
282 ± 49
440 ± 142
562 ± 44

20.69 ± 1.38
58.81 ± 4.30
61.76 ± 9.3
58.12 ± 11.88
55.92 ± 1.28
62.74 ± 8.5
52.37 ± 1.28
67.88 ± 2.58
63.57 ± 1.90

1.60 ± 0.22
3.53 ± 0.13
3.69 ± 0.08
4.35 ± 0.1
4.49 ± 0.29
4.34 ± 0.22
4.40 ± 0.28
4.41 ± 0.33
4.95 ± 0.15

t/⌧1 + A e t/⌧2 + ⌫ .
a h⌫
1
0 1 (t)i = A1 e
2

108

⌫1

15666.8 ± 4.5
15638.9 ± 0.9
15635.8 ± 9.4
15642.4 ± 6.1
15634.1 ± 10.8
15637.1 ± 18.8
15657.1 ± 21.3
15653.0 ± 17.6
15664.2 ± 3.2

Figure 4.7. Fluorescence Stokes shift time constants for ZnCytc at 22 C and pH 7.0
as a function of the Gdm+ concentration, as obtained from fits to Equation 4.6. Top:
Time constant ⌧2 , of the slower component, for the final shift to the red. Bottom:
Time constant ⌧1 , of the faster component, for the initial shift to the blue when
Gdm+ is present. The plotted values are listed in Table 4.3.

109

70

A 2 cm

1

60
50
40
30
20

10

A 1 cm

1

0

10

20

30

0

1

2

Gdm

3

4

5

M

Figure 4.8. Fluorescence Stokes shift amplitudes for ZnCytc at 22 C and pH 7.0 as
a function of the Gdm+ concentration, as obtained from fits to Equation 4.6. Top:
Amplitude A2 , of the slower component, for the final shift to the red. Bottom: Am-

plitude A1 , of the faster component, for the initial shift to the blue when Gdm+ is
present. The plotted values are listed in Table 4.3.

110

are shown in Figures 4.7 and 4.8 for the time constants and the shift amplitudes,
respectively. These plots suggest that Gdm+ affects the stability and dynamics of
the folded protein by saturating sites on the protein surface at low concentration
and that at least one folding intermediate is formed well below the overall unfolding
transition.
The bottom panel of Figure 4.7 shows that the time constant ⌧1 for the fast
component of the FSS response from ZnCytc exhibits two main changes as Gdm+
is added. As noted above, the red shift observed in water is converted to a blue shift
somewhere in the region above 80 mM Gdm+ , assuming a linear connectivity, and the
time constant is abruptly lengthened to 800 ps at 0.25 M. Subsequently, the blue shift
speeds up as Gdm+ is added except for an inflection in the 1.0 M region. The unfolding transition at 2.0 M Gdm+ is accompanied by a decrease in the fast time constant
from 700 ps at 1.0 M to 300 ps at 3.0 M. Above the unfolding transition, however, the
time constant gradually lengthens. Although the fast component observed in the FSS
response from ZnCytc in water is associated with motions of the hydrophobic core77
and are accordingly short ranged in mean-squared deviation,144 it is evidently rather
sensitive to global changes in structure or conformation.
The trend for the amplitude A1 for the fast component in the FSS response from
ZnCytc is shown in the bottom panel of Figure 4.8. The amplitude abruptly increases
in magnitude and changes sign as the fast part of the FSS response abruptly shifts
from the red to the blue as Gdm+ is initially added, but above 0.5 M Gdm+ it remains essentially constant. The unfolding transition at 2 M is followed, however, by
a significant jump in A1 ; the value at 3 M is statistically well resolved from those at
2 M and 4 M, which are indistinguishable. Thus, the trends in A1 and ⌧1 together
indicate that the internal structural dynamics in ZnCytc are markedly affected by the
presence of Gdm+ at concentrations that are well below the unfolding transition.

111

The top panel of Figure 4.7 shows that the time constant for the slow component
of the FSS response, ⌧2 , exhibits two main changes as Gdm+ is added to ZnCytc solutions. At low Gdm+ concentrations, ⌧2 exhibits a biphasic increase that resembles
a binding equilibrium that is saturated at 1 M, well before the unfolding transition.
The most rapid part of this increase accompanies the initial addition of Gdm+ to the
solution, and then a second phase of increase occurs over the 0.5–1-M range. The
trend in the amplitude for this component is shown in the top panel of Figure 4.8. It
also exhibits a response like that of a binding equilibrium, but only a single phase is
observed that saturates immediately, at 0.25 M Gdm+ , and then remains essentially
constant as Gdm+ is added over the range of the unfolding transition. The saturation of A2 at very low concentration suggests, but does not prove, that Gdm+ acts
initially either by binding to sites on the solvent-contact layer of the folded protein
structure and/or by altering the hydrogen-bonding structure of the hydration layer
that surrounds it.80 That the amplitudes A1 and A2 mirror each other as Gdm+ is
initially added (see Figure 4.7) is a strong indication that the transition to the biphasic character and the dramatic lengthening of the slow part of the FSS response mark
a global change in structure and dynamics. This transition occurs more rapidly than
the change in bulk viscosity (see Figure 4.9) that accompanies the addition of Gdm+
to the solution.
Figure 4.10 shows the dependence of the total amplitude of the FSS response
from ZnCytc, A1 + A2 , on the Gdm+ concentration. The trend in this plot should be
compared to that in Figure 4.2 of fluorescence peak maxima. The latter plot is of the
time-integrated fluorescence Stokes shift, whereas the former is obtained from the
time-resolved spectral response. The trend for A1 + A2 clearly projects out three distinct phases of structure and dynamics as Gdm+ is added to a ZnCytc solution. The
peak in A1 + A2 at 0.25 M Gdm+ apparently marks the initial saturation by Gdm+ of
the binding sites that induce the transition to a biphasic, blue/red FSS response. The

112

￿

1.4

1.3

Η ￿cp￿

￿

1.2

￿
￿

1.1

￿
1.0 ￿ ￿
0

￿
1

￿

2

3

￿Gdm ￿ ￿M￿

4

5

￿

Figure 4.9. Viscosity of aqueous solutions of guanidinium hydrochloride at room
temperature as a function of the Gdm+ concentration. From ref. 168.

113

￿

￿

40

￿

A1 ￿ A2 ￿cm￿1 ￿

￿

35

30

￿

￿

￿
￿
￿

25
0

1

2

3

￿Gdm ￿ ￿M￿

4

5

￿

Figure 4.10. Gdm+ concentration dependence of total fluorescence Stokes shift amplitude, A1 +A2 , in ZnCytc at 22 C and pH 7.

114

decreasing transition in A1 + A2 that follows over the 0.5–1.5-M Gdm+ range marks
the formation of an intermediate structure that precedes the overall unfolding transition. Finally, the unfolding transition at 2 M Gdm+ is accompanied by an increase
in A1 + A2 ; this increase matches the shift to the blue observed in Figure 4.2. It is interesting to note that the magnitude of the 95% confidence intervals for A1 + A2 , the
total range between the error bars, suggests the presence of an inhomogeneous ensemble especially at the 1-M and 2-M Gdm+ concentrations that mark the midpoints
of transitions. In contrast, the endpoints of these transitions, at 1.5 M and 3 M, respectively, suggest the presence of relatively homogeneous ensembles because they
have especially small 95% confidence intervals. Note that the precision of the measurements at all of the Gdm+ concentrations was comparable, given that the total
experimental time for counting of fluorescence photons was fixed for each transient,
and further that an effort was made to narrow the confidence intervals especially at
1 M Gdm+ by performing a large number of replicate experiments. In our hands,
then, it appears that the partially unfolded ensembles indicated by the intermediate points in Figure 4.10 are inherently inhomogeneous or that some of the dynamic
properties of these ensembles are controlled by external variables that we did not
control, despite considerable effort.

4.4 Discussion
The results show that the FSS response function from ZnCytc is especially sensitive
to the presence of Gdm+ in two concentration regimes: at the lowest concentrations, below 0.5 M, where the overall stability of the folded protein is altered so
that the ⇡

⇡⇤ transition of the intrinsic ZnII porphyrin becomes a significant lo-

cal perturbation of the motions of the surrounding protein and solvent, and at an
intermediate concentration, 1 M, where a transition-state-like intermediate structure

115

on the unfolding reaction coordinate is populated. The FA response, obtained using
the polarization information in the same data set, is surprisingly insensitive to the
low-concentration part of the Gdm+ response, but it is especially sensitive to the formation of the intermediate at 1 M Gdm+ . In the following, we compare the correlation
timescales obtained from the FSS response functions with those obtained from the
FA response. This comparison makes it clear that the FSS response is more sensitive
than the FA response to the overall stability of the folded protein.
In our previous work on the FSS response of fbCytc,144 we discussed how the
correlation timescale returned from the FSS response from an intrinsic fluorescent
probe can be taken as a measure of the amplitude of the equilibrium structural fluctuations made by the host protein. The FSS response function arises from the dielectric response of the probe’s surroundings, so it is sensitive to motions of charges or
dipoles, even at a considerable distance, that modulate the electric field sensed at the
probe’s location. Assuming that the optical transition of the probe does not impart
a significant perturbation on its surroundings so that the linear-response regime is
maintained,54–56 the fluctuation–dissipation relation allows one to equate the experimentally measured solvent-response function, S⌫ (t) (Equation 4.5), with the timecorrelation function for the fluctuations of the medium,
M(t) =

h !(0) !(t)i
,
h( !)2 i

(4.7)

where
!(t) = h!i

!(t)

(4.8)

relates the instantaneous ground-to-excited-state energy gap for the probe from that
averaged over time or averaged instantaneously over the ensemble.54–56
As a protein propagates on the protein-folding energy landscape, its structure
fluctuates owing to thermally driven passages over the activation barriers that divide
adjacent potential minima. We modeled this process as Brownian diffusion over a
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one-dimensional effective coordinate.144 The main result is that there is a linear
relationship between the correlation timescale for a fluctuation, ⌧, as obtained from
the FSS response function, and the mean squared displacement, hx 2 (⌧0 )i,
⌧ = (hx 2 (⌧0 )i/2D) exp( G‡ /RT )

(4.9)

The correlation time ⌧ is related by an Arrhenius equation to the characteristic
timescale, ⌧0 , at which the transition-state structure at the top of a barrier of height
G‡ is accessed owing to diffusion on the structural coordinate x at a given temperature T . The diffusion constant D is inversely proportional to the friction from
internal protein motion or from the surrounding solvent, so an increase in friction
causes a lengthening of the correlation time. The relation between the correlation
time for a particular fluctuation and the amplitude (mean-squared deviation) of the
associated motion assumes that the conditions are kept constant. Considering that
the barrier heights for motion on the energy landscape are likely to be strongly coupled to the conformational or folding state, it should be clear that Equation 4.9 can
be used only qualitatively in interpreting the correlation timescales.
As discussed previously, the FA response from ZnCytc directly detects the subset of fluctuations that impart angular deviations onto the ZnII porphryin from the
mean structure. We modeled the FA decays using the wobbling-in-cone (WIC) mechanical model introduced by Kinosita et al. to describe the dynamics of a fluorescent probe in lipid membranes.149, 150 Figure 4.11 shows how the correlation times
for internal angular motion, ⌧int and the limiting cone angle, ✓c , vary with the Gdm+
concentration in ZnCytc solutions. The cone angle plot reports the formation of the
intermediate structure at 1 M Gdm+ in terms of a transition to a significantly larger
range of angular motion for the ZnII porphyrin, such as that permitted by a less condensed fold. The ⌧int plot marks the intermediate as having a significantly longer
correlation time, 1.35 ns, than either the native state in water or the unfolded state
at Gdm+ concentrations above 2 M. Applying the relation above (Equation 4.9), the
117

Figure 4.11. Gdm+ concentration dependence of ⌧int , the correlation time for internal motion, and ✓c , the wobbling cone angle, from the picosecond anisotropy decays
observed with ZnCytc at 22 C and pH 7.0.

118

mean-squared deviations of the intermediate are almost twice as large as those in the
native state. It is notable that at 1 M Gdm+ , the ⌧int correlation time is quite comparable to the shorter of the two correlation time detected in the FSS from fbCytc, where
the fluctuations are especially enhanced in amplitude by the protein’s assumption of
a molten-globule-like, partially unfolded state.144
In comparison, the faster of the two timescales obtained for ZnCytc in water from
the FSS response function, ⌧1 , is significantly shorter than that obtained from the FA
response (see Figure 4.7). As Gdm+ is introduced, however, the ⌧1 timescale rises
abruptly and reaches a maximum at 0.25 M at approximately the same timescale,
⇠800 ps, as that in the FA plot. The intermediate at 1 M is not marked by a dominant
peak in the correlation time trend like the one observed in the FA response. Further,
the unfolding transition at 2 M is associated with a decrease in ⌧1 ; at the same time,
the ⌧int trend from the FA response remains essentially constant. These comparisons
show that the FA and FSS responses detect different types of characteristic fluctuations. The FSS response is apparently much more sensitive to the overall fold of the
protein than is the FA response. As mentioned in the previous chapter, the angular
motion of the ZnII porphryin would be expected to be particularly sensitive to the
presence or absence of the axial ligands. The 1-M intermediate may exhibit large
angular fluctuations because it is likely to be a four-coordinate structure without native or non-native axial ligands from the surrounding protein. Such an intermediate
would be transition-state-like in that an exchange of one axial ligand with another
would require a four-coordinate transition state if the ZnII porphryin binds only a
single axial ligand along the unfolding pathway.
A comparison of the faster of the two timescales obtained from the FSS response
in ZnCytc to the internal timescale from the FA response treats the former as if it
is really a correlation timescale rather than a relaxation or reaction timescale. That
the shift of the time-resolved fluorescence spectrum for this component is to the

119

blue, rather than the red, is a strong indication that the optical excitation of the ZnII
porphryin is a larger perturbation on its protein and solvent surroundings than expected by the assumption of linear response. Still, it is reasonable to consider the
timescales of the two components in the FSS response as indicating the range of
motion required to relax to the initial structure prior to the excitation. The shorter
timescale, ⌧1 , would be taken then as a shorter-range motion than that arising from
the longer timescale, ⌧2 . In water, the ⌧1 timescale is insensitive to the presence of
glycerol in the external solvent, so it was assigned previously to the hydrophobic core
of the folded protein. The glycerol dependence of ⌧2 recommended an assignment
to the motions of the solvent-contact layer of the protein, which would be expected
to exhibit longer-range motions than the core of the protein.77 These assignments
seem to be applicable even in the presence of Gdm+ . In particular, the blue shift associated with ⌧1 is best explained by the reduced polarizability of the protein/solvent
surroundings that would accompany an expansion of the ZnII porphyrin’s hydrophobic binding pocket in response to the optical excitation. The photodissociation of
the axial ligands from the methionine (M80) and histidine (H18) ligands76 probably
contributes to this response, but note that the lineshape of the time-resolved fluorescence spectrum in the presence of Gdm+ did not suggest that a large change in
the porphyrin’s structure occurs during the blue shift or during the subsequent red
shift.
That the transition from a normal, monotonic FSS response in water to a bidirectional FSS response occurs in ZnCytc at such low Gdm+ concentrations, below
0.25 M, suggests that Gdm+ alters the dynamics of the protein by acting directly on
the hydrogen-bonding structure of the hydration layer.80 The exposure of the ZnII
porphryin directly to the hydration layer is small169 and the ⇡ -electron density is
essentially orthogonal to the exposure, so a direct action of Gdm+ on the porphyrin
is less likely than a general effect on the protein stability. It would be especially in-

120

teresting, then, to probe how the structure and dynamics of the hydration layer are
altered in the presence of Gdm+ by placing a fluorescent probe on the surface of
ZnCytc or tethered at a distance away from the surface. Femtosecond spectroscopy
studies of this type are already underway in the Beck laboratory to explore how the
inertial and diffusive motions of water molecules in the hydration layer are correlated
with motions in the folded protein structure.

121

CHAPTER 5
Conclusion

5.1 Overview
This dissertation represents an attempt to obtain a better structural picture for the
motions that contribute to the FSS response detected by an intrinsic fluorescent
probe in the interior of a small globular protein. The first part of this project was
a comparison of the FSS response in fbCytc with ZnCytc, which had been previously
characterized in the Beck laboratory by Sanela Lampa-Pastirk. One of the main findings is that the FSS response function for fbCytc in water is much slower than that
obtained for ZnCytc in water. The FSS response for fbCytc in water is biexponential,
and the two time constants, 1.4 ns and 9.1 ns, are about 10 times longer than those
obtained for ZnCytc in water, where the slower time constant is 1.5 ns. The two correlation times describe the motions of the hydrophobic core and the solvent-contact
layer sensed by the intrinsic porphyrin probe. The correlation times were further
lengthened in the presence of 50% (v/v) glycerol. These results were best interpreted
using a Brownian diffusion model with thermally activated barrier crossings on the
folding energy landscape. The longer of the two correlation times in fbCytc arise from
increased mean-squared displacements of the core and surface fluctuations than in

122

ZnCytc. This finding supports the conclusion that fbCytc has some characteristics of
a molten globule with a dynamic, partially unfolded structure.
The fbCytc studies provide information about the nature of the fluctuations but
lack a detailed structural picture. The next phase of the project, a study of the motions associated with the unfolding of ZnCytc, was aimed at probing the dynamical
and structural origin of the equilibrium fluctuations. The motions associated with the
unfolding reaction coordinate were probed using the FA response in the presence of
the denaturant Gdm+ . The results show that the unfolding transition is preceeded by
the formation of a structural intermediate. The intermediate exhibits longer correlation times and an enhanced angular fluctuation of the porphyrin probe compared
to the native and unfolded states. The intermediate exhibits some of the properties
that would be expected for a transition-state structure along the folding/unfolding
reaction coordinate. The correlation time for internal angular motions for the intermediate obtained from the FA response is similar to that observed for the FSS
response of fbCytc. This comparison suggests that the intermediate has lost both of
its axial ligands for the ZnII porphyrin.
Even at the lowest concentrations studied, the presence of Gdm+ strongly impacts
the dynamics of ZnCytc by affecting the interaction of the protein with the hydration
layer. The FSS response obtained as ZnCytc is titrated with Gdm+ shows that the
presence of Gdm+ destabilizes the native fold of the protein; the optical excitation
of the ZnII porphyrin chromophore perturbs the motions of the surrounding protein
and solvent molecules such that they depart from the linear-response regime. The
deviation from the linear response regime is evident from the unusual bidirectional
FSS response observed in presence of Gdm+ . The action of Gdm+ appears to saturate
well prior to the formation of the intermediate at 1.0 M. These results imply that the
origin of the dynamical changes reported in the FSS response lies in the structural
changes in the hydration layer surrounding the folded protein.

123

5.2 Comparison to Other Studies
The established theory that proteins exhibit a hierarchy of conformational substates
was originally suggested by Frauenfelder et al.47 based on their studies on reaction rate of photochemical dissociation of carbon monoxide from myoglobin. These
studies suggested that the protein motions involve sampling a rough energy landscape with a hierarchy of barrier heights. Our results add the importance concept
that the fluctuations observed in proteins are the result of barrier-crossing events
on the folding energy landscape. As discussed in Chapter 2, the characteristic time
scales of fluctuations observed in the fluorescence experiments probably arise from
distinct structural motions near the native minimum of the energy landscape. Association of either of these motions along generalized structural coordinates with
unfolding/refolding reaction requires additional information.
Englander and coworkers,161, 162, 170–172 and Rousseau and coworkers164, 166
have extensively studied the intermediates populated along the folding/unfolding
reaction coordinate of FeCytc. Englander and coworkers170 and Myer167 showed
that the unfolding/refolding of FeCytc involves formation of rate-limiting intermediates. Myer’s work suggests that the nature of the unfolding process that is induced
by Gdm+ and urea arise from different kinds of interactions between the denaturant
and the protein. Maity et al.172 used equilibrium and kinetic hydrogen exchange
experiments to show that sequential assembly of small folding units called foldons
leads to progress along the folding reaction coordinate of FeCytc. These studies also
suggest that a discrete folding intermediate accumulates prior to the global unfolding.
The results discussed in this dissertation strongly support the conclusion that
discrete intermediates are populated prior to the unfolding of ZnCytc. The observed
correlation time scales and cone angles suggest the formation of at least one intermediate at 1.0 M Gdm+ well prior to the global unfolding transition. The ligand-exchange
124

studies by Yeh and coworkers173 suggest that the folding and refolding reactions in
cytochrome c involve more than one pathway and populate discrete intermediates
that have molten globule-like properties. The FSS response obtained for ZnCytc as a
function of Gdm+ in our experiments are consistent with this conclusion. The measured correlation times in the FA and FSS response functions suggest a change in
the compactness of the protein that is accompanied by axial ligand exchanges prior
to the global unfolding transition. The 1.0 M intermediate is more likely to be fourcoordinate transition state while the folded protein in the ground state is believed to
be six-coordinate structure.

5.3 Conclusions and Next Steps
This work shows that the FSS and FA response functions can be used to detect the
formation of intermediates during unfolding/refolding reactions in small proteins.
The FSS response function from ZnCytc shows it is more sensitive to the dynamical effects of Gdm+ at the low concentration of 0.5 M and 1.0 M region. In the 0.5 M
Gdm+ regime the overall stability of the folded protein is altered so that the local perturbation from the ⇡

⇡⇤ transition of the intrinsic ZnII porphyrin leads transiently

to the formation of nonequilibrium structures. At 1.0 M Gdm+ , a transition-state-like
intermediate structure is formed which exhibits longer range motions. The FSS response is sensitive to motions of the protein over long distances owing to the low
dielectric constant of the protein’s interior, whereas the FA response is more sensitive to local motions of the protein around the ZnII porphyrin. The transition of the
FSS response function from a normal monotonic response to the unusual biphasic
response observed even at very low Gdm+ concentrations suggests that Gdm+ may
act on the hydrogen-bonding structure of the hydration layer, which in turn alters
the dynamics of the protein.

125

An obvious next step to take in this line of research would be to consider how the
structure and dynamics of the hydration layer is altered by the addition of Gdm+ . We
suggest that one might consider this question using ultrafast spectroscopy using a
fluorescent probe tethered to the surface of the protein, which would be able to sense
changes in the inertial and diffusive motions of the water molecules in the hydration
layer. Work of this type is currently ongoing in the Beck laboratory.

126

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