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”FORMATION OF oxrmcm m TD WHYSH AS STUPID
BY THO-DIMENSIONAL NUCLEAR MIC RESONANCE

8!

ILRJIInIaIa

A DISSERTATION

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

MR OF PHILOSOPHY

Department of Chanistry

1987

WNFORNATION OF omncnl m TO WHYSIN AS SI'UDIED

BY TWO-DIMENSIONAL NUCLEAR MIC RESONANCE

BY

N.R.Nirna1a

The main focus of this work has been the study of the cyclic
nonapeptide Oxytocin when it is bound to the protein Neurophysin,
using two-dimensional Nuclear Magnetic Resonance Spectroscopy (2DNMR).
The concept of transferred Nuclear Overhauser Effects has been used in
our experiments.

An insight into the theory of 2DNMR has been obtained using the

product operator formalism in the 1/23, 12, 1+, I_ basis. The product

operator formalism was found much more convenient to use, especially
to examine theoretically the ZDCOSY and ZDNOESY experiments. Further,
the use of coherence transfer pathways was invoked to determine
effective phase cycling of the pulses of each pulse sequence.
Computer simulations were performed on a model ligand-protein
system to determine the nature and magnitude of transfer NOE’s
expected for various concentrations of ligand and protein for fast and

intermediate exchange rates.

Subsequently, a new technique developed in our laboratory for
the suppression of the solvent signal in an NMR experiment has been
discussed. This technique uses phase-coherent irradiation of the

solvent signal followed by a spin-echo pulse sequence for acquisition.

Suppression of the solvent signal by a factor of as much as 105 to 107
was obtained.

2DNOE experiments were performed on Oxytocin (free form) and on
Oxytocin in the presence of the protein Neurophysin. The transfer
NOE’s seen in the complex were analysed and the resonances assigned.
Comparison of the information from the ZDNOE data and the published
crystal structure of De-aminooxytocin revealed sOme important
differences in the backbone structure of the peptide. A model was
constructed based on the ZDNOE data and was found to be distinctly
different from the X-Ray structure.

Thus, using ZDNMR, it has been possible for the first time, to
arrive at a reasonable conformation for the bound peptide which is
flexible in the free form. Previous work on the same system using
lDNMR methods yielded only limited information. The potential of ZDNMR
has thus been realised in our studies of the Oxytocin-Neurophysin

system.

It is with great pleasure and respect that I acknowledge the
guidance, encouragement and support that I received from Prof. Klaas
Hallenga during the entire course of my study at Michigan State
University. In addition, the friendship and warmth that he extended to
me will be remembered and cherished for a long time to come.

I thank Kermit Johnson and Long Le for continuous support and
help with instrumentation in the NMR facility and Dr. Atkinson for his
help on the Vax. ,

I would like to thank Michigan Molecular Institute, Midland,
Michigan, for the use of their 360 MHz NMR spectrometer, The Upjohn
Chemical Company and Dr. Scaehill in particular, for the use of their
500 MHz NMR spectrometer.

I am grateful to Prof. L. R. Brown (School of Chemistry,
Australian National University, Canberra) whose collaboration
initiated this project, Prof. Kaptein (Dept. of Physical Chemistry,
University of Groningen, The Netherlands) who graciously provided us
with a software package for processing ZDNMR data on the VAX and Prof.
V. Hruby (Dept. of Chemistry, University of Arizona, Tucson, Arizona)
and his co-workers for providing us with samples of Oxytocin and
Neurophys in .

I am also grateful to the Department of Chemistry, Michigan
State University for financial support, without which my study in the

'U.S.A would have been impossible.

ii

Many thanks to Dr. Karabatsos for being my co-advisor and a
special mention must be made here of Prof. M. 1'. Rogers who took an
active interest in my progress by being on my committee inspite of his
then failing health.

Thanks are also due to all the secretaries in the Department
who were of immense help at times of need; to Martin Rabb, for being a
good friend; to Dr. Cukier and his group, for allowing me use of their
IBM-PCs; to U. Shin for helping with the word-processing software;
and to all the others who contributed in many different ways to my
progress.

A special word of thanks to the members of the Dye group -
past, present and future - for treating me as an honorary member of
their group and allowing me use of their equipment as and when the
need arose.

Thanks to all those special friends who made my stay here so
enjoyable - Mary, Carmen, Dan, Ed and many others. I

Thanks to Ravishankar for being sopatient during the last
few years and for helping me in the final stages of my thesis.

Finally, I would like to thank everyone in this department
for being so friendly and congenial. My stay at MSU is full of
pleasant experiences and I am very grateful for the opportunity to

have worked and studied in such a pleasant atmosphere.

iii

LIST OF FIGURES
LIST OF TABLES
CHAPTER 1
CHAPTER 2
CHAPTER 3

CHAPTER 4

CHAPTER 5
CHAPTER 6

CHAPTER 7

CHAPTER 8
APPENDIX

REFERENCES

TABLE'OF'CUNTENTS

INTRODUCTION
THE PRODUCT OPERATOR FORMALISM
THE COSY AND NOESY EXPERIMENTS

CHEMICAL EXCHANGE AND TRANSFERRED
NUCLEAR OVERHAUSER EFFECTS

A NEW TECHNIQUE FOR SOLVENT SUPPRESSION
THE EXPERIMENTS

THE OXYTOCIN-NEUROPHYSIN COMPLEX -
RESULTS AND DISCUSSION

FUTURE WORK

iv

vii

21

46
66

74

76
93
95

104

FIGURE

1

mum

.1A

.lb

.4A

.4B

.4C

LIST'OF’FIGURES

CAPTION
General scheme of a 2DNMR experiment
Some common pulse sequences in ZDNMR
Representative COSY spectrum for the I spin
Representative NOESY spectrum for the I spin

Foldover of N peaks over P when the carrier
is placed within the spectrum.

Coherence transfer pathways for a 90° single
pulse experiment

coherence transfer pathways for the COSY
experiment

Cbherence transfer pathways for the NOESY
experiment

Energy levels for an AX spin system
Model used to study ligand-protein interaction

Effect of inversion of the S spin on the I spin
magnetisation. Starting conditions for A, B, C
and D are given in Table 4.1 ‘

Effect of inversion of the S spin on the I spin
magnetisation. Starting conditions for A, B, C
and D are given in Table 4.1

Effect of inversion of the S spin on the I spin
magnetisation. Starting conditions for A, B, C
and D are given in Table 4.1

Effect of inversion of the S spin on the I spin
magnetisation. Starting conditions for A, B, C
and D are given in Table 4.1

Effect of inversion of the S spin on the I spin
magnetisation. Starting conditions for A, B, C
and D are given in Table 4.1

Effect of inversion of the S spin on the I spin
magnetisation. Starting conditions for A, B, C

PAGE

29

29

36

38

41

44

47

55

61

61

62

62

63

63

and D are given in Table 4.1

A: Normal presaturation and B, C, D and E: Phase
coherent irradiation. The solvent signal is at
4.765ppm.

Difference in phase between decoupler and
acquisition pulse for A: 0’, B: 90', C: 180°

and D: 270°. The solvent signal is at 4.765ppm
COSY spectrum of Oxytocin in H20 using A: Normal

presaturation and B: phase-coherent irradiation
Schematic depiction of ligand-protein binding
Oxytocin

ZD-NOESY spectrum of free Oxytocin in H20.

No cross-peaks are seen except in the tyrosine
residue and the B protons of the CYS residues

2D-NOESY spectrum of the 10:1 Oxytocin-
Neurophysin mixture in 020 (360 MHz). A few
cross-peaks are seen.

2D-NOESY spectrum of the 10:1 Oxytocin-
Neurophysin mixture in H20 (360 MHz). Only
the NH region is shown.

20-NOESY spectrum of the 10:1 Oxytocin-
Neurophysin mixture in H20 (500 MHz). This

spectrum shows the most detail by far and
has been analysed in detail.

vi

68

70

72

78
79

81

82

83

84

TABLE

2.1

7.2

7.3

7.4

.LIST'OF”TABLES
CAPTION

Product operators in the l/2E, Iz, Ix’ Ty
basis.

Effects of pulses and delays on the product
operators

I

Product operators in the l/2E, 12, 1+, -

basis.

Effects of pulses and delays on the product
operators of Table 2.3

Evolution of product operators for the COSY
pulse sequence

List of abbreviations used in the text

Evolution of product operators for the NOESY
pulse sequence

List of starting conditions used in the
simulations

Details of the experiments performed
Intra-residue cross-peaks
Inter-residue cross-peaks

Estimations of inter-proton distances based
on a knowledge of the distance between the

1
fl protons of the CYS residue and the magnitude

of the NOE between them

PAGE

13

18

19

20

23

26
33

59

75
87
87
89

contradictions between predictions of the existence 89

of NOE cross-peaks based on the X-Ray structure

and the actual NOE spectrum

Comparison of the dihedral angles in the X-Ray
structure of deamino-oxytocin and the proposed
conformation of bound oxytocin based on the 2DNOE

vii

91

spectrum

7.5 Cross—peak intensities for the 180 msec NOESY 91
experiments

viii

INTRODUCTION

.Nuclear Magnetic Resonance (NMR) has undergone tremendous
progress during the last decade. One must attribute much of this
progress to the introduction and development of Two-Dimensional NMR
(2DNMR). The first 2DNMR experiment was proposed in 1971 by J.Jeener
[1]. .It waS'ruat until several years later, however, that the theory
and most of the basic 2D experiments were published [2-4]. In recent
years, an avalanche of new experiments and results has been produced
by several groups [5-10] that show the great potential of 2DNMR for
structural elucidation of natural products, determination of protein
stnummres.nzsolution [11] and the study of interactions between
proteins and substrates in solution.

One-dimensional NMR spectra become increasingly complex as the
molecular weight of the substance under study increases. This is where
the usefulness of 2DNMR is realized - the spectral complexity is
considerably reduced and hence the analysis of the spectra of large
molecules is facilitated. 2DNMR is particularly useful in determining’
conformations of molecules in solution by using the concept of the
Nuclear Overhauser Effect [12]. The. subject of this thesis is the
study of the conformation of the peptide Oxytocin when it is bound to
the protein Neurophysin in solution.

This thesis will examine briefly the theory of 2DNMR by invoking
the product Operator formalism, after which the experiments and the

. results obtained will be presented.

The simplest description of a 2DNMR spectrum is that it is a
spectrum which is a function of two frequency variables, as opposed to
a lDNMR spectrum which is a function of only one frequency variable.
The 2DNMR spectrum could actually be called three-dimensional - two
frequency dimensions and a third dimension which gives the intensity
of the various resonances.

GENERAL FORMAT OF A ZD-EXPERIME'IH':

There are several ways in which a 20 experiment can be performed
[4]. However, the time space experiment is by far the most widely
used, and will be described briefly :

A 20 time space experiment is one which has two independent time

variables, t1 and q, , as a function of which the signal amplitude
S(t1,t2) is measured. A two-dimensional Fourier transformation of
S(t1,t2) gives a 20 spectrum S(w1,w2).

In very general terms, the basic experiment can be described as
follows (Figure 1.1a)

a) The preparation period: This consists of an initial delay
(which allows the system to reach equilibrium) followed by the
application of one or more radiofrequency pulses. These pulses prepare
the system for the experiment to be conducted.

b) The evolution period: At the end of the preparation period,
the system which is now in a non-equilibrium state, evolves under the
influence of the perturbation and assumes, at the end of this period,

a state that is a function of the evolution time t1.

c) The mixing period: At the end of the evolution period, a

pulse or several pulses are applied to the system and for a time cm,

the magnetization coherences undergo mixing. This mixing period is not

present in all ZDNMR experiments. It is optional.

d) The detection period: At the end of the evolution or mixing
period, an additional rf pulse is applied to the system to detect its

final state at time t1, or at time tm' This detection pulse creates

observable transverse magnetization which is measured during the time

t2 (analogous to the acquisition time in a lDNMR experiment).

Conducted just once, the above experiment would have little
value; the experiment must be repeated for various predetermined

values of CI in order to obtain a sampling of the ZD time function in
both variables t1 and t2. Thus, regular increments of t1 will yield
information about the system as a function of t1, while detection for
a certain time t2 in each experiment gives the behaviour of the spins
as a function of t2. A Fourier transformation with respect to t1 and
t2 should then give rise to a spectrum which is a function of two
frequencies ml and ”2°

Some pulse sequences commonly used in ZDNMR are given in Figure

1.1b.

REPRESENTATION OF 2D SPECTRA:

There are several ways to represent a 2D spectrum. Stacked
plotting is the most aesthetic of them all - the peaks are stacked
against one another. Contour plots of 2D spectra are similar to
geographical maps of mountain contours and are quite useful. One can
also plot out various cross sections of interest of the 2D matrix -

these cross-sections resemble 1D spectra.

General scheme of a 2DNMR experiment

PI P8 P8 '
~°~D~~D~-D .. »

D, =- relaxatlon delay t. a mixing time

t,=evolutlontlme P P '3‘?!
t, an acquisition time " " ’ '

FIGURE 1. la

 

Some common pulse sequences in. 2DNMR

Homonuclear correlated spectroscopy (008?):

”‘D i [I‘-

ZD-J resolved spectroscopy:

0, ”chat/.2 .t.

ZD-NOE spectroscopy (NOESY):

”'fl‘fl‘ 11‘-

Double quantum filtered 008?:

”"0" D‘- H‘-

FIGURE 1.1!)

ADVANTAfl'S OF 2DNMR SPEC'IW:

The main feature of a 2DNMR spectrum is that any information
obtained is spread over two dimensions instead of just one. This
implies that the complexity of the results obtained is reduced
considerably. This is especially desirable when one is dealing with
the spectra of large molecules such as peptides or proteins.

When coupling patterns are too complex to analyse easily, it is
routine practice in lDNMR spectroscopy to conduct a series of
decoupling experiments in which one resonance is irradiated in an
effort to determine to which other resonances it is coupled. However,
decoupling experiments are frequently difficult to perform, mainly
because, in the process of irradiating the resonance of interest, one
may perturb nearby resonances. One gets around this by using selective
pulses, but again, there are limits beyond which even selective pulses
cannot be used easily, especially in regions of the spectrum that are
very crowded.

The 2DNMR COSY experiment (see Figure l.lb) is the equivalent of
performing simultaneously, a series of decoupling experiments in which
every single resonance in the spectrum is decoupled. This is achieved
by the use of hard pulses. Thus, one does not have to deal with the
disadvantages and difficulties of using selective pulses. In addition,
one experiment gives us information on the coupling interactions of
each and every resonance in the spectrum.

Similarly, Nuclear Overhauser Effects (NOEs) are very commonly
studied using NMR spectroscopy. NOEs give information about spatial
relationships of the nuclei, especially protons, in a molecule. In
lDNMR, one uses techniques of selective irradiation to observe NOEs

and faces the same problems listed above. The 2DNOE experiment (see

Figure l.lb) achieves what a series of lDNOE experiments on each
resonance would; once again, hard pulses are used to create NOEs.

Another advantage of 2DNMR is the fact that the theoretical
description of 2DNMR experiments is much less complicated and much
more transparent than the formulation of the equivalent lD
experiments. This is particularly evident when a second irradiating
field must be used, as in decoupling, spin tickling, etc. The presence
of the second rf field causes energy levels to shift, resonance lines
to change intensity and new signals to appear. The use of simultaneous
excitation by hard pulses and evolution under a time-independent
Hamiltonian as is the case in 2DNMR, is easy to describe in a
transparent formalism.

Thus, in cases where the lDNMR experiment demands selective
irradiation, the 2DNMR experiment uses hard pulses. One 2DNMR
experiment replaces a series of lDNMR experiments. Aside from the
advantages mentioned, this results in a more efficient use of

instrument time .

SOME comes APPLICATIONS:
COSY experiments yield data on coupled nuclei. This gives rise

to the "connectivi ty" map of the molecule under study. A combination

of homonuclear (IH— 1H couplings) and heteronuclear (lH-uC couplings)
COSY experiments enables one to establish the backbone structure of a
molecule. This is used widely in the assignment of resonances of amino
acid residues in polypeptides and proteins.

2DNOE experiments are used to gather data on the spatial
relationships of nuclei in solution. The magnitude of the NOE is
' directly related to the distance between the two nuclei in question.

The 2DNOE map of a molecule, in combination with molecular dynamics

calculations gives one the three-dimensional conformation of the
molecule [12]. This application is very significant because it enables
the determination of conformations of molecules in solution. In many
instances, the structure of biomolecules in solution is of greater
relevance because it is the conformation in solution that is
biologically active and this structure may differ from the structure
one obtains from, say, X-ray crystallography. Proteins which cannot be
crystallised, peptides that have an active conformation in solution,
etc., are also ideal subjects for this technique. A combination of
COSY and NOESY experiments can be used to determine the 3D structures
of proteins.

Another important application of ZDNMR is in the field of
multiple quantum NMR [13]. 2DNMR methods enable one to create multiple
quantum coherences. This has led to several applications in solution
and solid-state NMR. COSY spectra can be simplified using multiple
quantum filters, for example [14].

In general, the approach to NMR experiments has changed
. drastically with the birth of 2DNMR spectroscopy. The use of 2DNMR has
also prompted the design of novel experiments in lDNMR. 2DNMR
experiments are now used routinely in the structural elucidation of

intermediate and large molecules.

THIS STUDY:

Oxytocin is a cyclic polypeptide (MWalIOO) that is responsible
for several functions in mammals - uterine contractions, milk
secretion etc [15]. It is transported from the pituitaries to the
various parts of the body by the protein Neurophysin. The conformation
of oxytocin when it is bound to the protein is of great interest to

pharmaceutical scientists who wish to design drugs that mimic the

functions of oxytocin. 2DNOE methods have been used to study the
confermation of bound oxytocin.

Chapters 2 and 3 present a quantum mechanical treatment of 2DNMR
experiments. The density matrix approach in combination with the
product operator formalism will be used. Chapter 4 describes the
theory underlying the process of chemical exchange and chapter 5 gives
a short description of the technique of solvent suppression used. The
final chapters discuss interpretation of the results obtained and
further studies that could be conducted on the Oxytocin-NeurOphysin

system in an effort to understand their interaction more completely.

THE mea' OPERATOR FORNALISN

The basic theory of 2DNMR was developed by Ernst and his co-
workers [2]. In general, to understand most NMR experiments, the
density matrix approach is useful.

Consider a system described by a wavefunction p at some instant
of time t. The expectation value of any operator A is given by

<A> - <¢|A|¢> (2.1)

If it can be expanded as a complete set of orthonormal functions un,
i.e.
yb - nz,:m cnun , then,

<A> - 2 chn<m|A|n> (2.2)

Thus to compute any observable, it is enough to specify the
coefficients or the products of the coefficients. Knowledge of the
products one; being more useful, one can arrange these products in the
form of a matrix. It can be shown that

<A> - Tr {0A} - Tr (AU) (2.3)
where a is defined as the matrix whose elements anm are the various
cncz. However, one is always more interested in expectation values of

ensembles of systems. If <A> is an ensemble average,

 

<A>-20c

*
n m <m|A|n> (2.4)

 

al-

The quantities cncm form a matrix which is called the density matrix,
often designated as an operator 0 or p. The density matrix is the
quantum mechanical equivalent of the classical density p of points in

space. A few features of the density matrix are worth pointing out :

10

l) The density matrix is Hermitian.
2) If 0(t) is the density matrix at time t,' and 0(0) is that

during equilibrium,

0(t) - U(t,0) 0(0) u'1(c,0) (2.5)
where U(t,0) - exp (3%; ) and H is the Hamiltonian of the system.

3) Any radiofrequency pulse applied to a system of spins acts as
a rotation over the appropriate angle and the resulting density matrix
-1
”R is given by 0R - R 0(0) R where R is the rotation matrix.

4) At equilibrium, the density matrix takes the form

- 1 '
a 2 ex? ( ’5?‘7
where Z is the partition function and T the temperature. In the high

temperature approxima tion ,

15020
0 - g (l — — 12) where w is the resonating frequency of the

kT

spins and 12 is the Z component of the spin angular momentum
operator. Since the unity matrix commutes with all operators, this
part of the density matrix will be omitted in all subsequent
calculations. -

For an AX spin system, the Hamiltonian is given by

- h(wA+ 8A)IZA+ h (ox-v- 8X)sz+ MAX IAIX (2.6)
where the w’s are the resonance frequencies,

the 6's are the chemical shifts and

J is the coupling between A and X nuclei.

All
At equilibrium, the density matrix 0(0) can be written as
he: no) '
_ .1. _ _d_ - _K
0‘ 1:1 ‘1 kT IZA kT sz ’ (2'7)
Since IZA and IZX can take values of either a or B, the density

matrix for an AX system will have a dimension of 4 x 4. The density

matrix 0. will have the following form :

ll

l°a> lafi> lfia> “33>
' <aa| r1 0 0 0]
<a8| 0 0 0 0

<pa|o o o 0

 

 

<pp| Lo 0 0 -1J
Thus, using the matrix forms of the operators, one can manipulate
matrices to study effects of radiofrequency pulses, delays between
pulses, etc. , to describe perturbations on spin systems. However, it
is immediately apparent that for a simple AX spin system, one has to
deal with several matrix multiplications even for a simple two-pulse
experiment. If one were to study slightly more complex spin systems,
th‘ p ocess becomes only more cumbersome and it is easy to lose track
of the physical insight of an experiment by becoming buried in lengthy
calculations.

It seems imperative therefore, especially with the advent of
2DNMR, in which multiple pulse experiments are the, norm, to use a
formalism which bypasses the tediousness of the density matrix
calculations while retaining their basic simplicity. This is where the
product operator formalism enters the picture [16-18]. For any multi-
spin system, the set of basis functions chosen usually consists of the
products of the individual wavefunctions. For example, for an All spin
system, the set of basis functions consists of products of the one-

spin system wavefunctions, i.e. ,

QAX - |mA,mX> ; <I>Ax(l) - |aa>
<DAX(2) - |aB>
can) - we»

¢AX(4) - lfifi>
Analogously, the operators for a two-spin system can be chosen to be

products of the one-spin operators. Two of the more common basis sets

12

for product operators are the (1/2)E, 12' 11' 1y [16] and (l/2)E,

I , I

z +. I- [18] bases. The former will be considered first :

we shall examine briefly the single element product operator
formalism with respect to the chosen basis in particular. The single
element product operator am can be expressed as a matrix whose
elements are given bv .

A

On - <¢i| 0n |¢.> where the ei’s are d ’s are the one-spin system

J

wavefunctions. In the (l/2)E, Iz, I , Iy basis, the following are

x
the single element product operators to be used for a weakly coupled
two-spin system.
” l . A _ l . A _l . A _ l _
(1/2)E v 2 l 0 , 12 2 l 0 , Ix 2 0 l , Iy 2 0 i
0 l 0 ~l l 0 i 0
The product operators are given by taking the direct products of the
single element operator wavefunctions. For example, the direct product
of two operators 01 and O, is given by:
01 x 02 - [a b] x [a’ b’] - [ aa’ ab’ ba’ bb’ 1
c d | ac’ ad’ bc’ bd’ |
ca’ cb’ da’ db’
cc’ cd’ dc’ 'dd’ J
Matrix expressions for the 16 product operators obtained in this

chosen basis are given in Table 2.1.

Some observations about product operators :

i) There are 22n operators for a system of n weakly coupled nuclei.
ii) A summation of all the product operators gives rise to the density
matrix.

iii) Product operator; are orthogonal, i.e.,

A A ,
T . . 0. - .. . w .. ' ' ' .
It (01) I J) nlJ 61] here nlJ is a normalisation constant

.A close inspection of the product operator matrices enables one

to see that they can be classified according to the order of coherence

13

TABLE.2.1

I BASIS

I .
x

2,

PRODUCT OPERATORS IN THE l/2E, I

AA

0 100

l
0
0
0

I
4

A

(l/2)EX(l/2)E -

AA

(1/2 nix;

A

I x(1/2)E -

1 000

0 100

0 010

0 001

X

0 001

01. 4

as

Ar

Ix

(1/2)E

y

 

0 010

000.

1.4

1 000

mu wlnunv

0 100

1 000

.174

(l/2)E

A
I x
2

AS

A.l

14

where a coherence is defined to exist when the appropriate matrix
element is non-zero. The density matrix for an AX spin-system can be
said to have the following orders of coherence : single, double, and

zero. The product operators for an AX system can be classified as

folle :

Populations : (1/2)E, Iz, $2, 1232

Single quantum coherences of spin I : Ix’ Iy' Isz, Iysz

Single quantum coherences of spin S : Sx’ Sy' Isz, Izsy

Double and Zero quantum coherences : Linear combinations of Ixsx’
I S , I S and I S
x Y Y x Y 7

Thus in order to perform calculations using product operators
one needs to know how each product operator is transformed under a
certain perturbation (such as pulses, delays, precessions, etc.).
Matrix multiplications and other tedious algebra will be completely
done away with in this new formalism. Complex pulse sequences can be
analyzed easily without losing track of the physical insight that each
result provides.
BASIC OPERATIONS USING PMDUCI' OPERATORS:

The time-dependence of the density matrix is described by the

following equation :

A
AA

H0 (2.8)

Q__ i
dt h

A
A

where B is the Hamiltonian superoperator given by

A
AA A A

Ha - [11, 0]

Solving (2.8), we have,

l5
0(t) - exp [-iBt/h]. 0(0)

-[1 +(-1nc/n)+%, {-th/h}2 + g, {-iBt/fils + ...1 0(0) (2.9)

Consider the basic NMR acquisition experiment - the Hamiltonian

during the application of a hard non-selective pulse takes the form

A

HP - #1816111): + 115x) (2.10)

At the onset of the experiment, the system in thermodynamic
equilibrium, is given by

1 IMO
0(0) - 2 (E + kT (12+ 32))

 

assuming 11-13.

E is invariant under all operations and will be omitted below. The

A

results of the operations on Iz alone will be considered.

A A A

Corresponding results on 82 can be obtained by permuting I and S.

Equation (2.9) can be written as

A
A A

0(t) - exp {—iflfit/h). 0(0)

A A A
A

.A l- ‘A 2 i .A 3
-c[ l + {-int/fz) + 2! {-int/h} + 3! {-int/fi) +...]Iz

(2.11)

A A A A
A A

. A A ‘1- ' A 2
-c[ l + (iqulax + S) t) + ”0181(1): + 8x) t) +...]I

X 2

where c = 7H0/4kT. stz - 0 ; Eqn. 2.11 can be reduced as

A A
A

- [cos(1BIIk) + isin(1BIIx)] Iz

 

16

A
A A

exp (iOIx).Iz where 0 - yBlt

A A A

.A l .A 2 l .A 3 A
-[1 + (191x) + 2!(191x) + 31(191x) +...]Iz
- ‘ ‘ L w; 2 2
- l 1 + 1911K. 12} + 2,(1 ) [ x,[ x. 211 + ..1
2A
-I +0I -'o'I
z y 212""

I cosO + I sin0
z X

A
A A A A

exp (161k).lz - Izcoso + IXSinfl

A

Thus, the product operator 12 on application of a 90° pulse along the

A

X-axis is transformed into Iy' This result is consistent with the

density matrix formalism and the vector model. Similarly, the effects
of pulses on other product operators are summarized in the first two
rows of Table 2.2.

Let us examine the effect of free precession in the X-Y plane on
product operators.The Hamiltonian for free precession is given by

H - - thIz - thSz + fiJIZSz (2.12)

Proceeding similarly as above, it can be shown that
A

exp [-iwI Izt] Ix - Ixcos(wIt) - Iysin(wIt) (2.13)

and so on, as listed in the last two rows of Table 2.2.

A A

In using the (l/2)E, 12, If, I- basis, one again obtains 22N(-

16) product operators. Table 2.3 lists the matrices for the sixteen
product operators obtained in this basis. These can be classified

according to their orders of coherence.

l7

Populations : (1/4)E, 12, $2, 1282

Single Quantum coherences of spin I : I

+’-+z 2
Single Quantum coherences of spin S : 5+, S_, S+Iz, S_Iz
Double Quantum coherences : I+S+, I_S_
Zero Quantum coherences : I+S_, I_S+

A cursory inspection of this classification reveals that the
coherence order of a certain product operator is obtained by adding +1

for every I+ operator, -1 for every I_ operator and 0 for every 12

operator. In the basis set used previously, this is not immediately
evident. This convenience will prove to be especially so when one is
dealing. with spin systems containing more than two spins. For
instance, in a four-spin system, the triple quantum coherence is

represented by the product operators Il+IZ+I3+I4z or 11+12+I3zl4+ or

I1212+I3+14+ and so on. In the basis set used previously, such an easy

visualization of the product operators is not possible. This feature

of the (l/2)E,Iz, I+,

I_ basis is attractive to 2DNMR spectroscopists
who routinely deal with the study of multiple quantum coherence in
their experiments. The results obtained from calculations in this
basis are easier to comprehend. Other advantages of this basis will
become evident presently. Henceforth, we will use this basis in all
our calculations. Table 2.3 lists the matrix expressions for the
product operators of this basis and Table 2.4 lists the results of

pulses, free precession, spin-spin coupling interactions on the

(1/2)E, Iz, I+, I- basis. These results may be derived either directly

from Tables 2.1 and 2.2 or from first principles.

18

we have now formulated a table that lists the effects of pulses
and delays on the product operators. we shall proceed to use this to

calculate results of some 2DNMR experiments in order to demonstrate

the ease of handling this formalism.

TABLE.2.2

Effect of pulses and delays on the product operators

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l . l I . .
x y z
I l | l l
1 2
101 I I coso - I sin0 I coso +I sin0
x x y z z y
I .. l l I I
iBI I coso + I sino I I cos0 - I sin0
x z y z x
I l l l l
2 2
i0’I I c050 - I sin0 I cosfl + I sin0 I
z x y y x 2
If AAI l I I
iAIzSz IxcosA+21yst1nA chosA-leszsinx Iz

 

 

l9

TABLE.2.3

A

(l/2)Ex(l/2)E -

 

 

 

 

 

 

 

 

 

 

I x (1/2)E

A

(1/2)E

IX
2

20

TABLE.2.4

EFFECT OF PULSES AND DELAYS ON THE PRODUCT OPERATORS OF TABLE 2.3

iBIx -isinBIz+ (l/2)(l + cosO)I++ (1/2)(l - cos0)I_

 

 

iOIy sinolz+ (1/2)(l + cosO)I+- (l/2)(l - cosfl)l_
l I I
2 f

iO’IZ (c050 + isin0)I+

 

iAI S cosAI - 2isinAS I
+ z -

 

 

 

 

 

191x isin9I2+ (1/2)(1 - coso)I++ (1/2)(1 + coso)I_

 

 

 

 

iOIy sinflIz- (1/2)(l - cosB)I++ (l/2)(l + cosfl)I_
l2 2 | I
i0'Iz (c050 + isin0)I_

 

iAI S 2isinASzI++ cosAI_

 

 

 

 

 

 

 

 

 

 

 

z z
.B I
z
I l I
”f 1
iOIx cosfilz- (i/2)sin01+ + (i/2)sin0I_
I . I I
MIy cosalz- (l/2)sin01+ - (l/2)sin0I_
l l l
2 1‘
19': I
z z
s A A
iAI S I
z z z

 

 

 

 

1 o-yBlt; 20’-w1t; 3A-Jt.

MWANDNOESYMERIHENTS

This chapter will lead us through the use of the product
operator formalism for the COSY and NOESY experiments. It must be
pointed out here that these calculations ignore spin-lattice and spin-
spin relaxation effects. The two-spin systems used are assumed to be
weakly coupled and the two spins are indicated as I and S spins.
TWO-DIHENSIONAL OORRELATD SPECI'IDSCOPY (00$!) EXPERIMENT:

One of the very first ZDNMR experiments proposed [1], COSY is a
two-pulse experiment whose pulse sequence is :

D1 " 90° "' t1 ' 90° 'tz (ACQ)
where D1 is a relaxation delay between successive scans, t1 is the
evolution period separating the two 90° pulses and t2 is the

acquisition time, namely, the time during which the signal, i.e. the
magnetization in the X-Y plane, is detected by the receiver. Table 3.1
lists the calculations.

At equilibrium, and at the start of each repetition of the

pulse sequence, the system is represented by 12 and $2. The relaxation

delay is assumed to be long enough that the system returns to
equilibrium by the time the pulse sequence is applied again. we will

follow the fate of the 12 operator through the COSY pulse sequence.

Results for the S2: operator are obtained by permuting I and S.

22

The first 90;_pulse :

,i l
12—» 21++21_ (3.1)

12 is the z magnetization which is converted to Iy under the influence

of a 90 pulse along the X-axis. -§ I+ + g I_ is indeed equivalent to

I .
7

The evolution period t1: Two processes occur in this period. One is
the free precession as a result of the Zeeman interaction and the
other is the interaction due to spin-spin coupling.

a) Free precession :

-g- 1+ + g I_ . - j exp(+iwIt1)I+ (3.2)

i .
+ 3 exp(-iwIt1)I_

where ml is the precessional frequency of the I spin.

b) Spin-spin interaction :

-é exp( iwIC1)I+ ‘2 '% eXp( iwIC1)(COS(Jt1/2) ' 21$in(Jtl/2)SZ)I+

+L exp(-iwIt1)I- 4 +j

2 exp(-iwIt1)(cos(Jt1/2) + 2isin(Jt1/2)SZ)I_

The second 90"pulse: Let 0J1 - cos(Jt1/2) ; 5J1 - sin(Jt1/2)
,i . ,. _i i - l l

4 2 exp( iwIt1)(CJ1 21 SJ1( 2 3+ + 2 S_ ))(-lIz +2 1+ +2 I_ )
i -. . __1. i . l 1
+2 exp( iwIt1){CJl+ 21 SJ1( 2 3+ + 2 S_ ))(+1Iz +2 1+ +2 I_ )

Inspection of the terms above indicates the presence of the following

terms:-
Single Quantum (SQ) : 1+, I_, S+Iz, S_Iz
Double Quantum (DQ) : S I 5.1

23

TABLE 3.1

Evolution of product operators for
the COSY pulse sequence

 

EQM 90’ 'r, 90‘ '1;
II longitudinal
I, 1, not detected f
1, 0.5.'.C,.C.I.+
1. 1.3. $339.3. +
is, not detected
1.8. 1.8. 20 I
1,3, on
1,3, 20
1,3, no
1.
1,3, za
1,3, no
1,3, 1,3, 2o
1,3, no
1,5, not detected
1. ' 1.8. 03.0.“ «8.8. '
I. 03.03 “0.1. '
I, I, not detected
1. longitudinal

20 - zero quantum. and DO - double quantum coherences;
'-Ppeaksand+ -Npeaks(pleasereierto'l‘ahle3.2ior
the full expressions). Solid lines indicate the N pathway
while the broken lines indicate the P pathway.

24

Zero Quantum (ZQ) : S+I_, S_I+

Immediately after the second 90" pulse, therefore, three different
types of coherences are created. However, the detector is capable of
detecting only single quantum coherences; so, we can omit the DO and

ZQ terms during the time t2( detection period). Furthermore, since
quadrature detection is used, only coherences of the type I-

correspond to observable magnetisation.

Rewriting the result, one obtains,

* i ' .‘L - e
i . l .

The above expression describes the conditions immediately after the
second 90" pulse. It is to be noted that a coherence that started out

as Iz now has evolved into I_ and S_ coherences. This is brought about

as a result of spin-spin interaction. In other words, the evolution
period causes a mixing of states that are coupled by the J-
interaction.

The detection period: During the detection period t2, the spins evolve

under the influence of the Zeeman interaction as well as the spin-spin

coupl ing .

1 1 2
Let exp(-iwItl) - e_I; exp(+iwIt1) - e1; exp(-iwItg) - e-I;

2
exp(+iwIt2) - el, and so on, for the S spins as well (Table 3.2).

a) Free precession :

1 2 l 1 2
2 ‘4 e1 8-1 CJII- ' 2 er e-s SJlS-Iz
A. 1 e1 2
*4 e -Ie -I 0011* 2 la SSJlSz I

25

b).Spin-spin interaction: Once again, one obtains terms that are

functions of 1-, S_, I_Sz, IzS_. Only the I_ and S_ terms convert into

observable magnetisation. We will omit the other terms from further

consideration.
112 3
2 ’4 ‘1 e-I CUlCJZI- ( '48)
1 1 2 3 4b
‘ 4 91 9-s SJISJZS- ( ' )
1 1 2 3 4
+ 4 e_Ie_I CJICJZI- ( . c)
112 3
+ 4 e_1e_ssjlsjzs_ ( .44)

We now have to deal with four terms. Recalling the original
expressions'for the various abbreviations used above, it is seen that

one obtains two terms in I_ and two terms in S-. The two terms in I-
and S_ differ only in the fact that while the precession of the I spin
during t1 is in the positive sense (3.4a) and (3.4b), it is in a

negative sense in (3.4c) and (3.4d). The first two equations give rise
to negative, or "N" peaks and the second two, to positive, or "P"
peaks.

Following the P peaks for the moment, one gets from the above

equations,

' c s c s s

.1.
2 c c C C I + 11 J1 52 J2 -

4 11 J1 12 J2 -

#ll-

1 c c s c I + i c s s s s

* 4 11 J1 12 J2 - 4 11 J1 52 J2 -
+ 1 s c c c I + i s s c s I
4 11 J1 12 J2 - 4 11 J1 52 J2 -

- 1. i. .
4 sIchlSIZCJZI- + 4 SIlSJlSSZSJZI- where the various

abbreviations given in Table 3.2 have been used.

Further simplification yields the following:

26

TABLE.3.2

LIST OF ABBREVIATIONS USED IN THE TEXT

ABBREVIATION EXPRESSION ABBREVIATION EXPRESSION
0J1 COS(Jt1/2) 0&2 COSCJt2/2)
8J1 SIN(Jt1/2) 5J2 SIN(Jt2/2)
1 2
e1 EXP(wIt1) eI EXP(wIt2)
1 2
e_I EXP(-wIt1) e_I EXP(-wIt2)
1 2
es EXP(wSt1) es EXP(wSt2)
1 2
e_s EXP(-wst1) e_S EXP(-wst2)
1 l 2 J
e(I:J) EXP((wIi 2)t1} 6(I1J) EXP{(wIt 2)t2)
1 EXP *1 2 J.
e-(ItJ) {-(wIi 2)t1) e-(IiJ) EXP{-(wIi 2)t2)
1 J 2. J
e(SiJ) EXP{(w31 2)t1) e(S:J) EXP((wSi 2)t2)
1 E l 2 l
e-(StJ) XPf-(wsi 2)t1) e-(StJ) EXP(-(wsi 2)t2)

27

“I6{GXP('1(°’I+2 )t,) + exp(-i(wI- ‘5 )t1)}{exp(-i(w1+‘21)t2) +
exp(-1(wI- % )t,)} I_
~13 exp(-i(w1+% )tl) - exp(-i(wI- 3]" )t1)} {exp(-1003+ % )tz) -

. J
exp(-1(ws- 3 )t2)} S_ (3.5)
The I_ term contains terms which precess with the same frequency
(war-col) in both the t1 and t2 time periods. Fourier transformation

of this term will give rise to a set of four peaks with frequencies as

shown in Figure 3.1. The peaks appear at (1.11.: J/2,wI§:J/2) in the

spectrum. These peaks are diagonal peaks.

The S- term contains terms which precess with a frequency of «II

in the t1 time period and a frequency o§ ms in the t2 time period.
Fburier transformation of this signal will give rise to a set of
four peaks that appear at (col: J/2, «as: J/2) - with a frequency of ”I

in the t1 time domain and a frequency of ”S in the t gtime domain.

These peaks are off the diagonal and are referred to as cross-peaks.

Similarly, the $2 spin gives rise to a set of P peaks on the
diagonal centered around (1.23, ms) modulated by the J-coupling. The

calculations for the N peaks are similar; the following expression is

obtained :

4 -12 {exp(+i(w1+% )tl) + exp(+i(wI- 3] )t1)} {exp(-1001+ '21 )t2) +

exp(-i(wI- % )t2)} I_

28

- I6 {exp(+i(w1+ ‘21 )t1) ' 8XP(+1(UI' 3% )t1l} {919(‘1'm34' % )tz)

-exp(-i(ws- =5 )c,)} s_ (3.6)

Figure 3.1 indicates both P and N peaks that will be obtained
for the I spin of the AX spin system.

These calculations can be extended with facility to a many-spin
system. Ultimately, one obtains, in COSY spectra, peaks on the
diagonal that resemble the lDNMR spectrum of the molecule, and peaks
off the diagonal are present only if the two corresponding spins are
correlated by spin-spin coupling.

As can be seen from equation 3.5, complex Fourier
transformation (FT) of the expression yields peaks which do not have a
simple lineshape since the FT will have real (absorptive component)
and imaginary (dispersive) parts superimposed on top of one another.
One of the earlier ways to get around this was to represent spectra in
the absolute value mode. This is done by taking the square of the
Fourier transformed spectrum so that the signal intensities in the

spectrum are given by

2 2 1/2
S(w1, (.02) - ( Real (wl, (1)2) )+ Imag(w1, w?) )

TWO-DIMENSIGIAL OVERHAUSER EFFECT MERINENT (2DNOE) :
The 2DNOE experiment has the following pulse sequence:

D1 - 90' - tl - 90" - tm- 90° - t2 (ACQ)
where D1 is the relaxation delay between successive scans, t2 is the
incremental delay or the evolution period, tm is the mixing period and
t, is the acquisition period during which time the receiver collects

the signal due to observable magnetisation.

29

 

 

+0); r - — - + 3
+6)!- " — "- + _ z
1 l l l
“I ”I “I; 0;
—m; - + + + -—
3
—m{ - + + - + .-
o;- 0.4/2 q- 0.4/8
o;- o,+J/2 U,‘- oft-Ill

REPRESENTATIVE COSY SPECTRUM FOR THE I SPIN

FIGURE 3. 1

.e_
E

PPEAKS

-wb _

 

REPRESENTATIVE NOESY SPECTRUM FOR THE I SPIN

FIGURE 3.2

30

Nuclear Overhauser Effects are a result of cross-relaxation
between spins A and B. In lDNMR, this is brought about by saturating
say, spin A, and observing cross-relaxation to B. If there is cross-
relaxation to B, this is indicated by an increase or decrease in the
intensity of the peak due to the B spin in the NMR spectrum, depending
on whether the NOE is positive or negative. The pulse sequence shown

above accomplishes the same in a 2DNMR experiment.

The first 90; pulse: As before,

I»-1I+-§I (3.1)
The evolution period t1: The calculations continue to be identical to

those for the COSY experiment except for the fact that the two spins
are considered not to be coupled to one another.

a) Free precession:

_1 1 _, -1 .
2 1+ + 2 I_ 2 exp(+iwIt1)I+

j, _ .
+ 2 exp( iwIt1)I_

where “I is the precessional frequency of the I spin. Once again, we

follow the I spin through the pulse sequence. A summary of the
calculations is shown in Table 3.3.

b) Spin-spin interaction: J - 0. One can ignore the effect of this
term on the product operators.

The second 90' pulse:

a - 1 exp(+iwIt1)I+(-ilz + g I + g I )
l l
2 2

2
+ 1‘ exp(-iw t )I (+iI +
2 I 1 - z

31

We are now left with terms that have the following coherences : 0, +1,
-1. Calculations for the 5 spin can be obtained similarly.

The mixing period: During this period, cross-relaxation between the
two spins occurs. The cross-relaxation can be represented as follows:
[12 (c - cm) ] _ [RH R13] [12 (c-0) ]

82 (t - ta) RSI RSS SZ (t-O)

The product operators Iz and 82 are modulated by the cross-relaxation

and, of course, the spin-lattice relaxation.

Iz (t - rm) - RII

Sz (t - cm) -- 123112 + RSSSZ

The 1+ and I_ product Operators that remain at the end of the second

12 + R1332

90' pulse will experience free precession and spin-spin coupling, if

any, in the X-Y plane during tm' Since it is the cross-relaxation that

gives rise to the NOE’s, we will trace only those product operators

that are modulated by the cross-relaxation, namely, the 12 and 82

product operators.

1 ‘ 1 ‘

-2 eIRIIIz ' 2 eIRISSz

1 l. 1
eoIRIIIz ' 2 e—IRISsz
1 l. 1
e.S'RSIIz - 2 eSIRSSSSSz

1 J- 1
e-SRSIIz ' 2 e-sRsssz

where the abbreviations used stand for the expressions given in Table

N'IH NF- NIH

3.2.

The third 90" pulse: This pulse converts the I2 and S2 product

operators (i.e. longitudinal magnetisation) into observable

magnetisation. This is followed by acquisition of the signal for a

32

time t2 during which time precession under the influence of Zeeman

interaction takes place in the X-Y plane. The resulting expression is
given by:

aL12 £12
2 ‘4 ale-IRIII- ' 4 ere-sRIsS-

.1 12 .1; 12
'4 e-Ie-IRIII- ' 4 e-Ie-SRISS-
112 £12
'4 eSe-IRISI- ’ 4 ese-sRsss-
i 12 i 12 S
’4 e-Se-IRISI- ' 4 e-se-sRss -
Again, the abbreviations have been expanded in Table 3.2 and the

superscripts refer to the respective time domains. The expressions

containing product operators 1+ and 8+ have not been carried through
because only terms containing I_ and S_ correspond to observable

magnetisation.
As in the COSY experiment, one obtains "P" and "N” peaks,

characterised by the sense of precession in the evolution period t1.

FT of the signal obtained gives rise to peaks at positions on the

diagonal at (1 w I) and (1; a) S) and off the diagonal at (i w

I’ w s' w I’

(or) and (i ”S’ (as) as represented in Figure 3.2. The intensities of

these peaks are modulated by the magnitude of the cross-relaxation

term RIS (-RSI). If cross-relaxation is absent, no cross-peaks can be

seen. Thus, the presence of cross-peaks in a 2DNOE spectrum indicates
the presence of NOE between the spins concerned. In effect, the 2DNOE
spectrum gives the 2DNOE map of the molecule under study.

It has been shown that the cross-relaxation rate is inversely
proportional to the sixth power of the distance between the two spins

in space [23]. The farther away the two spins are from one another,

 

33

TABLE 3.3

Evolution of product operators for

the NOESY pulse sequence
son 90' 'r 90' '1', 90' ’ 1',

R}, not detected

1

3.1. +
R.l_ Diagonal peak

R’s. not detected

3‘3;
R.S_ Croce-peak +

 

mo. W A!!!) Dom gum common

I' mnmm

 

 

 

12.1, not detected

R.l_ ‘ Diagonal peak .

3.3, not detected

+ - N Peaks and ‘ = P peaks. Solid lines indicate the N pathway while
broken lines indicate the P pathway.

34

the weaker is the NOE and the weaker is the cross-peak in the
spectrum. Using the ZDNOE spectrum along with the intensities of the
various cross-peaks, it is possible to generate three-dimensional
structures for molecules with the help of molecular dynamics
calculations.

Thus, use of product operators greatly simplifies the
calculations necessary to gain insight into any multiple pulse
experiment. This formalism facilitates the design of new pulse
sequences. Extension of the above calculations does not complicate the
calculations any further. One is just left with a few more terms to
handle.

The description of 2DNMR given so far has brought forth the
various advantages and features of the technique. However, every
experiment has its own disadvantages as well, and the practical use as
such, depends upon how easily and conveniently these disadvantages can
be overcome. Any instrumental technique suffers from instrumental
errors, from errors due to approximations made in the theoretical
formalism, errors in analysis, etc. For instance, the calculations
performed above neglect relaxation effects altogether, pulses are
assumed to be perfect, and so on.

It must also be remembered that the same pulse sequence gives
rise to different effects. The 2DNOE experiment, for example,
generates multiple quantum coherences at the end of the second pulse
which are converted into observable magnetisation at the end of the
third pulse. If one is not mindful of such details, the "2DNOE"
spectrum will contain artifacts due to multiple quantum coherences.

In addition, each experiment generates a set of P peaks and a
set of N peaks [19]. It is undesirable, in the absolute value mode

representation, to retain signals due to both P and N peaks since the

 

35

P peaks will appear folded on top of the N peaks in the spectrum if
the carrier frequency is positioned within the spectrum (Figure 3.3) .
One must therefore devise some means of separating P and N peaks, if
not eliminating one of them.

Finally, the calculations shown above ignore relaxation
effects. If the relaxation rates are high, longitudinal magnetisation
will deveIOp during the evolution period and the next 90° pulse
applied will convert this into observable magnetisation. This will

give rise to axial peaks, i.e. peaks which appear at m1 - 0.

The simplest method used to eliminate unwanted coherences and
artifacts, or to select desired coherences is by the phase cycling of
the pulses and the receiver [20]. Different coherences evolve with
different phases and by making appropriate choices for the phases of
the pulses used, one can cancel undesired signals. To be able to do
this effectively, it is necessary to study the coherence transfer

pathways of the pulses concerned [19].

commas TRANSFER PATHWAYS AND PHASE-CYCLING:
Coherence transfer pathways are most easily understood by the
use of coherence transfer diagrams. At equilibrium, the system can be

represented by the 12 and 52 product operators. These represent

longitudinal magnetisation and have a coherence of order zero. At the
end of the pulse sequence, during‘the detection period, only
coherences of order -1 will correspond to observable magnetisation.
Any pulse sequence visualised, therefore, should convert all desired
coherences into coherence of order -1 by the application of the

observation pulse. If Apn is the change in thecoherence order after

the nth pulse, then,

36

 

 

Foldover of N peaks over P when carrier is
placed within the spectrum

0 P peaks 0 N peaks
FIGURE 3.3

37

n
2 Apn- -l, where n is the number of pulses in the sequence
1

[19.].

Coherence transfer diagrams picture the coherence transfers in
the following manner: Each coherence order is represented as a level
equally spaced between the next and previous coherence levels (Figure
3.4a). With the application of a 90° pulse at equilibrium, the
longitudinal magnetisation is now converted into coherences of +1 and
-l, the latter corresponding to observable magnetisation. This is a
simple lDNMR experiment. In general, 90° pulses create coherences of
different orders while delays modulate the magnetisations within
coherences of the same order (Table 2.2). It is now possible to
construct coherence transfer pathways for the COSY and NOESY
experiments .

WRENCH TRANSFER PATHWAYS FOR 005? :

The coherence transfer diagram is as shown in Figure 3.4b. At

equilibrium, longitudinal magnetisation alone exists. Application of

the first 90’ pulse converts this into I +and I _coherences; namely,
coherences of orders +1 and -1 respectively (Table 2.2). During tl ,

these coherences are modulated by free precession and J coupling. At

the end of the t1 period, another 90° pulse is applied. This pulse

converts the +1 coherence into +1, 0, and -l coherences and the -l
coherence is converted into -1, 0 and +1 coherences.

During the t2 period, the -l coherence alone is observable.

This magnetisation is a result of the pathways 0 4 +1 -* -l and 0 -v -1
-* ~l. The former gives rise to N peaks and the latter to P.
It can be shown that the phase of a coherence is directly

proportional to the value of Ap for that coherence. Therefore,

38

90'

 

 

--——-—‘-—-

 

 

 

Coherence transfer pathways for a

90‘ single pulse experiment

FIGURE 3.4a

39

incrementing the phase of a pulse by, say, m will increment the phase
of a certain coherence by cp x Ap. In the case considered here, the P
and N peaks have the following values for Ap:

N P

First 90° pulse (m1) : +1 -1
Second 90° pulse (m2): -2 0
Thus, incrementing the phase of go: by 90° affects the phase of the N

type coherence by -l80‘ and leaves the phase of the P type coherence

unchanged. Taking two scans where the phase of «p, is shifted by 90° in

the second scan, and adding the two scans should cancel the signals
due to the N peaks. Conversely, subtraction of the two scans will
cancel the signals due to the P peaks. This addition or subtraction is
achieved by shifting the phase of the receiver appropriately. A 180°
shift will subtract the signals while keeping the receiver phase
constant during both scans will add them.

If spin-lattice relaxation has been significant during the t1

period, we will be left with some longitudinal magnetisation at the

end of the t1 period. The second pulse then creates observable

magnetisation which has not followed the COSY pathway. This will give

rise to the so-called axial peaks that appear at a.)1 - 0 in the 20
spectrum (no t1 dependence). To eliminate axial peaks, let us consider

their coherence transfer pathway. They follow the 0 -v 0 -' -l pathway.

Ap1 - O, Apg - -1. Therefore, incrementing cp2 by 180' and adding the

two scans will cancel axial peaks. This two-step cycle can be combined
with the previous two-step cycle to cancel both axial and P peaks. In

general, N peaks are selected because there is partial cancellation of

40

instrumental imperfections when a coherence precesses in opposite

senses in t1 and t2.

In practice, since radiofrequency(rf) shifts are subject to
systematic errors, the basic phase cycle is expanded 4 times to
include all possible combinations of phase shifts. However, selection

of N peaks alone presents some problems. The expression for the I_
product operator for diagonal N peaks at the end of t, has the

following form for the t1 dependent part:

exp(-(w, + fi )c,) + exp(-(w, - f )c,)

Complex Fourier Transformation (CFT) of an exponential function gives
a real part and an imaginary part:

exp (iwIt1} -> Re(wI) + iIm(wI)

where the real part gives rise to an absorption line and the imaginary
part gives rise to a Lorentzian line in dispersion. If a two-
dimensional CFT is performed on the product of two exponentials,

exp (iwltl) exp (iwztz) e {Re1(wl) + iIm1(w1)) exp {iw2t2)
(Re1(w1) + iIm1(w1)} (Re2(w2) + 111112002”

The real part of the above expression corresponds to

Re, (w1)Re2 ((0,) - rm, (w1)Im2 00,)

which is a mixture of absorption and dispersion components and results

in a phase-twisted lineshape at (wl, wz). As mentioned briefly above,

one way to get around this problem is to represent spectra in absolute
value mode. However, this carries the handicap of increasing the
linewidth at half-height of a Lorentzian line by a factor of J3 and
.increases the amplitudes of the wings of the peaks [21]. As a result,

if two peaks are very close to one another in a 2D spectrum, this

41

90° 90‘

 

 

 

 

 

 

F—-—-b----r

 

Coherence transfer pathways for the COSY
experiment. The phases are cycled as follows:
Pulse1:00221133
Pulsez :02021313
Receiver:00221 133
0,1,2 and 3 imply 0‘, 90', 180‘ and 270‘ phase
shifts. P and N pathways have been retained.
Axial peaks have been suppressed.

 

-——- P pathway and N pathway

FIGURE 3.4b

42

manifests itself as an apparent reduction in resolution.

It is therefore necessary and convenient to be able to generate
spectra which have pure absorption lineshapes. Examination of the
calculations indicates that if coherence transfer pathways
corresponding to both N and P peaks are retained (Figure 3.4b) , the

resulting expression at the end of t2 is as below:

e ' J
-o % {5111((01. + 3] )CI + $111001. - E )C1)(9XP(‘(QI + % )t2)

+ exp(-(«>1 - ‘3’ mm,
- % {cos(wI + % )t1 + cos(wI - % )t1}(exp('(ws + % )t2)
1
- exp(+(wS - 2 )t2))S-

The term corresponding to the t2 period is a complex function while
the term corresponding to the t1 period is a sine or a cosine. The

first CFT will give real (absorption) and imaginary (dispersive)
components. The imaginary component is zeroed before the second
transformation. The resulting expression will now have only the real

parts of both the t1 and t2 time periods [22].

However, it is to be noted that the term corresponding to the

diagonal peaks has a sine dependence in the t1 time period and will
have an absorptive lineshape in the «.02 frequency domain and a
dispersive lineshape. in the m1 frequency domain. The term
corresponding to the cross-peaks has a cosine dependence in the t1

time domain and will have a pure absorption lineshape in both

frequency domains. Since information contained in the cross—peaks is

43

of primary importance, the "mixed" lineshapes in the diagonal peaks

can be tolerated.

commas TRANSFER PATHWAYS FOR NOESY:
Coherence transfer pathways for NOESY are as in Figure 3.4c.
The first 90° pulse generates +1 and -1 coherences as before. These

are modulated during t1 by the free precession. The second 90° pulse

distributes these coherences into +1, 0 and -1 orders. Higher orders
are created if J coupling interactions are present. Thus at the end of
the second pulse, one has generated single quantum, double quantum and
zero quantum coherences in addition to creating longitudinal

magnetisation of the I and S spins. During the tm period, the

longitudinal magnetisations are modulated by the spin-lattice and
cross-relaxation. At the end of the mixing period, another 90° pulse
will bring the longitudinal magnetisation into the X—Y plane in the
form of +1 and -l coherences, of which the -l coherence is observable.
Thus the observable magnetisation contains information about cross-
relaxation in the off-diagonal, or cross-peaks. To selectively observe
this effect alone on the system, it is necessary to suppress other
coherence transfer pathways, notably the double quantum pathway.
Higher quantum coherences are generated, but their intensities are
considerably lower and can be ignored.

Longitudinal magnetisation follows the 0 4 +1 4 0 4 -l path for
the N peaks and the 0 4 -l 4 0 4 -l path for the P peaks. Double
quantum coherence follows the 0 4 -l 4 -2 4 -1 for the P peaks and the

_0 4 -1 4 -2 4 -l path for the N peaks.

44

90' 90‘

 

 

 

 

 

Coherence transfer pathways for the NOESY
experiment. The phases are cycled as follows:
Pulsel :02020202

Pulsez :0000000022222222
Pulsez :00221 133
Receiver:02201331200231 13
0.1.2 and 3 imply 0', 90‘, 180° and 270' phase
shifts. P and N pathways have been retained.
Axial peaks have been suppressed.

---- P pathway and --—— N pathway

FIGURE 3.40

45

Ap for 1’ peaks Ap for N peaks
‘Pi <02 ‘P3 ‘P1 (P2 P3
NOE pathway -1 +1 -1 +1 -1 -1
Double quantum pathway -1 -1 +1 +1 +1 -3

To cancel P peaks, two scans are taken with the phase of oz

shifted by 90° and the phase of the receiver shifted by 90°. Addition
of the two scans will cancel the N peaks while subtraction will cancel
the P peaks. If pure absorption lineshapes are desired, both P and N
peaks must be retained and one need worry only about suppression of

the double quantum coherence pathways. If the phase of gas is

increased by 90° in the second scan, together with a shift in the
phase of the receiver of 90°, the phase of the double quantum
coherences will be incremented by 1 180°. Addition of these two scans
will cancel these double quantum signals. Similarly, appropriate phase
cycles can be designed to suppress unwanted coherences of higher
orders. A combination of all these individual phase cycles will then
cancel out all unwanted signals. The phase cycling used for a NOESY
experiment is shown in Figure 3.4c. The phase cycling discussed here
involves only 90° phase shifts. It is possible to use non-90‘ phase
shifts as well in the phase cycling. However, instrumental features
available until recently only supported phase shifts that were
multiples of 90°.

Thus, the design of a ZDNMR experiment involves not only the
design of the pulse sequence but also the design of the appropriate
phase cycle to select the desired coherences. The product operator
fbrmalism and the concept of coherence transfer pathways greatly

.facilitate an understanding of the 2DNMR technique.

 

MICAL EXCHANGE AND mum NUCLEAR OVERHAUSR 373678

The study of protein-ligand interactions has been of great
interest in general, because of the scientific importance of the
applications pertaining to such studies. There are several techniques
available to carry out experiments that seek to know more about such
interactions; however, one may say without fear of exaggeration that
the use of NOE measurements in NMR is probably the single most
important method that yields information about the conformation of the
bound ligand. The fact that NOE measurements are capable of
determining proximities of nuclei in space has been well known and
documented. In the early seventies, Noggle and Schirmer analysed the
theory and listed the possible applications [23]. The subsequent
advances in NMR have, with the advent of 2DNMR, merely made the method
more convenient and easy to use (pl. see chapter 1). In fact, routine
three-dimensional structural analysis of proteins of molecular weights
of upto 10,000 have been recently reported in the literature [24].
There is an upper limit on the applicabilty of NMR to structural
elucidation because as the size of the molecule increases, the lines
are not very resolvable even at the highest fields currently
available. In addition, one is limited by the faster relaxations of
the protons in macromolecules.

In the case where protein-ligand interaction is under study,
the mode of approach to the problem must be slightly different. In

most cases, the signals of the bound ligand cannot be observed.

46

 

47

However, using the concept of transferred NOEs, it is possible to
study conformations of bound ligands.

In order to understand the use of Nuclear Overhauser effects
in conformational studies, a quick look at the underlying theory is
warranted.

Consider a weakly coupled AX spin system. The energy levels
are as given in Figure 4.1. The spins are labelled I and S. The energy

levels correspond to the following wavefunctions:

Level Spin I Spin S
1 la) |a>
2 |a> |p>
3 IE) |a>
4 m> lfl>

 

4 In)

Energy levels for an A! spin system

Figure 4. 1

48

In general, for the case of like spins, levels 2 and 3 have
nearly equal energies. Transitions occur between levels from states
with higher populations (i.e. lower energy) to states with lower
populations (or higher energy) in accordance with the selection rule
Am - i l where m is the spin quantum number. If the radiofrequency
field applied is very strong, the populations of the lower.and higher'
energy levels will be equalised, resulting in saturation.

There are several mechanisms by which the system returns to
equilibrium. All these mechanisms fall under the broad category of
spin-lattice relaxation.

If we denote W as the probability per unit time that a
transition will occur due to spin-lattice relaxation, we can define

several different types of such transitions [25]:

W11 : The single quantum transition rate for spin I t o

undergo a transition corresponding to Am - :_+_l

W13 : The single quantum transition rate for spin 5 t o

undergo a transition corresponding to Am - :1

W2 : The double quantum transition rate for I and S to flip

in the same sense i.e. an 4 EB or [BE 4 aa

W0 : The zero quantum transition rate for I and S to flip

in opposite senses, i.e. afl 4 he or he 4 on
These transition rates have also been depicted in Figure 4.1.
If the populations of the various states can be denoted by
appropriately subscripted P’s, the rate of change of the population of

'the on state can be written as

49

d? ° ° °
3:99 ' '0"11* ”15* V2)(Pea' Pan) * ”2(Pfip’ P55) ' w11(Pap' Pafi)
+ wls(P - Pfla) (41}

where the P ’s are the various equilibrium populations.
The intensities of the transitions are proportional to
population differences. Therefore, the intensity of the I transitions

are proportional to PI which is given by

PI - (Pea - Pfia) + (Pafl - P195) (4.2)
PS - (Pea - Pfla) + (Pafl - Pfifi) (4.3)
From equations 4.1 and 4.2,
dP; - -(w + 2w + w )(P - P°) - (w - w )(P - P.) (4 4)
dt 0 II 2 I I 2 0 S 3 °
“IL-wmw +W)(P-P°)-(W-W)(P-P°) (45)
dt 0 IS 2 S S 2 0 I I '
Rewriting 4.4 and 4.5 in more general terms,
d<I >
dc z - -pI[<Iz> - Io] - aIS[<sz> - so] (4.6)
«S >
dt 1 - -ps[<Sz> - so] - oSI[<Iz> - Io] (4.7)

where p1 - l/TII and p5 - 1/TSS; aIs - l/TIS and oSI - l/TSI.

The p terms are the spin-lattice relaxation terms and the 0 terms are
the cross-relaxation components of the spin-lattice relaxation. In
order for the 0’s to be non-zero, there must exist one or more

mechanisms which couple I and S such as

50

l) dipolar relaxation between I and S
2) chemical exchange between I and S

etc.

It is the cross-relaxation that makes the Nuclear Overhauser

Effect possible [25]. In the two-spin system, if spin 8 is saturated

and if.f is the enhancement in the intensity of the I signal,

fI(S) -(<Iz> - I0)/Io

At steady state, dIz - 0 equation 4.6 gives

 

dt
30
<Iz> - IO + OIS ;—
I
a S
i.e. fI(S) - I; 0
”I o

Zié S(S+l) Z§
pI I(I+1) 11

as I « I(I+l)7I and S

0 a 5(3*1)73'

0

where a is the cross-relaxation between spins I and S,

IS

1 the magnetogyric ratio of the subscripted nuclei,

and I and S are their nuclear spins.

For two like spins,

“A _ "240

W0 + ZWII + W

2

The various W’s can be expressed as follows:

2 2 2
3_ 7175“ ro

 

 

W ' e 2 2
II 20 r l + w r
I c
2 2 2
, W _1_msfi 1. ,_ I 7175“
0 10 r6 2 2 N 10

l +(wI - ws) 1c

 

(4.8)

(4.9)

(4.10)

51

2 2 2 2 2 2
W i 1I73h 'c ~ 717$fi Tc
2 ' 5 e 1 2 2 ~ 6 1 4(02 2
r +(wI + us) 'c r + 7c

ulna

In the extreme narrowing limit, i.e. wrc<< l (as in small

molecules),

 

222
-171 -
aIS - W2 - W0 I5 I Sh (6rc 10) (4.11)
r

It is seen that the majority of the contribution to 0 comes from the

W2 term.
When wrc >> 1, i.e. in the spin-diffusion limit (as in large

molecules),

 

 

 

1 2 2 2 6
013 - __ 717$h ( 2 2 - l )1c

10 6 l + 4w 1
r c
2 2 2 2 2 2 2 2

= l_ 1I1Sh ( 3 - 2w 1C ) ~ - l_ 1 1 fi 1

10 3 2 2 ~ 10 ° c

r 20 'c

(4.12)

The major contribution in this case is from the W0 process.In
other words, the W2 pathway for relaxation is the predominant pathway
in the case of small molecules while the zero-quantum W0 pathway

dominates the cross-relaxation mechanism for non-rigid molecules.

The cross-relaxation is given by,

1 I‘fiz 6'
a - - - 6 ( ’c - , 2 2 ) (4.13)
IS 10
r l + 4w r
IS c

where fc is the correlation time for the dipolar interaction given by

diffusive rotational motion of the molecules,

 

52

r15 is the distance between I and S,

and a) is the Larmor precession frequency.

The NOE will be equal to zero when 013 - 0. This condition is

satisfied when

67
c - ——9-.,—-; , i.e. wrc - 1.118
1 +41.) 'c

1'

When one << 1, i.e. in the extreme narrowing limit, f - +0.5.

This is the case for small molecules since the correlation times are
small. In the case of large molecules which usually have longer

correlation times, ore is much larger than 1. This is also the case in

situations where a ligand is bound to a large protein. The value of f
( i.e the NOE ) is now equal to +1. Thus under ideal conditions, NOEs
can range from +0.5 to -1.

When chemical exchange between free and bound ligand is
present, the equilibrium that exists between free and bound forms of
the ligand enables information pertaining to cross-relaxation to be
transferred from the bound to the free form of the ligand. The NOE
thus observed is referred to. as Transferred NOE (TRNOE) [26] .

Typically, in an NOE experiment, the S resonance is irradiated
( or selectively inverted) and the NOE develops as the S spin relaxes
to the steady state. The time this process takes depends on the rate
of cross-relaxation. The pulse sequence can be schematically depicted

as

90'

lawman T _ ACQ

 

53

The time r is the time during which the NOE develops. As seen in
Chapter 3, this time corresponds to the mixing time in a 2DNOE
experiment.

Normally, in the free ligand, NOE’s are either positive or

close to zero since the ligand is usually a small molecule (wrc << 1),
or one of intermediate size («orc - 1). However, upon binding, the
correlation times become longer and the value of the NOE changes

sign, becoming negative. Thus observation of negative NOEs on the free
ligand resonances is a consequence of TRNOEs. It is therefore clear
that the structure of the bound ligand can be studied in the presence
of free ligand by using TRNOEs. .
What follows below is a theoretical treatment of the case of a
ligand L binding to a protein P and how relaxation rates, association

'and dissociation constants etc. affect the TRNOEs observed.

”DH: Consider a ligand L binding to a protein P.

where kl and k_1 are the rates of association and dissociation. Let

us, for the sake of simplicity, consider two spins I and S on the
ligand and two spins X and Y on the protein. Spin X on the protein is
at the binding site while spin Y on the protein is at a site that
relaxes quickly. The model is depicted in Figure 4.2. This model is
based upon solvent proton spin-lattice relaxation studies of aqueous
protein solutions where it has been shown that the solvent
' magnetisation actually flows into the protein [27]. This situation can

be extrapolated to the case of a protein-peptide system.

54

The two protons on the bound ligand experience cross-

relaxation between each other (as), cross-relaxation with spin X on
the protein (ox) at the binding site, and are in chemical exchange

with I and S on the free ligand. In addition, spin-lattice relaxation
is also present. Cross-relaxation between I and S in the free ligand

is represented by 0F and cross-relaxation between protons X and Y on

the protein by a The rate constant for binding is k and for

XY'
dissociation is k_1. The equilibrium concentrations of the free ligand
and the protein are represented by [L] and [P] respectively.

Bloch equations representing the various z-magnetisations at

equilibrium are given by :

dnlfl
‘ dt ' ' ”13(HIB'HBO) + °B(”ss'"30) + a x(” x3 ”XBO) kJMIB
+ kllPJMIF
an
.45 .. - - - -
dt pIF(MIF ”Fo) + °F(”5F ”Fo) + k-1”IB k1IPIMIF
an
u-fl - a - n .
dt Pss(”sa ”30) * °B(”IB 30) ”X( XB ”XBO) k IMSB
+ k1[P]MSF
an
__$£ _ - _ _ _
dt ”5F(”sr MFG) * °F(”IF F0) + k-1MSB kIIPJMSF
an
a-fl - c - -
dt PXB(” XB ”xso) + ”xycnrs ”30) + °x(”IB ”30)
an
c—ZE - c .-
dt pXF(M xr ”XFO) * a XY(MYF ”XFo) + k 1”XB k1[L]”xr
an
-J _ _ _ -' - _
dt ”YB(”YB MYBO) + "XY(”YB ”130) "YB + k [LINN

55

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56

any
dt ' ' PYF(”YF'”XF0) + ”XY(”¥F‘”XF0) + k-1MYB ' k1[L]MYF

where H and ”F0 are the equilibrium magnetisations of the bound and

BO

the free forms of the ligand respectively, ”X80 and MXFO are the

equilibrium magnetisations of the bound and free forms of the protein.
The subscripts 18, IF, SB, 51", X8, XF, Y8 and YF refer to the bound
and free forms of the I and S spins on the ligand and the X and Y
spins on the protein. The various p’s are the spin-lattice relaxation
rates of the respective subscripted protons and are comprised of the

following rates: -

”In ' RIB + ”B + ”XY pXB ' RXB + ”KY * 20X
pIF ' RIF + ”F pXF ' RXF * ”XY
p88 ' R33 + ”B + ”xy pYB ' RYE * ”xv
93F ' RSF + ”F pYF ' RYF + ”XY

where the R’s are spin-lattice relaxation rates for the respective
subscripted protons and the 0’s are the respective cross-relaxation
'rates.

The solution of the eight differential equations with
different sets of starting conditions will yield values for the
magnetisation and can help one understand the buildup and decay of the
TRNOE’s.

The IMSL routine DVERK was used to iteratively obtain

solutions for ”13' ”88’ etc.

The values for the various relaxation rates, binding constants
etc. were chosen based on the following rationale:

k1 : rate of association of the complex - obtained from previous

work on the Oxytocin-Neurophysin complex [28].

57

k 1 : rate of dissociation of the complex - obtained similarly as

-1
RIB - RSB - RIF - RSF - 2.0 sec

This value was obtained based on values for spin-lattice relaxation

times for a and B protons of peptides obtained from the literature

[29] and an estimate using a re value of 10-103ec for a CH2 fragment.

_1
RXB - RXF - 2.0 sec

This value was used based on analogous values in the literature [30,

31] and can be considered the upper limit.

01“ - 0.5 sec -1: Cross-relaxation between the I and S protons in the
free ligand is negligible since wrc z 1 and therefore the NOE is
almost equal to zero. Hence a small value has been assigned for 01,.

-1
GB - 25.0 sec : The correlation time for the Oxytocin-Neurophysin

complex has been estimated previously to be approximately 10 nanosec.

Based on this and using equation 4.13, for an internuclear separation

-1
of 2.12A OB can be calculated to be 25.0 sec

_1
0X - 25.0 sec : Cross-relaxation between the protons of the bound

ligand and the bound protein has been known to occur and the rate has
been assumed to be comparable to the cross-relaxation between I and S

on the bound ligand. Hence this value.
,1
0XY - 30.0 sec : Cross-relaxation between X protons on the protein

and Y protons, acting as sinks for the magnetisation. This rate is

probably slightly higher than 0X since the X-Y distance on the average

will be shorter than the X-I and the X-S distances.

58
-1
RYB - RYF - 10 sec : We assume that the Y sites experience fast
internal motions (eg. methyl groups) allowing them to be efficient

relaxers. This rate was calculated by maximising fc in the expression

for p1. Using this value for r cand an internuclear distance of 1.72A

(protons in a CH2 group), the value obtained for the rate ranged

-1 -1
between 4 sec and 5 sec . In a protein, however, there are more
dipole-dipole interactions (eg. in a methyl group) that contribute to

the spin-lattice relaxation rate of a particular spin and therefore a

value of 10 sec.1 was chosen for the simulations.

Using the above-mentioned values in the differential
equations, different sets of solutions were obtained by varying each
parameter to suit relevant situations. Table 4.1 gives the sets of
starting conditions used.

The buildup of IB, IF, and IB+IF (i.e. Iav) was studied when

the S resonance was inverted selectively. Selective inversion
corresponds to a particular row of a 2DNOE experiment where at the end
of the evolution period, I and. S transverse magnetisation are out of
phase and are transferred into +2 and -Z magnetisation. For purposes
of this study, the I and S resonances are assumed to be in fast
exchange with respect to the chemical shift scale. That is to say that
individual resonances corresponding to IB, IF, SB, and SF cannot be
observed. Instead, one is able to observe only the average signals

lavand Sav' The differential equations are then solved for the

inversion of S .
. av

Figures 4.3 through 4.8 indicate the results of such

simulations .

59

148L314.1

LIST OF STARTING CONDITIONS USED IN THE SIMULATIONS

Peptide/ Off rate ax aXY Y sites Figure
protein
100:1 100 0 0 25.0 1 4.2A
100:1 100 25 0 25.0 1 4.28
100:1 100 25.0 25.0 10 4.20
100:1 100 100.0 100.0 90 4.20
100:1 5 0.0 25.0 1 4.3A
100:1 5 25.0 25.0 1 4.38
100:1 5 25.0 25.0 10 4.30
100:1 5 100.0 100.0 90 4.30
10:1 100 0 0 25.0 1 4.4A
10:1 100 25 0 25.0 1 4.48
10:1 100 25 0 25.0 10 4.40
10:1 100 100 0 100.0 90 4.40
10:1 5 0 0 25.0 1 4.5A
10:1 5 25.0 25.0 1 4.58
10:1 5 25.0 25.0 10 4.50
10:1 5 100.0 100.0 90 4.5D
2:1 100 0 0 25.0 1 4.6A
2:1 100 25 0 25.0 1 4.68
2:1 100 25 0 25.0 10 4.60
2:1 100 100.0 100.0 90 4.6D
2:1 5 0.0 25.0 1 4.7A
2:1 5 25.0 25.0 1 4.78
2:1 5 25.0 25.0 10 4.70
2:1 5 100.0 100.0 90 4.7D

All rates are in sec“ .

_1 -1
Other parameters used: Rate of association- 10000M sec .
Equilibrium magnetisations of the bound and free ligand
were normalised to add up to 1.0, i.e.,

 

 

[LPL
HBO - ”X30 - [LPJ/Ltotal - [L] + [LP]
[LL
"F0 ' [LI/Ltotal " [L] + [LP]
nxpo - nxso [PI/[LP] - nxao -%

where [L], [P] and [LP] are the equilibrium concentrations
of the ligand, protein and the complex.

60

It can be seen that the magnitude of the TRNOE’s observed is
influenced by the rate of cross-relaxation between the protons of the
bound ligand and the protein. If this rate is high, or in other words,
if the size of the protein increases, the magnitude of the ~TRNOE’s
observed will decrease correspondingly (Figures 4.3 through 4.8 ’A’
and ’8’).

The other mechanism that reduces the magnitude of the TRNOE’s
is the presence of Y sites on the protein. While one Y site lowers the
maximum in the curves fractionally, the presence of several Y sites
does considerable damage to the TRNOE's observed (see figures 4.3
through 4.8 0 and D). This is because the Y sites belong to groups
that experience fast internal motions and consequently relax faster
than the X'sites. Existence of cross-relaxation between the X and the
Y sites, therefore, will facilitate the rapid dissipation of the
ligand magnetisation through the protein. The greater the number of Y
sites, the faster is the dissipation through the 18 a X8 » Y8 pathway.
This results in the observation of TRNOE’s of lower magnitude.
Moreover, the maximum possible value for the TRNOE’s is attained in a
shorter period of time. Thus, the mixing time used in a 2D- NOESY
experiment is heavily dependent upon:

1. The existence of a considerable rate of cross-relaxation between
the bound ligand protons IB, SB and the proton X8 on the bound
protein.

2. The number of Y sites on the protein.

It is quite possible that in some ligand protein systems,
TRNOE’s are just not observable. Such systems are probably examples of
situations where there are a lot of rapidly relaxing Y sites which are
responsible for the reduction of the amount of NOE transferred from

the bound to the free ligand.

RATIO OF Pm! TO 930nm : 100:!
I“ (0" am) I No “C“. FAST new:

 

 

m (SIC)
FIGURE 4.3

RATIO OF PIP'I'IDI TO PROTEIN : 100:1
K4 (OF? RAT!) " 5 SIC". COIPMLI TO arm-Lame: MITCH um.

ODD-4; A

/

 

 

 

mm (SIC)
FIGURE 4.4

EFFECT OF INVERSION OF THE S SPIN ON THE I HAGNETISATION.
STARTING CONDITIONS FOR A, B, C AND D ARE GIVEN IN TABLE 4.1.

62

mm or 9mm: 1'0 pm : um
gamut!) - :oo sac-'Jmncmm

 

 

 

 

undo 63 36 1a 25
IHGURE4t5

um O? m: 1'0 rm : 10:1
L, (on It?!) - 6 SIC", OOIPM ‘I'O arm-um M110" RATIO.

9
8
L,

  
  

mum:
(Ills-Uflllto-lv)

a a

‘n‘ ‘E

 

:J

I. 1.:
an (ac)
new 4.5

030 0.5

EFTECT’OF INVERSION OF THE S SPIN ON THE I HAGNETISATION.
STARTING CONDITIONS FOR A, B, C AND D ARE GIVEN IN TABLE 4.1.

63

“110 0' 9mm: 1'0 new : 8:!
L. (0" RAT!) - 100 W. PAST m

fllllsdlflflbl
(loo-luhflro'lw)

 

 

r
0.0 0.5 1.0 L! 2.0
fillalu)

lflGURllt7

IANOO’PIPTDITOPW:2:1
L. (0" RATE) ' O SIO". comm TO amt-um“ M1108 urn.

 

 

0.504
A GAO-4
." .
O
:5...
+ +
l . w
i! I
mm
c
mm h
05 d3 15 as no
INCURE‘tB

EFFECT OF INVERSION OF THE S SPIN ON THE I HAGNETISATION.
STARTING CONDITIONS FOR A, B, C AND D ARE GIVEN IN TABLE 4.1.

64

Figures 4.3, 4.5, 4.7 indicate the evolution of the TRNOE’s
for ratios of 100:1, 10:1 and 2:1, of the peptide to protein when the
exchange is fast on the chemical exchange scale. In all the three
cases, the maximum is displaced toward short mixing times as the
number of Y sites is increased. However, this effect is the least
pronounced in the case of the 100:1 ratio. It may be concluded that in
cases where the presence of a large number of Y sites is suspected, it
may be better to work with larger amounts of peptide. Fortunately,
this is easier to do than to procure large amounts of protein. Even
though the TRNOE's are lower in magnitude in the 100:1 case, they are
nevertheless observable.

In the case where the exchange is comparable to the T1

relaxation rates (figures 4.4, 4.6 and 4.8), the trends are similar to
the the fast exchange situation. However, the damping of the TRNOE’s
at lower ligand: protein ratios is quite severe going from situation A
to D. In addition, the shift in the maximum towards shorter times is
more drastic than in the fast exchange cases. It seems evident
therefore, that working with larger ligand: protein ratios is even more
important when chemical exchange is slower. Since exchange
intermediate on the spin-lattice relaxation scale is likely to be
encountered for more selectively bound ligands, this case is quite
important for biological systems. As has been pointed out earlier
[26], there is no hope of observing TRNOE’s when the exchange rates

are significantly smaller than the Tl’s of the molecules involved.

One other aspect of all the curves is worth noting. They all
consist of a biphasic rise and fall pattern. This is almost invisible
for the lOO-fold peptide excess and fast exchange (Fig. 4.3) but

becomes more and more pronounced for slower exchange and smaller

65

peptide ratios (Figs. 4.6, 4.8). Under these circumstances, the TRNOE

buildup for I and IF become separated in time through the different

B

rates between the SB -* IB -9 X8 4 Y8 and the S 84 S 8-. I pathways.

For large ligands such as Oxytocin, it is unlikely that all
ligand protons will experience direct cross-relaxation to protein
protons. For those that do, the intensity of cross-peaks toward other
ligand protons will be reduced relative to those that are not in
contact with the protein. Indiscriminate interpretation of cross-peak
intensities into distances could lead to substantial errors. However,
the presence ‘of ligand protein cross-peaks allows one to correct
calculated distances for this effect.

To summarise, the simulations performed indicate that the use
of TRNOE’s in determining conformations of bound ligands is not
without drawbacks. However, most of the handicaps due to cross-
relaxation bemeen the bound ligand and the protein may be overcome by
working in the appropriate concentration ratios or in- pH ranges where
the exchange rate is favorable for the observation of TRNOE’s.
Previous studies along similar lines have not taken into account the

effect of ex and a xyon the TRNOE [26,32]. Hence, the predictions

regarding TRNOE’s have tended to be more optimistic than what we have
seen in our calculations as well as in our experiments [33]. In cases

where ex is small, the TRNOE method is, of course, relatively easy to

use. In some cases, the presence of significant cross-relaxation
between the bound ligand and the protein can actually provide
information about the binding between the ligand and the protein,
instead of leading to the conformation of the bound ligand. These
calculations were performed to gain an insight into the mechanism of

O

TRNOE’s and factors influencing their magnitude and evolution.

A NEW TECHNIWE FOR SOLVENT ”PRESSION

This chapter describes a new technique developed for the
suppression of solvent signals in an NHR spectrum. The experiments in

[1,0 were performed with a 90:102H 05D 0 ratio, thezD 0 providing the

lock signal. Due to the limited dynamic range available, the huge HDO
peak has to be suppressed in order to observe the signals of interest.

There are several methods in use today for suppression of the
solvent signal [34-36]. The most comon method is by presaturation of
the solvent resonance before the accumulation of the free induction
decay. Saturation of the solvent signal during the acquisition time
leads to Bloch-Siegert shifts [37] and hence is usually avoided. Since
the HBO z-magnetisation recovers during the acquisition period, it
must be irradiated before application of each detection pulse.

The intensity and length of the radiofrequency pulse necessary
for saturation of the solvent signal depend upon the width of the
solvent line. More power is required for a solvent line with shorter

T1 and T2; this tends to also saturate partially the resonances that

are close to the water line.
Considerable improvement upon this method has been made in our

laboratory by using presaturation coherent with the RF observation

4 5
pulse. Single scan suppression of 10 to 10 has been achieved.
Since a long presaturation pulse is in fact equivalent to a

continuous wave irradiation, the phenomenon is-well described by the

steady state solution of the Bloch equations [38]:
66

67

2 2
MOII + T260140) ]

 

 

 

Hz " 2 2 2 2
2
M018 1 T2021 -w)
U " 2 2 2 2
2
M0181 T2
v -

T: (“Hafiz + l + T112128:

where Hz, u and v are the z, x and y magnetisations in the rotating
frame. 1 is the gyromagnetic ratio of the nucleus in question, T1 and
T2 the relaxation times,18 the rotating field applied along the x
axis, "o the equilibrium magnetisation and (mi-w) is the difference in

the radiofrequency and the resonance frequency. Since the irradiation

is applied at the resonance frequency of the water line, (wi- w) is

equal to zero. The Bloch equations can be rewritten as

 

 

 

u - 0
2
140181 T2 M
V " 2 2 z
and
”0 M0
M2 - 2 2 z
1 1“ T1127 31 1311373113

If radiofrequency power of about 24 dB is used,

_1
500 sec

H

781

l
1000

 

o: l“

Thus, presaturation without perturbing more than a -_I-_50Hz region

might, at best give a suppression of the water signal by a factor of

68

 

E—JJJ'LJ'WI‘J—~“Jrlmfljw‘ht‘i‘a; .7, h .5 129 SC A N 5

n {L I la!
——‘““ L” ”LN \— 16 sows

 

g_,__,¢uJ

 

1...! ,"11 , R‘.‘,_,_-____,1 W! W. at! h A I.

 

11’.—

" l ‘ ’ l
'0 4 "' _# no
«I..--

 

L l
o. . c. s an 3.0 2.0 W

FIG 5.1. A: NORMAL PRESATURATION, B, C, D, E: PHASE-00m
IRRADIATION. THE SOLVENT SIGNAL IS AT 4.765PPH.

69

1000 (Figure 5.1a). This suppression is still not adequate when
dealing with millimolar solutions of peptides, proteins, etc.

One way to improve the suppression is to introduce a definite
phase to the irradiating pulse. The argument then, is that if the
phase of the detection pulse is the same as that of the irradiating
pulse, the detection pulse will then flip the residual x-y
magnetisation at the end of the presaturation pulse into the i. Z
directions. This minimises the solvent magnetisation in the x-y plane

during detection and increases the single scan suppression factor to

about 10‘ to 105 (Figure 5.lb).

Furthermore, phase-cycling of the presaturation pulse through
the X, -X, Y, -Y phases averages out phase imperfections and results.
in further reduction of the solvent signal by another factor of 10-100
(Figures 5.1c, d and e). In addition, application of a spin-echo
sequence instead of the acquisition pulse is effective in removing the
broad components of the solvent line (these broad components are

caused by 81 inhomogeneities) resulting in further reduction of the

solvent signal.

However, it is not easy to determine the phase of the solvent
magnetisation after irradiation 'for a time 1. It has been observed
that the phase of this magnetisation is not totally coherent with the
irradiating field. This can be explained by noting that presence of
phase glitches in the radiofrequency pulse can cause part of the water
magnetisation to spin-lock. Thus, when the acquisition pulse is
applied, it may be necessary to apply it with a phase displaced by an
angle 0 from the phase of the decoupler pulse. This angle 0 is
determined by the length of irradiation, the irradiating power used,

rf characteristics of the spectrometer etc. The angle 0 has been

 

 

 

 

 

 

 

1 L1 L 1 J Li L L 14

5.5 ‘r.5 3.5 2.5 1.5 .5
P PM
FIGURE 5.2. DIFFERENCE IN PHASE BETWEEN DECOUPLER AND ACQUISITION
PULSE FOR A: 0°, B: 90°, c: 180', 1): 270°. THE SOLVENT SIGNAL IS AT
4.765PPH.

71

determined empirically for the 360 NH: spectrometer used in our
experiments to be about 60'. In modern spectrometers where phases of
pulses can be varied in non-90' steps, a more precise measurement of 0
is possible. Figures 5.2a, b, c and d show the single scan spectra of

a sample of urine in 908 H20 with the acquisition pulse displaced 0',

90', 180' and 270' from the irradiating pulse.

Thus the phase-coherent solvent suppression has been found to
yield very good suppression of the solvent signal.

The basic technique can be applied in 2DNMR experiments also.

The COSY experiment for example, may be modified as follows:-

PHASE-
g COHER av

IMAblArtou

 

....?...-°

(Ace)

A=4m3

Figures 5.3 a and b show the COSY spectrum of Oxytocin with
presaturation and phase-coherent suppression of the water signal. The
water ridge is restricted to 0.05 ppm in 5.3b enabling one to see all
the NH-a proton connectivities close to the water signal.

It is slightly more difficult to apply this technique to ZDNHR
experiments involving longer pulse sequences because the water
magnetisation recovers before the detection pulse is applied. In
addition, any x-y magnetisation present is flipped back into the z-
direction by the penultimate pulse resulting in a huge water signal

with the application of the detection pulse.

72

 

 

 

 

 

 

 

 

 

 

 

 

 

r
O.“ 7.72 5.33 I O. 3.55 2.1. 0.7.

PPM
FIGURE 5.3. COSY SPECTRUM or OXYTOCIN IN 1120 USING A: NORMAL PRBSATURATION
AND B: PHASE-comm IEEADIATION OF THE SOLVENT SIGNAL.

73

One way to get around this has been by phase-coherent
irradiation of the solvent resonance during the mixing period. This
makes matters somewhat better but the suppression is by no means as
good as in the COSY experiment. It has been shown however, to be about
three times as good as simple presaturation [39]. This is due to the
fact that the water resonance has essentially no frequency dependence

in up, so that the w, and «a2 water ridges in the final 20 spectrum are

strongly reduced.
This method of solvent suppression is easy to use and gives
excellent results, particularly in lDNMR and in ZDCOSY experiments.

All the experiments in H20 conducted in this project have used this

method of water suppression. In view of the weak TRNOE’s observed due
to the reasons outlined in chapter 4, this method has proved

indispensable in our 2D NOESY experiments.

THE murmurs.

SAMPLE PREPARATION: Samples of the peptide Oxytocin (MW z 1100) and
the protein Neurophysin (MW as 10,000) were obtained from V.Hruby and
P.Hi11 of the University of Arizona, Tucson, AZ.

10 mM solutions in D20 of the pure Oxytocin (z 8 mg in 0.4m1)
were prepared by first lyophilising solutions from 020 and then adding

0.4ml D20 to the sample in a 5- NMR sample tube. The solutions in H20

were prepared using a 90:10 ratio for HZO:D20. The pH in both these

samples was adjusted to be between 2.0 and 2.5.

The complex was prepared by adding Neurophysin to the solution
of the peptide so that the resulting solution had a 10:1 molar ratio
of the peptide:protein. To obtain this, 7.95 mg of the protein were

added to the Oxytocin sample.

INSTRUMENTATION AND DATA PROCESSING: The 2DNMR experiments were all
performed on a Bruker WM 360 instrument in collaboration with
L.R.Brown at the Michigan Molecular Institute, Midland, MI. One NOESY
experiment on the complex was performed on a Bruker AM 500 at the NMR
facility of the Upjohn Chemical Company in Kalamazoo, MI. Data were
acquired on an Aspect 2000A computer at Midland and an Aspect 3000
computer in Kalamazoo. The data were subsequently transferred to tape
and then to the 11/750 Vax/VMS operating system at the Department of
Chemistry. Software provided by the Department of Physical Chemistry,

University of Croningen, The Netherlands was used to process the data.

74

75

The spectra were examined on a Tektronix 4014 and plotted on an

HP7550a plotter.

m EDERIMEITS: ZDCOSY experiments were performed on the pure peptide

in 020 and in H20 and on the peptide-protein complex in H20.

ZDNOESY experiments were performed on various samples as shown in
Table 6.1. Data matrices were of the size 1024 x 1024 words after the
two Fourier transforms. Experiments were done in the phase sensitive
mode using the Time Proportional Phase Incrementation method. The COSY
was done with 512 experiments while the NOESY was done with 300, 350
or 400 experiments depending on the spectrometer frequency, sample

etc. The experiments of the samples in H20 were done using the phase—

coherent solvent suppression described in Chapter 5. The phase
programs used for the solvent suppression the phase-sensitive COSY and
NOESY experiments, and the listing for the program used in Chapter 4

for the simulations are given in the Appendix.

TABLE 6.1

Details of experiments performed

Sample Temp. Mixing NMR freq. # of exp.
time (ms) (MHZ)
Oxytocin/H20 300K 180 360 300
Oxytocin/Neurophysin/DZO 300K 70 360 300
300K 100 360 300
300K 140 360 300
300K 180 360 300
300K 210 360 300
Oxytocin/Neurophysin/HZO 300K 70 360 300
300K 100 360 300
300K 140 360 300
300K 180 360 300
300K 210 360 300
300K 180 500 400

Neurophysin/H20 300K 180 360 350

THE OWIN-NEUMPHYSIN mm - m3 AND DISWSSION

PREVIGIS WORK:

A lot of interest has been displayed regarding peptide
hormones, especially Oxytocin, since it was the first peptide hormone
whose primary structure was determined [40] and then proven by
synthesis. It contains a 20-membered ring with a disulphide bridge
(residues 1-6) and a tripeptide side-chain (residues 7-9). In the
1960’s, Oxytocin was studied extensively using NMR. There have been
several NMR studies of Oxytocin in deuterated dimethylsulphoxide. With
the use of precursor peptide fragments, decoupling experiments and
deuterated derivatives, all the resonances in the NMR spectrum were

assigned. The first spectrum of Oxytocin in H20 was reported in 1971

but the complete assignment of the amide resonances was done later

using double resonance decoupling experiments in H20 and 020 [41].

Circular dichro--sm and laser Raman spectra of Oxytocin indicated the
possibility of more than one conformation for Oxytocin [42]. Studies

of rotamer populations about the Caz-CB bonds on Oxytocin also

concluded that Oxytocin was a conformationally flexible peptide [43].
Neurophysin is a protein found in the pituitaries and has a
molecular weight of about 10000. Oxytocin forms a 1:1 complex with
Neurophysin which dimerises at concentrations above 2mg/ml. Some
studies have been conducted on the Oxytocin-Neurophysin complex, using

NMR and other methods. The NMR work done by Balaram, Bothner-By and

76

 

77

Breslow indicates that the tyrosine residue is implicated in the
binding [44].

Recently, single crystal X-Ray data have been available for
Deamino-Oxytocin [45]. This structure has proved to be very useful in

analysing the data from our experiments.

PRESENT WORK:

Consider a conformationally flexible peptide as depicted in
Figure 7.1. The two protons labelled A and B are spatially distant and
so one would not expect to see any NOEs between them. However, on
binding to the protein, the peptide might acquire a conformation that
is definite and which brings A and B into i-ediate proximity. NOEs
between A and 8 will now exist in all likelihood, provided the cross-
relaxation rates are favorable (see 0h. 5). A comparison of the 2D-
NOESY spectrum of the free and bound peptide should throw light on the
conformation of the bound peptide.

2DCOSY experiments were performed on the Oxytocin molecule (Fig
7.2) to establish the nine residues present (see Figure 5.3). The
experiment was repeated for a sample of the Oxytocin:Neurophysin
complex and it was seen that one or two of the resonances of the
peptide shifted minimally while the others exhibited essentially no
shift.

Subsequently, 2DNOESY experiments were performed in D20 and
H20. Figure 7.3 shows the 2DNOESY of the pure Oxytocin inzH 0. There
are no NOE’s present, except for those between :
o 1 2
1) The 8 protons of the CYS , CYS , and TYR residues,

2
2) The aromatic protons of the TYR residue and

78

LIGA MID 'VROTEIN

1L

COMPLEX

 

FIG 7.1. SCHEMATIC DEPICTION 0F LIGAND-PROTEIN
BINDING.

79

 

I l
H-Cys-Tyr-IIe-GIn—Asn—Cys-Pro-Leu-Gly-NH2

123456789

COHOOH CH3—'CH3
|
NH; O CH: o Chi—CH,
l u l H l
CHr—CH— c —NH-—-—CH— c —NH—CH
I 1 2 a I
8 NH
A O O
I ° N 5 ll ‘ l

CHr—CH—NH— C —CH——NH— C -—CH—CH,—-CH,——CONH,

|
| c...

c=o l
l CONH,
CH1— N 7 0 a . O 9
\ H II
I /CH-—- c -—NH-—CH— c -—NH—CH,—coNH,
_ ~ |
CH' CH’ CH,

CH(CH.);

FIGURE 7. 2. mm

80

3) The ASN NHz’s and the CLN NHz’s.

This suggests a non-rigid conformation for the pure peptide,
confirming previous studies on Oxytocin.

Previous lDNMR studies on the Oxytocin:Neurophysin complex have
shown the presence of NOE’s between the tyrosine residue and the
protein. Few other NOE ’s were observed in these studies.

The 2DNOESY spectra (figures 7.4, 7.5, 7.6) exhibit several NOE

cross-peaks. The experiment performed in H20 on the 500 MHz

spectrometer shows the maximum detail and will be analysed below.
We will digress briefly to consider the kind of information
available from cross-peaks. As seen in Chapter 4 (Equation 4.11), the

cross-relaxation aij between protons i and j in the bound peptide is
inversely proportional to the sixth power of the distance between i

and j. Using an estimated value of 25 sec'1 (see Chapter 4) for a,

one obtains a value of 2.12A for rij'

The conditions for observation of TRNOE’s between the the
protons of the bound peptide can be summarised as follows:

1) The exchange between free and bound ligand should be much faster
than the spin-lattice (R?) and the cross-relaxation (0?) rates of the
free form.

. F
1.8. k_1 >> (K? + ai)°

At a pH of 2.5, k_ z 100 sec-1, of < 0.01 and R: < 5 sec-1. The above

1
condition is easily satisfied.

2) The magnetisation exchange in the bound form should be greater than
that in the free form in order for the NOE's to reflect the bound

conformation. If f is the fraction of the free form,

81

 

  
 

9
0

2‘ - .; con-0.- Vivflv -
'o‘ ' 7

.o. (.2

' e
9"- e
O

08
1
-o‘v"o 'o'.

o—‘fiof.-. C--'.-

I..‘.I
a
O

H“

 

 

 

:" ' . :
i
Pd '_ .' g
o : 2 ’
: I q’ ' '
' .1' - . "' l
‘ . a .
a“ .g . l
' : '~' . '- !
l ‘ ° . ' :
° . I '- i
' I
. 2 , l .
:4 o . a
. I
A '1 I
Jo c o To 0'» n u so a o 4 o 00

‘ rm

FIGURE 7.3. 2D-NOESY SPECTRUM OF FREE OXYTOCIN IN 11,0. NO GROSS-PEAKS

ARISIEXCEPTINTHBTYROSINBRESIDUEANDTHBBPROTONSOFTHEGYS
RESIDUES.

82

 

 

 

 

 

4794
PPM

.33

6

7.72

9.10

 

 

 

 

55.0

.4. zn-NOESY SPECTRUM or A 10:1 onTocIN-NEUEGPNYSIN NIETUEE IN
mix). A EEG GROSS-PEAES AEE SEEN.

7
60

neon
n,o (3

83

 

 

 

 

 

 

 

 

Il'nlull. ‘
.......l... 5.
m 2.
O b fl
. a II .I'. In. a. k I
o s
- . . . .2.
I o 0 d. .I.‘ I u .‘ 7
inflow.

. I
_ 7

I - - - - 1'

I. O.
G -o .

8 0 0 U
. .T...

L _

_

.- a- -. q- . ._- q... .. ..1. J ..
Mao a on. no.“ 56. an n am we n $5
21;

:1 OXYTOCIN-NEUROPHYSIN MIXTURE IN

E30 (360 KHz). ONLY THE Ell-REGION IS 8m.

FIGURE 7.5 ZD-NOESY SPECTRUH OF A 10

84

 

 

 

 

 

 

 

 

 

 

O
3;-
O O C ‘ '
o 0
o
q
o I. . '
on: 20‘ o 0 I
N . i .
. o 8 D
a u ' I z
s ' ' °
6'! O .
I -
..| I 3 .
‘ ‘5 "25‘. . o o
q O k r O ,‘ 'bl.e .. . . a 0' I
Z: 3 .
D- 0‘ -- a" ° . . r I
a. '4 . o '8
.5 n . [ i
q ' P ”I. . F
.3 - ‘b
a ,_. 1
“f- 0‘ "lb ‘ i
u " ' '
gr. : l e
2 .° ‘3 -' - 1| 9-
_ .. 000
s - " i
0‘ .. I
h __
_. . o 3
271-: -' 2:2: ° '
":1; ..: .' 0 d
g “ gt...
"1 __ 9.;- open.
0
A ":_ u " -_
I T 1 T j T j T 1 I r T T 1—
908 7.58 5 28 4 88 3 48 2.0. 0 38

FIGURE 7. 6. ZD-ROESY SPECTRUM OF A 10:]. OXYTOCIM-NEUROPHYSIN MIXTURE IN
E30 (500 MHz). THIS SPECTRUM SHOWS THE MOST DETAIL BY FAR AND HAS 3.!

ANALYS- IN DETAIL.

85

B F
(l-f)laijl > flaijl

If f-0.9 (10:1 molar ratio of peptide:protein), 01:} < 0.01 sec 'land

as. . > 1 sec :1 this condition is satisfied. A calculation of the

1J

. . B B -1
relationship between aij and rij shows that for aij - 25 sec , r. . -

1J

B -l . .
2.12A (rc- 10 nanosec). For 01-J- ' 1 SEC . rij - 3.7A. Thus it is

safe to say that trnoe’s will be observed only if the protons
concerned are separated in space by a distance of less than 3.7A,
while those cross-peaks of intensity higher thn 1% would be between
protons no more than 3.3A apart. Clearly, therefore, one cannot expect
very many cross-peaks across residues that are not adjacent to one
another unless they are situated across the ring from each other.

This knowledge of the relationship between the magnitude of a
cross-peaks and the distance between the protons involved will allow
conformational analysis based upon ZDNOE data.

The cross-peaks seen in the 2DNOE spectra can be broadly
classified into four categories:

1. Intra-residue cross-peaks: Cross-peaks between protons of the same
amino acid residue.

2. Inter-residue cross-peaks: Cross-peaks between protons of different
amino acid residues.

3. Protein-peptide cross-peaks: Cross-peaks between the bound peptide
and the protein.

4. Cross-peaks between protons on the protein.

Of these, type 1 cross-peaks serve to supplement information in
the COSY spectrum and to a limited extent, give us information about

the orientation of the side chain in the amino acid residues. Type 2

86

cross-peaks are crucial for obtaining the conformation of the bound
peptide . Cross-peaks of type 3 indicate which peptide residues are
very close to the protein. Cross—peaks of type 4 are relevant for
studying the structure of the protein and will not be considered here.
In addition, cross-peaks of type 4 are very weak as compared to other
peaks and it will be necessary to use pure protein in larger
concentrations (2-3mM) and a 500 MHz spectrometer to study its
solution structure. Eventually, a combination of cross-peaks of type 3
and 4 will help one dete mine the structure of the binding site.

A closer look at Figure 7.6 indicates the kind of cross-peaks
present. These are summarised in Tables 7.1a and b (an exhaustive
list of cross-peaks observed and their intensities is given in the

Appendix). Most of the inter-residue cross-peaks present (Table 7.1b)

are from the ith residue to the (i+l)th residue, i.e. , they are short-
range cross-peaks. The only type of long-range inter-residue cross—
peaks is from the TYR residue to the ASN residue. Since this is a
peak that occurs across the ring, it may prove crucial in determining
the conformation of the bound Oxytocin.

The following calculation was made to obtain an estimate of

inter-proton distances based upon NOE intensities. The distance

between the 8 protons on the CYS1 residue is about 1.8A and the NOE

seen is about 40%. Using the fact that NOE’s are inversely
proportional to the sixth power of the. distance between the protons in
question, one can calculate expected NOE intensities for different
inter-proton distances and this is tabulated in Table 7.2. This
calculation is based upon the assumption that the correlation times
for all the protons are the same. Although this assumption may not be

strictly true, the table is useful to obtain an approximate

 

87

TABLE 7.1A

INTRA-RESIDUE CROSS-PEAKS

TYPE RESIDUE TYPE RESIDUE TYPE RESIDUE
NH-a ILE a-fl CYSl E-p CYSl
NH - a GLN ILE TYR
LEU GLN CYS6
GLY PRO PRO
CYS6 LEU p - 7 ILE

NH - p TYR CYS6 GLN
ILE a - 1 ILE PRO
GLN GLN p - 6 TYR
ASN PRO PRO
CYS6 LEU a - e TYR
LEU

NH - 1 GLN 5,e - NH TYR 6 - e TYR

TABLE 7. 13

INTER-RESIDUE CROSS-PEAKS

TYPE RESIDUES TYPE RESIDUES

NH ~ a TYR - CYSl NH - NH TYR - ILE

GLN - ASN ILE - GLN

LEU - PRO ASN - GLN

GLY - LEU NH - 6 ILE - TYR

NH - B TYR - CYSl 0YS6 - PRO

TYR - ASN 6 - a PRO - CYS6

ASN - GLN TYR - CYSl

LEU - PRO 8 - 8 TYR - ASN

GLY - LEU 8 - 6 ILE - TYR

ILE - TYR 6 - e ILE - TYR

GLN - ILE 1 — 8 GLN - ASN

NH - 1 GLN - ILE 1 - a ILE - GLN
ASN - GLN

LEU - PRO

88

correspondence between inter-proton distances and NOE intensities in
the spectra.

A model of the Deamino-Oxytocin molecule was constructed based
on. the X-Ray structure. Examination of this model reveals that the

strongest cross-peak in the 2DNOE spectrum should be that between the

e
TYR-NH proton and the CYS -a proton since the inter-proton distance in

the X-Ray structure is only l.lA. However, such a cross-peak does not

exist. Probably, in the bound form of the Oxytocin molecule, the CYS6
residue is pulled away from the TYR-NH.

Similarly, the model based on the X—Ray structure indicates
that the ASN-8 is z 4.8A away from the TYR-NH. This means that one
should not be able to observe the corresponding cross-peak in the
spectrum. However, a cross-peak is indeed observed between ASN-8 and
TYR-NH where the cross-peak is about 1.4% of the intensity of the
diagonal peak. Table 7 .3 summarises the various contradictions between
the X-Ray and the 2DNOE data.

When a model is constructed with the dihedral angles of our
proposed model, as given in Table 7.4, it is seen that the 2DNOE data

are consistent with those predicted by this model. Furthermore, the

CYSG-a - TYR-NH are about-5A apart while the ASN-8 moves closer to the
TYR protons, explaining the absence of cross-peaks in the former case
and the presence in the latter. This model is also consistent with the
fact that all the cross-peaks seen but not compatible with the X-Ray

structure can be expected based on the inter-proton distances. The

1 2 3
dihedral angles of the CYS , TYR , ILE and CYS‘ residues are

drastically different from those in the X-Ray structure. In addition,

 

89

TABLE 7.2

Estimations of inter-proton distances
based on a knowledge of the distance

between the two 8 protons of the CYS‘
residue and the magnitude of the NOE
between them.

a

Inter-proton 1/r 0'5, 8 N O E

distance (A) expected Intensity
1.72 3.86E46 40.0
2.0 1.56E46 16.0
2.5 4.10E45 4.2
3.0 1.37E45 1.42
3.5 5.44E44 0.56
4.0 2.44E44 0.25

TEBLE 7.3

Contradictions between predictions of the existence of NOE.
cross-peaks based upon the X-Ray structure and the actual NOE
spectrum.

Protons involved X-Ray Cross-peak Cross-peak
distance A expected? observed?
0
TYR NH - CYS a 1.1 YES NO
TYR NH - ASN B 3.8 NO YES
ASN 8 - GLN NH , >5.0 NO YES
0
ASN B - CYS NH ,4.0-4.5 NO YES
ILE NH - TYR NH 4.7 NO YES
ILE NH - GLN NH 4 7 NO NO
TYR NH - TYR 82 3 7 Very Weak Strong

6
CYS a - CYS a 1.5 YES NO

 

90

1 e
the tail, consisting of PRO , LEU and CLY’, a1 undergoes some

1 a
change that gives rise to a strong PRO -a - LEU -NH cross-peak.

Thus it is possible to assign a definite conformation for the
bound Oxytocin based upon the inter-residue cross-peaks and the

single-crystal X-Ray data .

The information obtained in the D30 experiments serves to
substantiate information from the NOESY experiments in H20. Since the

molecule is a relatively small peptide, the NH-a, NH-B and NH-NH
cross-peaks offer the maximum information on inter-residue spatial

relationships. However, the presence of a very strong cross-peak
o 1

between the CYS a and the PRO 8 is to be noted in the 020 spectrum.

This strong cross-peak is possible only if the configuration of the

1
PRO residue is trans. This is also borne out by the X-Ray structure
and by previous structural studies on Oxytocin. In addition, since it
is possible to look at really low contours in the ZDNMR spectrum

(unlike the spectra of Oxytocin-Neurophysin complex in H20 where the

solvent peak is so intense that peaks of lower intensity can just not
be seen very easily without interference from the solvent ridges), one
can see cross-peaks between the peptide residues and the protein.

A comparison of the cross-peak intensities done using the 360
MHz spectrometer and the one using the 500 MHz spectrometer indicates
that the cross-peaks are more intense in the latter case. An
inspection of the equations in chapter 4 tells us that in the case of

We << 1 or m c>> 1, the NOE intensities are independent of o. In

other words, the intensities of the NOE cross-peaks observed should be

91

TABLE 7.4

COMPARISON OF THE DIHEDRAL ANGLES IN THE X-RAY STRUCTURE
OF DEAMINO-OXYTOCIN AND THE PROPOSED CONFORMATION OF
BOUND OXYTOCIN BASED ON NOE DATA

4 5
X ~RAY STRUCTURE

RESIDUE couromnou
BASED on 201101:
1 0 i 4»
CYS! - +101 - +165
TYR2 -126 +164 -130 -120
ILE: +125 -65 +10 +80
GLN‘ +29 +56 +20 +60
ASNB -158 +66 -160 +60
0Y3“ -123 +96 +120 +120
P1201 -73 -12 -73 -12
LED -77 -33 +165 +30
611°

the same in both the 360 and 500MHz experiments. This is not so, and
can be explained as being due to the fact that the correlation time

for the bound Oxytocin is still not large enough that wrc>> l,

contrary to predictions for NOE '5 based on correlation times estimated
for the Oxytocin:Neurophysin dimer. A few sample intensities of NOE
cross-peaks for the various experiments are given in Table 7 .5.

TABLE 7.5

CROSS-PEAK INTENSITIES (8) FOR 180 MSEC NOESY EXPERIMENTS

CROSS- D20/ 360 MHz H20 '/ 360 MHz H20 / 500 MHz
PEAK
TYR 6-6 4.1 9.5 14.6
CYSla-fl 2.3 - 3.5
TYR-NH - CYSl a - 5.1 8.2
ASN NH - CLNa - 1.8 3.1
GLN NH - GLN 8 - 1.8 4.1
CYSl 8 - 8 21.0 - 40.0
GYS6a -PRO& 1.7 - 1.7

92

The other type of cross-peaks relevant to the configuration of
the bound Oxytocin is the type 3 cross-peak, i.e., cross-peaks between
Oxytocin and the protein. These tell us about the mode of attachment
of the peptide to the protein.

An examination of the spectra and the tabulated data reveals
cross-peaks between the TYR residue, the GLN residue, the ILE and the
ASN residues and the protein. This information, in addition to the
suggested conformation for the bound Oxytocin shows that the peptide-
protein NOE’s are all on one side of the Oxytocin molecule. It may be
speculated that the mode of approach of the peptide towards the
protein is from the side containing the abovementioned residues.
However, this premise needs further verification by means of some more
experimentation before one can say anything more definite.

Thus the TRNOE experiments have proved invaluable in the
determination of the conformation of the bound peptide. The method is
not without its limitations, as described in Chapter 4, but under the
right combination of experimental conditions, is powerful in the study

of ligand-protein interactions .

FUTURE FORE

The results obtained so far suggest several promising areas of
research for the Oxytocin-Neurophysin system. First of all, a
rigorous, unique conformation for the bound Oxytocin may be obtained
using distance geometry algorithms. Once this is done, the protein can
be studied and its conformation determined as best as possible using
currently available 2DNMR methods, or devising new experiments, since
the protein is really at the upper limit of what is possible by 2DNMR.
In addition, the results could lead to a more definite knowledge of
the nature of the binding site.

Next, the complex could be studied at the slow exchange limit
(pH z 6.5) using the same experiments as described in Chapters 6 and
7. It is suggested that the nature of the system, the magnitude of the
NOE’s expected etc. , warrant the use of a high field instrument for
the experiments. The study of the protein especially, is possible only
with the use of a spectrometer of atleast 500MHz operating frequency.
It is also to necessary to design a good solvent suppression scheme
that can be used in the 2DNOE experiments that can be used with even
greater success than has been achieved so far.

The rates of cross-relaxation could be determined by a more
detailed analysis of the NOESY experiments done with different mixing
times and comparing cross-peak intensities as a function of the mixing
times. This could also give us a measure of the strength of the
binding and a clearer understanding of the reason for the weak nature

of the TRNOE’s observed.

93

94

Finally, these experiments can be extended to the analogues of
Oxytocin like Vasopressin, for example, another peptide hormone of
pharmaceutical interest.

The theory of 2DNMR using the product-operator formalism
presents some intriguing possibilities, some of which are already
under investigation at this time. A basic understanding of the theory
will probably lead to the design of novel pulse sequences applicable

to this system in particular.

APPENDIX

 

95

APPENDIX

PROGRAM USED FOR SIMULATION OF CHEMICAL EXCHANGE AND TRANSFER NOEs.

0010

0011
0100
0200

PROGRAM DIFF

INTEGER*4 N,IND,NW,IER,K

REAL*B Y(8),0(24),W(8,12),X,TOL,XEND
REAL*B EMBO,EMFO,EMXBO,EMXFO
EXTERNAL FCNl

EMBO-0.09
EMFO-0.91
EMXBO-EMBO
EMXFO-0.01

NWh8
N-8
x-0.0

Y(1)-EMBO

Y(2)-EMFO

Y(3)--EMBO

Y(4)--EMFO

Y(5)-EMXBO

Y(6)-EMXFO

Y(7)-EMX80

Y(8)-EMXFO
TOL-.0001

IND-l .

WRITE(6,200)X,Y(1),Y(2),Y(3),Y(4),Y(5),Y(6),Y(7),Y(8)

DO 10 K-l,200

XEND-FLOAT(K)*0.01

CALL DVERK(N,FCN1,X,Y,XEND,TOL,IND,C,NW5W,IER)

IF (IND.LT.0.0R.IER.GT.0) GO TO 11

WRITE(6.200)X.Y(1) .Y(2) .Y(3) .Y(4) .Y(5) .Y(6) .Y(7) .Y(8)

CONTINUE

STOP

CONTINUE

FORMAT(2X,I4)
FORMAT(2X,F7.4,8(1X,F7.4))
STOP

END

SUBROUTINE FCN1(N,X,Y,YPRIME)
INTEGER*4 N
REAL*8 SIGMAX,SIGMAB,SIGMAF,SIGMXY,EMXBO,EMBO,EMFO,EMXFO,PROT

RHOl,RHOZ,RHO3,RHO4,RHO5,RHO6,RHO7,RHOB,R1,R2,R3,ELIGND

REAL*B Y(N),YPRIME(N),X
REAL*B Kl,KINVl

Rl-2.0
R2-2.0
R3-10.0

 

96

SIGMAF-0.2
SIGMAB-25.0
SIGMAX-0.0
SIGMXY-30.0

EMBO-0.09
EMFO-0.91
EMXBO-EMBO
EMXFO-0.01

Kl-100000
KINVl-IOO

PROT-0.0001
ELIGND-0.0091

RHOI- R1+SIGMAB+SIGMAX
RHOZ-R1+SIGMAF
RHO3-R1+SIGMAB+SIGMAX
RHO4-RHOZ
RHOS-R2+SIGMXY+2*SIGMAX
RHO6-R2+SIGMXY
RHO7-R3+SIGMXY
RHOB-RHO7

0 YPRIME(l)--RH01*(Y(1) -EMBO)+SIGMAB*(Y(3) -EMBO)+SIGMAX*(Y(5) -
EMXB )
* -KINVl*Y(l)+K1*PROT*Y(2)
YPRIME(2)--RH02*(Y(2)-EMFO)+SIGMAF*(Y(4)-EMFO)+XINV1*Y(1)
* -X1*PROT*Y(2)
YPRIME(3)--RHO3*(Y(3) ~EMBO)+SIGMA8*(Y(1) -EMBO)+SIGMAX*(Y(5) -
EMXBO) .
* -KINV1*Y(3)+K1*PROT*Y(4)
YPRIME(4)--RHO4*(Y(4)-EMFO)+SIGMAF*(Y(2)-EMFO)+KINV1*Y(3)
* -KI*PROT*Y(4)
YPRIME(5)--RHO5*(Y(5)-EMXBO)+SIGMXY*(Y(7)-EMXBO)
* +SIGMAX*(Y(1)+Y(3)-2*EMBO)-KINV1*Y(5)+K1*ELIGND*Y(6)
YPRIME(6)--RHO6*(Y(6)-EMXFO)+SIGMXY*(Y(B)-EMXFO)+KINV1*Y(5)
* -K1*ELIGND* Y(6)
YPRIME(7)--RH07*(Y(7)-EMXBO)+SIGMXY*(Y(5)-EMXBO)-KINV1*Y(7)
* +K1*ELIGND*Y(8)
YPRIME(8)--RH08*(Y(8)-EMXFO)+SIGMXY*(Y(6)-EMXFO)+KINV1*Y(7)
* -X1*ELIGND*Y(B)

RETURN
END

97

PHASE PROGRAM FOR THE SOLVENT SUPPRESSION SEQUENCE:

l
2

NOQVmUivau

PHI

ZE

(P3 PH3):D:E

P1 PHI
02

P2 PH2
02
60-2
WK #1
EXIT

- A0 A0 A2

PH2 - A0 A2 A2

PH3

PH4

PH5
PH6

A2 A0 A0
81 B3 83
80 82 82
82 80 80
83 81 81

A2
A0
A2
81
80
82
B3

A1
A1
A3
82
81
B3
82

A1
A3
A1
80
B3
81
80

A3
A3
A1
80
83
81
80

,‘ PHASE-COHERENT SOLVENT IRRADIATION
;(PHASE CYCLE PH3, 4, 5 OR 6)
; SPIN-ECHO PULSE SEQUENCE FOR ACQUISITION
; D2 - 1 MSEC.

A3 A2 A2 A0 A0 A3 A3 Al Al
Al A1 A3 A3 A1 A2 A0 A0 A2
A3 A3 Al Al A3 A0 A2 A2 A0
82
81
83
82

PHASE PROGRAM FOR THE COSY EXPERIMENT (PHASE-SENSITIVE - TPPI METHOD)
H20 USING PHASE-COHERENT IRRADIATION FOR SOLVENT SUPPRESSION.

IN

‘OQVQ‘nkUNH

PHI

PH2 - A0

PH3

PH4 -

PH5

ZE

(P3 PH3):D:E

P1 PHI
D0

P2 PH2
D2

P4 PH4
DZ
GO-Z PH5
NR #1
IF #1
IPHl
IPH3
INil
EXIT

- A0

- 80
0

>

EEEREEE
EEEESER
Efitégtt

£8:

Al
A1
81
Al
A0
R1

EEEBEE:
EBREEEE
EBEEEBE

PHASE-COHERENT IRRADIATION OF SOLVENT
PREPARATION PULSE

INCREMENTAL DELAY

DETECTION PULSE, PART OF THE SPIN-ECHO
SEQUENCE THAT SERVES AS THE ACQUISITION
PULSE.

v. u. h. n. b. u.

 

98

PHASE PROGRAM FOR THE NOESY EXPERIMENT (PHASE-SENSITIVE - TPPI METHOD)
IN H20 USING PHASE-COHERENT IRRADIATION OF THE SOLVENT SIGNAL.

1 2E

2 (P3 PH3):D:E

3 Pl PHl

4 D0

5 P1 PH2

6 (P4 PH4):D:E

7 Pl PH5
8 D2 :

9 P2 PH6 ;

10m
11 60-2 PH7
12 Wk #1
13 IF #1
14 IPHl
15 IPH3
16 IN-l
17 EXIT
PHl - A0 A2
PH2 - (40),. (A2)1°

PH3 81 B3 83 81
PH4 BI 83 B3 81
PH5 A0 A0 A2
PH6 A

I I I l
O
m>>tg

HQH

A2
A2
A

in

A3
R2 R

Bhttg
Etta:
Egttg

A0 A2
A3 A1
PH7 - R0 R2

0

v. v. n. u. h. h.

PHASE-COHERENT IRRADIATION OF SOLVENT
PREPARATION PULSE

INCREMENTAL DELAY

MIXING PULSE

MIXING TIME, SOLVENT IRRADIATED AGAIN
DETECTION PULSE, PART OF THE SPIN-ECHO
SEQUENCE THAT SERVES AS THE ACQUISITION
PULSE.

Al A3 A3 A1 A2 A0 A0 A2
A2 A0 A0 A2 A3 Al Al A3
R2 R0 R0 R2 R3 R1 R1 R3

99

LIST OF GROSS-FEARS AND DU'ENSITIES FOR THE 2DNOESY mm H 520 AT
500 ME: OPERATING FREGIENCY.

 

RESIDUE .DIAGONAL.PEAK’ amass PEAKS ASSIGNNENT INTENSITY
PPM INT PPM INT (PERCENT)
1-CYS a 4.29 6.746E8 8.985 2.365E7 TYR NH 3.5
1
3.473 2.195E7 CYS 6, 3.2
1
3.297 2.36367 CYS 6, 3.5
1
p, 3.464 1.34466 3.292 5.944E7 ch 6, 44.0
1
4.28 1.09667 CYS a 8.2
6.969 4.49766 TYR NH 3.3
1
62 3.292 1.36266 3.471 5.64667 CYS 6, 41.4
1
4.293 1.12167 CYS a 8.2
8.989 6.63066 TYR NH 4.9
TEE a --8LEACHED--
p, 3.164 1.26266 3.009 4.713E7 TYR 6, 37.0
6.672 1.67266 TYR e 1.3
7.937 2.56266 ILE NH 2.0
7.219 1.213E7 TYR 6 9.6
8.990 4.94266 TYR NH 3.9
T2218, 3.009 1.46666 3.1634 4.42267 TYR 6, 3.0
7.219 1.29367 TYR 6 6.6
6.990 7.63766 TYR NH 5.3
7.55 1.67666 1.3
7.939 1.96466 ILE NH 1.4
TYR 6 7 219 7.511E8 6.659 5.79767 TYR e 7.7
6.99 2.05067 TYR NH 2.7
4.262 5.07666 CYS a 0.7
3.165 2.37467 TYR 6, 3.2
3.007 2.69767 TYR 6, 3.6
2.656 5.34666 ASN 6 0.7
0.666 2.93066 ILE 6 0.4
T1: e 6.659 4.47166 6.990 4.03666 TYR NH 0.9
7.217 6.53467 TYR 6 14.6
6.320 5.42666 PROTEIN? 1.2
4.262 3.56266 l0Y6 a 0.6
3.162 3.45266 TYR 6, 0.6
3.006 4.12766 TYR p, 0.9

100

.RESIDOE DIAGUNAL.PEAI amass PEAKS ASSTGNNENT INTENSITY
.PEN INT’ .PPN INT' (PERCENT)
0.645 2.66466 ILE 6 0.6
7.962 4.54466 ILE NH 1.
TYR.NH 8.990 2.13366 7.937 2.52266 ILE NH 1.2
7.216 1.19467 TYR 6 5.6
1
4.266 1.75367 CYS a 6.2
1
3.269 6.50666 CYS 62 4.0
1
3.466 6.06666 CYS 61 2.9
3.161 6.23766 TYR 61 2.9
2.999 1.15367 TYR 62 5.4
2.646 3.07066 ASN 6 1.4
ILE'a '4.062 3.13466 6.204 1.46367 CYS6/GLN NH 4.7
7.936 1.19367 ILE NH 3.6
1.910 1.61767 ILE 6 5.6
1.214 1.59467 ILE 1,(cn,) 5.1
1.001 9.64066 ILE 12(CH2) 3.1
0.652 1.94567 ILE 1 (0H,) 6.2
6 1.919 3.791E8 6.169 4.66166 GLN NH 1.3
7.935 9.69166 ILE NH 2.6
4.051 1.34467 ILE a 3.5
1.216 6.64766 .ILE 11(CH2) 2.3
0.653 1.848E7 ILE 1 (CH3) 4.9
1.001 5.95266 ILE 12(CH2) 1.6
ILE NH 7.936 1.43366 6.995 2.53466 TYR NH 1.8
6.711 1.66166 PROTEIN? 1.2
6.639 1.65366 PROTEIN? 1.3
6.166 4.66366 GLN NH 3.3
7.212 2.07766 TYR 6 1.5
4.057 1.12767 ILE a 7.9
3.156 2.73166 TYR 61 1.9
1.913 1.37267 ILE 6 9.6
1.219 - 3.06766 ILE 1,(on,) 2.2
0.995 3.06166 ILE 12(0H2) 2.2
0.661 1.26367 ILE 1 (CH3) 6.9
2.999 1.95466 TYR 62 1.4
CLN'a 4.097 4.54366 6.319 1.12267 ASN NH 2.5
6.194 1.63967 GLN NH 3.6
2.399 1.63067 GLN 1 4.0
2.044 3.36567 GLN 6 7.5
0.666 6.34266 ILE 1 (CH3) 1.4
6 2.055 4.612E8 6.329 4.25366 ASN NH 0.9
8.189 1.04067 GLN NH 2.3

 

RBSIDUF

NH

CYS a

#1

I92

DIAGUNAL.PEAK

PRU

2.394

8.190

2.847

8.335

3.228

2.971

INT

4.09838

5.15238

--BLEACHED--

7.14838

2.44838

--BLEACHED--

2.28838

1.79438

101

amass Pills
RR! INT
6.655 3.19336
5.226 2.36736
4.094 1.93437
2.391 3.02537
8.319 2.25536
8.194 6.19836
4.098 1.50037
2.049 2.51337
2.847 3.21336
4.087 2.13837
2.401 6.32136
1.224 2.41236
0.994 2.39336
0.863 1.87137
8.987 3.51236
8.326 1.61437
8.194 7.64336
7.579 1.78636
7.217 3.00836
4.086 1.93336
also to
8.194 2.61437
4.102 7.69036
2.849 1.43637
2.049 5.81336
8.199 7.8536
4.865 3.26036
3.702 9.08036
3.472 3.36436
2.968 9.00137
8.198 9.40736
4.864 2.04136
4.063 2.12836
3.705 4.19036
3.227 7.14537

7

PROTEIN?

GLN a
GLN 1

ASN NH
GLN NH
GLN a
GLN 8
ASN fl

GLN a
GLN 1

ILE 11(CH2)
ILE 12(032)
ILE 1 (CH3)

TYR NH
ASN NH
GLN NH?
ASN NH,

TYR 8
TYR e
GLN NH?
GLN a

ASNB
GLNfl

6
CYS NH

6
CYS a
PROS

1
crs 62
6
CYS 32

6
CYS NH
6

CYS a

PRO 5
6
CYS 51

33

W88

to Q OHk QQWHO “#00

GO QHNO

lx§oiux1 ”wk mainly.

'oxiu'u'w

be
§

FAWN
WUIW§

3 .

U: ‘0
N

kahaho
m UNH

39.

@51me

61th3..

ASSIGNEENT’ INTENSITY

RESIDUE

NH

28010

2.

52:72

NH

DIAGONAL REA!

PP”

8.19

2.286

1.918

4.293

1.605

8.449

.15238

.13238

.62238

.71838

.45438

.74638

.50938

.54838

102

Cl088.236l3
RR! INT
4.869 1.41536
3.726 2.84736
3.224 5.27436
2.973 9.70736
8.449 2.92637
2.283 4.95537
1.974 1.50437
1.878 1.29437
8.449 2.52036
4.441 1.62537
3.718 5.30736
1.919 5.42437
2.28 5.03537
8.435 2.98136
8.189 4.35736
4.44 7.08836
3.717 6.28636
4.862 4.22536
3.228 8.33436
2.953 4.70336
2.283 5.39636
1.913 7.38336
8.444 8.19136
8.354 1.27937
1.607 1.43337
0.884 1.50237
8.449 5.46936
4.305 9.24236
4.438 2.15437
4.297 8.92936
2.283 2.91736
2.027 2.56936
1.921 3.97336
1.671 1.42537

ASSIGIHEIT

6
CYS 0
PRO 6

6
CYS 51

6
CYS 52

LEU NH
PRO 61

PRO 1
PRO 52

LEU NH

PRO a
PRO 6
PRO 1932

PRO 51
LEU NH

6
CYS, GLN NH
PRO a
PRO 6

6
CYS a
6
CYS 51

6

CYS 52
PRO 51
PRO 52: 12

LEU NH
GLY NH

LEU He

LEU NH

PRO 0

PRO 51
PRO 71
PRO 52.1
LEU 61

0°
0 cu»

you

QNG

2 .

13.

HHH O

N LON

N
QNW§V

be

NNNH

‘wiako bx L.o.«ar~

zuioko 561m

616 kkhk

#NQQNQNN

INTENSITY
(REIGENT)

QNVQUIH

 

RESIDUE

Me

NH

1L3 11

DIAGUNIL.REAK

PEN

1.662

0.931

3.924

8.358

1.21

INT

2.99538

2.92039

Ln

.12138

to

.67938

1.0538

‘ 1L3 1 (CH3) 0.6606 2.4169

ILE 1

PRO 11

GLN a falls

2.019

6.89938

Ambiguous cross-peaks:

O
crs/cznxnn

8.19

5.15238

CROSS Ellis

.32! INT'

8.45 6.08736
4.3 2.61436
3.001 3.35436
2.072 1.24537
0.930 9.00736
1.684 1.40437
1.635 1.41937
8.368 1.19037
4.449 1.37636
4.305 1.00037
3.929 6.05836
3.862 9.74736
1.648 2.83136
7.934 1.55736
4.045 7.13336
1.915 4.67136
0.991 2.57437
8.1962 1.71237

.41

.316
.44

.711
.28

.327
.845
.75

.047
.919

under ILE a 1L3 1

MN #90 N

#NHMW

)

ASSIGNMENT' INTENSITY

(PERCENT)
LEU NH 2.0
LEU a 0.9
7 1.1
7 4.2
LEU He 3.0
LEU 8 0.5
0.5
GLY NH 2.3
PRO 0 0.4
LEU a 2.7
GLY a 1.6
GLY a 2.6
LEU 8 0.8
1L3 NH 1.5
1L3 a 6.8.
1L3 8 4.4

(Dispersion signal)

cross-peak)

.34336

.00836
.29036

.39137
.02537

.5537

.56736
.52136
.50237
.72536

GLN NH 0.7
LEU NH 3.4
7 4.4
PRO a 6.2
PRO 34.5
PRO 8 29.0
ASN NH 6.9
ASN 8 1 1
ASN a --

PRO 1,IL3 87 2.9
PRD82,... 0.9

 

104

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