{IMIIHHVWHHHIIHWWW“WWI

   

IVERS IBTYLI

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

3 1293 00910 86

IIILIIIBIIIII

 

 

 

 

This is to certify that the

thesis entitled

Electron Nuclear Double Resonance
Characterization of Plastocyanin

presented by

Matthew Paul Espe

has been accepted towards fulfillment

of the requirements for

Maiden;— degree in Chem i s t ry

g/W
S/z/fio.

07639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

 

 

 

 

 

 

 

F
LIBRARY I
Michigan State

; University J

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.

DATE DUE DATE DUE DATE DUE

___I
___I
+7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r—I

 

 

 

 

 

 

MSU Is An Affirmative Action/Equal Opportunity Institution
cmmnt

 

 

ELECTRON NUCLEAR DOUBLE RESONANCE CHARACTERIZATION OF
PLASTOCYANIN

By

Matthew Paul Espe

A THESIS

Submitted to
Michi an State Universi
in partial fu lment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Chemistry

1990

(945- "70"?/

ABSTRACT
Electron Nuclear Double Resonance Characterization of Plastocyanin
By
Matthew Paul Espe

Electron nuclear double resonance (ENDOR) has been used successfully in
obtaining structural insight into small complexes but its application to biological
macromolecules has been limited. In this work the technique of ENDOR is
developed so as to be useful in obtaining structural information on proteins. The
protein under study, plastocyanin, was isolated from spinach.

By using the crystal structure for poplar plastocyanin the hyperfine coupling
(hfc) constants for the protons near the copper site were determined. These
calculated hfc constants were then compared to the experimental values in order to
assign the ENDOR resonances.

The ENDOR spectrum of spinach plastocyanin consists of seven sets of
resonances, four of which could be assigned. These assignments indicate that the
protons are in a portion of the protein that is structurally very similar between the
two species. The inability to assign the other three resonances indicates that there

are some structural differences near the copper site.

ACKNOWLEDGMENTS

First, I would like to thank Dr. Chris Bender for all his help in maintaining
the spectrometer and teaching me to use it correctly. I would also like to thank all
the members of the lab who have assisted me in this project. Most importantly I
want to acknowledge Dr. G.T. Baboock for all his spiritual and financial support.

iii

TABLE OF CONTENTS

 

 

 

 

 

 

 

 

 

Page
LIST OF TABLES v
LIST OF FIGURES - vi
INTRODUCTION 1
MAGNETIC RESONANCE THEORY 13
COMPUTER APPLICATIONS _ - _ 29
RESULTS - 34
EXPERIMENTAL 34
DISCUSSION _- _ _ _ - 49
FUTURE WORK _ -- 53
APPENDIX A: SOURCE CODE OF TENSOR.FOR 55

 

REFERENCES - -- - - - 62

 

iv

Table 1

Table 2
Table 3
Table 4

Table 5
Table 6

LIST OF TABLES

 

 

 

 

Page
Bond lengths and bond angles from PROTIN and neutron
diffraction for histidine and cysteine 30
Input for TEN SOR 33
Parameters for simulating the EPR spectrum of spinach PCy ........... 38
Pairs of resonances from the ENDOR spectrum of
spinach PCy 39
Spin density distribution used in calculating hfc tensors 43
Protons assigned to the ENDOR spectra and their complete
hfc tensors 47

 

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

LIST OF FIGURES

Energy levels of a Cu(II) ion at constant
magnetic field. The four EPR transitions
are indicated by the arrows

 

(a) A re resentation of the g-tensor axis
system s owing axial symmetry. (b) A similar
representation of the Cu(II hyperfine
coupling tensor and its co-lmearity with

 

the g-tensor axis system

 

Computer generated EPR spectrum for a
Cu( ) ion with parameters similar to PCy

Energy levels of a dogen atom at constant
magnetic field. Bot the EPR and ENDOR
resonances are displayed

 

(a) Observed linesha for an axial hfc
tensor. (b) Observe lineshapc for a
rhombic hfc tensor

 

(a) EPR spectrum of PCy at 10 K. Conditions:
microwave wer, 2.07 mW; 12.5 KHz modulation
am litude, .4 Gpp; microwave frequency,
9.4 543 GHz; swee time, 200 sec.

b)blSir;1ulation of (2) using parameters in

a e

 

ENDOR s ctra of PCy for the positions marked
A, B, and in Figure 6. Conditions:

RF power, 90 W; modulation frequency, 40 KHz;
microwave wer, 20.7 mW; microwave frequency,
9.43556 G ; sweep time, 200 sec

 

ENDOR spectra of P for the positions marked
D and E in Figure 6. nditions: same as in

 

Figure 7

vi

Page

15

19

20

22

37

40

41

INTRODUCTION

Biophysics is a unique field of study in that it incorporates not only the areas
of biology and biochemistry but also many areas of chemistry and physics. One of
the most active areas within this field is the study of structure-function dynamics.
That is, what particular structural characteristics of a biological species, such as a
metalloprotein, correspond with biological functions. Whereas the biologist or
biochemist can determine the composition of the species, such as number and type
of amino acid and metal cofactors, and in some cases the location and function of
these constituents, their techniques generally do not give direct information on the
structure of the species.

With the use of a large variety of spectroscopic techniques though, a
thorough description of biological macromolecules and their active sites can be
obtained. Once the detailed picture of the active site in a protein has been
produced, a study of structure-function relationships can be carried out.
Experiments can be done to determine what structural or electronic changes occur
when the protein undergoes such biological activity as electron transfer, binding to
substrates, or enzymatic activity. Environmental effects on the protein, such as
changes in pH or temperature, can also be studied.

In the study of the metal sites in metalloproteins one area of extensive investigation
is the location and catalytic relevance of nearby protons. These protons are well
studied because of the wealth of physiological information that can be obtained.

Such information includes the presence of hydrogen bonds, whether the system

2

under study is involved in proton pumping, structural changes that occur upon
binding with substrates, and geometric and electronic structure at a metal site.

The work presented in this thesis describes the application of Electron
Nuclear Double Resonance (ENDOR) in the study of protein structure, both
geometric and electronic, at the copper containing metal site in the protein
Plastocyanin (PCy). The work is aimed at providing information on the structural
characteristics of the metal site, in particular on protons near the metal, and on the
distribution of the unpaired electron spin density in PCy. In this case, methods that
have been applied to the study of smaller molecules will be extrapolated to and
tested to see if they are also applicable to the study of metalloproteins.

Plastocyanin from spinach (Spinacia oleracea L.) was chosen for this study
for several reasons. First, PCy is a biologically interesting protein that is available in
high purity and concentration. Also, the high resolution (1.8 A)1 crystal structure
has been solved for the plastocyanin isolated from the closely related species,
poplar. This allows comparison of the crystallographic data with the experimental
magnetic resonance results. Last, the metal atom under study in PCy is copper, the
properties of which make it ideally suited for ENDOR studies.

Plastocyanin is a member of a group of small, 10,000 to 25,000 Dalton, single-
copper-containing proteins known as Type 1 or blue copper proteins (BCP). BCP
were first discovered in 1958 and are found in bacteria where they are commonly
called azurins, and in blue-green algae and higher plants where they are commonly
called plastocyaninsz. In all three groups the function of the protein is to mediate
electron transfer between two other redox active species.3

The crystal structures of a higher plant BCP and two bacterial BCP have
been resolved.1’4’5 The crystal structure in each case showed that the copper atom

is ligated to two nitrogens from histidines, the sulphur atom of cysteine, and the

3

sulphur atom of methionine. The metal site coordination geometry, which is nearly
the same in all three proteins, is best described as a flattened tetrahedron.

The primary optical characteristic of BCP is an absorption maxima near 600
nm with an absorption coefficient of 3000-5000 M' 1cm' 1, which gives the proteins
their characteristic blue color. The EPR spectra of BCP also have several
characteristic features that include axial or slightly rhombic spectra, g. > g1 > 2.00,
and smaller than normal copper hyperfine coupling. The redox potential of BCP
are spread over a wide range, from 184 mv to 390 mv, all of which are higher than
that for tetraaquo Cu(II), which occurs at 153 mv.3

The function of the BCP in bacteria is not well understood except that they
are electron transfer agents.3 In higher plants the role of BCP is to mediate
electron transfer from photosystem 11 (P811) to photosystem I (PSI). P811 and PSI
reside in the thylakoid membrane of the chloroplast whereas PCy, a water soluble
protein, is loosely bound on the luminal side of the membrane. The role of PCy in
photosynthesis is the transfer of electrons between cytochrome f in the cytochrome
b5/ f complex and the redox active chlorophyl complex in the reaction center in
PSI.3

Many techniques have been used in the study of protein structures in
metalloproteins. Each technique reveals unique pieces of information, the
collective body of which produces much insight into the structure of the protein.
Below is a brief description of several of the physical methods used to study PCy.
Along with a discussion of the results obtained by each of the techniques is a
consideration of its advantages and disadvantages.

Absorption Spectroscopy

A large quantity of information on the metal sites in transition metal
complexes can be obtained from absorption spectroscopy, particularly when used
with the complementary techniques of circular dichroism and magnetic circular
dichroism.6 In this kind of study the metal d-d transitions are of greatest interest
and usefulness. The number and energy of these transitions can reveal information
that allows the assignment of the point group of the metal site.

Early work had indicated that the ligands in PCy are probably nitrogen and
sulfur.7’8 Studies of PCy have shown that the d-d transitions occur below 11,000

cm'l

, which is quite low in comparison with most copper complexes with nitrogen
and sulfur ligands.9 The d—d transition energies for octahedral complexes with six
nitrogen ligands have been reported in the range 13,400-14,300 cm’1 and 17,100-
17,500 cm'l.10 The square pyramidal complex, Cu(NH3)52+, has its transitions at
11,400 and 15,000 cm'l, which are still higher than PC3510 Spectra observed for
square planar Cu(II)-amino acid complexes show d-d transitions in the ranges
15,40017,700 cm’1 and 17,500-20,600 cm'1.11 Exchanging two sulfur ligands for
two nitrogens, giving a N282 donor set, shifts the energies to 13,000 and 21,000 cm'1
for the square planer complex. 12 These results were used to rule out 5- and 6-
coordinate and square planer 4-coordinate complexes as the coordination geometry
for the metal site.

The exact geometry of the metal site can not be determined from the
absorption spectra of PCy but the results allowed the elimination of many
possibilities. The remaining possible geometries include trigonal 5- and 4-
coordinate and distorted tetrahedral complexes. The ligands to copper are also not

identified from these results but the low transition energies would indicate such

ligands as nitrogen, sulfur, or oxygen. 13

Electron Paramagnetic Resonance (EPR)

EPR spectroscopy is useful in determining structure at the metal site as well
as revealing insights into the ground electronic state of the metal site. EPR results
can give information as to the type and number of ligands and the particular (1
orbital in which the unpaired electron resides. The EPR spectra of PCy are
characterized by the following: a) g. > g1 > 2.0, b) axial or nearly axial g-tensor, and
c) small copper hyperfine coupling (hfc) values. 14 The ordering and magnitude of
the g tensor values are the most useful parameters in the spectroscopic
determination of the metal site geometry.

Both 5- and 4- coordinate trigonal structures, dicussed above as possible
geometries for the metal site in PQ', have the unpaired electron located in the dz2
orbital.15’l6 This electronic configuration typically gives g values that have g. ~ 2.0
< 31. , which are opposite to those seen for PCy. 17,18 The PCy EPR spectra is
consistent with the unpaired electron residing in a d,‘2_y2 orbital, which is the
expected electronic ground state of a distorted tetrahedron. 19 Attempts to fit the
experimental g values with this geometry have produced good results.19

The unusally small copper hfc constant, along with the lack of any other hfc
in the ESR spectra, gives information about the distribution of the unpaired
electron spin density about the metal site. In the case of Cu-EDTA, where the spin
is located completely, or nearly completely, on the copper atom, A I is 588 MHz,
compared to 180 MHz for PCy. The small value of AI in PCy indicates that a
significant portion of the spin density is removed from the copper atom. Many
inorganic copper complexes with nitrogen ligands show nitrogen hfc in their EPR
spectra.20 Since nitrogen hfc are not detected in PCy the amount of spin density
delocalized onto the nitrogen ligands must be small. The unpaired spin must be

located on atoms with zero nuclear spin since hfc from atoms other than copper are

6

not seen in the EPR spectra. Theoretical calculations indicate that a significant
portion of the spin density (35 %) is delocalized onto the cysteine sulfur ligand.21
Since 33S (natural abundance 0.76%) is the only sulfur isotope with a nuclear spin,
the exact spin density on the sulfur has not yet been determined.

EPR spectroscopy provides a qualitative indication of the delocalization of
the spin density and has been used in conjunction with the analysis of the optical
absorption spectrum to provide a good description of the geometry of the metal site.
Providing detailed molecular structure from the results obtained with these methods
has not been possible though, due to the low resolution of these two techniques.

Hydrogen atoms, for example, are not resolved at all in the EPR spectra of PCy.
X-Ray Absorption Spectroscopy

The methods of X-ray absorption spectroscopy (XAS) and extended x-ray
absorption fine structure (EXAF S) have been used to provide extensive insight into
metal site structure in metalloproteins. Information is contained in two regions of
the x-ray absorption spectrum, the absorption edge and the EXAF S. The
absorption edge reveals information on the oxidation state and site symmetry of the
metal, and in some cases the type of liganding atoms. Typically however, edge data
are only used to determine the oxidation state of the metal.22 The EXAF S spectra
give more detailed insight, such as a more accurate prediction of ligand type, and
interatomic distance between ligand and metal. EXAF S can still not tell the exact
type of ligand atom but can limit it to an atomic weight range i.e. C,N, or O.

XAS results provide little information on the copper in PCy, showing only
that the oxidized form of PCy contains copper in the + 2 state.22 A study of the
reduced form of PC shows copper to be in the + 1 state in this form of the enzyme,

.7

supporting the fairly obvious conjecture that redox activity is mediated by the
copper atom.

The EXAFS technique was first applied to azurin (Ps. aeruginosa) and the
following results on the identity and distance of the nearest atoms to the copper
were obtained: 2.6 atoms (N,O) at 1.97 A, 1.3 S at 2.10 A, and 0.6 S at 2.24 A. 23 The
second sulfur atom is not well detected and the distance determined is a best
estimate. Except for the second sulfur atom, these results compare well with the
crystal structure data, which indicate 2N at 2.11 A, 1 s at 220 A, and 1 s at 2.79 x 4
Similarily, a good correlation between the EXAF S results and the crystal structure
was also seen for p0plar PCy.24 Again in this case the sulfur atom farthest from the
copper could not be detected well and the possibility that there is a large error in
this result was noted.

The application of XAS techniques both confirms previous data and provides
new insight into the metal site geometry. The EXAF S data confirmed the type of
atoms liganding to the copper as nitrogen and sulfur and provided information on
the bond distances between the copper atom and its ligands. EXAF S does have
some problem in determining the exact stochiometry of the liganding atoms as the
azurin results show. Also, EXAFS seems to be limited in the amount of structural
information it can provide as there are no reports of information on the positions of

other atoms in BCP other than the ligands to the copper.22

X-Ray Crystal Structure

The techniques described above can give much information about the
structure of metalloproteins but suffer from several important drawbacks. The
results are either not completely specific-for example, EXAF S can only narrow the

type of liganding atom to a small group-or the results must be interpreted in terms

8

of model compounds-as in the case for absorption and EPR spectroscopy. In order
to obtain an accurate 3-dimensional structure of a protein, x-ray diffraction
techniques must be used. X-ray crystallography, when used in conjunction with the
amino acid sequence, can determine the position and type of each atom in the
protein.

The crystal structure of oxidized PCy was determined first to 2.7 A25
resolution and later refined to 1.6 A resolution. 1 At this level of refinement many of
the ambiguities remaining for the metal site structure were resolved. The metal site
in PCy was shown, as previously predicted, to be a modified tetrahedron. Previous
studies of the metal site, though predicting N and S ligands, could not determine the
exact number of each or if there were any other ligands to the metal. The crystal
structure resolved the uncertainty in the nature of the liganding atoms by showing
that there were only four ligands to copper, 2 N and 2 S. The crystal structure also
showed that there were no water molecues at the copper site and none within the
protein.

The distorted tetrahedral geometry of the metal site in PCy is unusual for
copper complexes.1 Further crystallographic work has shown that this geometry is
the result of the polypeptide. Comparison of the crystal structure of the apoprotein
(1.8 A resolution)26 with that of the oxidized form shows only small differences near
the copper site. The crystal structure has also been determined for the reduced
form of PCy27 as well as for the Hg(II) substituted protein28. In each case only
small structural differences are seen near the copper site. The polypeptide thus
provides the optimum geometry for the metal site to facilitate electron transfer most
effectively.

X-ray diffraction methods provide a wealth of data but also suffer from
several drawbacks. First, in order to study a protein, a single crystal must be grown.
In the case of BCP many species were attempted until PCy from poplar was

9

crystallized.1 Second, the crystal structure determined is a static description of the
protein. Studies of the structure of the protein under different conditions, such as in
different oxidation states, at different pH values, or interacting with other systems,
require a single crystal be grown under each new condition. This has been done for
PC at different pH27 values but could prove to be very difficult or impossible for
PCy-redox partner systems. Techniques are needed that are capable of studing
protein structure in liquid and frozen solutions that allow comparison of the results

with the crystal structure.
Nuclear Magnetic Resonance (NMR)

N MR has been used in the solution study of many aspects of protein
structure and dynamics. Metal binding site characteristics”, interaction sites of
redox partners”, and global structure31 have all been studied in PCy by NMR.
NMR titration experiments of the histidines in PCy showed that their pKa values
shift from their normal values of around seven to five, indicating that these amino
acids are ligands to the metal.7 Substitution of 113Cd for copper in BCP followed
by 113Cd N MR provided qualititive information on the metal binding site.29 The
113Cd chemical shift for azurin is significantly different from that of PCy. This
indicated that the copper sites in these two BCP are different. The refined crystal
structure of azurin (Alcaligines denitrificans)5 showed that it may also have a long
copper-oxygen bond, in addition to the long copper-sulfur bond.

The most important advance in N MR studies of relatively low molecular

weight, soluble proteins is the ability of the technique to determine the complete 3
dimensional structure.32 With the use of a variety of pulse sequences and muti-
dimensional techniques that are now available, nearly every proton in a low

molecular weight protein can be assigned. These assignments, in conjunction with

10

N OE studies, which give relative distances between protons, and distance geometry
algorithms allow the tertiary structure of the protein to be determined.32 A
complete assignment has been carried out for both French bean31 and spinach
PCy33 and for French bean the tertiary structure has also been obtained. The
overall solution structure is similar to the crystal structure for poplar PC, but there
are some local differences}1
Even though NMR can be used to obtain the tertiary structure of a protein,
there are some limitations. With proteins comparable in size to PCy the proton
NMR spectra become very complex and a complete assignment of the spectra is
difficult and time-consuming. The assignment of the spectra for PCy required the
application of a large number of N MR techniquies. So far the largest protein to be
completely mapped out is French bean PCy which contains only 99 amino acids.31
This technique then is currently limited only to the study of those metalloproteins

that are no larger than my.
Electron Nuclear Double Resonance (ENDOR)

Many of the biological systems under study have not yet been crystallized and
thus the crystal structures are not known. Except for NMR, none of the methods
discussed above is able to resolve spatial coordinates for protons near a metal site in
a metalloprotein in solution. ENDOR, as for NMR, is a method well-suited for the
study of soluble proteins that contain paramagnetic metals. Besides being able to
study proteins in solution ENDOR also has several other advantages. It has been
shown in previous experiments on organometallic compounds that metal-proton
distances determined by ENDOR are accurate to 0.1 A34 ENDOR can also be
used to study all nuclei within a system that have a net nuclear spin. This would

include H, N, P, and many transition metals. ENDOR can also be used to obtain

11

information on the ground electronic state of the metal. In particular, it can be used
to determine whether the unpaired spin is isolated on the metal atom or distributed
onto the protein ligands.

ENDOR, as with the other techniques, has its limitations and difficulties. In
order to detect ENDOR resonances the nuclear relaxation times must be slowed
down sufficiently to allow them to compete with the electronic relaxation times.35
Achieving this condition for transition metal complexes requires cooling the sample
to 20 K or lower. This necessitates the use of a liquid helium cooling system. The
generally low concentration of isolated proteins, along with the small sample
volumes, results in a very low concentration of paramagnetic centers. This low
concentration, together with the inherent weakness of ENDOR signals, results in
signal to noise ratios that are often quite low.

Unlike NMR the complete tertiary structure of the protein can not be
determined from the ENDOR results. ENDOR can only be used to study that
portion of the protein that is within approximately 8 A of the paramagnetic site.
Even though the entire protein can not be studied by ENDOR this technique has an
advantage in that it looks fairly specifically at the active site. The spectra, then, are
easier to interpret and do provide detailed structural information. With the simpler
spectra, structural changes that occur near the active site under different conditions
can be easily detected. ENDOR, then, is a technique that is very capable of
addressing the questions raised at the beginning of this chapter.

Whereas ENDOR has been used sucessfully in obtaining structural insight
into small organometallic complexes,34’36’37 its application to biological
macromolecules has been limited. In this work the ENDOR technique used to
study inorganic complexes is developed so as to be useful in obtaining structural
information on proteins such as PCy. Previous ENDOR work on BCP has

concentrated only on the nitrogen ligands and those protons with strong isotropic

12

couplings”,39 Study of the much weaker dipolar interactions can be used to
provide insight into the structure of the protein farther from the paramagnetic
center than previously possible . PCy was chosen for this study for two reasons.
First, since the crystal structure has been solved, the structural information
determined by ENDOR can be compared with the crystallographic data. Second,
for my biological approaches such as biosynthesis and molecular biology can be
applied to help in the interpretation of the ENDOR results.

In the chapters that follow, the application of ENDOR to PCy is described in
detail. In chapter 2 the theory that underlies the EPR and ENDOR experiments is
discussed. This is followed by an introduction into the computer techniques used to
help make assignments within the ENDOR spectra and determine structral
information about PCy. Finally in chapter 4 the results obtained about the
structural and electronic environment around the copper site in PCy are displayed

and discussed.

MAGNETIC RESONANCE THEORY

EPR and ENDOR spectra are interpreted with the use of a Spin
Hamiltonian. This Hamiltonian acts upon spineonly wave functions and predicts
their energies for the particular system under study. Allowed transitions between
these energy levels can be induced by electromagnetic radiation of the appropriate
frequency. The resonances present in EPR or ENDOR spectra represent the
transitions between these energy levels. The Hamiltonian for EPR and ENDOR
that is applicable for frozen solution samples of Cu(II) complexes is discussed in this

chapter.
EPR
The Hamiltonian that describes the EPR spectral characteristics is:40

14 =fieH8T'S'8NflNH'I‘I'S'AT'I (1)
H = Hamiltonian operator
31‘ = electron g-tensor
fie = electron Bohr magneton
gN = nuclear g value
an = nuclear Bohr magneton
H = Zeeman field (externally applied magnetic field)
AT= hyperfine coupling tensor

S = electron spin angular momentum operator

13

14

I= nuclear spin angular momentum operator

The first term of the equation, the electron-Zeeman term, describes the
interaction between the unpaired electron and the externally applied magnetic field
(Zeeman field). The effect of this interaction is to split the degeneracy of the two
spin-only wavefunctions for the unpaired electron. This splitting, the Zeeman
splitting, is the largest interaction of the unpaired electron in a Cu(II) complex and
is diagrammed in Figure 1. Since the electron-Zeeman term is a function of the g-
tensor its magnitude will be orientationally dependent and thus anisotropic. That is,
the magnitude of this interaction will depend on the direction of the Zeeman field
relative to the g-tensor. The g-tensor is diagonal in at least one coordinate system
and this coordinate system will be the primary axis system used in the discussion of
EPR and ENDOR.

The second term in equation 1 is the nuclear-Zeeman term which represents
the interaction between the nuclear spin and the Zeeman field. This term is non-
zero only for those nuclei that have non-zero nuclear spin. Unlike the electron-
Zeeman term the nuclear g value is taken as isotropic. The nuclear-Zeeman
interaction is directly analogous to the electron-Zeeman interaction except that in
this case the degeneracy of the nuclear Spin wavefunction is split. The splitting of
the two wavefunctions is the nuclear-Zeeman splitting and is shown in Figure 1.

The third term in equation 1 describes the interaction between the unpaired
electron and non-zero spin nuclei. This interaction is referred to as the electron-
nuclear hyperfine coupling (hfc). For many Cu(II) complexes, including PCy, the
only hyperfine coupling seen in the EPR spectra is to the nucleus of the copper
atom. The hfc term is comprised of two components, equation 2, the orientationally
independent (isotropic) Fermi contact coupling and the orientationally dependent

dipolar coupling. The dipolar coupling is described by the tensor T and the Fermi

15

 

 

 

 

 

 

 

 

 

 

 

 

 

mI=-3/2 / I}
mI=-l/2
—

ms=+l/2 fit

mI=+l/2

mI=+3/2 ?

m13‘3/2

mI=-l/2 it
m8=-1/2 A I}

mI=+1/2

mI=+3/2
Electron- Nuclear-Zeeman Hyperfine
Zeeman Interaction Coupling
Interaction

Figure 1 Energy levels of a Cu2+ ion at constant magnetic field. The four EPR
transitions are indicated by the arrows.

16

contact coupling by the sealer quantity a. The total coupling is the sum of the two

components.

s-AT-I = a(S°I) + s-Tr-r
(2)
= Aiso + Anip

Fermi contact coupling results from unpaired spin density being located at
the nucleus of the coupled atom, equation 3-a. In order for the unpaired spin
density to be at the nucleus of the atom it must be located in an s orbital. The
coupling of the unpaired electron to the copper nucleus in copper (II) complexes
shows an isotropic component. Spin polarization by the unpaired electron in the 3d
orbital causes unpaired spin density to reside in the inner shell 5 orbitals of the
copper atom resulting in the Fermi contact coupling. Spin polarization by the
unpaired electron can also cause unpaired spin density at the nucleus of atoms
bonded to the atom containg the unpaired electron.

The dipolar coupling is a through space interaction between the unpaired
electron and neighboring nuclei, equation 3-b. In the Cu(lI) ion case, along with the
Fermi contact coupling described above, there is also a dipolar coupling between
the unpaired electron and the copper nucleus. Since the dipolar coupling is
described by the tensor T it is anisotropic and the magnitude of the hfc tensor A is
dependent on the orientation of the Zeeman field relative to the Aotensor axis
system. The effect of the hfc on the energy of the wave functions is shown in Figure
1.

Aao=3tgeficgNflN'I(0)l 25 '1 (3'3)

17

w| (0)| = wavefunction evaluated at the nucleus
Amp = so 133ng M3608” A- 1)/r 3 (343}

go = nuclear g-value
pro = nuclear Bohr magneton

r = magnitude of vector r between the electron spin and nuclear spin
0 A = angle between r and the Zeeman field

In the X-band EPR study of Cu(II) complexes it is assumed that the high
field approximation is applicable.40 In this approximation both the unpaired
electron spin and the nuclear spins are quantized along the Zeeman field. In this
case ”sharp” eigenvalues are obtained from the spin operators S and I acting on the
spin only wavefunctions. The eigenvalues obtained from these operators are the
spin angular momentum in the direction of the Zeeman field. Under these
conditions the scalar quantities, ms and In}, can be substituted for the operators S
and I in the Hamiltonian, equation 1. A Cu(H) ion with one unpaired electron and
a nuclear spin of 3/2 will have m5= 11/2 and m1=-_r-_3/2, _-_r-_1/2, depending on the
electron and nuclear spin states.

In the EPR experiment the selection rules are am1= 0, Am s= 1 and the
allowed EPR transitions are labelled in Figure 1. In an EPR transition the
electronic spin undergoes a "spin flip" resulting in a one quantum change in the spin
angular momentum. The energy of such transitions usually fall in the microwave
frequency range. These transitions are detected in the EPR experiment and show up
as peaks in the EPR spectrum.

The dominant features of the EPR spectra of frozen solution samples of

Cu(II) complexes are dictated by the g- and copper hfc tensors. The g-tensor for

18

many copper complexes is axial, that is gx=gy=gl and & =8! , where g x: g y, and
g z are the principal values of the g-tensor. If the unpaired electron is located in
the dx2-y2 orbital of copper then the x and y axis of the tensor are located in the
plane of this orbital and the z axis is perpendicular to this plane. In this electronic
configuration the the g-tensor axis system and the frame of reference of the d-
orbitals are colinear, Figure 2. The hfc tensor for coupling to the Cu nucleus in
copper complexes also is axial in many cases. Similar to the g-tensor, Ax=Ay=Al
and Az=AI where A x, A y, and A z are the principal components of the hfc
tensor. The hfc tensor is also closely related to the geometry of the metal d orbitals
and in many cases is colinear with the g-tensor, Figure 2.

In frozen solution samples of Cu(H) complexes the molecules are oriented in
all possible directions. Each molecular orientation relative to the Zeeman field will
have a scalar effective value for the g and hfc- tensors which are labelled geff and
Aeff. Substitution of these effective values into the spin Hamiltonian results in a
different EPR spectrum for each molecular orientation. The experimentally
detected EPR spectrum is then a composite of the individual spectra and is referred
to as a powder pattern spectrum. Figure 3 is a computer generated powder pattern
EPR spectrum of a Cu(II) ion characteristic of a BCP. The primary feature in the
spectrum is the e0pper nuclear hyperfine coupling. Since copper, nuclear spin 3 / 2,
has four nuclear spin states, there are four hyperfine manifolds in the EPR
spectrum. The splitting of these manifolds is dictated by the hfc tensor. The low
field portion of the spectrum corresponds to those molecules oriented with their 2-
axis aligned along the Zeeman field, g=gl . The hyperfine coupling for this
orientation is A. and the hyperfine manifolds are centered abouth . Similarly, the
high field portion of the spectra corresponds to those molecules oriented such that
the Zeeman field is in the molecular x,y plane. The hyperfine coupling is then A .L

19

 

 

 

 

z 9 9“
2+
Cu v. 9.1.
X, 9;
9"- Au
2+
9.1.: Ar.
Figure 2 a) A representation of the g—tensor axis system showing axial

symmetry. b) A similar representation of the Cu(II) hyperfine
coupling tensor and its co-linearity with the g-tensor axis system.

20

 

 

 

 

 

 

 

 

 

 

 

 

AJ. I

Figure 3 Computer enerated EPR spectrum for a Cu(II) ion with parameters
similar to Cy.

21

and centered about g. The powder pattern spectrum, Figure 3, clearly shows the
orientational effects of the g and copper hfc tensors.

Besides hyperfine coupling to the copper nucleus there is also coupling
between the unpaired electron and other nearby nuclei. The nuclei of interest in
this work are the protons surrounding the metal site. These protons are generally
not detected in the EPR spectra of Cu(II) complexes since their hyperfine coupling
constants are very small compared to the large linewidth of the copper hyperfine
coupling manifolds. In order to investigate these smaller hyperfine interactions a
more sensitive technique with narrower linewidth is needed. ENDOR is well-suited

for the study of these interactions.
ENDOR

The Hamiltonian that describes the ENDOR experiment is exactly the same
as the one used for EPR.35 Since the Hamiltonian is the same in both experiments
the energy levels are also the same for the system under study. The difference in the
two experiments is that the ENDOR experiment promotes and detects transitions
between nuclear spin states rather than between electronic spin states as in EPR.

In discussing the ENDOR experiment we shall consider the case of an
unpaired electron interacting with a single proton. This is the type of interaction
that is detected when ENDOR is used to study PCy. The hyperfine coupling to the
proton is described in equation 3. The energy level for this system is shown in
Figure 4. Transitions between energy levels 1 and 3 and energy levels 2 and 4 are
the EPR transitions. In the ENDOR experiment the selection rules are m1: 1,
Ams=0 and the system under study undergoes a nuclear spin flip. The ENDOR
transitions then are between energy levels 1 and 2 and between energy levels 3 and

4. The splitting of these energy levels falls in the radiofrequency range. In

Figure 4

22

 

 

 

 

 

 

mI=-1/2
m3=+l/2 EPR#1 ENDOR#1
I
mI=+1/
EfR#2
mI=-l/2
mS=-l/2 ENDORIZ
mI=+1 2
Electron- Nuclear-Zeeman Hyperfine
Zeeman Interaction Coupling

Interaction

Energy levels of a hydrogen atom at constant magnetic field. Both the
EPR and ENDOR transrtions are displayed.

23

ENDOR, unlike EPR, the effect of the RF radiation on the EPR resonances are
detected rather than direct detection of the absorption of RF power at frequencies
corresponding to ENDOR# 1 and ENDOR#2.

The Zeeman field strength is adjusted so that one of the EPR transitions,
EPR# 1, is in resonance. The microwave power is then increased to partially
saturate this EPR transition. This has the effect of equalizing the populations of
energy levels 2 and 4. The system is next irradiated with a swept radiofrequency.
When the frequency of the RF fulfills the resonance condition of ENDOR# 1, the
transition will be saturated and the population of energy levels 3 and 4 will be
equalized. This results in a lowering of the population of level 4 and a desaturation
of the EPR#l transition. The EPR transition will then increase in intensity and this
change in intensity is detected as a peak in the ENDOR spectrum. A second
ENDOR peak is detected when the RF fulfills the resonance condition for the
ENDOR#Z transition. The ENDOR spectrum is, thus, simply the change in EPR
intensity plotted as a function of RF frequency.

The ENDOR spectrum for this system consists of two peaks centered at v N
the free proton resonance. u N is equal to the nuclear-Zeeman splitting, Figure 4.
The splitting between the ENDOR resonances is A, the value of the hfc tensor for a
particular molecular orientation. The energy at which the two ENDOR peaks will
occur is predicted by equation 5,

by = uni |A/2| (5)

The ENDOR spectra of a spin system in a frozen solution will have distinct
features depending on whether the hfc tensor is ardal (Ax=Ayt-AQ or rhombic
(AxtIAyuA 9- The lineshape that appears for an axial hfc tensor, shown in Figure 5,
is comprised of a pair of absorptive shaped peaks and a pair of derivative shaped
peaks.41 For a hfc tensor that is purely dipolar, equation 3 predicts that A. , with

24

 

 

 

 

 

 

 

2

 

 

>
'—
.Il-

 

 

JIJ

 

 

 

 

 

 

I j—Az ‘I

Figure 5 a) Observed lineshape for an axial hyperfine cou ling tensor. b)
observed lineshape or a rhombic hyperfine coup ing tensor.

25

0A=0°, will be twice as large as A. with o A=90 0. The absorptive shaped peaks
are then split by an amount equal to A. and the derivative shaped peaks by A. .
The lineshape for a rhombic hfc tensor is shown in Figure 5. The absorptive shaped
peaks are split by AZ, the derivative peaks by Ay, and the rhombic shaped peak by
Ax, where AZ >Ay>Ax.41

Structural Information

In the previous section the values of g and A were shown to be a function of
the angle beween the Zeeman field and the z-direction of their respective tensors.
In the case of a spin system with axial tensors the scalar quantity of these tensors for

a particular molecular orientation are described by equation 6,42

8eff = (ngsinzon + g. Zoos» ti 1”

(6)
Aeff = (A12 sinzoa + A. 2cos’0 ,9 l/2

The angle 0 n is the angle between the Zeeman field and g. for the g-tensor and o A
is the analogous angle for the A-tensor. Using the Cu(II) ion as an example, Figure
2, the value of the g-tensor when the Zeeman field is along the atomic z-direction,

0 “=00, is g . and when the Zeeman field is along the x—direction, 0 “=90 (Z g= g..

In between these two extrema the value of g is determined from equation 5.

The situation is quite different for the A-tensor. Experimentally it is
observed that the effect of changing a Ais not to change the value of A as in the g-
tensor case but its effect is to modulate the intensity of the peaks in the ENDOR
spectra. When the Zeeman field is along the z—direction of an axial A-tensor,

a A= 0°, a pair of absorptive shaped peaks are detected with a coupling of A. and

26

when the Zeeman field is in the x,y plane, a A=90°, a pair of derivative shaped
peaks are detected with a splitting of A i' As 0 Aincreases from 0° to 90°, the
intensity of the peaks separated by A. will decrease while at the same time the
intensity of the peaks separated by A .I. will increase. Regardless of the value of a A
no additional peaks will appear in the ENDOR spectra from the proton.

In the spin system of study in this work, PCy, the hfc tensors are not axial but
rhombic. The change in ENDOR peak intensity for a rhombic hfc tensor is a
straightforward extension of the axial case. The only difference is that a rhombic
lineshape, Figure 5, will be detected. The intensity of these peaks will change as the
Zeeman field is more closely aligned along or farther away from the principal
directions of the hfc tensor just as for an axial hfc tensor.

The angles 0 A and 0 ”can be changed by taking ENDOR spectra at a series
of Zeeman field values within the EPR spectra. As ENDOR spectra are aquired at
increasing Zeeman field, increasing 0 n , each spectra will correspond to a different
value of 0 A, Correlation of the lineshape of the ENDOR peaks-absorptive,
derivative, or rhombic-with their change in intensity allows an assignment of the
peaks corresponding to a particular proton. Knowing the principal values of the hfc
tensor and using equation 3 for hyperfine coupling the distance r between the
unpaired electron and the proton is determined. Also, following the intensity
changes of the ENDOR peaks versus o it give an approximate angle between the
vector r and the direction of g. . This angle, along with the distance to the proton,
gives an accurate description of the position of the proton relative to the metal
atom.

Application of the technique of ”angle selection" ENDOR on compounds
ranging from simple organics to organometallic complexes has provided a wealth of
information. With the use of ENDOR spectroscopy the molecular geometry of the
spin label 2,2,5,5,-tetramethylpyrroline-1-oxyl-3-carboxylic acid in a frozen solution

27

was determined.43 Comparison of the ENDOR results with those obtained from
crystal structures and molecular modeling showed only a 5% discrepancy in the
structure of the compound.

Several groups have also used this technique to study the planar complex
bis(acetylacetonato) copper (II) (Cu(acac)2).36’44 The difference between the
experimentally determined proton hfc tensors for a frozen solution sample and
single crystals was minimal. The hfc tensors from a powdered crystal, where copper
has been doped into crystals of Pd(acac)2, also compared well with those from
single crystals. The powdered crystal sample also showed two additional pairs of
ENDOR peaks not detected with the frozen solution sample. These peaks result
from the interaction of the unpaired electron on the copper atom with the
methylene proton on a neighboring Pd(acac)2 molecule. This coupling was purely
dipolar and the the magnitude of the two couplings were A. and A. . By using these
couplings along with the formula for dipolar coupling the distance from the metal
atom to the proton was determined. Comparison of this distance with the distance
calculated from the crystal structures of Cu(acac)2 and Pd(acac)2 showed good
agreement.

This technique has also been extended to study non-planar organo-metallic
complexes. The ligand environments around the Gd3 'I' 37and V02 'I' 34 ions have
been studied in frozen solutions of methanol or methanol /water cosolvent. The
ENDOR results revealed insight into the ligand geometry along with the type of
ligand, CH3O’, HO’, or H20, and to some extent, their stochiometries. ligand
geometries determined by ENDOR were very close to those from crystal structures
of similar compounds.

In the work cited above the unpaired electron is localized on the metal atom
or in the spin label system roughly half way between the N and O of the nitroxide

group. As discussed above this is not the situation for PCy, where a portion of the

28

unpaired spin density is delocalized onto several of the liganding atoms. The angle
selection technique is still applicable for this system but structural information for
protons nearby the metal atom can not be calculated from the hfc tensor in a
straightforward manner. When the unpaired spin density is delocalized over several
atoms there is a hfc tensor for the interaction of a proton with the unpaired spin
density on each of these atoms. The total hfc tensor for the proton is the sum of
these individual hfc tensors. From the crystal structure of poplar my the individual
and total hfc tensors can be calculated. Using the angle selection technique along
with the principal values of the hfc tensor the peaks in the ENDOR spectra can then
be assigned to particular protons. Calculation and interpretation of the total hfc
tensor is discussed in chapter 3.

COMPUTER APPLICATIONS

With the unpaired spin density in PCy delocalized over several atoms the hfc
tensors for the protons in PCy can not be calculated in the straightforward manner
discussed in chapter 2. In this situation the calculation of these tensors becomes
more complex. Adding to the difficulty of the problem is the fact that the crystal
structure for PCy does not include the coordinates for the protons. These
coordinates are needed in order to extract their hfc tensors. In order to solve this
problem the application of computers is necessary. The methods used to determine
the nuclear coordinates of the protons and their hfc tensors along with the computer

programs used in this effort are described below.
Crystal Structure

The nuclear coordinates from the crystal structure of the oxidized form of
PCy were obtained from the Protein Data Bank. These coordinates are listed in
units of angstroms and are relative to the crystallographic axis system. This axis
system is orthogonal with its origin located outside the protein structure. The crystal
structure was solved by using X-ray radiation, which does not allow the nuclear
coordinates for protons to be determined.

The nuclear coordinates for the protons were therefore calculated by using
the program PROTIN45 in conjuction with the crystal structure. This program uses
idealized coordinates for the nuclei, including the protons, for all the amino acids.

These coordinates are overlayed onto the protein’s crystal structure and the

29

30

coordinates of the protons are calculated relative to the crystal axis system. The
coordinates from PROTIN were compared to those from neutron diffraction studies
of single crystals of the individual amino acids“,47 Comparison of geometric
parameters such as bond lengths and bond angles showed good agreement. The
results for the amino acids histidine and cysteine are listed in Table 1. The
coordinates calculated for the protons are assumed to be accurate simulations of the

true proton coordinates.

Table 1: Bond lengths and bond angles from PROTIN and neutron diffraction for

 

 

histidine and cysteine
Amino Acid Geometry PROTINa N eutrona
Diffraction

bCysteine c 1 -H 2 1.067 1.077
C 1 -H 3 1.068 1.076
C 2 -H 4 1.045 1.104
LS-C(1)-H(2 107.3 1073
LH(3)-C(l)- (2) 109.2 107.8

cHistidene N 3 —H.10) 1.080 1.026
N 2 -H 9) 1.060 1.070
c 6 -C(5) 1.080 1.075
LCE63-Né3iH210; 125.5 127.9
LC 5 -N 3 -H 10 123.6 123.0

.3; Bond lengths are in angstroms and bond angles in degrees

Ref 46
c Ref 47
Tensor Calculation

The calculation of the total hfc tensor first involves calculating the individual
hfc tensors for each component of unpaired spin density in the system. For PCy the
spin density is delocalized onto the ligand atoms (His37)N, (His87)N, (Q584)S and

the copper atom.21 The protons studied in this work are not bonded to amino acids

31

that contain unpaired spin density or are sufficiently removed from it that they have
no isotropic component to their hyperfine couplings. The hfc for these protons is
taken as purely dipolar and the coupling to the four sources of unpaired spin density

is calculated with equation 7.

ADip = g )9 “198600820 A-1)/r 3 (7)

Solving equation 7 for values of o A of 0° and 90° yields the principle components
A. and A. , respectively, for the hfc tensor. The axis system for this tensor is
defined such that the vector connecting the unpaired spin density with the proton is
labelled the Y direction. Since the tensor is axial the directions of the X and Z axis
are arbitrary and are defined so that a right handed orthogonal axis system is
established.

The second step in calculating the total hfc tensor is the addition of the
individual tensors. The difficulty of this process arises from the fact that the
individual hfc tensors, each in its own axis system, must all be in a common axis
system before they can be summed. The individual tensors must first then be
rotated into the common axis system. Any axis system is suitable to be used as the
common axis system. For PCy the principal axis system of the g-tensor was chosen
as the common axis system. The g tensor for PCy is slightly rhombic but for this
work it is assumed to be axial. The error resulting from this assumption is minimal
since the difference between gx and gy is very small. This axis system, then, has only
one unique directional component gz. Single crystal EPR work has placed the Z-
direction of the axis system colinear with the vector between the copper atom and
the sulphur atom of the methionine ligand.48 The X and Y directions are defined
so that a right handed orthogonal system is constructed.

32

The values of the components of the hfc tensor after rotation into the

common axis system are calculated by using equation 8.
AT(I)ij = 22a Hall AT (1)0 (8)

AT(I)k1 = hfc tensor in its principle axis system
AT(I)ij = hfc tensor in common axis system
an, a],- = direction cosines

1,2,3 = X, Y, Z

For the direction cosine terms the first subscript refers to the hfc system and the
second to the common axis system.
With all the hfc tensors rotated into the common axis system the tensors are

then summed, equation 9.
ATij = 2 AT (IQij (9)

AT = total hfc tensor
Ara.) = kth individual tensor

The final step is to solve for the eigenvalues and eigenvectors of the total hfc
tensor. This is accomplished by using the the IMSL49 subroutines for matrix
diagonalization. The resultant eigenvalues are the principal components of the hfc
tensor, AxAyAz and the eigenvectors define the axis system of the tensor relative
to the common axis. The value of the principal components along with their
directions can now be compared with the angle selection ENDOR results to assign
the ENDOR peaks to protons within the protein.

33

Program: TENSOR

The program TENSOR calculates the total hfc tensor and solves for its
eigenvalues and eigenvectors by following the steps described above. The program
was written in Fortran 77 and run on a VAX 11 / 750. The matrix diagonalization
was accomplished by using the IMSL49 subroutine EVCRG. The IMSL subroutines
WRRRN and WRCRN,49 which print out the results from EVCRG, were also used.
The input needed for the program is listed in Table 2 and the number of individual
tensors that can be calculated is only limited by the resources of the computer.

Table 2: Input for TEN SOR

 

zx, Z3, Z2 The coordinates of the Z axis of the common
axis system relative to the crystal structure

NT number of individual tensors to be calculated

Hx, Hy, Hz coordinates of proton

Sx, Sy, Sz coordinates of atom containing unpaired spin
density

ISO isotropic coupling for the proton

D quantity of unpaired spin density

 

The last three lines of input are repeated for each atom containing unpaired
electron spin density. The output of the program consists of the total hfc tensor and
the tensor’s eigenvalues and eigenvectors. A listing of the program is given in

Appendix A.

RESULTS AND DISCUSSION

EPR and ENDOR spectra were recorded for the blue copper protein
Plastocyanin. The ENDOR measurements focused on the matrix region, the region
of the spectra near the free proton resonance. The ENDOR resonances in this
region are from protons that are within approximately 6 A of the copper site and
show purely dipolar hfc.5° The ENDOR spectra were recorded at a series of
magnetic fields within the EPR spectrum so that the angle selection technique in
conjunction with the computational techniques discussed in chapter 3 could be
applied. Assignment of the peaks in the ENDOR spectra to particular protons is
possible by comparison of the experimental hfc values with those that were
calculated. The results derived from using this technique along with consideration
of the applicability of the angle selection technique to protein systems such as PCy
are discussed below. The EPR spectrum was also thoroughly studied by accurately
simulating the spectrum. These simulations allow the values of the terms in the spin
Hamiltonian to be determined. The results from these simulations are also
discussed below.

EXPERIMENTAL

The EPR spectrum was recorded at X-band on a Bruker ER200D series
spectrometer by using a Bruker TE102 cavity. During the EPR experiment the
magnetic field is modulated at 100KHz which results in the first derivative spectrum

being recorded. The EPR spectrum was recorded at sample temperatures of 10 -_t_ 3

34

35

K. These temperatures were achieved by using an Oxford Instruments helium flow
cryostat (ESR900) connected to an Oxford digital temperature controller (DTC-2).

ENDOR spectra were recorded at X-band with a Bruker ER250 Endor
accessary and a Bruker ER250ENB cavity. The ENDOR coil is home built and is a
modification of the design of Hurst et al.51 The coil consists of 19 turns of silver
wire connected to brass fittings on either end. The coil and cavity are fitted to an
Oxford Instruments continuous flow helium cryostat (ESR900); spectra were
recorded at sample temperatures of 10 i3 K. Radiofrequency power is supplied to
the coil by an ENI 3100L amplifier driven at RF frequencies generated by a
Wavetek (3000-446) synthesizer. The RF power is frequency modulated, which
produces a first derivative ENDOR spectra.

In the ENDOR experiments on PCy the frequency modulation (FM) of the
RF power used was i 40 KHz. FM values lower than this did not reveal any better
resolution within the ENDOR spectra; higher F M values resulted in line broadening
and lower resolution.

In order to obtain accurate simulations of the EPR spectra the microwave
frequency and magnetic field values must be known accurately. These values were
measured directly by using a Bruker ER035 M NMR gaussmeter and a Hewlett-
Packard 5424 counter / 5255 3-12 GHz converter, respectively.

Plastocyanin protein was isolated from spinach leaves using previously
established procedures.°° The final concentration of the protein was 100 rtM. In
the deuterium substitution experiment the protein was redsuspended in an excess of
D20 for 24 hours. After this period the protein was concentrated back to its

original concentration.

36

EPR

The X-band EPR spectrum of PCy recorded at 10 K is shown in Figure 6 and
the instrument parameters are listed below the spectrum. The EPR characteristics
of BCP, g. > g. and a small copper A. , are clearly illustrated in the EPR spectrum
of PCy. At X-band the slight rhombicity in the g-tensor is not detected, instead the
derivative shaped portion of the spectrum appears with an effective g 1 between that
of gx and gy. Also, the A 1. component of the copper hfc tensor is unresolved.
Accurate values of the principal components of the g- and hfc tensors can not be
determined from the experimental spectrum but must be obtained from computer
simulations.

The EPR spectrum was simulated by using the program QPOW.52 The
input for the program is divided into two groups. The first group includes the
experimental parameters, the microwave frequency and the magnetic field. The
second group is the hamiltonian components gT, gN, AT, and the Euler angles
defining the non-alinment of the tensors. Using these parameters the spin
hamiltonian is solved to determine where the EPR resonances will occur. Since the
samples used are frozen solutions the hamiltonian is solved for all molecular
orientations to obtain the powder pattern spectrum.

The parameters in the second group are adjusted after comparison of the
experimental and simulated spectra until an accurate simulation is obtained. That
is, we employ an interative fit with human judgement in the feedback loop. The g.
and g 1 portions of the spectrum were expanded independently to aid in producing a
more accurate simulation. The same parameters used in these simulations were
also used in the simulation of the complete EPR spectrum. The simulated spectrum
is shown in Figure 6 and the parameters used to simulate the spectrum are listed in
Table 3.

37

 

I l J J
2850 3050 3250 3400

Figure 6 a) EPR spectrum of PCy. Conditions: microwave power, 2.07 mW;
12.5 KHz modulation amplitude, 0.4 G p; microwave frequency,
9.45543 GHz; sweep time, 200 see. b) rmulation of (A) using
parameters in Table 1.

3 8
Table 3: Parameters for simulating the EPR spectrum of spinach PCy.a

 

u u H II II II
N
|+|+|+|+|+

. 333W 9:

x = 5230 MHz
Y = 52.0 MHz
Z = 70.0 MHz
The g— and A-tensors are colinear

Frequency = 9.465 GHz

 

aThe error reported for these values are determined by visual inspection of the
simulations

Even though the experimental spectrum shows axial g-tensor characteristics a
good simulation could not be obtained without using a rhombic g-tensor. The g.
region of the spectrum was also very sensitive to variation in gx and gy. Changes of
less than 1% in the values of gx and gy caused significant distortion in the lineshape.
The values of gx and gy reported in Table 1 are very close to those obtained from Q-
band EPR spectra of PCy where gx=2.042 and gy= 2.059.21 The value of g. has a
slightly larger error due to the significant amount of g- and A-strain present in this
portion of the spectrum.53 The value we determined for g. is slightly larger than
the previosly measured value of 2.23 for PQI at 25 K54 The difference is probably
a result of the fact that the authors of the earlier study were unable to measure
accurately the microwave frequency or magnetic field.

The hfc tensor components were similar to the g values in that the error in
A. is approximately 1.5% where the error in A. is larger at about 3%. The larger
error in A. is again the result of g- and A-strain. Our value for A. of 180 MHz is
very similar to the previosly reported value of 189 MHz.54 For A. previous work

39

could only estimate its magnitude to be less than 51 MHz.14 The present work
shows that A. is 30 MHz.

On the EPR spectra in Figure 6 are marked the positions (A-E) where the
ENDOR spectra were recorded. ENDOR spectra were recorded over the entire

range from g. to g. so that the angle selection technique could be applied.
ENDOR

The ENDOR spectra of PCy recorded at positions A-E on the EPR spectrum
are shown in Figures 7 and 8. From these spectra seven sets of proton ENDOR
resonances were observed. The magnitude of the hfc constant for each set of peaks
along with their lineshape types are listed in Table 4. Assignment of the ENDOR
resonances to protons within the protein was based on two criteria, comparison of
the experimental ENDOR couplings with the calculated hfc tensors and the value of

o p for the tensor components.

Table 4: Pairs of resonances from the ENDOR spectra of spinach PCy.

 

Peak pair hfc constant(MI~Iz)a Lineshape
a,a ’ 5.13 absorptive
b,b’ 3.19 absorptive
c,c ’ 2.30 absorptive
d,d’ 2.14 absorptive
e,e’ 1.61 derivative
f,f’ 1.15 derivative
g,g ’ 0.92 rhombic

 

”The error in these values is discussed in the text

The hfc tensors for these protons were determined by using the coordinates
obtained by the procedure discussed in chapter 3. These coordinates, though, are
based on the crystal structure of plastocyanin from poplar. The spinach and poplar

40

 

0n=0°

 

 

 

 

 

 

 

 

 

 

 

 

 

M.
M
opal

 

MHz

Figure 7 EiNDORs sgectra of PCy. for the positions marked A,B, and C in
gure 6. onditions: microwave power, 20. 7 mW; microwave
frle uency, 9. 4355 GHz; RF power, 90 W; RF modulation frequency,
40 ;sweep time 200 sec.

M II II ”=45.

 

 

 

 

 

 

 

 

 

 

Figure 8 ENDOR spectra of for the positions marked D and E in Figure 6.
Conditions: same as in igure 7.

42

forms of the protein both have 99 amino acids and only differ in amino acid type at
2210cations.55 The majority of these amino acid substitutions involve conservative
changes and surface residues. These types of changes in amino acids should not
cause significant differences in the tertiary stuctures of the two proteins. NMR
experiments, in particular NOE techniques, have been used to determine any
structural differences between spinach plastocyanin and the crystal structure of
poplar plastocyanin.33 A qualitative comparison of the NOE data obtained for
spinach PG! and inter-proton distances calculated from the crystal structure showedA
no inconsistencies. The NOE data included backbone-backbone short- and long
range interactions as well as sidechain-sidechain interactions. From this large set of
data it was concluded that the structure of poplar plastocyanin is conserved in
spinach even with the amino acid substitutions. The proton coordinates calculated
by using the poplar plastocyanin crystal structure are thus assumed to be the same
or nearly the same for PCy.

Of all the protons in PCy there are 28 that are near enough to the copper site
to give ENDOR peaks that are resolvable. The criterion used to select these
protons was that they have at least one component of their hfc tensor equal to 1
MHz or greater. This is the minimum coupling that is resolvable within the
ENDOR spectra. The 28 protons are located on eight amino acids including the
four ligand amino acids. These eight amino acids are conserved between the poplar
and spinach forms of the protein.

Since the exact distribution of the unpaired spin electron density is not
known the hfc tensors were calculated by using a series of different distributions. As
a starting point, the calculated distribution by Penfield and co-workers of Cu 45%, S
35%, N 10% and N 10% was used.21 An ENDOR study of a large number of
pseudoplanar copper complexes with nitrogen and oxygen ligands showed that the
spin density on the nitrogen was between 6% and 10%.20 The different

 

43

distributions we used in calculating the hfc tensors had low or no spin density on the
nitrogen ligands and varied the majority of the spin density between the copper and
sulphur atoms. The different spin density distributions (SDD) groups are listed in
Table 5.

Table 5: Spin density distributions used in calculating hfc tensors.

 

SDD groupa %Cu %S %N %N
1 55 35 5 5
2 65 35 0 0
3 50 50 0 0
4 70 30 0 0
5 45 35 10 10

 

aSDD = spin density distribution

Along with calculating the hfc tensor for the 28 protons the orientation of the
tensor relative to the g-tensor axis system is also determined. Since the g-tensor is
treated as axial in this work the only unique axis is g. . The only orientational
information then that is relavent is the angle 0 p, which is the angle between the
direction of the tensor component and the direction of g. . As the value of o H , the
angle between the applied magnetic field and g. , increases, and the applied
magnetic field becomes closer aligned along the direction of the hfc tensor
component, the intensity of the ENDOR peaks will increase. The intensity of the
peaks then will be a maximum when 0p=o n. The value of 0 p is then used to find
that proton whose hfc tensor would best match the intensity changes seen in the
experimental spectra.

The error in the calculated hfc tensor components was determined from the
error reported for nonbonded atom contact in the crystal structure. This error was
estimated to be 0.5 A. 1 Coordinates were then determined for the atoms containing

44

unpaired spin density such that the distances from these atoms to a proton were
equal to the crystallographic distance i025 A. The hfc tensor was then calculated
by using the longest distances and again using the shortest distances. These two sets
of data repesent the maximum and minimum results for the calculations, while the
results from using the crystallographic coordinates were generally half way between
the two extrema. The spread in the results was considered to be the error for these
calculations and was found to be 20%. This calculation was carried out for several
protons, both close and far from the unpaired spin density, and the error was always
found to be about 20%. The variation in o p is much less sensitive to the change in
distances between atoms discussed above. The value of a p changes by only a few

degrees between the maximum and minimum result data sets.

ASSIGNMENTS

Reliable assignment of the ENDOR peaks to one particular proton, or in
some cases two protons with nearly identical characteristics, is possible for four of
the pairs of ENDOR resonances. In the other three cases, due to discrepancies in
both hfc values and o p the assignment of the ENDOR resonances was not possible.
These assignments along with the complete hfc tensor for the protons are listed in

Table 6.

Peaks a,a’

The peak pair a,a’ have an absorption lineshape and a coupling of 5.13:1
MHz. The intensity of these peaks shows an increase up through 0 H = 45° and
nearly the same intensity at 0 F 80°. This intensity change indicates that o pis

located between these two values of 0 it. There are two protons that match these

45

characteristics, the amide proton on asparagine 38 (A38H) and a proton on the )3-
carbon of histidine 87 (H87I-IB1). For H87HB1 the hfc values range from 4.23-5.33
MHz while a pvaries from 66°-68° for the five spin density distributions. The hfc
values for A38H vary from 4.59-4.98 for SDD groups 1,2,4,5 while the value for
SDD group 3 is much larger at 6.22. The angle 0 p again varied little, 59 °-62 °. With
the small difference in hfc and 0 pvalues assignment of the peaks to one proton or
the other is not possible.

Peaks b,b’

This pair of peaks, with a coupling of 3.19:0.60 MHz, also has an absorptive
lineshape. These peaks first appear when a n =25 ° and the intensity is increasing
even when 0 n= 80° indicating that 0 pmust be at or near 90 °. Five protons have
values for the absorptive components of their hfc tensors that are near 3.20 MHz.
Only the proton on the p-earbon of histidine 37 (H37HB2) has the correct value of
o pwith 90°. For the other protons o pranged from 67 °down to 20 °. The value of
this tensor component for H37HB2 varies from 3.07 to 3.75 MHz for the five SDD

groups whereas the value of a pvaries by only a few degrees.

Peaks d,d ’

These peaks, with an absorptive lineshape and a coupling of 2. 14 i 0.36 MHz,
are present as shoulders on peaks e,e ’. The peaks are first present when 0 “=25 °
and increase in intensity until 0 n= 45 °. When 0 “=80 °the intensity of these peaks
has decreased. The value of 0 pshould then be in the range of 45 °-80 °. Once again
a series of protons, five, have the correct hfc values for the ENDOR coupling.

Three of these protons have a p values that are too small, 18 °-37 °, while one is too

46

large, a F 80 °. The proton that meets both criteria is the second proton on the )3-
carbon of histidine 87 (H87HBZ). For SDD groups 1,2,4 and 5 the hfc values range
from 1.77-1.83 MHz and o pvaries from 63 °-67 °. For SDD group 3 the hfc value is
too low at 1.65 MHz.

Peaks f,f’

Peak pair f,f’ are derivative shaped peaks with a coupling of 1.15:0.20
MHz. The intensity changes of these two peaks is very much like that of the pair
d,d ’. The intensity of the peaks is increasing when 0 “=45 °but the peaks are very
small or not present at all at 0 n=80°. Again this will place 0 within this range.
Two protons with nearly identical characteristics are assigned to these peaks. The
proton on the 19an of methionine 92 (M92HB2) has hfc values that range from
0.94-1.01 MHz and a 0 p that ranges from 37°~40° for SDD groups 14. The hfc
value for SDD group 5 is lower at 0.88 MHz.

The second proton is the terminal -CH3 group of the methionine 92 side
chain. At a sample temperature for these spectra of 10 K, the methyl group is
assumed to be rotating freely. The three protons are then magnetically equivalent
and the methyl group is represented by a single proton at the average position of the
three protons. EPR studies of organic radicals such as the chloroacetylalanine5°
and 4-methyl-2,6-ditertbutylphenol57 free radicals have shown that methyl groups
can be freely rotating even at temperatues of 4.2 K. The methyl groups of
bis(acetylacetonate) copper (II) in frozen solutions have also been shown to be
freely rotating at 25 K as determined by ENDOR.“ A study of the PCy crystal
structure also shows that the -CH3 group is located in a pocket where there is no

protein structure to hinder its rotating.

47

The hfc and o pvalues for M92CH3 are very similar across all five SDD
groups. The hfc values range from 1.22-1.34 MHz while 0 1: only changes slightly
from 57°-59°. As in the case for peaks a,a’ the hfc and 0 pvalues for the two
protons are so similar that assignment of peaks f,f’ to just one proton is not

possible.

Peaks c,c’;e,e’is.8’

For each of these sets of peaks a reasonable assignment to one or more of
the protons in PCy was not possible. It was possible to assign one or more protons to
each set of peaks on the basis of hfc values alone but in each case the values of o p
were significantly in error. Possible explanations for the inability to assign these

peaks are discussed later in this chapter.

Table 6: Protons assigned to the ENDOR spectra and their complete hfc tensors.

 

 

Peaks Proton A! Ay AZ
a,a’ H87HBI -1.9 -2.9 5.1
a,a’ A38H -2.1 -2.6 4.7
b,b’ H37HB2 -1.3 -2.1 3.5
d,d’ H87HBZ -0.8 -1.0 1.8
f,f’ M92HBZ -0.8 -1.0 1.8
f,f’ M92CH3 -1.1 -1.3 2.4

DEUTERATION

In conjunction with the calculated hfc tensors another method that would
assist in the assignment of the ENDOR spectra would be deuterium substitution. If

a deuterium could be substituted for a proton whose peaks were present in the

48

ENDOR spectra, those peaks would disappear. There are several exchangeable
protons near the copper site that could possibly be substituted.

The ENDOR spectra for the deuterated sample of PCy were taken at
magnetic fields similar to those for the protonated sample. These spectra showed
no difference when compared with those taken for the protonated sample. All
seven sets of peaks were present and they showed the same hfc constants. The
intensity changes as a function of magnetic field of the peaks seen in the spectra of
the protonated sample were reproduced in the spectra of the deuterated sample.
These results are consistent for the four sets of peaks in which assignments were
made since all these protons are covalently bonded and are not expected to
exchange. Of the 28 that are near the copper site only five, all backbone amide
protons, are expected to be exchangable. NMR studies of PCy have shown that four
of these five protons are non-exchangeable even after dissolving the protein in a
D20 buffer for 24 mm.” The only proton that did exchange was the amide
proton on histidine 87. The deuteration experiments are thus consistent with the
assignments made above for the peaks labelled aa’, bb ’, dd’, and ff’. Moreover,
the deuterium work allows us to conclude that the three sets of unassigned peaks
are not derived from the amide proton of histidine 87.

SPIN DENSITY DISTRIBUTION

The different SDD groups used to calculate the hfc tensors are listed in
Table 5. It was expected that one of these groups would consistently prevail over
the other groups in giving the correct hfc constants and o pvalues and thus the
correct SDD could be determined. This approach was used in the study of the
unpaired spin distribution in benzoquinone and the tyrosine radical in
ribonucleotide reductase. The distribution was changed until the calculated hfc

49

tensors for each proton matched the experimental values determined using
ENDOR. By using an iterative process the distribution of the unpaired spin was
determined.

The hfc tensors for H87HB1, H37HB2, M92HB2 and M92CH3 showed little
difference when the different SDD groups were used in their calculation. The
calculated tensors in each case gave reasonable results for all five SDD groups. The
only exceptions were the protons A38H and H87HBZ. For H87HB2 the hfc tensor
component with SDD group 3 was 1.65 MHz, which is significantly lower than the
values for the other four SDD groups and below the range of 1.78-2.50 MHz for this
hfc constant. Similar results were seen for A38H except that in this case the tensor
component was much larger, 6.22 MHz, which is outside the range of 4.13-6.13 MHz
for this set of peaks. There also were no situations where a proton assignment could
be made only by using the hfc tensor calculated using SDD group 3. The SDD
group 3 only gave viable results in those cases where the calculated tensor was
insensitive to the spin density distribution. From these results it appears that the
distribution with the unpaired spin density split equally between the copper and
sulphur atoms is incorrect. The best results are obtained with a greater portion of
the unpaired spin density on the copper atom versus the sulphur and when the
distribution on the sulphur atom is no more than 35%. Any higher resolution of this

unpaired spin density is not possible from these results.

DISCUSSION

The technique of angle selection ENDOR has proved succesful in assigning
many of the resonances in the ENDOR spectra of PCy. The complete hfc tensors
for the protons that have been assigned to the ENDOR spectra are listed in Table 6.

In each case, though, only one component of the hfc tensor could be identified.

 

50

There are several possible reasons why the other components were not detected.
The ENDOR resonance for each hfc tensor component will have its own properties
with respect to relaxation. That is, the transitions between nuclear spin states giving
rise to the ENDOR resonances (Figure 4) have different relaxation rates. If this
relaxation is fast on the ENDOR time scale then the ENDOR resonances will be
broadeded out and, in extreme cases, not detectable. The intensity of ENDOR
peaks is dependent on several factors including microwave power, RF power and
temperature. In this experiment these parameters were varied over a modest range
about the optimum conditions without resolving any new resonances.

A second explanation is the high density of resonances within this region of
the spectrum. The four protons that have been assigned have ten resonances, of
different lineshapes, with couplings of less that 3 MHz (Table 6). In many cases
tensor components from two different hfc tensors are nearly the same. If one of the
resonances is present but is severely broadened, as discussed above, and has a low
intensity relative to a second resonance, with a large intensity, the first resonance
may not be detected. In this system the reason that some of the hfc tensor
components are not detected is most likely a combination of both effects.

For the three ENDOR resonances that could not be assigned to any protons
the most likely reason is small structural differences between poplar and spinach
PCy. While the N MR NOE studies indicate that the overall structure of the two
proteins are very similar, these experiments do not have the resolution to detect
small differences in structure. For a long side chain amino acid such as methionine
or histidine a slight change in several bond angles could cause a moderate change in
the position of a hydrogen bonded to the sidechain. The discussion on the errors in
the calculated hfc tensors showed that even the relatively small shifts in atomic
position of 0.5 A can cause a significant change in the tensor components. These

results then indicate that while the magnitude may be small there is probably some

 

 

51

structural differences between poplar and spinach PCy. Since the exact unpaired
spin density distribution could not be determined it was not possible to determine
which protons had moved or the direction and amount of the movement.

Several different BCP, including two species of PCy have previously been
studied by ENDOR.3&39 In these experiments ENDOR was used to detect and
study the nitrogen ligands to the copper and to study the proton resonance with a
coupling of 27 MHz. This large coupling was proposed to come from the methylene
group of the amino acid cysteine 84, which also contains the sulphur ligand. This
coupling is large as a result of the significant amount of unpaired spin density on the
sulphur atom, which gives these two protons a large isotropic component to their hfc
constant. This same resonance was also seen in the present work (spectrum not
shown). The ENDOR spectra for PCy from the species bean and poplar were found
to be very simialr in all aspects. The spectra from these experiments, though, were
very low in resolution and showed only one set of proton resonances near the free
proton resonance. No attempt was made to acheive higher resolution spectra or to
study intensity changes of the resonances. The present work is the first attempt to
detect and assign the matrix region couplings in the ENDOR spectra of a PCy.

It has been shown here that structural and electronic information can be
obtained for biological species by using the angle selection ENDOR technique. It is
also important to note that the information was obtained from frozen solution
spectra and not from single crystals. Since single crystals have not been produced
for many of the biological species under study there are many systems where this
technique could prove very useful. In this work two sets of structural data were
determined. First, for those protons that could be assigned to the ENDOR spectra
their positions within the protein are the same as the corresponding proton in
poplar PCy. Second, this work has also shown that there are some structural
differences, although probably small, between the poplar and spinach forms of PCy.

52

With the use of several other techniques, including molecular biology and
biosynthesis, it is expected that assignments made in the ENDOR spectra can be
made less equivocal. That is, for those ENDOR resonances where two protons were
assigned or for those resonances in which no assignments could be made, these
methods will help in determining the exact assignment. These approaches are
considered briefly in the following chapter.

FUTURE WORK

The assignments to the ENDOR spectrum discussed in the previous section
were based on solid theoretical approaches. Since no substitution occurs in the
deuterium exchange experiment it was not possible to confirm these results. Our
future efforts are aimed at securing a technique in which deuterium substitution can
be accomplished and the exact site of substitution can be controlled. Substitution of
a proton that already has been assigned will be the most useful in confirming the
results obtained in this work. One possible approach for achieving the goal of
selective deuteration is the use of amino acid auxotrophs.

Auxotrophs are mutants of a species that require the addition of a certain
amino acid in the grth medium for the species to grow. Unfortunately, there are
few reports of plant amino acid auxotrophs.61 However, there are auxotrophs for
photosynthetic cyanobacteria, which also contain the protein plastocyanin. The
cyanobacteria strain Anabaena variabilis has a methionine auxotroph.62 Peaks f,f ’
in the ENDOR spectrum of PCy have been assigned to either a proton on the 13-
carbon or the protons of the terminal methyl group of methionine 92. Use of this
mutant with perdeuterated methionine and methionine selectively deuterated at the
positions discussed above would allow exact assignment of these peaks in the
ENDOR spectrum. The procedure can be followed for other auxotrophs to confirm
or determine other assignments in the ENDOR spectrum.

Upon confirmation of the proton assignments ENDOR will be used to study
PCy when it is bound to its redox partner cytochrome f. There is currently some
disagreement as to the binding site of cytochrome f on PCy.°3’64 The two proposed

53

54

sites are the acid patch consisting of amino acids 42-45 on the ”east" side of the
protein and histidine 87 on the "north” side of the protein. If binding was to occur at
the acid patch, which is approimately 12 A from the copper site, little or no
structural changes would be expected at the copper site. However, if the binding
occurs at histidine 87 significant structural modifications may occur. ENDOR will
be used to study the structural difference, if any, that occur near the copper site in
PCy after binding to cytochrome f.

Efforts are also underway to carry out site-directed mutagenesis on PCy.
One proposed modification is to substitute a cysteine for one of the non-cysteine
ligands to the copper. The purpose of this experiment is to determine if a blue
copper protein with two cysteine ligands mimics the CuA in cytochrome oxidase.
ENDOR, then, will be used both to determine if this substitution causes any
structural changes and, more importantly, to acertain whether a second cysteine

ligand causes any change in the distribution of the unpaired spin density.

APPENDIX

APPENDIX A

Program Listing for TENSORFOR

COOOOOCIC30.333...$338.83...Oit...ICOIOIIOOOIICOCCIOIICOCOCCCIOCOOIOOIC

This program will calculate a theoretical dipolar hyperfine coupling tensor, in
any axis tem. If there are several nuclei rnteractmg with the udpaired spin
densi e tensors will be rotated into a common axis system an then
adde. The total tensor will then be diagonalized and the direction cosines
from the common axis system and the axis system that diagonalized the
tensor.

Matthew Espe

Babcock research group
Dept of Chemis

Michigan State niversity

Ct3‘833338.3‘883I33883CIICOOICCCCCOCCOIIICIOCICCOOIICIOOCIIICCICIOOCICI

00000000000

REALHCE 2 $13.31.,)CGC,R(3 3), HCR(3, LENA(3, D, A53 ,,3) LVC(3), T(3, 3),
3,,3) NG(3), ),AC(33R 1123,,3) snnéil’ao 3), A3,,3) ISO, LPC,
Egéccm ,,3) MC(361’), PC(3 1’), MP, TH, s cm, VN, 6, AF, 11(3),
(TER'B INPUT,OUT‘PUT
CHARACTER’I no

INTEGER I,J,K,N, NA,B,LDA,LDEVEC,ITRING,NCA,NRA
COMPLEX EVAL( AL(3i:EVEC()3O ,3.
DATAAS ,,THFC,A, VC/9‘O , *0.0,9*0.0,9*0.0,3'0.0/

PRINT’,’THIS IS THE PROGRAM ROTATE. IN ORDER TO USE ’
PRINT’,’THE PROGRAM THE USER MUST HAVE’

PRINT ',’ALREADY SET UP AN INPUT FILE WITH THE CORRECT
SPECIFICATIONS.’

PRINT ‘,’PLEASE SEE THE DOCUMENTATION FOR HELP ON
USING THE PROGRAM.’

DATA INPUT FOR EVCRG SUBROUTINE

N = 3

LDA = 3

LDEVEC = 3

C

8 ENTERING NAME OF INPUT AND OUTPUT FILES

2000 WRITE(6,1)

000

55

(30(300‘l 9‘ 000

O

OOOOH
8

120
C

56

FORMAT(/, ,1X,’ENTER NAME OF INPUT FILE-UP TO 8
LETTERS’, /

READ(5,2) UT

FORMAT A8)

WRITE(6, )

FORMAT(/1X,’ENTER NAME OF OUTPUT FILE UP TO 8
LETTERS’,/ ’0

READ(5,) 4) UTPUT

FORMAT(A8)

CALL UMACH .19)

CALL UMACH -2,12

OPEN.UNIT=9, =INPUT,STATUS=’OLD’
OPEN UNIT=12,FILE=OUTPUT,STATUS =’ W’)
READ 1N DATA
READ(9, 7..IA (R(3, I), 1: 1,3)
READ 9 6N
FORMAT( r3
READ(9, 7) 8C(I),=l 1 ,3)
FORMAT(3
CALCULATE G-AXIS SYSTEM
DETERMINE G-X AXIS
R.1:2= ,1 =1 .0
R13

 

--R(31\14)INER(3’3§AXI

R2,1= 21,‘R1,3-R 28‘R3,3

R2,2 =R1,1 ’R3,,3-R31 ‘R 1,3

R 2,3 =R 3,1 ‘R 1,2 -R 1,1 ‘R 3,2
LENG O S

OF G-AXISVE
LENG 1 =SQRT R 1,1 "2+R 1,2 "2+R 1,3 "2
LENG 2 =SQRT R 2,1 ”2+R 2,2 “2+R 2,3 ”2
LENG 3 =SQRT R 3,1 "2+R 3,2 ”2+R 3,3 “2
100 = ,
DO 1001=1,3

RJ,I =R 1,1 LENGJ
CO I ) ( )/ ()

151833.? G AXIS SYSTEM SO THAT IT IS THE ABSOLUTE AXIS
THE COORDINATES FOR THE HYDROGEN ARE ROTATED IN
THE NEW G AXIS SYSTEM.

Do 1201- 1,3
DO 120 J=
HCR(21)= HCR(I)+R(I,J)’HC(J)
Do 120 0x= 1,3
GCR(I,J)= ’GCR(1,J)+R(J, K)*R(I,K)
CONTINUE

 

000‘”
§

000 000g 0% 00005:

000

name
93

57

WRITE 10,3000 GCR 1,1,OCR 1,2 ,GCR 1,3
WRITE 10,3000 GCR 2,1 ,OCR 2,2 ,OCR 2,3
WRITE 10,3000 OCR 3,1 ,GCR 3,2 ,GCR 3,3
FORMAT(3F8. ,/)

MAIN LOOP TO CALCULATE A-TENSOR AFTER ROTATION

DO 1000 B= 1,NA
READ(9,10 (SD(I),l=1,3)
FORMAT( F8.4)
READ(9,11 ISO
FORMAT 3)
READ(9, 1 .D
FORMAT( 63)

THIS SECTION DETERMINES THE x131, AND 2 COORDINATES OF
THEX,Y, ANDZAXISOFTHEHYP RFINETENSOR

D014OI=1,3

Do 140 J =13
CO SDR I)=SDR(I)+R(I,J)‘SD(J)

D’ACaz’ i: IHCRO) SDR(I)
CON-ilNiiE
DETERMINATION OF 2 AXIS
AC 3,1 =0 0
AC 3, ’2 _ --AC(2,3)/AC(2,2)
AC 33 —1.0
DETERMINATION OF x AXIS

AC 1,1 =AC 2,2 -AC 3,3 -AC 2,3 'AC 3,2
AC 1,2 =AC 2,3 ‘AC 3,1 -AC 2,1 ‘AC 33
AC 1,3 =AC 2,1 ‘AC 3,2 -AC 3,1 ‘AC 2,2
CONVERSION TO UNIT VECTORS

LENA 1 =SQRT AC 1,1 "2+AC1,2 "2+AC 1,3 "2
LENA2 =SQRT AC 2,1 "2+AC 2,2 ”2+AC 2,3 "2
LENA3 =SQRT AC 3’ 1 "2+AC 3, 2 "2+AC 3’3 "2

1801=1,3
D01801=

1,3
0AC5 IJ)= A(3(I.J)/1-15’N"-(1)

CALCULATION OF A TENSOR DIAGANOL COMPONENTS

I-IFC1,1 8.4'D)/LENA(2)”3
IIFC§2,2E7 gig. 4'2. 0‘D)/LENA(2)“3
HFC 3 3 C(1, 1)

OOOO§OOO

47
320

360

58

CALCULATION OF DIRECTIONAL COSINES
CONTINUE

ROTATION OF A-TENSOR INTO CRYSTAL G-AXIS SYSTEM
AND ADDITION OF THE A-TENSORS

DO 2401= 1,3
DO 240 J =1,3
T 1,1) AC(k, $91322 0 KTI’Fka)
= 1 t a
(1.1 =AS(IJ)+TIB;

$1.12] = A(I.J) + AS(IJ)

PRINTING OUT THE RESULTS

WRITE(10,20 B

FORMAT 1 COMPONENTS OF A-AXIS AND DIRECTION COSINES
FO ATOM’,12,/}

WRITE(10,25) (AC(1,I), =1,3

FORMAT(1X,’X AXIS IN A- NSOR SYSTEM’,3(1X,F11.7))

WRITE(10,30 (AC(2,I),I= 1,3

FORMAT(1 ’Y AXIS IN A- NSOR SYSTEM’,3(1X,F11.7))

WRITE(10,3)52 %AC(3,I),I= 1,3

FORMAT(1 ' AXIS IN A- NSOR SYSTEM’,3(1X,F11.7))

PRINTING OUT A TEN SOR

WRITE(10,36)
FORMAT(/,10X,’HYPERFINE COUPLING TENSOR’,/)
DO 260 I=1,3

WRITE(10,37 (HFC(I,J ,J=1,3)

FORMAT(1 3(F85,3X )
CONTINUE

PRINT OUT DIRECTION COSINES
COMPONENTS OF A MATRIX AFTER ROTATION

WRITE(10,46)
Eglggafin /, 31X,’COMPONENTS OF A TENSOR AFTER ROTATION’, /)
= 1,
WRITE(10,47 (AS(I,J),J=1,3)
FORMAT(1 3(F8.5,3X))
CONTINUE
DO 360 I=1,3
SDR I =0.0

000 000000000300

0

1200

000

2005
2010
3500
2020
2030
2040
2050

59
END OF MAIN LOOP

CONTINUE

3.3.000COOIOOCOCOOISIOOOOI.Cttttttttttttt33$Ittttlttttittttttlttlt

EVCRG IS AN IMSL LIBRARY SUBROUTINE WHICH CACULATES
THE EIGENVALUES AND EIGENVECTORS OF A MATRIX. THE
SUBROUTINES UMACH AND WRCRN ARE ALSO IMSL ROUTINES
EgAT CONTROL THE OUTPUT OF THE DATA FROM THE EVCRG

OCOIIOOIOOOOO3.3.00...I$8..tlttttltttfitttttttttttttOCIIIIIOOCIOIOO

CALL EVCRG(N,A,LDA,EVAL,EVEC,LDEVEC)
PRINTING OUT RESULTS

call WRRRN(’TOTAL A-TENSOR’,3,3,A,LDA,0)
CALL WRCRN E’EIGENVALUE’,1,3,EVAL, 1,0)
CALL WRCRN ’EIGENVECTOR’,3,3,EVEC,3,0)

DO 12001=1,3
EVL(GI=) RlEAL(EVAL(I))
DO 1200 J=
EGVC(I,J)= REAL(EVEC(I,J))
CONTINUE
LVC 1 =SQRT EOVC 1,1 "2+EGVC 2,1 "2+EGVC 3,1 "2
LVC 2 =SQRT EOVC 1,2 "2+EGVC 2,2 "2+EGVC 3,2 "2
LVC 3 =SQRT EOVC 1,3 "2+EGVC 2,3 "2+EGVC 3,3 "2
DO 14001=1,3
DO 1400 J= 1,3
EGVC(J,I) = EGVC(J,I)/LVC(I)
CONTINUE

CALCULATE ENDOR FREQUENCIES

6,2005
FORMA’I'(8X,’ YOU WISH TO CACULATE ENDOR
FREQUENCIES [Y/N]?’)
READ(5,2010 O
FORMAT(A1
IF (G.EQ.’Y’. R.G.EQ.’y’) THEN
WRITE(6, 2020)
FORMAT(SX,’ENTER ANOLE BETWEEN MAO FIELD AND gz-AXIS’)
READ(5, 2030) TH
FORMAT F5. 2)
WRITE(6, 040)
FORMAT(SX,’ENTER MAGNETIC FIELD VALUE’)
READ(5,2050) MF
FORMAT(F7.2
3%??1113817) 5
cm =COS TH)
VN=4.2577 E-3‘MF
H(3) =CIH

 

 

2200

2300

2350
2100

2410
2420
2430

2450

2455

3100

3150

00

60

DO 21001= 1,360
ANO =I‘0.01745
HE1;=STH‘COS(ANG)
H 2 =STH"SIN(ANG)
DO 2200 J = 1,3
DO 2200 K=1,3
LH J) =H(K)'EGVC(K,J) + LH(J)

DO 2300 I=1,3
AF=EGVL(J)'LH(J)"2+AF
LH J =0.0

MC(3= -VN + (AF/2)
=VN- (AF 2)

(11, ,2(3502 PC(I).I.MC(I), I
FORMAT(1X,2 F11 .6 ,I6))
AF=0.0
CONTINUE
LPC= 1
SPC=PC 1
LMC=MCél
SMC=MC 1
DO 24001 ,360
IF PCEIE. .GT. LPC) LPC= PCIf)

 
  

LT. SPC SPC= PC
.O.T C) LMC= CI)
IF MCI .L.T SMC)) SMC= MC(

WRITE(12,2410

FORMAT(/,10 ’ENDOR COUPLINOS')

WRITE(12,2420)

FORMAT(/,1X,’POSITIVE COUPLINO')

WRITE(12,2430) LPC,SPC

FORMAT(/,1X,’LARGE COUPLING = ’,Fl 1.6,’SMALL COUPLING =

’,F11.6
(12,2440)

FORMAT(/1X,’NEGATNE COUPLING’)

WRITE(12,2450) LMC,SMC

FORMAT(/,1X,’LARGE COUPLINO- - ' F,11.6,’SMALL COUPLING —

’,F11.6
WR (12,2455 VN
’FREE PROTON RESONANCE =

FORMAT(/,/,1

TH= TH/o. 01745

WRITE( 12,2460 MF, TH

%%A;F§7,om ,/, 1 MAGNETIC FIELD = ’,F7.2,’ ANGLE THETA= ’,FS.2)
FORMAT(6X,’)CALCU1ATE ANOTHER SET OF ENDOR
FREQUENCIES’)

READ(5,3150 O

FORMAT(AI

OOTO 3500

ENDIF

RETURN TO TOP TO RERUN PROGRAM

’,F6.3)

1570
1580

1590

1610
1620

1700

61

WRITE(6,1580
FORMAT(/, YOU WISH TO ENTER A NEw SET OF DATA

Egéhl’(15,1590 I?

FORMAT(A1
IF (F. EQ. ’Y’ .O.R F. EQ. y’) then
DO 1620 J= 13
HCR J’)= 0.0
SDR( )=0.0
DO 1610GCRK=1,3
J,=Ko)= 0. 0

$1in %366
CXDDFFHVIHE
(ECYT()2000
IflLSEE
CKDTT)I700
IHVEHI?

STYJP
IHVI)

BIBLIOGRAPHY

 

1)
2)

3)

6)
7)

8)
9)

10)
11)
12)

13)

14)
15)
16)
17)

18)

BIBLIOGRAPHY

Guss, J .M.; Freeman H.C., J. Mol. Biol.,1983,169,521-563

Adman, E.T., "Metalloplroteins Part 1: Metal proteins with redox roles";
Pauline Harrison Ed.; erlog Chemie:Weinhcim, Germany, 1985; pp 1-48

”Copper Proteins and Copper Enzymes"; Rene Lontie Ed.; CRC Press, Baco
Raton, FL 1984, pp 184

Adman, E.T.; Jensen, L.H., Isr. J. Chem, 1981, 21, 8-12

Norris, G.E.; Anderson, B.F.; Baker, E.N., J. Am. ChemSoc., 1986, 108,
2784-2785

Solomon, E.I., Comments Inorg. Chem, 1984, 3, 227-320

Markle , J .K.; Ulrich, E.L.; Berg, S.P.; Krogmann, D.W., Biochemistry, 1975,
14, 44 -4433

Solomon, E.I.; Clendening, PJ.; Gray, H.B.; Grunthaner, F .J ., J. Am. Chem.
Soc., 1975, 97, 3878-3879

Solomon, E.I.; Hare, J .W.; Gray, H.B., Proc. Natl. Acad. Sci. USA, 1976, 73,
1389- 1393

Hathaway, BJ.; Tomlinson, A.A.G., Coord. Chem. Rev., 1970, 5, 1-46
Bryce, G.F., J. Phys. Chem, 1966, 70, 3549-3555

Corri an, M.F.; Murray, KS; West, B.O.; Pilbrow, J .R., Aust. J. Chem, 1977,
30,24 5-2462

Huheey, J. "Inor am'c Chemistry Principles of Structure and Reactivity";
Harper & Row: ew York, 1983: pp3 -385

Fee, J .A., "Structure and Bonding”; Springer Verlag: N ewYork, 1975, 23, 1-60
Hatfield, W.E.; Jones, E.R.Jr., Inorg. Chem, 1970, 6,1502-1508
Wood, J .S., J. Chem Soc. A, 1969, 1582-1590

Slade, R.C.; Tomlinson, A.A.G.; Hathaway, BJ.; Billing, D.E., J .Chem. Soc.
A, 1968, 61-69

Barbucci, R.; Bencini, A.; Gattcschi, D., Inorg. Chem, 1977, 16,2117-2221

62

19)

20)
21)

22)

23)
24)
25)

26)
27)
28)
29)
30)

31)
32)

33)
34)
35)

36)
37)
38)

39)

63

Solomon, E.I.; Hare, J .W.; Dooley, D.M.; Dawson, J .H.; Stephens, PJ.; Gray,
H.B., J. Am Chem Soc., 1980, 102, 168-178

Iwaizumi, M.; Kudo, T.; Kita, S., Inorg. Chem, 1986, 25, 1546-1550

Penfield, KW; Gewirth, A.A.; Solomon, E.I., J. Am Chem Soc., 1985, 107,
4519-4529

"Copper Proteins and Copper Enzymes"; Rene Lontie Ed., CRC Press, Boca
Roton, F1, 1984, pp 94

Tullius, P.F.; Hodgson, KO., Proc. Natl. Acad. Sci. USA, 1978, 75, 4069-4073
Tullius, T.D., Ph.D. Thesis, Stanford University, 1979

Colman, P.M.; Freeman, H.C.; Guss, J .M.; Murata, M.; Norris, V.A.;
Ramshaw, J .A.M.; Venkatappa, M.P., Nature, 1978, 272, 319-324

Garret, T.P.J.;C1in eleffer, DJ .; Guss, J .M.; Rogers, SJ.; Freeman, H.C., J.
Biol. Chem, 1984, 9, 2822-2825

Guss, J.M.; Harrowell, M.M.; Norris, V.A.; Freeman, H.C., J. Mol. Biol.,
1986, 192, 361-387

Church, W.E.; Guss, J .M.; Potter, J.P.; Freeman, H.C., J. Biol. Chem, 1986,
261, 234-237

Esnzgéeseth, H.R.; McMillin, D.R.; Otvos, J.D., J. Biol. Chem, 1984, 259, 4822-

Armstrong, F.A.; Driscoll, P.C.; Hill, H.A.O.; Redfield, C., J. Inorg.
Biochem, 1986,28,171-180

Chazin, WJ.; Wright, RE, J. Mol. Biol., 1988, 202, 623-636

Wuthrich, K. "NMR of Proteins and Nucleic Acids"; John Wiley and Sons:
N ewYork, 1986

Driscoll, P.C.; Hill, H.A.O.; Redfield, C., Eur. J. Biochem 1987, 170, 279-292
Mustafi, D.; Makinen, M., Inorg. Chem, 1988, 27, 3360-3368

Kevan, L.; Kispert, L. “Electron Spin Double Resonance Spectroscopy"; John
Wiley and Sons: New York, 1976, 1-57

Kirste, B.; van Willigen, H., J. Phys. Chem, 1983, 87, 781-788
Yim M.B.; Makinen, M.W., J. Mag. Res., 1986, 70, 89-105

Roberts, J .E.; Cline, J.P.; Lum, V.; Freeman, H.; Gray, H.B.; Peisach, J .;
Reinhammcr, B.; Hoffman, B.M., J. Am Chem Soc., 1984, 106, 5324-5330

Roberts, J .E.; Brown, T.G.; Hoffman, B.M., Peisach, J ., J. Am Chem Soc.,
1980, 102, 825-829

64

40) Abragam A.; Bleaney, 3.; "Electron Paramagnetic Resonance of Transition
Ions", Dover Publications, New York, 1970, pp 27

41) Atkins, P.W.; Symons, M.C.R. "The Structure of Inorganic Radicals";
Elsevier: Amsterdam 1967; pp 268-270

42) Gordy, W. "Theo and plication of Electron Spin Resonance"; John
Wiley and Sons: ew Yor 1980; pp 48-68

43) Wells, G.B.; Makinen, M.W., J. Am Chem Soc., 1988, 110, 6343-6352
44) Baker, G.J.; Raynor, J .B., J. Chem Soc. Dalton Trans., 1986, 2663-2667

45) The program PROTIN was used in the laboratory of Dr. A. Tulinsky, Dept.
of chemistry, Michigan State University, East Lansing, MI

46) Kerr, KA.; Ashmore, J.P., Acta. Cryst., 1975, B31, 2022-2026
47) Fuess, H.; Hohlwein,D.; Mason, S.A., Acta. stt., 1977, B33, 654-659

48) Penfield, KW.; Ga , R.R.; Himmelwri t, R.S.; Eickman, N.C.; Norris, V.A.;
Freeman, H.C.; So omon, E.I., J. Am em Soc., 1981, 103, 4382-4388

49) IMSL Fortran Subroutines, IMSL Software Systems, Houston Tx, USA

50) Kevan, L., and Kispert, L., in "Electron S in Double Resonance
Spectroscopy", John Wiley & Sons, New ork, 1976, pp 240

51) Hurst, G.; Kraft, K; Kreilick, R., J. Magn. Reson., 1982, 49,159-165
52) Nilges, Ml, PH. D. thesis, University of Illinois, 1979

53) Groeneveld, C.M.; Aasa, R.; Reinhammer, B.; Canters, G.W., J. Inorg.
Biochem, 1987, 31, 143-154

54) Malkin, R.; Bearden, AJ., BBA, 1973, 292, 169-185

55) Scawan, M.D.; Ramshaw, J .AM.; Boulter, D., Biochem J ., 1975, 147, 343-349
56) Wells, J .W.; Box, H.C., J. Chem Phys., 1968, 48, 2542-2546

57) Clough, S.; Poldy, F ., J. Chem Phys., 1969, 51, 2076-2084

58) O’Malley, PJ.; Babcock, G.T., J. Am Chem Soc., 1986, 108, 3995-4001

59) Bender, C.J.; Sahlin, M.; Babcock, G.T.; Barry, B.A., J. Am Chem Soc.,
1989, 111, 8076-8083

60) Egezfgsoné3\g.L; Ulrich, E.A.; Krogman, D.W., Methods in Enzymology, 1980,

61) Ne 'tiu, 1.; De Brouwer, D.; Dirks, R.; Jacobs, M., MOI. Gen. Genet., 1985,
1 , 330-337

 

65
62) Currier, T.C.; Haury, J .F.; Wolk, C.P., J. Bacteriol., 1977, 129, 1556-1562

63) Farver, 0.; Shahak, Y.; Pecht, 1., Biochemistry, 1982, 21, 1885-1891
64) Burkey, KO.; Gross, E.L.; Biochemistry, 1982, 21, 5886-5893

"llllllltl'lllllfitl“