EPR studies of the dynamics of rotation of dioxygen in model cobalt(II) hemes and cobalt-containing hybrid hemoglobins

Article abstract of DOI:10.1021/jp9711306

Earlier we showed that the shapes of the EPR spectra of cobalt(II) porphyrinate(nitrogen base)(dioxygen) complexes in fluid solution were sensitive to the rate of rotation about the Co-O bond (Walker, F. A.; Bowen, J. H. J. Am. Chem. Soc. 1985, 107, 7632). We have now extended these studies to four metal-substituted hybrid hemoglobins in an attempt to determine whether EPR spectroscopy is sensitive to differences in the mobility of dioxygen in the α and β subunits of the T and R quaternary states. For purposes of this study, [α₂(CoO₂)β₂(FeO₂)] and [α₂(FeO₂)β₂(CoO₂)] were used as R-state models and [α₂(CoO₂)β₂(Zn)] and [α₂(Zn)β₂(CoO₂)] were used as T-state models. EPR spectra were recorded for samples of each of the above hybrids, equilibrated with 1 atm of O₂ gas, as a function of temperature. The progress toward averaging of the EPR signals of the Co-O₂-containing subunits was measured as the difference in field positions, ΔH, for the midpoint of the low- and high-field extrema of the derivative EPR spectra. A plot of ΔH vs temperature for each hybrid shows that the [α₂(Zn)β₂(CoO₂)] hybrid is unique in averaging more slowly than the other three (all of which behave similarly), indicating more restricted rotation of dioxygen in T-state β-chain pockets than in the heme distal O₂-binding pockets of any other form. This finding is consistent with X-ray crystallographic data which show that valine E11 on the distal side of the T-state β-chain pocket partially blocks the dioxygen binding site (Perutz, M. F.; Fermi, G.; Luisi, B.; Shaanan, B.; Liddington, R. C. Acc. Chem. Res. 1987, 20, 309). Simulation of EPR spectra as a function of jump time provides semiquantitative estimates of the rate of dioxygen rotation in these mixed-metal hemoglobin-dioxygen samples; these rates are in the 1 × 10⁸ s^-1 range for three of the hybrids at 35-37°C, and about one-third that value for T-state β(CoO₂) centers. These results provide new insight into the highly dynamic nature of dioxygen bound to the metal centers of hemoglobin at physiological temperatures.

Full text of DOI:10.1021/jp9711306

J. Phys. Chem. B 1997, 101, 8683-8691
8683
EPR Studies of the Dynamics of Rotation of Dioxygen in Model Cobalt(II) Hemes and
Cobalt-Containing Hybrid Hemoglobins
James H. Bowen,† Nikolai V. Shokhirev,‡ Arnold M. Raitsimring,‡ Daniel H. Buttlaire,† and
F. Ann Walker*,‡
Department of Chemistry and Biochemistry, San Francisco State UniVersity, San Francisco, California 94132,
and Department of Chemistry, UniVersity of Arizona, Tucson, Arizona 85721
ReceiVed: March 31, 1997; In Final Form: July 28, 1997X
Earlier we showed that the shapes of the EPR spectra of cobalt(II) porphyrinate(nitrogen base)(dioxygen)
complexes in fluid solution were sensitive to the rate of rotation about the Co-O bond (Walker, F. A.;
Bowen, J. H. J. Am. Chem. Soc. 1985, 107, 7632). We have now extended these studies to four metal-
substituted hybrid hemoglobins in an attempt to determine whether EPR spectroscopy is sensitive to differences
in the mobility of dioxygen in the R and â subunits of the T and R quaternary states. For purposes of this
study, [R2(CoO2)â2(FeO2)] and [R2(FeO2)â2(CoO2)] were used as R-state models and [R2(CoO2)â2(Zn)] and
[R2(Zn)â2(CoO2)] were used as T-state models. EPR spectra were recorded for samples of each of the above
hybrids, equilibrated with 1 atm of O2 gas, as a function of temperature. The “progress toward averaging”
of the EPR signals of the Co-O2-containing subunits was measured as the difference in field positions, ∆H,
for the midpoint of the low- and high-field extrema of the derivative EPR spectra. A plot of ∆H vs temperature
for each hybrid shows that the [R2(Zn)â2(CoO2)] hybrid is unique in averaging more slowly than the other
three (all of which behave similarly), indicating more restricted rotation of dioxygen in T-state â-chain pockets
than in the heme distal O2-binding pockets of any other form. This finding is consistent with X-ray
crystallographic data which show that valine E11 on the distal side of the T-state â-chain pocket partially
blocks the dioxygen binding site (Perutz, M. F.; Fermi, G.; Luisi, B.; Shaanan, B.; Liddington, R. C. Acc.
Chem. Res. 1987, 20, 309). Simulation of EPR spectra as a function of jump time provides semiquantitative
estimates of the rate of dioxygen rotation in these mixed-metal hemoglobin-dioxygen samples; these rates
are in the 1 × 108 s-1 range for three of the hybrids at 35-37 °C, and about one-third that value for T-state
â(CoO2) centers. These results provide new insight into the highly dynamic nature of dioxygen bound to the
metal centers of hemoglobin at physiological temperatures.
Introduction
hemes in the â-chains of the crystals studied were oxidized to
the inactive met form.9 In the T state, the crystal structures
Since the report of the crystal and molecular structure of the
tetrameric heme protein methemoglobin by Perutz and co-
workers in 1968,1 there have been a number of further structural
studies that have provided detailed insight into the structural
basis for the cooperativity of binding of dioxygen that has been
observed in the kinetics and equilibria of dioxygen binding and
release2-5 for many years. The two-state allosteric mechanism
originally proposed by Monod and co-workers6 was first
interpreted in terms of a structural model by Perutz in 19707
and has been elaborated and extended several times since.8,9
The two states are described as the deoxy or “tense” (T) form
and the oxy or “relaxed” (R) form, and each form has a distinct
3-dimensional structure. The dioxygen binding affinity of the
T structure is slightly less than that of the R structure.9 The T
and R structures differ in the relationship of the four subunits
(two R and two â chains, each of which contains a protoheme
molecule that can bind one molecule of O2) to each other, as
well as in the conformation of the individual subunits. The
quaternary TfR transition causes a rotation of one Râ dimer
relative to the other by 12-15° and a translation of one dimer
relative to the other by about 0.8 Å.9 Binding of O2 to the R
subunits in crystals of deoxyhemoglobin causes movement of
the R-chain Fe atoms toward the porphyrin by 0.15 Å, though
the porphyrin remains domed, and approximately 30% of the
have shown that the distal valine E11 obstructs the binding site
for O2 in the â-chain hemes.9 From this and many studies of
the kinetics of dioxygen binding, the impression has arisen that
O2 binds more readily to the R-chain than to the â-chain hemes.
This is an oversimplification, however, as pointed out by the
detailed studies of Ackers et al.,5 who find that of the eight
partially ligated states of hemoglobin, quaternary switching from
T to R occurs whenever binding to the hemes creates a tetramer
with at least one ligated subunit on each dimeric half-molecule.
Recent use of the Laue method, coupled with fast laser flashes
to break the Fe-CO bond, have allowed visualizing the Fe out-
of-plane, histidine and protein chain movements that occur on
very short time scales when CO is flashed off the heme centers
of crystals of the related monomeric protein, myoglobin.10,11
Metal-substituted hemoglobins, especially the “hybrid” he-
moglobins having different metals (or different oxidation states
of the same metal) in the porphyrin rings of R and â subunits,
have been extremely useful in obtaining detailed information
concerning cooperativity in the binding of dioxygen (and other
ligands) to hemoglobin. Dynamic properties, spectroscopic
signatures and static structures have been studied for a large
number of metal-substituted hemoglobins and myoglobins.12 For
these techniques to be used, methods had to be developed for
preparation of the mixed-metal proteins in pure form. Yonet-
ani13 used the acid-butanone method first reported by Teale14
to show that hemin could be removed from both cytochrome c
peroxidase and methemoglobin by this method, and that the
† San Francisco State University.
‡ University of Arizona.
X Abstract published in AdVance ACS Abstracts, October 1, 1997.
S1089-5647(97)01130-9 CCC: $14.00 © 1997 American Chemical Society

8684 J. Phys. Chem. B, Vol. 101, No. 43, 1997
Bowen et al.
former protein in tris-HCl buffer at pH 8.0 could be reconstituted
with hemin dissolved in 0.1 M NaOH.13 Shortly thereafter, the
first reports of the oxygen binding characteristics of hybrid
hemoglobins having one type of subunit in the cyanomet
form15,16 or simply mixed oxidation state hybrid hemoglobins17
were reported, and not long after those reports, Waterman and
Yonetani reported the first mixed metal hybrid hemoglobins,
the [R2(FeCO)â2(Mn3+)] and [R2(Mn3+)â2(FeCO)] hybrids.18
At about the same time, Hoffman and Petering19 reported the
preparation of “coboglobins”, the cobalt-protoporphyrin com-
plexes of myoglobin and hemoglobin, and showed that they bind
O2 reversibly. (Hoffman has since reviewed the preparation
and study of metal-substituted hybrid hemoglobins.12) Because
of the odd-electron configuration of Co(II) (d7), the dioxygen
complex is EPR-active, while the Fe(II)-O2 center is not.
Hence, EPR spectroscopy could be used to investigate questions
related to the effects of the allosteric mechanism of O2 binding,
although mixed-metal Co, Fe hybrid hemoglobins were not
reported until 1977.20 Single-crystal EPR spectroscopy of the
dioxygen complex of cobalt(II)-containing myoglobin21-24 and
its deoxy precursor25 have been reported. In addition, EPR
spectra of Co,Fe hybrids of hemoglobin show that there are
slight differences in the EPR spectra of the Co-O2 centers of
the T- and R-state forms of oxyhemoglobin.26
for the changes.) Hence, it was clear to us that the rotation of
dioxygen in the heme pocket of CoMbO2 is hindered (either
due to H-bonding between the distal histidine and O2 or to
crowding of distal pocket protein residues against the bound
O2) that the rates of rotation of dioxygen are slow but
measurable on the EPR time scale, and that the rate of rotation
might be measureable by EPR line-shape analysis techniques.
We thus decided to extend our studies to Co-substituted
hemoglobins, for which, by proper choice of partner metals,
we could stabilize the T or R quaternary state and attempt to
discover whether there were differences in the rate of rotation
of bound O2 in the R and â subunits in the two different
quaternary states. Although the experimental work reported
herein was completed some time ago,34 they have not previously
been published in the formal scientific literature, and methods
for analyzing the EPR spectra to determine the rates of rotation
of bound dioxygen have been developed only recently and are
also reported herein.
As partner metals, to stabilize the T- and R-state conforma-
tions, we chose Fe(II) to stabilize the R state in [R2-
(FeO2)â2(CoO2)] and [R2(CoO2)â2CoO2)] hybrids and Zn(II) to
stabilize the T state in [R2(Zn)â2(CoO2)] and [R2(CoO2)â2(Zn)]
hybrids. Zn(II) hemoglobin has previously been shown to be
in the T state,12 and, of course, Zn(II) does not bind O2. With
foresight we might have chosen as the T-state models the Ni-
(II) complexes rather than Zn(II), but the extensive studies of
(Ni,Fe) hybrid hemoglobins9,35-38 that show the strong stabiliza-
tion of the T-state conformation were not available when the
experimental part of this work was carried out. For the Zn(II)
hybrids that we have studied, we find that one of the T-state
hybrids, [R2(Zn)â2(CoO2)], is unique in having much slower
rotation of dioxygen about the Co-O2 bond than do the other
three hybrids.
We were among the first investigators to study the EPR
spectrum of synthetic porphyrinatocobalt(II)-dioxygen com-
plexes in detail,27 and we have extended these studies over the
years to investigate the equilibrium constants for binding
dioxygen to 5-coordinate cobalt porphyrinates,28 the effect of
organic π-complexing agents on the Co-O2 EPR spectral
parameters,29 the relationship between equilibrium constants for
binding dioxygen and the CoIII/CoII reduction potentials of a
series of 5-coordinate cobalt porphyrinates30 and the effect of
hydrogen-bonding from a porphyrin substituent to the terminal
oxygen atom of coordinated O2 on the dynamics of rotation of
dioxygen about the Co-O bond.31 In the latter work striking
differences in the shape of the EPR signal were observed for
two monoacetamide (NHCOCH3) substituted TPPCo(N-MeIm)-
(O2) complexes as a function of temperature: The mono-p-
NHCOCH3 derivative, like all other Co(II) porphyrinates studied
previously, exhibits a rhombic, powder-type spectrum having
at least 17 resolved lines below the freezing point of the solvent
(toluene, -95 °C), while it exhibits an “isotropic” 8-line EPR
signal above the freezing point of the solvent.31 In comparison,
the mono-o-NHCOCH3 derivative exhibits a quite different
temperature-dependent behavior, in which the same rhombic,
powder-type EPR spectrum is observed below the freezing point
of the solvent, but above -95 °C the EPR spectrum first loses
the 59Co hyperfine structure and then slowly broadens further,
with the outermost “wings” of the spectrum slowly moving
toward the center (as shown on the right-hand side of Figure 1
of ref 31). Only near room temperature, where, unfortunately,
the dioxygen complex is not very stable, does the eight-line
“isotropic” spectral pattern develop.31 We interpreted this
behavior as being due to slow rotation of the dioxygen moiety
due to hydrogen-bonding between the amide N-H proton and
the terminal O of the coordinated O2,31 which is bound at a
Co-O-O angle of approximately 145°.32,33
Experimental Section
General Techniques. All organic solvents and reagents not
described in the following were purchased from Aldrich, E. M.
Scientific, Sigma, or Mallinckrodt. TPPCo(II) and its N-
methylimidazole (N-MeIm) and dioxygen adducts were prepared
as described previously.27,31
Hybrid Hemoglobins. Unless otherwise stated, the following
procedures were carried out at 6-8 °C. The heme-free form
of human hemoglobin A (Sigma, 0.3-0.5 mM in heme site),
hereafter called apoHb, was prepared by a modification of the
acid-butanone method.13 The changes in the procedure are as
follows. Following heme removal at pH 3.0 the apoprotein
solution was dialyzed 12 times against ice-cold distilled water
for 20 min each followed by two dialyses, 45 min each, versus
4 °C buffer (50 mM bis-Tris, pH 8.0 for CoHb preparation,
and 10 mM bis-Tris, pH 6.65 for ZnHb preparation). The
solution was then dialyzed overnight against 50 mM bis-Tris,
pH 8.0 for CoHb, and 10 mM bis-Tris, pH 6.65 for ZnHb. The
absorption spectrum of the globin is that of a typical protein
spectrum with a band centered at 280 nm; the ꢀmM at 280 nm
is 12.7 for human apoHb,39 and we have used this value for
determining protein concentrations in the reconstitution proce-
dures below.
Reconstitution. ZnHb:40 Globin solution, pH 6.65, 10 mM
bis-Tris, was cooled to 0 °C with ice. A 1.1 equivalent amount
of Zn(II) protoporphyrin (Zn(II)Por) was dissolved in a mini-
mum amount of 0.1 N KOH (0.5-1.0 mL), diluted 10-fold with
distilled water, and also chilled. The Zn(II)Por solution was
added dropwise to the gently stirring globin solution (0 °C);
the pH rose but was maintained between 8 and 9 by addition
of dilute 4 °C HCl. After the addition of Zn(II)Por the solution
In that same study we also extended our investigation from
synthetic cobalt(II) tetraphenylporphyrinates to the dioxygen
complex of cobalt-substituted myoglobin, CoMbO2, and showed
that a similar loss of hyperfine structure, followed by slow
collapse of the rhombic signal occurs in this case as well.31 (A
detailed report of these spectral changes for CoMbO2 had
appeared earlier,24 but the authors had not recognized the reason

Dioxygen in Model Cobalt(II) Hemes
J. Phys. Chem. B, Vol. 101, No. 43, 1997 8685
was left to stir for 1 h at 0 °C. A small amount of precipitate
formed and was removed by centrifugation at 10 000 rpm for 1
min.
The supernatant was cooled to 4 °C, titrated with dilute 4 °C
HCl to pH 6.65 and applied to a 1.5 × 5 column packed to a
height of 3 cm with CM-trisacryl (LKB) which was equilibrated
with 10 mM bis-Tris, pH 6.65. The column was washed with
the same buffer until the eluate was clear. Then ZnHb was
eluted with pH 6.65, 10 mM bis-Tris, plus 0.5 M NaCl. ZnHb
catalase for 2 h. The mixture of R-pMB, dithiothreitol, and
catalase was passed through a 4.5 × 30 cm column packed to
25 cm with Sephadex G-25 (coarse) which was equilibrated
with 10 mM phosphate buffer, pH 6.6. The red-colored R-SH
fraction was loaded onto a 2.6 × 50 cm column packed to 10
cm with CM-trisacryl which was equilibrated with 10 mM
phosphate buffer, pH 6.6. The R-SH chains stuck at the top of
the column. The column was washed with the same buffer.
Following this washing the R-SH chains were eluted with pH
7.4, 50 mM phosphate buffer.
concentration was determined spectrophotometrically using ꢀmM
-
The mixture of â-pMB chains, dithiothreitol, and catalase was
passed through a 6.0 × 40 cm column packed to 30 cm with
Sephadex G-25 (coarse) which was equilibrated with pH 8.67,
50 mM tris buffer. The red-colored â-SH fraction was loaded
onto a 1.6 × 30 cm column packed to 7 cm with DEAE-trisacryl
which was equilibrated with 7 mM Tris buffer, pH 8.6. The
â-SH chains stuck at the top of the column. The column was
washed with the same buffer, and then the â-SH chains were
eluted with 50 mM phosphate buffer, pH 7.4. After the buffer
was changed from 50 mM phosphate, pH 7.4 to 50 mM Tris,
pH 7.4, the regenerated chains were stored aerobically at -60
°C.
Recombination of Subunit Chains.39 The R-SH and â-SH
chains were incubated with dithiothreitol (2 mg/mL) for 1 h in
the presence of 10 µM catalase before recombination. The R-SH
chains containing one metal were mixed with a 1.2-fold excess
of â-SH chains containing another metal to produce the [Fe,-
Co] and [Zn,Co] hybrids. After about 2 h, the mixture was
passed through a 4.5 × 30 cm column packed to 25 cm with
Sephadex G-25 (coarse) which was equilibrated with 10 mM
phosphate buffer, pH 6.9. The mixture was then applied to a
1.6 × 30 cm column and packed to 7 cm with DEAE-trisacryl
equilibrated with the same buffer. The excess â-SH chains stuck
to the column while the recombined tetramer eluted from the
column. After the buffer was changed from 10 mM phosphate,
pH 6.9 to 50 mM bis-Tris, pH 7.4 the hybrids were stored
aerobically at -60 °C.
(550 nm) ) 8.37. The solution was stored aerobically at 4-6
°C.
Zinc protoporphyrin IX was prepared from zinc acetate and
protoporphyrin IX by refluxing 100 mg of the free base and
456 mg of zinc(II) acetate tetrahydrate in 50 mL of a mixture
of chloroform-methanol (4:1). The reaction was monitored
by recording visible spectra of aliquots withdrawn from the
reaction flask. The reaction was completed within 10 min. Upon
completion, the solution was placed in a separatory funnel and
washed with five 100 mL portions of distilled water and
evaporated to dryness.
CoHb: CoHb was prepared from apoHb and cobalt proto-
porphyrin IX (Sigma) as described by Yonetani et al.41 The
reduced cobalt porphyrin in aqueous pyridine was added
dropwise to gently stirring globin solution under argon at 0-5
°C. After 30 min, the reconstituted CoHb was applied to an
anaerobic 6.0 × 40 cm column packed to 30 cm with Sephadex
G-25 (coarse) which was equilibrated with 10 mM bis-Tris, pH
6.0, and 0.25 M NaCl. This step removes the excess dithionite
and reaction products from the reconstituted protein. The
concentration of oxy CoHb was obtained spectrophotometrically
using ꢀmM(422) ) 120.
Preparation of Subunit-pMB Chains. A modification of
the methods of Geraci et al.42 and Ikeda-Saito et al.43 was used.
FeHb or CoHb in the oxy form, or ZnHb (1-2 mM in Zn-
substituted heme and 60-80 mL volume) was allowed to react
overnight with p-hydroxymercuribenzoate (pMB, Sigma; 10-
fold excess per Hb tetramer) at pH 6.0-6.1 in the presence of
0.25 M NaCl. When the exposed groups (-SH) in position
93(â), 112(â), and 104(R) of hemoglobin were reacted with
pMB dissociation into single-chain molecules occurred almost
completely.39 The next morning the pMB-Hb solution was
centrifuged at 10 000 rpm for 10 min to remove any precipitate.
To obtain the R-pMB subunits, one-half of the solution was first
applied to a 4.5 × 30 cm column packed to 25 cm with
Sephadex G-25 (coarse), which was equilibrated with 0.01 M
phosphate buffer at pH 8.0. Following elution of the first red
band the eluate was filtered onto a 2.6 × 40 cm column packed
to 35 cm with DEAE-trisacryl (LKB) which was equilibrated
with 0.01 M phosphate buffer at pH 8.0. The R-pMB subunits
were eluted with the same buffer.
To obtain the â-pMB subunits the other half of the solution
was applied to a 6.0 × 40 cm column packed to 30 cm with
Sephadex G-25 (coarse) which was equilibrated with 0.01
phosphate buffer at pH 6.6. Following elution of the first red
band the eluate was filtered onto a 2.6 × 40 cm column packed
to 30 cm with CM-trisacryl which was equilibrated with 0.01
phosphate buffer at pH 6.6. The â-pMB subunits were eluted
with the same buffer. The pMB subunits were stored aerobically
for 24-48 h at 4-6 °C before pMB removal and subunit
recombination.
Evaluation of the Preparations. The purity of the recom-
bined hybrids was checked by electrophoresis on a Gelman
Separatic cellulose acetate (Sephapore) gel using buffer at pH
8.8. Hybrid samples [Fe,Co] and [Zn,Co] were electrophoreti-
cally compared with normal Hb A. The presence of proteins
was ascertained by treating the cellulose acetate strips with
Ponceau S protein stain. Comparison of the hybrid samples
with the control (Hb A) showed a very similar mobility,
indicating the presence of tetrameric hybrids and a satisfactory
preparation.
Spectroscopy. UV-visible spectra were obtained on a
Hewlett-Packard 8451A diode array spectrophotometer at 22
( 1 °C using 1.0 cm quartz cuvettes. X-band EPR spectra of
hybrid hemoglobin solutions at pH 7.4 in 50 mM bis-Tris were
recorded immediately following concentration to approximately
10 mM. EPR studies of the hybrid hemoglobins were carried
out on a Varian E-12 X-band spectrometer equipped with a
flowing nitrogen temperature controller at San Francisco State
University. Field sweep was calibrated using a Varian weak
pitch sample (g ) 2.0027) or a sample of DPPH (g ) 2.0036).
Temperature calibration was carried out using a small-gauge
copper-constantan thermocouple referenced to distilled ice
water. Cobalt(II)-containing hybrid hemoglobin samples were
placed in thin-walled gas-permeable Teflon microtubing (Zeuss
Industrial Products, 1.2 mm o.d. × 0.05 mm wall) which was
folded in half and inserted into an open-ended quartz EPR
sample tube. The sample tube was then placed into the
microwave node in the EPR cavity. Oxygen was used as the
Removal of pMB.39 The removal of pMB and subsequent
recombination of subunit chains was accomplished by the
method of Ikeda-Saito et al.39 The R-pMB or â-pMB chains were
incubated with 20 mM dithiothreitol in the presence of 5 µM

8686 J. Phys. Chem. B, Vol. 101, No. 43, 1997
Bowen et al.
thermostating gas in order to maintain the hybrid hemoglobin
sample saturated with oxygen throughout the experiment.31
Q-band EPR spectra of [TPPCo(N-MeIm)(O2)] in toluene
glasses were obtained at 77 K at the National EPR Center in
Madison, WI.
ν0 is the microwave frequency, P is the transition probability:
2
P ) Tr(Gˆ 2) - (beTGˆ 4be)/geff
(5)
and geff is the effective g-factor:
EPR Simulations
T
2
x
geff
)
be Gˆ be
(6)
The most rigorous method for the simulation of the EPR
spectra of molecules undergoing reorientational and other
motions is the stochastic Liouville theory.44,45 This approach
allows one to take into account both quantum dynamics of the
electron and the nuclei and classical motion of the molecule.
However, the computational complexity of this approach
increases considerably with the increase in the number of both
classical and quantum degrees of freedom. Thus, instead of
using one universal method, we have developed several simpli-
fied methods taking into account specific features of the systems
of interest to this work. In particular, the complexes under
consideration have very high nuclear spin, I ) 7/2, and in
addition to the rotation of the molecules as a whole, there is an
extra degree of internal rotation around the Co-O axis. In all
complexes both g and A tensors are associated with the O-O
fragment and not with the porphyrin molecule itself.21,23
The following types of motion (and corresponding simulation
methods) were used: (1) Slow rotation of both the molecule
and the O-O group (averaging over orientations). (2) Fast
rotation of the O-O group around the Co-O bond, but slow
motion of the molecule. (3) Arbitrary rotation of the O-O group
but slow rotation of the molecule. (4) Fast rotation of the
molecule (and arbitrary rotation of the O-O group).
The ranges of applicability of some of these particular cases
overlap and several methods were used for testing the consis-
tency of the methods.
The total spectrum was calculated as the sum of eq 3 for
different transitions averaged over magnetic field orientations.
For the averaging, two-dimensional pseudo-random numbers
bꢀ uniformly distributed in the unit square were used,47,48 so that
the vector
sin θ cos φ
be ) sin θ sin φ
(7)
(
)
cos θ
is uniformly distributed on a unit sphere. Here
cos θ ) 2ê1 - 1
φ ) 2πê2
(8)
The number of points were 213 (8192) and 214 (16384).
This method for the calculation of EPR spectra was ac-
complished by creating a computer program for an IBM-
compatible PC with visual control of the simulation. The
additional broadening was performed in an interactive regime
in a separate program for the post-simulation processing by
convolution with the Gaussian or Lorentzian functions.
Method 2: Fast Rotation of the O-O Group around the
Co-O Bond, but Slow Motion of the Molecule. For the
simulations of this case, the above procedure for averaging is
applied to the system with already averaged g and A tensors
due to the fast rotation over the Co-O bond (axis bn). The new
(averaged) g tensor is an axial one with the principal axis bn
and the value
In all methods the Hamiltonian in the magnetic field scale
was used:
gNâN
Hˆ ) BSTGˆ BB + BSTAˆBI -
BI TBB
(1)
geâ
This expression is obtained by dividing the Hamiltonian in the
energy scale by geâp. In the above Hamiltonian, spin operators
are dimensionless, while the tensor of hyperfine interaction and
eigenvalues of (1) have the dimension of magnetic field strength.
The sign T denotes transpose, all other notations have the
conventional meaning. In further calculations it is assumed that
g| ) bnTGˆ bn
(9)
and two axes perpendicular to the axis of rotation and the values
g ) 1/2(TrGˆ - bnTGˆ bn)
(10)
EeZeeman . EeN . ENZeeman
(2)
The same expressions are valid for the partially averaged A
tensor. This type of averaging is also incorporated into the EPR
simulation program.
Method 3: Arbitrary Rotation of the O-O Group but
Slow Rotation of the Molecule. The simplified variant of the
stochastic Liouville equation was used (in fact, it is reduced to
the modified Bloch equations (spectral exchange) for transverse
magnetization). The angles between the directions of the
external magnetic field be and the axis of rotation bn were chosen
to be equally spaced:
HFI
The above condition is satisfied for the complexes under
consideration. Transition energies ∆(BB) (in linear magnetic field
scale) were calculated up to the second order of perturbation
theory.
Method 1: Slow Rotation of Both the Molecule and the
O-O Group. The contribution to the spectrum for a given
orientation of the external magnetic field be relative to the
molecule was calculated as46
B0 - ∆(Bbe)
P
geff
π
K
1
2
F(B)
f
(3)
θk ) k -
k ) 1, ..., K
(11)
(
)
(
)
b
Here f is a line-shape function (assumed to be of the Gaussian
or Lorentzian type), b is the line width (in gauss), and B0 is the
resonance field:
for each k the number of orientations (angles of rotation φ) Mk
were chosen proportional to the area between k-1/2 θk+1/2
:
π
K
1
2
Mk ) 2K sin k -
(12)
B0 ) hν0/geâ
(4)
(
)

Dioxygen in Model Cobalt(II) Hemes
The total number of points is
N ≈ (4/π)K2
J. Phys. Chem. B, Vol. 101, No. 43, 1997 8687
(13)
In the calculations K ) 64 and 128 (N ) 5215 and 20 860)
were used.
Thus, the following equations were solved:
-bτFm-1 + [i(B0 - ∆(BBm) + b + 2bτ]Fm - bτFm+1 ) ic
(14)
with the cyclic condition
FM +1 ) F1
(15)
k
Here b is initial line width (phase relaxation), and bτ is the rate
of jumps between adjacent orientations in the magnetic field
scale. This rate can be connected with the time of jumps τ and
the angular diffusion coefficient D:
2
B0
B
Mk
bτ )
)
0D
(16)
( )
ν0τ ν0 2π
where c is proportional to the longitudinal relaxation and the
scanning magnetic field strength. In eq 16 the definition
Figure 1. Experimental and simulated spectra of the 5-coordinate
deoxy complex, [(p-OCH3)4TPPCo(Pyridine)].27 The simulation pro-
gram developed for this work does not include superhyperfine splittings.
2
1
1 2π
τ Mk
D ≡
)
(17)
τ(∆φ)2
( )
was used.
This method was used only as a limiting case for the
comparisons with the other methods.
The contribution to the spectrum for a given θk is
Method 1 was first tested on the EPR spectrum of the deoxy,
5-coordinate complex [(p-OCH3)4TPPCo(pyridine)].27 The
previously reported spectrum,27 including 14N superhyperfine
structure from the pyridine ligand, and the calculated spectrum,
for which 14N shf is not included, are compared in Figure 1.
As is apparent, the simulation is quite acceptable. However,
the present treatment does not properly simulate the EPR spectra
having large second-order corrections, including the 4-coordinate
precursor of the above-mentioned complex.27
m)1
Mk
F(θk) )
Im Fm
(18)
The total spectrum is obtained by summation over all k.
Comment on the Rate of Rotation. The angular diffusion
coefficient D may be connected with the “rate” of stochastic
rotation R by the following relation:
1
D
σ
DT ) σ,
R ≡
)
(19)
T
Results and Discussion
Here σ is a numerical constant. It was chosen in the following
way: The average square of the angle as a function of time is
EPR Experimental Results. In Figure 2 are shown the EPR
spectra obtained for the four hybrid hemoglobins as a function
of temperature. The resolution of the frozen spectra at 77 K
(not shown) was not as good as has been reported by others,25
because no glassing agent (methanol, ethanol, ethylene glycol,
etc.) was added that might interfere with our desired study of
the temperature-dependent collapse of the powder-pattern
spectrum. As expected, and as can be seen, the “wings” of the
glassy EPR spectrum (marked by arrows) move inward as the
temperature is increased (Figure 2). Zn(II)-containing hybrid
hemoglobins readily developed a free radical signal, likely from
the creation of protoporphyrinatozinc(II) cation radicals and O2•-
due to electron transfer from the zinc porphyrin to Co-O2
centers or to O2 itself, that became significant above tempera-
tures of -5 °C. Even in the presence of this interfering free
radical signal, the trend toward collapse of the “glassy” EPR
signal as the temperature is raised is clearly evident. Spectra
were analyzed qualitatively as shown in Figure 3, where the
distance between the half-rise of the derivative Co-O2 EPR
signal at low-field and the half-fall of the same signal at high
field was measured and defined as ∆H, a qualitative measure
of “the progress toward averaging” of the EPR signal. This
“progress toward averaging” is plotted as a function of tem-
perature above the freezing point of water in Figure 4 for each
of the hybrid hemoglobins studied. As is apparent from Figure
(-1)m
π2
2
φ2
)
+ 4
e-Dm t
(20)
∑
m2
3
m)1
At Dt ) π2/10 ≈ 0.986 96 the average angle θ defined as
φ ) φ2
(21)
x
x
reaches 0.7434 of its limiting value π/ 3. At this point
x
2Dt 0.4472π or 80.5°.
The value π/10 was chosen for σ. In this case, taking into
account the definition (19), bτ can be expressed in terms of the
rate of rotation R:
B0RM2k
bτ )
(22)
ν040
Method 4: Fast Rotation of the Molecule (and Arbitrary
Rotation of the O-O Group). In this case both tensors are
isotropic with the following g value and HFI constant:
g ) 1/3Tr(Gˆ ),
a ) 1/3Tr(Aˆ)
(23)

8688 J. Phys. Chem. B, Vol. 101, No. 43, 1997
Bowen et al.
Figure 4. “Progress toward averaging”, ∆H, of the CoO2 signal as a
function of temperature above the freezing point of the solvent for the
four hybrids of this study, measured by the method shown in Figure 3.
Note that the T-state â-chain CoO2 signal is uniquely retarded in
averaging as compared to the other three.
Figure 2. X-band EPR spectra of hybrid hemoglobins in 50 mM bis-
Tris at pH 7.4 in the presence of 1 atm of O2, recorded as a function
of temperature: (left to right) (A) [R2(CoO2)â2(Zn)], (B) [R2(CoO2)â2-
(FeO2)], (C) [R2(Zn)â2(CoO2)], (D) [R2(FeO2)â2(CoO2)]. The sharp peak
centered in the “perpendicular region” of the spectra of the [Zn,Co]
hybrids (A and C) is absent when zinc is absent or when the sample
has not been exposed to oxygen for long periods of time, and is believed
to be due to ZnP+• and/or O2-•, both of which can be formed by electron
transfer from ZnP to O2. The arrows on either end of the spectrum
indicate the approximate starting and ending points of the spectrum
and the fact that they move inward as the temperature is raised; the
method used for measuring these points is shown in Figure 3.
that the distal valine E11 blocks the binding site of O2 in
hemoglobin T-state â-chains;9 if it blocks the binding, it must
certainly block the rotation of O2 about the Co-O2 bond.
Hence, the retardation in the “progress toward averaging” for
this hybrid is consistent with steric hindrance from the distal
valine E11;9 it is not consistent with stronger H-bonding from
the distal histidine to the O2 of this hybrid than for the others,49
since no H-bonding between the distal histidine and O2 has been
detected by X-ray crystallography for the â-chains of HbO2.50
EPR Spectral Simulation Results: Estimation of the Rate
of Rotation of Dioxygen. Because of better resolution in frozen
toluene solvent, we have chosen to estimate the rates of rotation
of dioxygen to which the EPR spectrum is sensitive by using
the glassy EPR parameters of the toluene-soluble tetraphe-
nylporphyrinatocobalt(II) N-methylimidazole dioxygen complex,
[TPPCo(N-MeIm)(O2)], rather than the hybrid hemoglobins.
However, because of the extreme similarity of the EPR signals
of cobalt heme-dioxygen species, the rates estimated using this
model heme are expected to be very similar to those of the Co-
containing hybrid hemoglobins of Figures 1-3; we are thus
overlooking the very minor differences in EPR parameters
reported for T- and R-state CoHbO2 centers.26
The EPR spectrum of [TPPCo(N-MeIm)(O2)] at Q-band is
shown in Figure 5, together with the simulation of this spectrum.
As in the case of the EPR spectrum of the deoxy complex shown
in Figure 1, the simulation is quite good, with the main
differences being the widths of each of the branches of the
spectrum. Because of the large g-value dispersion at Q-band,
it is possible to clearly discern the three g values and to estimate
the hyperfine coupling constants (even though two are not
resolved at this frequency). Tests of these values on the X-band
EPR spectrum shown in Figure 6 confirm the values of the
hyperfine coupling constants that are not resolved at Q-band.
We have defined the three branches of the rhombic spectrum
in the order 2, 1, and 3 from low-field to high-field end,
indicating, in agreement with the structures of model hemes32,33
and the single-crystal EPR results of Chien and Dickenson,21
that the middle g value, g1, is aligned along the O-O bond at
an angle of 35° to the normal to the porphyrin plane. The
high-field part of the derivative spectrum is difficult to simulate
precisely because of extensive overlap between the g1 and g3
branches; in particular the “intensity” of the highest-field
derivative line is not reproduced by the simulation, nor are the
unresolved features in the 3370-3400 G region of the experi-
Figure 3. Enlargement of the EPR spectrum of [R2(CoO2)â2(FeO2)]
at 40 °C, illustrating the method of measurement of ∆H, the “progress
toward averaging” of the EPR signal: The points of half-rise and half-
fall of the EPR signal were chosen as the most accurately measureable
features of these cw spectra. Experimental error in this measurement
is estimated to be (2 G or less.
4, the “progress toward averaging” is reasonably linear and of
similar slope in all cases, although we have refrained from fitting
the data to a straight line, because the complex behavior of EPR
line shapes when undergoing dynamic averaging, while they
may be appear to be linear over some temperature ranges, are
not in general expected to vary linearly with temperature. It
can be seen that three of the hybrid hemoglobins behave
similarly while the EPR signal of one is offset from the other
three and thus averages more slowly. The two R-state models,
[R2(FeO2)â2(CoO2)] and [R2(CoO2)â2(FeO2)], as well as one
of the T-state models, [R2(CoO2)â2(Zn)], all show very similar
progress toward averaging as a function of temperature, while
the Co-O2 EPR signal of the fourth hybrid, [R2(Zn)â2(CoO2)],
is retarded in the degree of averaging at any given temperature.
This is consistent with the findings of Perutz and co-workers,

Dioxygen in Model Cobalt(II) Hemes
J. Phys. Chem. B, Vol. 101, No. 43, 1997 8689
Figure 7. Simulated EPR spectra for Co-O2 centers assuming (a)
fast isotropic rotation of the entire molecule and (b) slow isotropic
rotation of the entire molecule but fast rotation about the Co-O bond,
where the middle g value is aligned along the O-O bond at an angle
of 35° to the normal of the heme plane.
Figure 5. (a) Q-band EPR spectrum of [TPPCo(N-MeIm)(O2)] in a
toluene glass at 77 K. (b) Simulation of this spectrum using the
parameters listed in Table 1.
to the normal to the porphyrin plane, “apparant” a values of
polycrystalline or frozen samples reported previously are smaller
(∼17-18 G for a2)19,27,31 than those determined using this
angular relationship in the simulations, or those determined from
single-crystal EPR studies.21-23
The z-axis of the g tensor of the Co-O2 complex, which is
aligned along the O-O bond vector, the middle g value,21-23
is thus inclined at an angle of about 35° to the axis of rotation
about the Co-O2 bond. The g and hyperfine tensors are also
noncoincident, with the same 35° angle relating gzz and Azz.21
Using these results, in Figure 7 the calculated spectra obtained
for the condition of fast rotation about the Co-O2 bond (the
molecular z-axis) and fast isotropic rotation of the entire
molecule are compared. As is clear from the two curves of
Figure 7, the resulting spectra are qualitatively similar but have
different separations of lines, with fast rotation about the
molecular z-axis creating a somewhat wider spacing of hyperfine
lines and a difference in the broadening of the spectrum at the
two ends. The latter features can be seen in the -81 to -61
°C spectra of the left-hand side of Figure 1 of ref 31, but at
higher temperatures the eight-line pattern of the model cobalt
heme O2 complex is symmetrical, suggesting isotropic averag-
ing. This 3-dimensional, isotropic averaging due to rapid
molecular tumbling requires that the rotational correlation time
τc be short compared to the inverse of the microwave frequency
in angular units, or ωτc , 1,51,52,53 and we have shown that
even for the small model complexes of ref 31, it is only at or
above room temperature in toluene solution that the rotational
correlation time is short enough to produce complete isotropic
averaging of the EPR signal.31 This is made all the more clear
Figure 6. (a) X-band EPR spectrum of [TPPCo(N-MeIm)(O2)] in
toluene at 77 K. (b) simulation of this spectrum using the parameters
listed in Table 1.
mental spectrum of Figure 6. Nevertheless, the line spacings
and positions of the first and last lines are well reproduced.
The best values of the g- and A-tensor components obtained
from the simulations at Q- and X-band are shown in Table 1,
first entry. As is apparent from the data of Table 1, the EPR
parameters of the model heme complex are well within range
of those reported from the single-crystal EPR data of CoM-
bO2.21,22 It should be noted that because of the 35° angle of g1
TABLE 1: EPR Parameters Obtained from Q- and X-band EPR Spectral Simulations of [TPPCo(N-MeIm)(O2)] in a Toluene
Glass and Comparison to Literature Values for the Co-O2 Center of Cobalt-Substituted Myoglobin
b
complex
Θa (deg)
g1
g2
g3
a1 (G)
a2 (G)
a3 (G)
a
b (G)
g
ref
[TPPCo(N-MeIm)(O2)]
CoMbO2, species 1
35c
35
21
35
17
2.004
2.00
2.03
2.006
2.008
2.083
2.081
2.08
2.083
2.085
1.985
1.99
1.98
1.989
1.983
4.6
13.1
7.2
9.33
8.2
21.5
23.5
23.2
16.7
17.3
3.8
8.8
11.6
5.95
7.2
10.0
2.022
2.023
2.03
2.026
2.025
TWd
21
22
21
22
15.1
14.0
10.7
10.9
CoMbO2, species 2
a Angle between the normal to the heme plane and the O-O bond vector. b Calculated by averaging the powder pattern parameters. c Angle
assumed for the spectral simulations of Figures 5-8. d This work.

8690 J. Phys. Chem. B, Vol. 101, No. 43, 1997
Bowen et al.
toward averaging” for both R(CoO2) and one â(CoO2) centers,
however, argues that such hydrogen-bonding may not be
significant at ambient temperatures. Although more stable state-
of-the-art EPR spectrometers with digital data storage would
allow accurate fitting of the experimental and calculated spectra,
these qualitative estimates have already provided us with new
insight into the dynamics of bound dioxygen in the heme pocket
of cobalt-substituted hemoglobin. The idea of dioxygen rotating
at a rate of ∼108 s-1 while bound in the distal pocket to the
metal center of hemoglobin is certainly a concept different from
that provided by the static structure of HbO2!50
Acknowledgment. The support of the National Institutes of
Health, Grant DK-31038, and the University of Arizona
Materials Characterization Program are gratefully acknowledged.
The authors wish to thank the personnel at the National EPR
Center for the use of their facilities for obtaining the Q-band
EPR spectrum of [TPPCo(N-MeIm)(O2)]. F.A.W. wishes to
thank Professor Daniel Kivelson for the inspiration he provided
while she was an NIH Postdoctoral Associate in his laboratory
in 1966-67, where the first EPR spectrum of [TPPCo(N-
MeIm)(O2)] was recorded.
References and Notes
(1) Pertuz, M. F.; Muirhead, H.; Cox, J. M.; Goaman, L. C. G.;
Mathews, F. S.; McGandy, E. L.; Webb, L. E. Nature 1968, 219, 29.
(2) Gibson, Q. H. Prog. Biophys. Biophys. Chem. 1956, 9, 1.
(3) Imai, K. Allosteric Effects in Haemoglobin; Cambridge University
Press: Cambridge, 1982.
(4) Gibson, Q. H. J. Biol. Chem. 1989, 264, 20155.
(5) Ackers, G. K.; Doyle, M. L.; Myers, D.; Daugherty, M. A. Science
1992, 255, 54 and references therein.
Figure 8. Simulated EPR spectra for Co-O2 centers assuming rates
of rotation about the Co-O bond of 3-200 MHz. Note the strong
similarity of this series of calculated spectra to those of the model
complex shown on the right side of Figure 1 of ref 31 as well as to the
hybrid hemoglobin samples of Figure 2.
by comparison of the left- and right-hand panels of Figure 1 of
ref 31, where the hydrogen-bonded Co-O-O‚‚‚HNCOCH3
structure prevents fast rotation about the Co-O2 bond of the
ortho-substituted isomer. For the hybrid hemoglobins, whose
rotational correlation times are at least a factor of 100 longer,
isotropic averaging on the EPR time scale cannot occur at any
temperature studied. This prediction is consistent with the
spectra of these protein samples obtained at temperatures as
high as +60 °C, which still look qualitatively similar to
broadened powder patterns (Figure 2).
(6) Monod, J.; Wyman, J.; Changeaux, J. P. J. Mol. Biol. 1965, 12,
88.
(7) Perutz, M. F. Nature 1970, 228, 726.
(8) Perutz, M. F. Proc. R. Soc. London Ser. B 1980, 208, 135.
(9) Perutz, M. F.; Fermi, G.; Luisi, B.; Shaanan, B.; Liddington, R. C.
Acc. Chem. Res. 1987, 20, 309.
(10) Schlichting, I.; Berendzen, J.; Phillips, G. N.; Sweet, R. M. Nature
1994, 371, 808.
(11) Sˇrajer, V.; Teng, T.; Ursby, T.; Pradervand, C.; Ren, Z.; Adachi,
S.; Shildkamp, W.; Bourgeois, D.; Wulff, M.; Moffat, K. Science 1996,
274, 1726.
(12) Hoffman, B. M. In The Porphyrins; Dolphin, D., Ed.; Academic
Press: New York, 1979; Vol. 7, pp 403-472.
(13) Yonetani, T. J. Biol. Chem. 1967, 242, 5008.
(14) Teale, F. W. J. Biochim. Biophys. Acta 1959, 35, 543.
(15) Enoki, Y.; Tomita, S. J. Mol. Biol. 1968, 32, 121.
(16) Haber, J. E.; Koshland, D. E. Biochim. Biophys. Acta 1969, 194,
339.
(17) Banerjee, R.; Cassoly, R. J. Mol. Biol. 1969, 42, 351.
(18) Waterman, M. R.; Yonetani, T. J. Biol. Chem. 1970, 245, 5847.
(19) Hoffman, B. M.; Petering, D. H. Proc. Natl. Acad. Sci. U.S.A. 1970,
67, 637.
(20) Ikeda-Saito, M.; Yamamoto, H.; Yonetani, T. J. Biol. Chem. 1977,
252, 8639.
(21) Chien, J. C. W.; Dickenson, L. C. Proc. Natl. Acad. Sci. U.S.A.
1972, 69, 2783.
(22) Hori, H.; Ikeda-Saito, M.; Yonetani, T. Nature 1980, 288, 501.
(23) Dickenson, L. C.; Chien, J. C. W. Proc. Natl. Acad. Sci. U.S.A.
1980, 77, 1235.
(24) Hori, H.; Ikeda-Saito, M.; Yonetani, T. J. Biol. Chem. 1982, 257,
3636.
In Figure 8 are shown spectral simulations of the Co-O2
center for varying (slow) rates of rotation about the Co-O2
bond. As was observed for both the model compounds of ref
31 and the hybrid hemoglobins of Figure 2, as the rate of rotation
increases the first observation is a loss of 59Co hyperfine
structure on the low-field end of the spectrum (3 MHz), followed
by loss of the high-field hyperfine structure (30-60 MHz), and
a simultaneous movement of both the low-field and high-field
extrema (∆H of Figures 3 and 4) toward the center (3-100
MHz), and finally, at quite high rates of rotation (200 MHz),
the emergence of the (broadened) eight-line pattern, which is
broader on the low-field end. This is qualitatively the same as
the series of changes that occurred to the hydrogen-bonded
model complex of the right-hand panel of Figure 1 of ref 31,
and we can estimate that at -61 °C the rate of rotation of
dioxygen in this hydrogen-bonded CoO2 complex, [(o-
NHCOCH3)TPPCo(N-MeIm)(O2)], is approximately 30 MHz
(∼3 × 107 s-1). For the hybrid hemoglobins of Figure 2 we
can estimate that at 35-37 °C dioxygen bound to three of the
hybrids is rotating at a rate of about 100 MHz (∼1 × 108 s-1),
while for the T-state â(CoO2) centers the rate is about one-
third that value. The potential effect of the hydrogen-bond
between Nꢀ of the distal HisE7 and the terminal oxygen atom
in the R- but not the â-chains seen in the crystal structure of
(25) Hori, H.; Ikeda-Saito, M.; Froncisz, W.; Yonetani, T. J. Biol. Chem.
1983, 258, 12368.
(26) Inubushi, T.; Yonetani, T. Biochemistry 1983, 22, 1894.
(27) Walker, F. A. J. Am. Chem. Soc. 1970, 92, 4235.
(28) Walker, F. A. J. Am. Chem. Soc. 1973, 95, 1154, 7928.
(29) Walker, F. A. J. Magn. Reson. 1974, 15, 201.
(30) Walker, F. A.; Beroiz, D.; Kadish, K. M. J. Am. Chem. Soc. 1976,
98, 3484.
(31) Walker, F. A.; Bowen, J. H. J. Am. Chem. Soc. 1985, 107, 8639.
(32) Lauher, R. G.; Ibers, J. A. J. Am. Chem. Soc. 1974, 96, 4447.
(33) Collman, J. P.; Gagne, R. R.; Reed, C. A.; Halbert, T. R.; Lang,
G.; Robinson, W. T. J. Am. Chem. Soc. 1975, 97, 1427.
50
HbO2 on the rate of rotation of bound O2 is not specifically
detectable in these measurements; the similarity in the “progress

Dioxygen in Model Cobalt(II) Hemes
J. Phys. Chem. B, Vol. 101, No. 43, 1997 8691
(34) Bowen, J. H. M.S. Thesis, San Francisco State University, 1987.
(35) Shelnutt, J. A.; Alston, K.; Ho, J.-Y.; Yu, N.-T.; Yamamoto, T.;
Rifkind, J. M. Biochemistry 1986, 25, 620.
(44) Freed, J. H. Theory of Slow Tumbling ESR Spectra for Nitroxides.
In Spin Labeling: Theory and Applications; Berliner, L., Ed.; Academic
Press: New York, 1976; Vol. I, pp 53-132.
(45) (a) Sneider, D. J.; Freed, J. H. AdV. Chem. Phys. 1989, 73, 387-
527. (b) Sneider, D. J.; Freed, J. H. Calculating Slow Motional Magnetic
Resonance Spectra: A User’s Guide. In Biological Magnetic Resonance;
Berliner, L. J., Reuben, J., Eds.; Plenum Press: New York, 1989; Vol. 8,
pp 1-76.
(36) Shibayama, N.; Inubishi, T.; Morimoto, H.; Yonetani, T. Biochem-
istry 1987, 26, 2194.
(37) Shibayama, N.; Imai, K.; Morimoto, H.; Saigo, S. Biochemistry
1993, 32, 8792.
(38) Shibayama, N.; Yonetani, T.; Regan, R. M.; Gibson, Q. H.
Biochemistry 1995, 34, 14658.
(39) Ikeda-Saito, M.; Inubushi, T.; Yonetani, T. In Methods in Enzymol-
ogy; Antonini, E., Rossi-Bernardi, L., Chiancone, E., Eds.; Academic
Press: New York, 1981; Vol. 76, pp 113-120.
(40) Scholler, D. M.; Wang, M. R.; Hoffman, B. M. Methods in
Enzymology; Fleischer, S., Parker, L., Eds.; Academic Press: New York,
1978; Vol. 52C, pp 487-492.
(41) Yonetani, T.; Yamamoto, H.; Woodrow, G. V. J. Biol. Chem. 1974,
249, 682.
(42) Geraci, G.; Parkhurst, L. J.; Gibson, Q. H. J. Biol. Chem. 1969,
244, 4664.
(46) Pilbrow, J. R. Transition Ion EPR; Clarendon Press: Oxford, 1990.
(47) Sobol, V. M. The Numerical Monte Carlo Methods; Mir: Moscow,
1979; p 125.
(48) Raitsimring, A. M.; Basu, P.; Shokhirev, N. V.; Enemark, J. H.
Appl. Magn. Reson. 1995, 9, 173.
(49) Perutz, M. F., personal communication.
(50) Shaanan, B. J. Mol. Biol. 1983, 171, 31.
(51) Pople, J. A.; Schneider, W. G.; Bernstein, H. J. High-Resolution
Nuclear Magnetic Resonance; McGraw-Hill: New York, 1959; pp 218-
225.
(52) (a) Kivelson, D. J. Chem. Phys. 1960, 33, 1094. (b) Wilson, R.;
Kivelson, D. J. Chem. Phys. 1966, 44, 154. (c) Atkins, P. W.; Kivelson, D.
J. Chem. Phys. 1966, 44, 169.
(43) Ikeda-Saito, M.; Yamamoto, H.; Imai, K.; Kayne, F. J.; Yonetani,
T. J. Biol. Chem. 1977, 252, 620.
(53) Freed, J. H.; Fraenkel, J. J. Chem. Phys. 1963, 39, 326.