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PROTEINS: Structure, Function, and Genetics 25:425-437 (1996)
Oxygen Binding by Single Crystals of Hemoglobin: The
Problem of Cooperativity and Inequivalence of Alpha
and Beta Subunits
Stefan0 Bettati,' Andrea Mozzarelli,' Gian Luigi Rossi,' Antonio Tsuneshige? Takashi Yonetani?
William A. Eaton: and Eric R. Henry3
'Institute of Biochemical Sciences, University of Parmu, 43100 Parma, Italy; 'Department of Biochemistry and
Biophysics, University of Pennsylvania School of Medicine, Philadelphia, Pennsylvania 191 04-6059;3Laboratory of
Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health,
Bethesda, Maryland 20892-0520
ABSTRACT
Oxygen binding by the human hemoglobin tetramer in the T quaternary
structure is apparently noncooperative in the
crystalline state (Hill n = 1.01, as predicted by
the two-state allosteric model of Monod, Wyman, and Changeux (MWC) (Mozzarelli et al.,
Nature 351:416419, 1991; Rivetti et al., Biochemistry 322888-2906, 1993). However, cooperativity within the tetramer can be masked by
a difference in affinity between the a and (3 subunits. Indeed, analysis of the binding curves derived from absorption of light polarized along
two different crystal directions, for which the
projections of the a and p hemes are slightly
different, revealed an inequivalence in the intrinsic oxygen affinity of the OL and p subunits
(p50(a)= 80 torr, p50(p) = 370 torr at 15°C)that
compensates a small amount of cooperativity
(Rivetti et al., Biochemistry 322888-2906,1993).
To further investigate this problem, we have
measured oxygen binding curves of single crystals of hemoglobin (in a different lattice) in
which the iron in the a subunits has been replaced by the non-oxygen-binding nickel(I1).
The Hill n is 0.90 f 0.06, and the p50 is slightly
different for light polarized parallel to different
crystal directions, indicating a very small difference in affinity between the two crystallographically inequivalent p subunits. The average crystal p50 is 110 & 20 torr at 15"C,close to
the p50 of 80 tom observed in solution, but
about threefold less than the p50 calculated by
Rivetti et al. (Biochemistry 32288S2906, 1993)
for the p subunits of the unsubstituted tetramer. These results suggest that Rivetti et al.,
if anything, overestimated the a l p inequivalence. They therefore did not underestimate the
cooperativity within the T quaternary structure, when they concluded that it represents a
small deviation from the perfectly noncooperative binding of an MWC allosteric model. Our
conclusion of nearly perfect MWC behavior for
binding to the T state of unmodified hemoglobin raises the question of the relevance of the
0 1996 WILEY-LISS,INC. *This article is a US Government
work and, as such, is in the public domain in the United States
of America.
large T-state cooperativity inferred for cyanide
binding to partially oxidized hemoglobin (Ackers et al., Science 25554-63,1992).
0 1996 Wdey-Liss, Inc.*
Key words: nickel-iron hybrid hemoglobins,
two-state allosteric model, single
crystal absorption spectra, Bohr
effect, multisubunit proteins, quaternary structure
INTRODUCTION
In spite of numerous claims to the contrary, the
two-state allosteric model of Monod, Wyman, and
Changew (MWC), together with the structural
mechanism of Perutz (P) and its statistical thermodynamic formulation by Szabo and Karplus (SK),
provides an accurate description of a wide variety of
structural, equilibrium, and kinetic data on cooperative oxygen binding by
Nevertheless, there remains the question of the exact magnitude of the deviations from the MWC-PSK model.
Since hemoglobin in the R quaternary structure
binds oxygen with a high affinity, similar to that of
the free chains, the question of the mechanistic origin of the apparent increase in affinity with increasing oxygen pressure toward the affinity of the free
chains has centered on the binding properties of the
low-affinity T quaternary structure. The question
can therefore be restated as: How much cooperativ-
Abbreuiations: oxyHb, oxyhemoglobin; deoxyHb, deoxyhemoglobin; metHb, methemoglobin; PEG, polyethylene glycol;
DPG, 2,3-&phosphoglycerate; IHP, inositol hexaphosphate;
nickel-iron hybrid, hemoglobin in which the iron of the a
hemes has been replaced by nickel(I1).
Received December 15, 1995; revision accepted March 8,
1996.
Address reprint requests to Dr. Andrea Mozzarelli, Institute
of Biochemical Sciences, University of Parma, 43100 Parma,
Italy, or Dr. Eric R. Henry, Laboratory of Chemical Physics,
Building 5, National Institute of Diabetes and Digestive and
Kidney Diseases, National Institutes of Health, Bethesda, MD
20892-0520.
426
S.BE'ZTATI ET AL.
ity is there in oxygen binding to the T quaternary
structure, and how does this compare to the increase
in oxygen affinity generated by the change in quaternary structure from T to R?
Much of the controversy surrounding this question
derives from the fact that the structural studies have
been carried out on hemoglobin in crystals, while the
functional studies have been performed on hemoglobin in solution. We have been making direct comparisons by measuring oxygen binding on single
crystals of human hemoglobin, which remain in the
T quaternary structure upon full o~ygenation.'~~-''
We previously found that the oxygen binding by the
T quaternary structure in the crystal is apparently
noncooperative,with a Hill n of almost exactly l.0,199
in keeping with the MWC-PSK model. More recently,
Shibayama and Saigo" have found that oxygenation
of deoxyHb encapsulated in a silica gel exhibits noncooperative oxygen binding, while deoxygenation of
encapsulated oxyHb results in noncooperative dissociation and a 500-fold higher affinity, as expected for
the R state. Thus, the crystal and gel experiments
appear to provide a striking confirmation of the most
basic features of the MWC-PSK model.
Noncooperative binding by the T tetramer could,
however, arise from fortuitous cancellation of an arbitrarily large amount of cooperativity by a large
inequivalence in binding by a and p subunits. This
effect is most easily demonstrated by considering a
tetramer in the T quaternary structure that has cooperative interactions between a and p subunits
within the ap dimers related by the twofold symmetry axis.13*14For a cooperative $I dimer in a tetramer binding with a Hill n = 1, the relation between the ratio of subunit affinities, g, and the
subunit interaction parameter, 6, is given by
(1)
Dodson and c o ~ o r k e r s , ~on
~ , 'the
~ basis of their
x-ray crystallographic studies a t a single oxygen
pressure, had suggested that only the a hemes bind
oxygen, while Ackers and coworker^,^^ as a result of
their tetramer-dimer dissociation studies on metalsubstituted hemoglobins, proposed that the increase
in affinity in binding a second ligand to the T quaternary structure is comparable to the increase associated with the change from the T to the R quaternary structure.
To address this question, Rivetti and colleagues'
took advantage of the small difference in the projections of the a and p hemes onto the crystal axes of
their measurements to estimate the inequivalence
in binding and the cooperativity. They found that g
= 5 (p50(a) = 80 torr, p50(p) = 370 torr a t 15°C)and
6 = 2,compared to values between 140 and 370 for
the ratio of the R:T state affinities in solution at pH
7.4 in the presence of chloride or phosphate an-
ions." However, the calculation of 6 depended sensitively on small differences in heme orientation and
assumptions about the orientation of the oxygenated
p hemes, which was not observed in the electron
density maps. This question therefore required further investigation. In this work we resolve most of
the ambiguity about compensation of cooperativity
by subunit inequivalence from measurements of the
single crystal oxygen binding curves of the p subunits alone in a metal hybrid T-state tetramer. In
this metal hybrid the iron(I1) ion in the a hemes has
been replaced by the non-oxygen-binding nickel(I1)
ion.19-22
MATERIALS AND METHODS
Preparation of Crystals
The nickel-iron hybrid of human hemoglobin,
a(Ni(II))2p(Fe(II))2,was prepared and purified by
using a modification of the method of Shibayama
and coworker^.'^ Samples were stored as the carbon
monoxide complex a t -80°C. The CO was removed
by photolysis under a stream of humidified helium.
Crystals of the deoxygenated species were grown by
a modification of the method used by Luisi and ass o c i a t e ~to~ ~obtain crystals of the CO complex.
Crystals suitable for measurements were obtained
from a solution of the following composition: 24-32
mglml hybrid hemoglobin, 1mM IHP, 10 mM potassium phosphate, 30 mM sodium dithionite, and
15.5-17.5% (w/w) PEG 1000 M, (Hampton Research, Riverside, CA), pH 6.8,a t 20°C. Crystals appeared within 24 hours. The crystals were elongated
plates. Precession x-ray photography confirmed that
they were the same space group, P2,, reported by
Luisi and coworkersz3for the CO complex, and that
they were flattened on (001) with the a and b axes
parallel and perpendicular to the elongation direction, respectively.
To prevent dissolution a t full oxygenation, the
crystals were transferred anaerobically to a solution
containing 50% (w/w)PEG 1000,l mM IHP, 10 mM
potassium phosphate, 30 mM sodium dithionite, pH
7.5, and were stored in a n anaerobic flask a t 20°C.
Before spectral measurements, crystals were resuspended at least six times in a deoxygenated dithionite-free solution containing 50% (w/w)PEG 1000,l
mM IHP, 10 mM potassium phosphate, 6000 U/ml
catalase, pH 7.5. Polarized absorption spectra using
a Zeiss MPM03 microspectrophotometer and oxygen
pressure measurements were performed as described previously.'
Analysis Procedure
Rivetti and coworkers' outlined the optical theory
and analytical procedures required for the spectrophotometric determination of the fractional saturation of the iron hemes as a function of oxygen pressure in hemoglobin crystals. Because these crystals
undergo variable amounts of progressive oxidation,
427
OXYGEN BINDING BY HEMOGLOBIN CRYSTALS
5
a
4 c4---~
1 2 1 0
2 I 0
_I
I
3
1
:::
JE l l a '
500
wavelength (nm)
600
wavelength (nm)
700
wavelength (nm)
Fig. 1. Reference spectra and polarization ratios (PR). The prominent peaks at about 520 nm and 560 nm are due to the absorption of
the non-oxygen-binding nickel porphyrins of the a subunits.
accurate determination of the fractional saturation
requires optical density measurements at many
wavelengths as a function of oxygen pressure
[S@,h)l and the fitting of these spectra to linear combinations of reference spectra [Sx(A)l for the pure
oxidized species and the reduced oxygenated and
deoxygenated species. That is,
S@,A)
= coxy(P)soxy(h)
+
+ cdeoxy(P)sdeoxy(A)
cmet(P)Smet(A)
(2)
where the fractional saturation y@) is defined as
(3)
In the nickel-iron hybrid molecule under consideration here, however, the absorption spectrum of the
hybrid molecule in the 450-700-nm wavelength region is dominated by the absorption due to the
nickel porphyrins (Fig. 1). It is, therefore, important
to suppress the influence of very high optical densities due to nickel porphyrin absorption and of small
changes in the nickel porphyrin absorption due to
iron ligation-dependent spectral changes. To this
end we have chosen a simple scheme in which the
contribution to the fit of the absorbance at each
wavelength is weighted in proportion to the fractional contribution of the Fe hemes to the overall
absorption by the hybrid molecule a t that wavelength. The overall scale of such a wavelength-dependent weighting function has no effect on the results of the fit; the essential feature for the fit is the
variation of the weighting function with wavelength. We can therefore estimate the wavelength
dependence of the fractional contribution of the
heme absorption to the overall absorption by com-
puting the wavelength-by-wavelength ratio of some
representative spectrum of (unsubstituted) hemoglobin to a spectrum for the nickel-iron hybrid. The
former spectrum may be constructed as linear combinations of reference spectra of unsubstituted hemoglobin for the three absorbing species in proportions determined by the supposed populations of
these species in the hybrid molecule. That is,
s F e ( h ) = Cox$oxy(h)
+
+ cmetSmet(A)
CdeoxySdeoxy(h)
(4)
where cx and S , are the fractional population in the
hybrid molecule and the reference spectrum, respectively, of species X.*
The wavelength-dependent weighting function is
then
*These weighting functions should be produced independently for spectra measured with polarizations along the two
different crystal directions. In the present case, the space
groups of the unsubstituted molecule and the nickel-iron hybrid are different, and a rigorous procedure for combining polarized spectra for polarizations along principal directions of
the two crystals in this way requires complete knowledge of the
polarized spectra: If spectra were available for all three principal directions of the all-iron crystal, it would be possible to
transform them to produce spectra appropriate for the principal axes of the nickel-iron hybrid crystal, thereby allowing
direct combination of spectra from the two molecules. In the
absence of such complete information, and with the expectation that shape differences between spectra measured along
different polarization directions will not affect the resulting
weighting functions in an important way, we have chosen to
simply directly combine spectra for the more strongly absorbing directions of the two crystals, and similarly for the less
strongly absorbing directions.
428
S. BE'ITATI ET AL.
In addition, because of nonlinearities arising from
stray light, the weighting function was set to zero
for those wavelengths a t which the optical density
was greater than 2.0. In practice, each measured
hybrid spectrum was fit as linear combinations of
reference spectra for the three species (plus a constant offset), using a wavelength-dependent weighting function calculated from Equations 4 and 5, assuming some representative set of populations cxo.
The fit produces a new set of populations c,', which
are used to recalculate the weighting function with
Equations 4 and 5. The new weighting function is
used in repeating the fit, producing a new set of
populations cx2, and so forth. This procedure (c,' +
weighting function + refit -+c X i +') is repeated until
a self-consistent set of populations (cxi = cxi ' =
c,) is produced; convergence to self-consistency is
accomplished within about five iterations. This iterative determination of populations cx is repeated for
all measured hybrid spectra of both polarizations,
with appropriate choices of both all-iron reference
spectra (for computing the weighting function) and
hybrid reference spectra (for the actual fit) for each
polarization.
+
Determination of Reference Spectra
The reference spectra for the nickel-iron hybrid
molecule with the hemes in the oxidized, oxygenated, and deoxygenated states were determined using the procedure described by Rivetti and colleagues.' Reference spectra for the oxidized and
reduced deoxygenated species were measured on the
same crystal. The crystal was first reduced by washing with a deoxygenated 50% (w/w) PEG solution
containing 30 mM sodium dithionite for the measurement of the deoxy spectrum. After washing
away the dithionite with buffered PEG, the crystal
was then oxidized by washing with a 50% PEG solution containing 5 mM potassium ferricyanide. The
progress of the oxidation reaction was monitored
spectrophotometrically at the peak of the metheme
absorption band at 630 nm for a period of up to 6
hours, after which the oxidizing agent was removed
by washing with a 50%PEG solution before the measurement of the met spectrum. In some experiments
it was observed that longer exposure to potassium
ferricyanide resulted in a decrease in the 630-nm
peak and the appearance of a shoulder a t 610 nm.
As in the earlier work, the determination of the
reference spectrum for the oxygenated species was
complicated by oxidation and by the incomplete saturation of the reduced hemes even a t 1 atm of oxygen. In order to produce a reference spectrum for the
fully oxygenated molecule, it was therefore necessary to extrapolate a series of spectra of the incompletely saturated molecule to infinite oxygen pressure. The basic extrapolation procedure has been
discussed previously.' Briefly, a series of spectra
was measured a t high oxygen saturations (150 torr
< pOz < 760 torr, saturations between 80% and
95%) a t 5°C to increase the affinity and minimize
oxidation, and difference spectra between these
spectra and that of the fully deoxygenated species
were calculated. At each wavelength, the amplitudes of these difference spectra as a function of
pressure were fit by using a simple hyperbolic form
describing noncooperative oxygen binding, constraining all wavelengths to have the same pressure
dependence (i.e., p50). The value of p50 was varied
to minimize the overall sum-of-squares of the hyperbolic fits a t all wavelengths. The hyperbolic curve at
each wavelength corresponding to this optimal
value of p50 was then extrapolated to infinite oxygen pressure to produce the absorbance of the extrapolated difference spectrum a t that wavelength.
The spectrum measured a t zero pressure was then
added back to this extrapolated difference spectrum
to produce the extrapolated spectrum of the fully
oxygenated species. The presence of small amounts
(54%) of the spectrum of the oxidized molecule in
the extrapolated spectrum was corrected for by first
subtracting variable amounts of the oxidized reference spectrum until the absorption peak at 630 nm
was eliminated and then rescaling the oxyheme
spectrum.
For the present case of the nickel-iron hybrid molecule, this basic extrapolation procedure was modified slightly in order to minimize deleterious effects
of the very intense nickel porphyrin absorption on
the extrapolation (see above). In determining the optimal p50 for the fitting a t all wavelengths, the contribution of each wavelength to the deviation from a
hyperbolic binding curve was weighted in proportion to the estimated contribution of the hemes to
the absorption at that wavelength. An iterative procedure similar to that described above was used,
with the wavelength-dependent weighting function
at each iteration determined in a similar manner
from the current set of estimated species populations
and a set of reference spectra for the all-iron molecule. In this case, however, the population of the
oxidized species (cmet in Eq. 2 ) was set to zero for
simplicity. Also, in order to make the multiwavelength fitting during each iteration as efficient as
possible, a single set of coefficients coxy and cdeox,,
(and therefore a single weighting function) was applied to all of the spectra in the extrapolation, based
on the average saturation of the whole data set computed in the previous iteration. The extrapolated
spectrum produced by one iteration was also used to
update the oxy reference spectrum for the next iteration, until a self-consistent spectrum and weighting function were obtained.
The final reference spectra for the three species of
the hybrid molecule are shown for both polarizations
in Figure 1. The absorption of light polarized parallel to the b crystal axis is much greater than that for
light polarized parallel to the a crystal axis. The
OXYGEN BINDING BY HEMOGLOBIN CRYSTALS
assignment of the crystal axes was based on the
heme orientations derived from the x-ray crystallographic structure of the carbon monoxide c~mplex.'~
As noted earlier, the absorption of linearly polarized light by the crystal will not be the same for
polarization directions parallel to the different crystal axes because the heme planes do not project
equally onto the different axes. For this reason the
apparent saturations (and therefore the apparent affinities) will depend on the polarization direction of
the measuring light. The optical theory presented by
Rivetti and associates' describes the optical properties of the oriented hemes in a hemoglobin crystal,
which may exist in a mixture of several distinct species i, from which apparent saturations and afinities may be determined. This theory begins with the
following equation relating the measured optical
density (OD) for light polarized parallel to crystal
direction p to the species populations and the orientations of the hemes relative to this direction:
.
Y
OD,(x,y)
=
-c
8
4
l f& sin2
~ zgp~
Table I. Projections of Heme Planes Used
in Calculations in Nickel-IronHybrid
Hemoglobin Crystals
Hemoglobin
Carbonmonoxyf
The Relationship of Apparent Affinities to
Subunit Affinities
(6)
i j=l
where c and 1 are concentration and pathlength, respectively, &. is the fractional population of heme j
in species i, Ei is the isotropic heme molar extinction
of species i at the specified wavelength, and zGp is
the angle between the crystal direction p and the
normal zti to the plane of heme j in the crystal structure of species i.
The use of this equation to analyze polarized absorption spectra of the nickel-iron hybrid molecule
requires that the heme normal directions for all
three species be known. For the hybrid molecule
with the p hemes oxygenated, we used the x-ray
structure of the carbon monoxide complex, a(Ni),p
(Fe-CO),, determined by Luisi and associate^.'^
Both the deoxygenated and p-oxygenated nickeliron hybrid crystallize from PEG in the space group
P2,, as determined by x-ray precession photographs.
For the nickel-iron hybrid with deoxygenated and
oxidized hemes, the structures of deoxyHb and
metHb crystallized from PEG were used.24 Both
these species crystallize from PEG in a different
space group (P2,2,2), so, before computing the heme
normal directions, it was necessary in each case to
orient the molecule in the axis system of the
liganded derivative by least-squares superposition
of all the backbone atoms of the tetramer onto the
corresponding atoms of the liganded derivative. At
most wavelengths in the near-ultraviolet-visible region hemes behave like nearly perfect planar absorbers of linearly polarized light.25,26The crystal
extinction coefficient for light linearly polarized par-
429
Subunit
sin' zia sin' zib sin2zic*
a1 "1)
a2 Ni(I1)
p l Fe(II)-CO
p2 Fe(II)-CO
0.134
0.398
0.384
0.117
0.927
0.602
0.627
0.900
0.939
0.999
0.988
0.983
a1 Fe(I1)
a2 Fe(I1)
0.158
0.426
0.316
0.067
0.897
0.576
0.700
0.936
0.998
0.984
0.996
0.150
0.458
0.355
0.084
0.892
0.544
0.666
0.921
0.957
0.998
0.979
0.996
Deoxy'
p l Fe(I1)
p2 Fe(I1)
0.945
Metg
a1 Fe(II1)
a2 Fe(II1)
p l Fe(II1)
p2 Fe(II1)
'Protein Data Bank File lNIH.23The atomic coordinates provided for the a(Ni),p(Fe-CO), molecule (8= 98.4") are given in
the a*bc axis system, so it was necessary to transform these
coordinates to the abc* axis system before computing the heme
normal directions.
'Protein Data Bank File lHGA, oriented in unit cell of lNIH.24
'Protein Data Bank File lHGB, oriented in unit cell of lNIH?4
allel to a particular crystal axis is therefore proportional to the projection of the heme plane onto that
crystal axis, and thus proportional to the magnitude
of the sin2 values for the heme normals. These values are given in Table I.
Given this heme orientational information, the
optical theory then allows us to compute apparent
saturations measured by using light of different polarizations from the actual saturations of the individual subunits:
where a and b represent the two crystal directions
for which spectra were measured, and for each
chemical species i and crystal axis p:
Equations 7 and 8 are analogous to Equations 11
and 9 given by Rivetti and colleagues,' where equivalent binding was assumed for the two a subunits
and for the two p subunits.
The magnitude of the deduced inequivalence in
subunit binding affinities depends on the difference
in apparent saturations in a way that is sensitive to
the detailed orientations of the hemes involved in
ligand binding. We have estimated this dependence
430
S. BE’ITATI ET AL.
both for the unsubstituted (P2,2,2) hemoglobin
crystal studied by Rivetti and colleagues’ and for
the hybrid crystal studied in the present work by
performing numerical simulations using the heme
orientational information determined for both systems from x-ray crystallographic data. These simulations were performed using the following procedure: A fixed value of the average P subunit p50 was
chosen for the nickel-iron hybrid molecule. From
these chosen p50’s and with Hill n values regarded
as adjustable parameters, P-subunit binding curves
were synthesized on a logarithmic pressure scale
over the wide range 0.01-10,000 torr. A set of pairs
[p5O(Pl),p5O(P2)]were then produced such that the
corresponding noncooperative binding curves for the
two P subunits combined to produce an overall
P-subunit binding curve, which optimally matched
the synthetic binding curve; the apparent Hill n
value of the combined binding curve (which will be
less than 1 for inequivalent subunit binding) was
also adjusted to optimize the match. The pairs were
produced by selecting a set of p50(@2)values in steps
downward from the chosen average p50; for each
p50(P2),the corresponding p50(Pl) (greater than the
average p50) was determined by least-squares fitting such that the average of the known P2-subunit
binding curve derived from the specified p50(P2) and
the binding curve derived from the variable p50(Pl)
produced the best fit to the synthetic binding curve
having the specified p50 and optimized Hill n. The
individual subunit binding curves corresponding to
the specified p50(P2) and the derived p50(Pl) were
then used to construct apparent overall binding
curves along the two measured crystal directions, by
evaluating the expressions from Equation 7 a t each
pressure. The resulting apparent binding curves for
the two directions were fit to the Hill equation to
produce apparent p50’s and Hill n’s for the two directions. Ratios of the various derived pBO(P1)’s to
their corresponding p50(P2)’s were paired with the
ratios of the corresponding computed apparent p50’s
and n values. A similar procedure was applied to
unsubstituted hemoglobin to relate inequivalence in
binding to the a and P subunits to apparent p50’s
and Hill n values for the two crystal directions, assuming equal affinity for the two a subunits and
equal affinity of the two P subunits.
RESULTS
Figure 2 shows a representative data set, in which
spectra were measured for light linearly polarized
parallel to the a and b crystal axes as a function of
oxygen pressure between 7 and 746 torr. The nickel
porphyrins of the a subunits dominate the absorption, resulting in relatively small changes on oxygen
binding to the P hemes. The nickel-porphyrin spectrum is that of a four-coordinate species,” indicating that the nickel-histidine bond is broken as
found by Luisi and coworkersz3in the x-ray struc-
500
600
700
wavelength (nm)
Fig. 2. Spectra as a function of oxygen pressure between 7
and 746 torr at 15°C.
ture of the carbon monoxide complex, a(Ni),p(FeCO),. Figure 3 shows the fit of the observed spectra
with a linear combination of reference spectra for the
completely oxygenated, deoxygenated, and oxidized
species. To reduce the interference of the nickel porphyrin absorption, weighting factors were applied to
the data in an iterative procedure described in the
“Methods” section. These weighting factors were determined by the relative contribution of the heme
and nickel porphyrin to the absorption at each wavelength (Eq. 3). For the a-axis data, the fit is almost
perfect, while for the b-axis data there are significant
deviations a t the nickel porphyrin peak at 560 nm,
where the optical density is greater than 2.0. These
deviations are mostly due to nonlinearities in the
spectrophotometer at these high optical densities,
and optical densities greater than 2.0 were not included in the fit (zero weighting factor). There is a
small shift in the nickel porphyrin peak a t 560 nm,
suggesting that there are changes in electronic interactions among metal-porphyrin chromophores in
the crystal as the spectra of the hemes change.
The fractional saturation of reduced hemes with
oxygen was determined from the fit coefficients using Eq. 3. The resulting saturations are shown in
Figure 4, together with the fraction oxidized to
methemes. The experiments were performed by increasing the oxygen pressure up to 746 torr, and
then lowering the pressure to 160 torr to demonstrate reversibility of the binding curve. During this
period there is continuous oxidation of the Fe(I1)
hemes to Fe(II1) methemes up to about 10%. A separate experiment showed that the fractional saturation a t a fixed oxygen pressure is independent of the
fraction of methemes (data not shown).
Hill plots of the binding curves from this experiment, as well as Hill plots from titrations of three
other crystals, are shown in Figure 5. The average
Hill n is 0.90 2 0.06 (the uncertainty is the standard
deviation from the mean of the eight determina-
431
OXYGEN BINDING BY HEMOGLOBIN CRYSTALS
E II b
,
7-1
2
I \
316torr
I
-
_J
0
A
2
700
wavelength (nin)
E II a
Fig. 3. Fit of measured spectra (continuous curves) at various oxygen pressures with linear
combinations of oxy, deoxy, and met reference spectra. The dashed curves in each panel represent the contributions of each of reference spectra of Figure 1 to the fit. The weighted sum of these
reference spectra is the dashed curve that superimposes on the observed curve at most wavelengths.
1
432
S.BETTATI ET AL.
I
L
-0
//saturation
methemes
0.2
saturation
0.6
-1
0
200
400
600
800
p02 (torr)
Fig. 4. Fractional saturation of reduced hemes with oxygen as a function of oxygen pressure
and fraction of methemes. (open circles) fractional saturation obtained upon increasing oxygen
pressure; (open squares) fractional saturation determined at end of titration; (filled circles)fraction
of methemes measured at each oxygen pressure; (filled squares) fraction of methemes at end of
titration.
tions), indicating no positive cooperativity in oxygen
binding to the p hemes. The p50 for the binding
curve measured with light polarized parallel to the b
crystal axis is 102 10 torr, while that for the a
crystal axis is 123 24 torr. The projection of the p l
heme on the a crystal axis is 3 to 4 times greater
than the p2 heme, while both p hemes have comparable projections, and therefore comparable contributions to the absorption, for light polarized parallel
to the b crystal axis (Table I; Fig. 6). The higher p50
for a axis data therefore indicates that the p l heme
has the lower affinity.
To evaluate the magnitude of this inequivalence,
simulations of the crystal binding curves were calculated to obtain the relation between the p50's
measured for light polarized parallel to the two different crystal axes and the p50's of the individual p
subunits. The results of these simulations, described
in detail in the "Methods" section, are shown in Figure 7. They show that a ratio of 1.2 in the crystal
p50's can arise from about a 1.6 ratio in the p heme
affinities. The corresponding Hill n's predicted for
measurements along the crystal axes are larger
than 0.99 (Fig. 7b), and therefore cannot possibly
account for the observed value of 0.90. In contrast,
for unsubstituted hemoglobin crystals,' a small difference in the p50's for the two crystal axes corresponds to a very large difference in the affinities of
the ci and p subunits (Fig. 7c) (assuming equivalence
of the two ci subunits and equivalence of the two p
subunits).
A limited study of the pH dependence was carried
out by determining the fractional saturation as a
function of pH a t a fixed oxygen pressure (Fig. 8).
These results show that there is no Bohr effect in the
crystal. An apparent enthalpy of binding was deter-
*
*
mined by measuring the fractional saturation as a
function of temperature a t a fixed oxygen pressure,
and calculating the p50 assuming a binding curve
with a Hill n = 1.0 (Fig. 9).
Binding measurements were performed on solutions of the nickel-iron hybrid hemoglobin in the
same buffer and at the same temperature as the
crystal experiments. The instrument used is an
improved versionz7 of the automatic oxygenation
apparatus of Imai and colleagues.'' The measurements were carried out as in the work of Shibayama's
except that optical absorption was
measured a t 430 nm instead of 432 nm, and the protein concentration was increased from 4 to 15 FM
tetramer. Experiments were performed in the presence and absence of PEG 1000 a t a concentration of
25% (w/v). This was the highest concentration of
PEG under the experimental conditions that could
be used without precipitating the protein. Oxygenation curves for the nickel-iron hybrid hemoglobin
at pH 7.5 in the absence and presence of PEG are
shown in Figure 10. Oxygen binding measurements
were also carried out at pH 6.0 and 9.0. The deoxygenation and reoxygenation curves matched each
other well. The results are given in Table 11. The p50
values in the absence and presence of PEG are 71
and 80 t o r r at pH 7.5 (the pH of the crystal experiments), and the Hill n's are 1.00, and 1.04, respectively. As in the crystal, there is no Bohr effect near
pH 7.5 in solution.
DISCUSSION
Our objective in this study has been to determine
the affinity of the p subunits of hemoglobin in the T
quaternary structure. We chose the nickel-iron hybrid hemoglobin, ci(Ni(II))zp(Fe(II))~,because the
433
OXYGEN BINDING BY HEMOGLOBIN CRYSTALS
I1 b
Ella
d
I ,
I
a3
0
p50 = 108 torr
I
2
3
I
2
3
I
2
3
I
2
3
I ,
0
graphically inequivalent subunits; there is no Bohr
effect in keeping with the x-ray finding that the relevant salt bridges remain intact upon ligand binding2sZ3;the enthalpy of oxygen binding is the same
as that measured previously for the (unsubstituted)
hemoglobin crystal; the affinities are nearly the
same in crystal and solution; and the average affinity of the p subunits in the crystal is higher
than that calculated previously by Rivetti and
colleagues' for the p subunits in unsubstituted
hemoglobin. All of these results point to the conclusion that cooperativity in the T quaternary structure of unsubstituted hemoglobin is small, possibly
smaller than previously estimated by Rivetti and
colleagues.'
One of the obvious criticisms of our crystal oxygen-binding experiments, as well as the x-ray structural analysis of crystals, is that the lattice forces
impose constraints that are not present in solution.
This is an old criticism, and has often been misused
in discussing the results of x-ray crystallography.
There are, however, only a few cases where crystal
and solution kinetic or equilibrium properties have
been rigorously compared.29 A striking example is
the study of oxygen binding to the dimeric hemoglobin from the clam Scapharca inaequivalvis, where it
is found that both the p50 and the Hill n are identical in crystal and solution.30In unmodified human
hemoglobin, the lattice forces prevent the transition
from the T to R quaternary structure, but the p50 of
the crystal T state is less than a factor of 2 different
from the p50 under solution conditions where strong
allosteric effectors are used to stabilize the T quaternary conformation.' In the present case of the
nickel-iron hybrid, not only is the p50 in solution of
80 torr close to the value of 110 20 torr found for
the crystal, but there is no cooperativity in either
crystal or solution binding (see below). [In this context we should also point out that there is no Bohr
effect near pH 7.5 in either crystal (Fig. 8) or solution (Table 111.1 Therefore, our conclusions concerning crystal binding are indeed directly relevant to
the behavior of hemoglobin in solution.
The mean Hill n observed for four crystals was
0.90 with a standard deviation of 0.06 from the eight
determinations (two binding curves of different polarization for each crystal) (Fig. 5). Because of the
uncertainties resulting from the intense nickel porphyrin absorption, we do not regard this Hill n as
significantly different from 1.0. Other causes of a
low Hill n seem improbable. The p subunits are not
in contact, except through the IHP bound in the
cleft, so that intersubunit negative cooperativity,
which has never been observed in a hemoglobin, is
unlikely. The one possibility that we investigated in
some detail is that a low Hill n could arise from
inequivalence in the affinity of the two crystalIographically distinct p subunits. This was motivated
by the fact that these two p subunits contribute un-
*
I
I
2
3
log p 0 2 (torr)
Fig. 5. Hill plots of oxygen binding curves. A,B: Data from
Figure 4.
nickel porphyrins do not bind oxygen, the molecule
remains in the T quaternary structure in the crystal
upon oxygenation of the heme containing p subunits, and the x-ray structure of the carbon monoxide complex has been determined.23 The complicating factor, in addition to oxidation to methemes, is
that the spectral changes upon oxygenation are relatively small because of the intense absorption by
the nickel porphyrins (Figs. 1 and 2). It has been
possible to overcome this problem by making very
precise absorption measurements over a wide wavelength range, and by fitting the data with wavelength-dependent weighting factors (Figs. 3-5).
The results are strikingly simple. The binding
curves are noncooperative; there is little difference
in the oxygen affinity between the two crystallo-
434
S. BETTATI ET AL.
Figure 7, but also included cooperative binding, and
found a 4.6 0.4-fold higher affinity for the a subunits with a corresponding S = 1.8 & 0.3. They also
pointed out that the uncertainties were larger than
the quoted values (the standard deviations from the
mean of experiments on three different crystals) due
to uncertainties in the orientation of the hemes of
the fully oxygenated molecule.
What can we say about their estimate of cooperativity within the T quaternary structure from the
present results? First, the apparent p50 for binding
to the two @ subunits in the nickel-iron hybrid crystal is only 110 t o r r compared to the average value of
about 140 torr observed for the crystal of unsubstituted hemoglobin.' From this result we can immediately conclude that the p subunit affinity in the
nickel-iron hybrid crystal is higher than in the unsubstituted hemoglobin crystal, since both the experiments of Rivetti and colleagues' and the x-ray
s t ~ d i e s ' ~ , ' ~indicate
,~'
a higher affinity for the a
subunits. Looking at the results in more detail, we
obtain p50's calculated from Equation 7 for the individual @ subunits of about 150 torr and 95 torr,
yielding a combined p50 of 120 ton-.+This is about
threefold less than the value of about 370 torr calculated by Rivetti and colleagues' (from the fits to
the data in their Figure 15, but not explicitly quoted
in the paper) for the @ subunits. From this comparison we suggest that Rivetti and colleagues' did not
underestimate the inequivalence in the affinity of
the a and p subunits, and therefore did not underestimate the cooperativity within the T quaternary
structure in their crystal.*
An obvious limitation of the analysis of Rivetti
and associates' is their assumption about equivalence of the affinity of the two a subunits and equivalence of the affinity of the two p subunits. In this
P2,2,2 crystal the asymmetric unit of the crystal is
the tetramer. The a (and @)subunits are not strictly
equivalent because they have different crystal contacts. There are, therefore, four distinct subunit affinities. Since only two binding curves for the crystal
were measured, one for each polarization, only two
binding curves could be extracted from the data, and
it was most reasonable to assume that the largest
inequivalence was between the a and @ subunits, as
suggested by the x-ray results, and not, for example,
between one of the a subunits and the other three
subunits. But there is a precedent for this latter scenario. In an early crystallographic study on the carbon monoxide complex of the mutant hemoglobin
Kansas in the T quaternary structure (space group
*
Fig. 6. Projection of iron hemes of p subunits and nickel
hemes of a subunits onto the ab crystal face of the optical measurements.
equally to the spectra measured with light linearly
polarized parallel to the crystal axes, particularly
the a crystal axis. Simulations of the binding show
that the 1.2-fold difference in the p50 measured for
the two crystal axes results from about a 1.6-fold
inequivalence in the affinity of the two f3 subunits
(Fig. 7A). As shown in Fig. 7B, in the absence of
positive or negative cooperativity this difference
barely lowers the apparent crystal Hill n's, from 1.0
to a value greater than 0.99.
The situation with inequivalence of binding to the
a and p subunits in the unsubstituted hemoglobin
crystal of Rivetti and colleagues' is quite different.
If we make the critical assumption that the difference in the apparent p50's for light polarized parallel to the different crystal axes arises solely from a
difference between the a and p subunits, then for
noncooperative binding a large difference in affinity
makes only a small difference in the apparent p50's
for the two different crystal axes, but a substantial
reduction in the apparent Hill n's (Fig. 7C,D). Rivetti and coworkers' assumed that the difference in
the apparent p50's of about lo%, in the face of apparent Hill n's of 1.0, resulted from the simultaneous occurrence of alp inequivalence, which lowers
the apparent Hill n's, and positive cooperativity,
which raises the apparent Hill n's (Eq. 1).They used
the simplest possible model for cooperativity within
a tetramer, by assuming a cooperative ap dimer
(14,15), which has a binding polynomial, Q:
where 6 is the interaction parameter. Rivetti and
coworkers' performed a detailed simulation of the
crystal binding curves, of the type used to create
+Thep50 calculated for a binding curve of two p subunits
with these individual p50's is 120 tom, compared to the average of the measured p50's along the two crystal axes of 110
torr.
*One caveat in this comparison is that the nickel-histidine
bond in the Q subunits is broken, which may influence the
oxygen affinity of the p subunits.
435
OXYGEN BINDING BY HEMOGLOBIN CRYSTALS
I
0 99
n 98
c
0 96
0 95
I
3
2
D
E 09 -
Fig. 7. Relation between apparent crystal binding curves and
subunit binding curves. a: Ratio of p50's observed for light polarized parallel to a and b crystal axes as a function of the ratio of p l
and p2 subunit affinities of nickel-iron hybrid of the present work.
b: Hill n values observed for light polarized parallel to a (heavy
broken curve) and b (heavy solid curve) crystal axes, as well as
the isotropic average (light broken curve), as a function of ratio of
p i and p2 subunit affinities. c: Ratio of p50's observed for light
polarized parallel to a and c crystal axes as a function of the ratio
of Q and p subunit affinities of unsubstituted hemoglobin of Rivetti
et al.' d: Hill n observed for light polarized parallel to a (heavy
solid curve) and c (heavy broken curve) crystal axes, as well as
the isotropic average (light broken curve) as a function of ratio of
Q and p subunit affinities; see "Methods" section for a description
of the calculation.
I
I
I
t
I
I
0
9
6
PH
Fig. 8. Fractional saturation as a function of pH at 15°C at an
oxygen pressure of 155 torr.
P2,), only three of the four hemes showed carbon
monoxide bound.32The difference between the relevant projections of the two 01 hemes in the P2,2,2
crystal of Rivetti and coworkers' is much greater
than the difference between the sum of the projections of the cx hemes and the sum of the projections of
the f3 hemes used in their analysis. The point is that
a small amount of inequivalence between the two a
3 '
0.0033
I
I
I
0.0034
0.0035
0.0036
1/T (x lo3
(OK).')
Fig. 9. van't Hoff plot of p50 calculated from saturation measurements at a single oxygen pressure. Each point and corresponding error bars represent the mean and standard deviation,
respectively, of at least 10 values of the p50 calculated from a p
parent saturations measured for the b (filledcircles) and a (open
circles) crystal directions at a fixed oxygen pressure of 155 2 2
torr. The AH,calculated from the slope using the van't Hoff relation, d In p50/d(l/T) = AH/R, is -12.1 L 0.8 kcal/rnol.
hemes could make a significant contribution to the
difference between the crystal binding curves measured by Rivetti and coworkers' in the two polariza-
436
S. BE'ITATI ET AL
Table 11. Oxygenation Data for Nickel-Iron
Hybrid Hemoglobin a(Ni(II))2f3(Fe(II))2
in Solution*
1
?
-.
-
PH
p50 (torr)
Hill n
6.0
7.5
9.0
76.2
70.7
64.2
1.01
1.00
6.0
7.5
9.0
85.8
79.6
67.8
1.05
1.04
1.02
No PEG
0
h
v
x
a0
1.01
25% PEG
0
I
-2
0
2
I
1
*Experimental conditions: protein concentration 15 p M tetramer (60 pM on metal basis), 10 mM potassium phosphate,
25% PEG (w/v) PEG 1000, 1 mM IHP, 15°C.
log p 0 2 (torr)
Fig. 10. Solution binding curves in presence (filledcircles)and
absence (open circles) of 25% (w/v) PEG 1000. Solution conditions: 15 pM protein (60 pM metal basis),10 mM potassium phosphate, pH 7.5, 1 mM IHP, 15°C.
tions. As a result both the d p subunit inequivalence
and the magnitude of the cooperativity parameter 6
required to produce the observed crystal binding
curves would be smaller.
Recent experiments on crosslinked nickel-hybrid
hemoglobins give additional insight into this problem.21,22Crosslinking the two p subunits eliminates
tetramer-dimer dissociation, permitting the construction of asymmetric hybrid molecules. Crosslinking has only a small perturbation on the properties of unsubstituted hemoglobin33and the nickel
hybrid hemoglobins.21,22The work on the hybrids
suggests that the alp inequivalence in the oxygen
affinity of the T quaternary structure (K,) is about
a factor of 3, compared to the calculated crystal
value of about 5.l Interestingly, in the ctp dimer
(XL[a(Fe)P(Fe)][ct(Ni)P(Ni)I)
the maximum Hill n =
1.03 a t pH 6.4. This is the dimer of the cooperon
model (Eq. 9) used in analyzing the crystal results.
We assume that the structure remains T after binding the second ligand, so that both the subunit inequivalence, q (-3 for the crosslinked hybrid, 5 for
the crystal) and the cooperativity parameter, 6 (-1.3
for the crosslinked hybrid, 1.8 for the crystal) of
Equation 1 are similar for hemoglobin in the crystal
and crosslinked hemoglobin in s o l ~ t i o n . ~
What then is the significance of the large apparent cooperativity for ligand binding in the T quaternary structure inferred from tetramer-dimer dissociation experiments, mainly on cynanomet hybrid
hemoglobins17?From the preceding discussion it is
*Crystalcontacts may contribute to the difference in affinity
between a and p subunits in the crystal. There have been some
suggestionsfor the structural ori in of the inequivalence from
examination of crystal contacts,2 .34 but any definitive conclusion will have to await a more rigorous theoretical analysis.
f
clear that there is now considerable evidence that
the cooperativity is very small and represents only a
slight perturbation of the key feature of the MWC
two-state model. This raises the question of the relevance of the cyanomet hybrids as models for intermediate ligation states of hemoglobin. If the mechanism for the apparently exaggerated cooperativity
in the cyanomet hybrid hemoglobin is the same that
produces the small amount of cooperativity in oxygen binding to the T quaternary structure of unmodified hemoglobin, studies of the cyanomet hybrids
could help in searching for the origin of this, albeit
small, effect.
ACKNOWLEDGMENTS
This work was supported in part by a NATO Collaborative Research Grant (No. 930826),by the Target Project on Biotechnology and Bioinstrumentation of the National Research Council of Italy (No.
93.01080.PF70), and by NIH grant HL14508.
We thank Martino Bolognesi and Menico Rizzi for
the x-ray measurements that identified the space
group and the Miller indices of the crystal face used
in our measurements.
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