Critical Review

Evolution of Allosteric Models for Hemoglobin

William A. Eaton1, Eric R. Henry

1, James Hofrichter

1, Stefano Bettati

2, Cristiano Viappiani

3and

Andrea Mozzarelli2

1Laboratory of Chemical Physics, National Institute of Diabetes, Digestive and Kidney Diseases,National Institutes of Health, Bethesda, Maryland, USA2Department of Biochemistry and Molecular Biology, University of Parma, Parma, Italy3Department of Physics, University of Parma, Parma, Italy

Summary

We compare various allosteric models that have been proposed to

explain cooperative oxygen binding to hemoglobin, including the

two-state allosteric model of Monod, Wyman, and Changeux

(MWC), the Cooperon model of Brunori, the model of Szabo and

Karplus (SK) based on the stereochemical mechanism of Perutz, the

generalization of the SK model by Lee and Karplus (SKL), and the

Tertiary Two-State (TTS) model of Henry, Bettati, Hofrichter and

Eaton. The preponderance of experimental evidence favors the TTS

model which postulates an equilibrium between high (r)- and low (t)-affinity tertiary conformations that are present in both the T and R

quaternary structures. Cooperative oxygenation in this model arises

from the shift of T to R, as in MWC, but with a significant

population of both r and t conformations in the liganded T and in the

unliganded R quaternary structures. The TTS model may be

considered a combination of the SK and SKL models, and these

models provide a framework for a structural interpretation of the

TTS parameters. The most compelling evidence in favor of the TTS

model is the nanosecond – millisecond carbon monoxide (CO)

rebinding kinetics in photodissociation experiments on hemoglobin

encapsulated in silica gels. The polymeric network of the gel

prevents any tertiary or quaternary conformational changes on the

sub-second time scale, thereby permitting the subunit conformations

prior to CO photodissociation to be determined from their ligand

rebinding kinetics. These experiments show that a large fraction of

liganded subunits in the T quaternary structure have the same

functional conformation as liganded subunits in the R quaternary

structure, an experimental finding inconsistent with the MWC,

Cooperon, SK, and SKL models, but readily explained by the TTS

model as rebinding to r subunits in T. We propose an additional

experiment to test another key prediction of the TTS model, namely

that a fraction of subunits in the unliganded R quaternary structure

has the same functional conformation (t) as unliganded subunits in

the T quaternary structure.

IUBMB Life, 59: 586–599, 2007

Keywords Hemeproteins; hemoglobin; protein function; proteinstructure; structural biology.

INTRODUCTION

It is a pleasure for us to contribute to this special issue in

honor of a truly outstanding scientist and international leader

in biochemistry and biophysics, Maurizio Brunori. Brunori

has been at the center of research on heme proteins for over 40

years. He has been a major contributor to the development of

the subject from his own research (see Preface to this issue)

and also because of his intellectual leadership and support of

others, particularly young scientists.

Brunori’s favorite heme protein is of course hemoglobin,

the paradigm for cooperative systems in biology, so it is only

fitting that this fascinating molecule be the subject of this

article. Brunori has had a love affair with hemoglobin for

almost half a century (1), beginning with his work as a young

researcher with the brilliant biochemist, Eraldo Antonini (2).

His long-standing interest also stems from his connection to

Jeffries Wyman, one of the founding fathers of biophysical

chemistry (3) and co-developer of the famous allosteric model

with Jacques Monod and Jean-Pierre Changeux (4). Wyman

was Brunori’s teacher, colleague and friend during his 25 years

in Rome, and introduced him to the world of rigorous

thermodynamic analysis of protein function (5).

The study of hemoglobin is a vast and complicated subject

(6 – 18), so we only discuss one aspect of the problem – the

evolution of allosteric models for cooperative oxygen binding,

Received 10 February 2007; accepted 11 February 2007Address correspondence to: William A. Eaton, Laboratory of

Chemical Physics, Building 5, National Institute of Diabetes,Digestive and Kidney Diseases, National Institutes of Health,Bethesda, MD 20892-0520, USA. E-mail: eaton@helix.nih.govThis work was presented at the Symposium on ‘International

Visions on Blood Substitutes. Hemoglobin-based Oxygen Carriers:from Chemistry to Clinics’, University of Parma, 17 – 20 September2006.

IUBMBLife, 59(8 – 9): 586 – 599, August – September 2007

ISSN 1521-6543 print/ISSN 1521-6551 online � 2007 IUBMB

DOI: 10.1080/15216540701272380

a subject of much controversy and of great interest to Brunori.

Four models, in addition to the original two-state model of

Monod, Wyman, and Changeux (4), have been selected for

analysis and comparison: the Cooperon model of Brunori and

coworkers, which is a more exact formulation of the MWC

model, the model of Szabo and Karplus (19), based on the

stereochemical mechanism of Perutz (20), the generalization of

the Szabo-Karplus model by Lee and Karplus (21, 22), and the

Tertiary Two-State model of Henry, Bettati, Hofrichter and

Eaton (23), which is a limiting case of the very general model

of Herzfeld and Stanley (24). To simplify the discussion, the

focus will be primarily on cooperative oxygen binding

(homotropic effects). Although understanding the regulation

of oxygen affinity by heterotropic effectors is of more general

applicability to other allosteric systems, to include analysis of

the effects of protons, carbon dioxide, chloride and 2,3-

disphosphoglycerate in any detail introduces too much

complexity to consider in this brief account.

In the following we briefly describe each model or a

simplified version thereof, and point out the key experimental

results that have provided their motivation and/or support.

We conclude with a brief comparison of the models and

suggest a new test of the TTS model, the only existing model

that is consistent with all of the major experimental results.

We shall see that in spite of an enormous amount of

experimental and theoretical work, some of the most basic

questions concerning structure-function relations in hemoglo-

bin remain unanswered.

THE QUATERNARY TWO-STATE ALLOSTERIC MODELOF MONOD, WYMAN, AND CHANGEUX

The subject begins with the legendary paper by Monod,

Wyman, and Changeux (4). Monod and Changeux were

interested in the regulation of the activity of multi-subunit

enzymes, and sought a model to explain how enzyme activity

could be regulated by the binding of effector molecules at sites

different from the substrate binding site and also result in

cooperative interactions (25). In formulating a quantitative

model, studies on hemoglobin influenced their thinking in two

ways (5, 26). The first was the discovery by Perutz and

coworkers in the initial low-resolution X-ray structural studies

that hemoglobin has a symmetric arrangement of its 4

subunits and that the quaternary structures of deoxy and

oxyhemoglobin are different (Fig. 1) (27, 28). The second was

the extensive discussions that Monod had with Wyman, who

introduced him to linked thermodynamic functions, the

mathematical relations that describe the interactions between

Figure 1. Schematic structure of hemoglobin showing the difference in quaternary structures (adapted from Dickerson and Geis

(76)).

EVOLUTION OF ALLOSTERIC MODELS FOR HEMOGLOBIN 587

substrate and effector binding (29). The result was the famous

paper that appeared in 1965 and which has been referred to

more than 5,000 times, one of the most highly cited theoretical

papers of all time.

The basic idea of the MWC model is that there is an

equilibrium between two quaternary conformations, one

called T (for ‘tense’) having a low reactivity and another

called R (for ‘relaxed’) having a high reactivity, corresponding

in the case of hemoglobin to the X-ray structures of deoxy-

and oxyhemoglobin with low and high oxygen affinity,

respectively. Cooperativity arises from a shift in the equili-

brium from T to R as successive ligands bind with increasing

oxygen pressure, p. The partition function for hemoglobin was

given by Monod et al. as:

X ðMWCÞ ¼ Lð1þ KTpÞ4 þ ð1þ KRpÞ4 ð1Þ

where L¼ [T]/[R], KT is the oxygen affinity of the T con-

formation, KR is the much higher affinity of the R conforma-

tion, and p is the oxygen pressure (Fig. 2). The sigmoid oxygen

Figure 2. Relative probability for individual subunit species for allosteric models of hemoglobin at alkaline pH where all salt

bridges containing an ionizable proton are broken. Empty symbols correspond to unliganded and filled to liganded subunits. In

the SK, SKL and TTS models, the green arrow for the deoxy T subunit conformations represents the inter-subunit salt bridge

(see Fig. 4 for details). For the TTS model, there is a correspondence with SKL parameters, shown in green in parentheses, but

with a different structural interpretation. See text for definition of parameters and Fig. 5 for a more complete picture of the TTS

model.

588 EATON ET AL.

binding curve arises from two non-cooperative binding curves,

one to the low-affinity T state that dominates at the lowest

oxygen pressures and another to the high affinity R-state that

dominates at the highest oxygen pressures (Fig. 3).

According to the model, small molecules that regulate

activity, so-called heterotropic allosteric effectors, bind at a

distance from the active site. They do not directly affect the

reactivity of the T or R conformation, but act indirectly by

shifting the T-R equilibrium, inhibitors preferentially binding

to T and activators to R. Protons lower the oxygen affinity of

hemoglobin by binding preferentially to T, i.e., they alter L

but do not affect either KT or KR. At the time of the MWC

paper, 2,3-DPG had not yet been discovered, and the effect of

pH on binding to the T quaternary structure was not

established with any certainty. Moreover, Monod et al.

anticipated that their explanation of the Bohr effect might be

an oversimplification, as it was already well known that the

reactivity of many monomeric proteins is affected by pH.

The partition function, equation (1) requires that all 4

subunits be equivalent, presumably motivated by the low-

resolution X-ray finding of approximate orthorhombic (D2,

222) symmetry (30), where any pair of subunits is related by one

of three orthogonal two-fold rotation axes. However, hemoglo-

bin contains two chemically different subunits, a and b, andpossesses only a single exact two-fold rotation axis of sym-

metry (the rotation axis that interchanges ab dimers) (Fig. 1).

Nevertheless,MWCcould fit the fractional saturation (y) versus

oxygen pressure curve at a fixed set of conditions well with just

3 parameters (L, KT, and KR) using the saturation function,

y ¼ 1

4

d ln Xd ln p

¼ LKTpð1þ KTpÞ3 þ KRpð1þ KRpÞ3

Lð1þ KTpÞ4 þ ð1þ KRpÞ4ð2Þ

An important property of this saturation function is that it

predicts perfectly non-cooperative binding to each qua-

ternary structure. Under conditions where only one

quaternary structure is populated, the saturation functions

are simply:

y ¼ KTp

1þ KTpor y ¼ KRp

1þ KRp; ð3Þ

i.e., the binding curve for each quaternary conformation is

hyperbolic with a slope in a Hill plot (log(y/17y) versus p) of

exactly 1.0 (Fig. 3).

Introducing inequivalence of a and b subunits does not

change the fundamental idea of MWC that binding to each

quaternary structure is independent of the number of ligands

already bound (7). The partition function for the model

including a –b inequivalence is given by:

X ¼ Lð1þ KaTpÞ

2ð1þ KbTpÞ

2 þ ð1þ KaRpÞ

2ð1þ KbRpÞ

2 ð4Þ

An important manifestation of a – b inequivalence is that the

slope of the Hill plot for binding to a single quaternary

structure is less than 1.0.

By the middle 1970s the bulk of the experimental evidence

favored the MWC model over the competing sequential model

(7, 8), introduced in a remarkable paper by Pauling (31), and

elaborated upon by Koshland, Nemethy, and Filmer (32). As

discussed in recent historical reviews by Shulman and Eaton

et al. (16, 33), the principal experimental results favoring

MWC from the early studies were the finding that the oxygen

affinity is independent of the number of oxygen molecules

bound per se, but depends only on the quaternary structure,

and the demonstration by Hopfield, Shulman, and Ogawa

that the MWC model explains, at least qualitatively, the

complex ligand binding and dissociation kinetics (34) in the

Figure 3. Hemoglobin oxygen binding curve and Hill plot of a

perfect MWC molecule (L¼ 107, KT¼ 0.01 torr71, KR¼ 10).

The binding curves approach asymptotes at low and high

oxygen pressures, corresponding to binding to the T and R

states.

EVOLUTION OF ALLOSTERIC MODELS FOR HEMOGLOBIN 589

experiments of Gibson, Antonini, and Brunori (35 – 37). The

most telling results that finally settled the issue are the oxygen

binding measurements in crystals and gels. Measurements of

oxygen binding to the T quaternary structure of hemoglobin in

single crystals (38, 39), known from the X-ray crystallographic

work of Dodson and coworkers to remain in the T quaternary

structure with oxygen bound (40), showed perfectly non-

cooperative binding (Hill n¼ 1.0). Subsequently, Shibayama

and Saigo showed that hemoglobin trapped in either the T or

R quaternary structure by encapsulation in silica gels also

exhibits non-cooperative oxygen binding (Hill n slightly less

than 1.0) (41). These experiments effectively ruled out a

sequential model.

THE COOPERON MODEL OF BRUNORI

The ‘Cooperon’ model of Brunori and coworkers (42, 43) is

an important extension of theMWCmodel, and was motivated

by a new type of experiment. Smith and Ackers used chemical

analogues (cyanomethemoglobin as a model for oxyhemoglo-

bin) to investigate the properties of ligation intermediates by

determining the free energy of dissociation of the tetramer into

two ab dimers for all 10 ligation microstates (44). The

difference in the tetramer-to-dimer dissociation free energies

for ligation microstates is the same as the difference in the free

energy of binding ligands to the tetramers compared to the

dissociated dimers. Since the free dimers bind oxygen non-

cooperatively and have nearly the same affinity as the R-state

tetramer, these free energy differences are measures of

cooperative interactions associated with ligating each micro-

state, and were called ‘cooperative free energies’.

Brunori and coworkers showed that the MWC model could

account for the cooperative free energies for 8 of the 10

microstates (43). The two outliers were the doubly liganded

species (a1x)a2(b1x)b2 and (a1x)a2b1(b2x) (x denotes a liganded

subunit). To explain these data, they introduced the cooperon

model, which allows cooperative interaction within the abdimer. The partition function for this model is:

XðCooperonÞ ¼ L 1þ KaT þ Kb

T

� �pþ dTKa

TKbTp

2� �2

þ 1þ KaR þ Kb

R

� �pþ dRKa

RKbRp

2� �2

ð5Þ

where dT and dR are the increases in affinity for binding the

second ligand to an ab dimer in T and R, respectively.

Equation 5 should be regarded as the exact MWC partition

function since it recognizes that hemoglobin has only a single

axis of symmetry, as well as a –b inequivalence (Fig. 1).

The cooperon model was able to explain all the observed

cooperative free energies except that for (a1x)a2b1(b2x).However the cooperative free energy for this species was

incorrectly determined (45), so the agreement with the

cooperon model (unknown to Brunori and coworkers at the

time) was excellent. The value of dT required to fit the data,

however, was 170 (dR was assumed to be 1.0, as was also

assumed in the analysis of the tetramer-dimer dissociation

data). That is, according to this model the second molecule of

oxygen binds to the ab dimer in the T quaternary structure

with an affinity 170 times greater than the first, only * 6-fold

less than the *1000-fold ratio of the fourth to first binding

constants, a result that is inconsistent with oxygen binding

curves (46). Analysis of more recent tetramer-dimer dissocia-

tion experiments of Ackers and coworkers, using chemical

analogues that much more closely retain the properties of

unaltered hemoglobin (14), have indicated that dT is as small

as 4 (33). However, the results of these experiments have been

called into question by Morimoto and coworkers (47), whose

kinetic measurements lead to an even smaller value for dT.In the presence of a –b inequivalence, which reduces the

value of the Hill n, the finding in the crystal of n¼ 1 requires

some cooperativity (for n¼ 1, dT¼ (qþ 1)2/4q, where q is the

ratio of a to b affinity constants (39)). From the ratio of the

binding constants measured for light polarized along ortho-

gonal axes, which have different projections of the a and bhemes, Mozzarelli and coworkers estimated q and therefore

that dT5 3 (48, 49). In the subsequent discussion we ignore

this small effect, and assume the binding to both quaternary

structures is perfectly non-cooperative.

THE MODEL OF SZABO AND KARPLUS

The model of Szabo and Karplus (SK) (19) is based on the

stereochemical mechanism described in the two famous 1970

papers by Max Perutz (20, 50) (Fig. 4). After obtaining atomic

resolution structures of deoxyhemoglobin and oxyhemoglobin

(actually methemoglobin, assumed at the time to have the

same globin conformation of oxyhemoglobin), Perutz spent

several years connecting the differences in the two structures to

the known functional properties of hemoglobin. His most

novel conclusion was the assignment of a functional role for 6

inter-subunit salt bridges, 4 connecting the two a subunits, and2 connecting a and b subunits on opposite dimers (Fig. 4). He

also emphasized the importance of an intra-subunit salt bridge

in the b subunits. The inter-subunit salt bridges are present

in the T but not the R conformation. According to his

mechanism oxygen binding to the T conformation moves the

iron from a position out of the porphyrin plane to one that is

more coplanar, requiring concomitant motion of the bound

(‘proximal’) histidine and its associated F helix, resulting in

breakage of both inter- and intra-subunit salt bridges

originating from the carboxy-termini (Fig. 4). The salt bridges

play several key roles in the Perutz mechanism. The low

affinity of the T conformation is attributed to the tension

transmitted to the heme from the constraints of 2 salt bridges

per subunit. The inter-subunit salt bridges also stabilize the T

quaternary structure relative to R, so breakage shifts the

quaternary equilibrium toward R. Two of the inter-a-subunit salt bridges contain ionizable protons, as does the

590 EATON ET AL.

b intra-subunit salt bridge (Fig. 4). Their uptake upon oxygen

dissociation contributes to the Bohr effect – the pH

dependence of the overall oxygen affinity that facilitates

release of oxygen at the more acid pH of the tissues.

Another important conclusion of Perutz was that the

conformational change at the heme is transmitted to the sub-

unit interfaces, but no farther, as suggested earlier by Shulman

and coworkers (51). That is, according to his mechanism

conformational changes in one subunit do not directly

influence the oxygen affinity of a neighboring subunit, as they

do in a sequential model. So as far as oxygen binding is

concerned, Perutz’s mechanism is consistent with the basic idea

of the MWC model that the affinity only depends on the

quaternary structure and not the number of molecules bound.

The SK model is the statistical thermodynamical formula-

tion of the Perutz mechanism. To make the description of

cooperative oxygen binding in the Perutz mechanism more

clear, we only consider oxygen binding at high pH, where all 4

of the salt bridges of the T quaternary structure that contain

ionizable protons are broken and the protons dissociated,

leaving 4 intersubunit salt bridges at complete deoxygenation

(Fig. 2). Under these conditions binding oxygen to a subunit

breaks one salt bridge and the SK partition function for this

model, ignoring a –b inequivalence, is (19):

X ðSKÞ ¼ QS4ð1þ KRp=SÞ4 þ ð1þ KRpÞ4 ð6Þ

where Q is the (hypothetical) quaternary equilibrium constant,

with all 4 remaining inter-subunit salt bridges broken, and S is

the strength of a salt bridge. This partition function makes the

elegantly simple connection between the MWC model and the

Perutz mechanism that L¼QS4 and KT¼KR/S, showing

quantitatively how the salt bridges stabilize T and lower its

oxygen affinity compared to R.

According to the MWC model, binding of allosteric

effectors, such as protons, does not alter either KT or KR,

but influences the overall affinity by changing L. However,

protons and 2,3-DPG do lower the affinity of the T

conformation (52), inconsistent with the explanation of

heterotropic effects by MWC. Szabo and Karplus used their

model to successfully fit oxygen binding data as a function of

pH, thereby demonstrating quantitative consistency of the

Perutz mechanism with, albeit limited, experiments.

THE GENERALIZED SZABO-KARPLUS MODELOF LEE AND KARPLUS

The SK model was generalized and revised later by Lee and

Karplus (SKL) (21, 22), motivated by two results. First, X-ray

crystallography of the mutant hemoglobin Kansas showed

that the salt bridges do not break in the crystal upon CO

binding to the T quaternary structure, in sharp contrast to the

prediction of the Perutz mechanism. Second, Karplus and

coworkers revisited the Perutz stereochemical mechanism

using energy minimization to map out a reaction path from

the hemes to the subunit interfaces upon oxygen binding (53,

54). From the latter they concluded that the low affinity of

subunits in the T quaternary structure is not due to the tension

at heme, as proposed by Perutz, but to the strain induced in

what they called the ‘allosteric core’ upon oxygen binding,

particularly the steric repulsion between the proximal histidine

and the pyrrole nitrogens of the porphyrin ring associated with

motion of the iron into the heme plane.

Figure 4. Salt bridges that are present in deoxyhemoglobin and

broken in oxyhemoglobin, key elements of Perutz’s stereo-

chemical mechanism. Residues that increase their pK as a

result of salt bridge breakage (dissociating protons) and

therefore contribute to the Bohr effect are V1 (amino terminal)

of the a chains and H146 (imidazole) of the b chains. From

Perutz (15, 20, 50).

EVOLUTION OF ALLOSTERIC MODELS FOR HEMOGLOBIN 591

For the present purposes, there are two major differences

between the SK and SKL models. The first is that ligand

binding to the T quaternary structure strains but does not

break salt bridges,1 a major departure from Perutz’s 1970

stereochemical mechanism. Instead, T-quaternary structure

salt bridges break only upon neutralization by hydroxyl ions,

or, in the case of inter-subunit salt bridges break, when the

quaternary structure switches to R. A second major difference

from SK is that the intrinsic affinity of the T quaternary

structure is no longer assumed to be the same as in R.

The high pH version of their model corresponds to the

simple partition function:

X ðSKLÞ ¼ QS4ð1þ KrpÞ4 þ ð1þ KRpÞ4 ð7Þ

where K is the intrinsic affinity of the T quaternary structure

(the affinity in the absence of salt bridges), r (r in the SKL

notation) is the additional parameter that accounts for strain

in the salt bridges and has the property that 14 r4S.2 In the

SK model r¼ 1/S and K¼KR.

From fitting an improved set of experimental data on the

pH dependence of oxygen binding, and allowing the salt

bridges to have unequal strength, Karplus and coworkers

found that K5KR, from which they concluded that there are

additional constraints on ligand binding to T in addition to the

salt bridges, which is presumably the strain in the allosteric

core postulated by Gelin et al. (22, 53, 54).

THE TERTIARY TWO-STATE MODEL OF HENRY ET AL.

The tertiary two-state model (TTS) was motivated by two

series of experiments. The first concerned experiments on the T

quaternary structure, and the second experiments on the R

quaternary structure. Mozzarelli and coworkers found that the

oxygen affinity of the T quaternary structure in the crystal is

lower than the affinity of the T quaternary structure in solution,

corresponding to the binding constant for the first oxygen

molecule (38, 39). They found, moreover, that the crystal

affinity is not affected by changes in pH, consistent with

Perutz’s proposal that salt-bridge breakage is associated with

the Bohr effect, since the X-ray result of Dodson and

coworkers showed that they remain intact upon oxygenation

(40). Rivetti et al. therefore proposed that there are two

extreme affinities for subunits in the T quaternary structure –

one for binding to subunits with intact salt bridges in both the

liganded and unliganded states, as in the SKL model, and a

second much higher affinity for binding to subunits with

broken salt bridges in both unliganded and liganded states.

Subsequent experiments by Bettati and Mozzarelli and by

Bruno et al. showed that hemoglobin encapsulated in silica gels

in the T quaternary structure in the presence of allosteric

effectors binds oxygen non-cooperatively with the same low

affinity as found in the crystal and an almost absent Bohr effect.

Furthermore, hemoglobin encapsulated as T in the absence of

allosteric effectors exhibits a higher affinity and the same Bohr

effect as found for T hemoglobin free in solution (55, 56). These

results showed that the non-cooperative binding is not an

artefact of the crystal lattice, and supported the proposal of

Rivetti et al. of two functionally different tertiary conforma-

tions of liganded subunits in the T quaternary structure (39).

The second motivation for the TTS model was the finding

in nanosecond-resolved Raman (57) and optical spectroscopic

experiments (58) of a tertiary relaxation following photo-

dissociation of carbon monoxide (CO) from hemoglobin in the

R quaternary structure. This sub-microsecond relaxation was

detected in the optical experiments as a spectral change that is

indistinguishable from the R-T spectral change, but could be

assigned as a pure tertiary relaxation because its rate and

amplitude are independent of the degree of photodissociation

(59). The relaxation also exhibits a stretched exponential time

course (60), as was found in myoglobin (61, 62), where the

conformational change had been established to dramatically

change the CO rebinding rate (63). A final key result was the

finding, using singular value decomposition of the time-

resolved CO-deoxy difference spectra in which CO-hemoglo-

bin was fully photodissociated, that there are only two deoxy

basis spectra. Since there is significant R to T switching in full

photolysis experiments, the finding of only two deoxy spectra

(60) suggested that the functionally relevant part of the relaxed

deoxy subunit conformations in T and R could be the same.

These results, together with elements borrowed from the

very general model of Herzfeld and Stanley (24), motivated

Henry et al. to suggest a Tertiary Two-State (TTS) allosteric

model (Figs 2 and 6) (23). The model postulates that high and

low affinity conformations of individual subunits, which are

called r and t, exist in equilibrium within each quaternary

structure. The model is similar to MWC in spirit, but differs in

that an equilibrium of tertiary conformations plays a key role.

In the MWC model tertiary-quaternary coupling is complete,

while in the TTS model tertiary-quaternary coupling is

incomplete, as previously considered by Szabo, Karplus,

Lee, Herzfeld and Stanley. In the TTS model the affinity state

of a subunit is solely determined by its tertiary conformation

and is the same in both T and R quaternary structures. The

quaternary structure influences the affinity by biasing the t-r

conformational equilibrium, the T conformation favoring t

and the R conformation favoring r. In both R and T ligand

binding favors r. The net result is that cooperativity arises

from the shift of T, containing deoxy subunits in the

t conformation and liganded subunits in both the r and t

conformations, to R, containing deoxy subunits in both r and t

conformations and liganded subunits in the r conformation

(Fig. 6). The partition function for this model (under a fixed

set of solution conditions) with equal a and b affinities is (23):

X ðTTSÞ ¼ L0

l4T1þ Krpþ lTð1þ KtpÞð Þ4

þ 1þ Krpþ lRð1þ KtpÞð Þ4 ð8Þ

592 EATON ET AL.

where L is the ratio of the T to R populations in which all the

subunits of T are unliganded t and all the subunits of R are

unliganded r, lT is the ratio of t to r populations of the

unliganded subunits in the T quaternary structure, lR is the

corresponding equilibrium constant in the R quaternary

structure, and Kt and Kr are the affinities of the subunits in

the t and r conformations in which the liganded subunits

remain in t and r, respectively (Fig. 6). In this model,

heterotropic effectors can influence L, lR, and lT, but not Kr

or Kt.

In the limit where lT is large and lR small, equation 8 is

identical to the MWC partition function (equation 1) with

L¼L, KT¼Kt and KR¼Kr. Notice also that the mathematical

forms of the partition functions in equations 1, 6, 7 and 8 are

the same, and therefore provide identical fits to equilibrium

oxygen binding data in the absence of allosteric effectors (e.g.,

at alkaline pH), or at saturating concentrations. At non-

saturating effector concentrations, however, this simple MWC

form will break down and apparent cooperative oxygen

binding to single quaternary structures can result.

The TTS model not only provides an excellent fit to the

time-resolved spectral data, where the tertiary relaxation

following CO photodissociation was interpreted as an r-t

relaxation, but the parameters used to fit the kinetic data are

consistent with the CO binding curve and determination of the

populations of intermediate ligation states by Perrella and

coworkers using low temperature electrophoresis (23, 64, 65).

Since the model was proposed in 2002, there are two new

important experimental findings that support it. One addresses

the prediction of the model that the lowest possible affinity

corresponds to binding to t without ligation causing a change

in conformation to r. This prediction is borne out by the recent

finding that the oxygen affinity of the T quaternary structure

in the crystal is identical to that of T hemoglobin, saturated

with the strong allosteric effectors, inositol hexaphosphate and

bezafibrate, either free in solution (see Fig. 1F in Yonetani

et al., 2002 (66)) or trapped in T by encapsulation in a silica gel

(67). The second new experimental finding, and the most

compelling evidence in favor of the TTS model, derives from

measurements of the kinetics of CO rebinding in gel-

encapsulated haemoglobin by Viappiani et al. (67), described

in the next section.

DISCOVERY OF R-LIKE LIGANDED CONFORMATIONSIN T AND COMPARISON OF MODELS

As pointed out earlier, encapsulation in gels to slow

quaternary changes, and thereby investigate the equilibrium

properties of the T and R quaternary structures, has played a

very important part in clarifying allosteric mechanisms (41,

55). Viappiani et al. recently extended this work to investigate

the kinetic properties of hemoglobin encapsulated in either the

R or T quaternary structures (67). Following photodissociation

of the CO complex encapsulated as R, only 2 kinetic phases

were observed, one corresponding to geminate rebinding and a

second corresponding to bimolecular rebinding (Fig. 7a). Since

the gel enormously slows the R to T transition, the slow phase

observed in solution corresponding to T-quaternary structure

rebinding is absent. Following photodissociation of the CO

complex encapsulated as T (by adding CO after the encapsula-

tion of deoxyhemoglobin in the presence of saturating

concentrations of inositol hexaphosphate and bezafibrate),

again only 2 phases were observed – a nearly zero-amplitude

geminate phase and a single bimolecular phase, as observed for

T hemoglobin in solution (Fig. 7a).

The new striking result was the time course of rebinding

following photodissociation of the CO complex of T

hemoglobin in the absence of allosteric effectors with a

Figure 5.Heme environment (from (54). (a) Key residues of allosteric core. (b) Projection showing steric clash between imidazole

of proximal histidine and porphyrin pyrrole nitrogens.

EVOLUTION OF ALLOSTERIC MODELS FOR HEMOGLOBIN 593

geminate phase and biphasic bimolecular rebinding kinetics.

Both the geminate and faster of the two bimolecular phases

have the same relaxation rates as R-encapsulated hemoglobin

(Fig. 7b). Furthermore, the relaxation rate of the slower

bimolecular phase is the same as that observed for T

hemoglobin encapsulated in the presence of the strong

allosteric effectors (in experiments at different pH’s the slow

phase is slightly faster, attributed by Viappiani et al. to a

different distribution and lack of complete equilibration of

conformational substates). The time course is an almost

perfect linear combination of the time courses observed for R

encapsulated hemoglobin and T hemoglobin encapsulated in

the presence of allosteric effectors (Fig. 7b).

How can T hemoglobin contain a fraction of its liganded

subunit conformations with kinetic properties almost identical

to those of liganded subunits in the R quaternary structure?

Figure 6. Tertiary Two-State model of Henry et al. (23). See text for description. Only one representative species from the most

probable microstate, defined by the number of liganded and unliganded r and t subunits, is shown.

594 EATON ET AL.

The most straightforward interpretation is that gel encapsula-

tion markedly slows tertiary as well as quaternary conforma-

tional changes to an extent that the conformation prior to

photolysis remains throughout the course of CO rebinding. By

preventing any tertiary conformational changes on the sub-

second time scale, encapsulation in the polymeric network of

the gel allows the subunit conformations prior to photolysis to

be determined from their CO rebinding kinetics.

The TTS model readily explains these results (Fig. 7),

recalling that fast and slow CO rebinding kinetics correspond

to high and low oxygen affinity, respectively (8, 68). In the

presence of allosteric effectors all of the liganded subunits of

the T quaternary structure are in the t conformation, as in the

oxygenated crystal of T hemoglobin. In their absence both r

and t conformations are present in liganded T, in a proportion

that changes with concentration of allosteric effectors through

their effect on the tertiary equilibrium constant, lT. Measure-

ment of the relative amplitudes of the geminate phase, or of

the fast and slow bimolecular phase, precisely counts the

average fraction of subunits in the r conformation. Further-

more, as predicted by the TTS model, there is a very good

correspondence between the fraction of liganded subunits in r

determined from the photodissociation and oxygen equili-

brium experiments (67). To explain the observation that

equilibrium is achieved in oxygen binding measurements on

the same gels, which are carried out on the tens-of-minutes

Figure 7. Photodissociation experiments on gel-encapsulated hemoglobin and interpretation using the TTS model (from

Viappiani et al., 2004) (67). Empty symbols represent unliganded subunits and filled symbols subunits liganded with CO. The

conformation of the subunit is indicated by a t (squares) or r (circles). In (a) the upper (blue) time course is for CO rebinding to

hemoglobin encapsulated as deoxy with saturating concentrations of allosteric effectors followed by saturation with CO (Tþ gel),

while the lower (red) curve is CO rebinding to encapsulated CO hemoglobin (R gel). In (b) the light blue time course is for CO

rebinding to hemoglobin encapsulated as deoxy without allosteric effectors at pH 7.6 followed by saturation with CO (T- gel).

The black curve is a linear combination of the 2 curves in (a), with the relative proportion determined from the best fit.

EVOLUTION OF ALLOSTERIC MODELS FOR HEMOGLOBIN 595

time scale and show low affinity and non-cooperative binding

for T-encapsulated hemoglobin, Viappiani et al. carried out

detailed kinetic modeling. Using the conformational rates

determined from an analysis of solution kinetics by Henry

et al. (23), they estimated that a slowing factor for tertiary

conformational changes of 105 – 106 would trap tertiary

conformations until the completion of CO rebinding, but

allow complete equilibration in the oxygen affinity measure-

ments (67).

Can other allosteric models also explain these results? The

basic finding of liganded subunits in T with the same kinetic

properties as liganded subunits in R is inconsistent with the

MWC and Cooperon models. The SK model does not

consider the possibility of binding without salt bridge break-

age (Fig. 2), so it can be ruled out by the equilibrium crystal

and gel data. Nevertheless, the SK model makes an intriguing

prediction concerning the kinetics of rebinding in the gel

experiments. In the SK model ligation of all 4 subunits of the

T quaternary structure breaks all 8 salt bridges. Since the salt

bridges are the sole source of the low affinity of T, liganded

subunits in T are functionally in the same conformation as

liganded subunits in R. Consequently, the SK model predicts

that following photodissociation 100% of the subunits in

liganded T (in the presence or absence of allosteric effectors)

will rebind with relaxation rates identical to those of R, as

observed, but the model is inconsistent with the observations

of no fast phase in the presence of strong allosteric effectors

and 40 – 85% in their absence.

In the SKL model the liganded form in the T quaternary

structure contains strained salt bridges as well as a strained

allosteric core. The SKL model would correctly predict the

observed monophasic kinetics for rebinding to T at saturating

concentrations of allosteric effectors by assuming that all

liganded conformations were those with strained salt bridges

and allosteric cores. In the absence of allosteric effectors the

SKL model predicts two liganded conformations at neutral

pH where ionizable salt bridges can be protonated – one with

both the ionizable and un-ionizable salt bridges intact, and

one with only the un-ionizable salt bridge intact. It therefore

predicts biphasic kinetics for rebinding to T in the absence of

allosteric effectors, with an amplitude for the geminate and

faster bimolecular phase that increases with increasing pH, as

observed. However, the relaxation rate of the faster phase

would not be that of liganded subunits in the R quaternary

structure, because in the SKL model the liganded T structure

that could produce this phase contains both a strained salt

bridge and a strained allosteric core (see endnote 2).

STRUCTURAL INTERPRETATION OF THE TTS MODEL

It is instructive to use the SK and SKL models to give a

structural interpretation to the parameters of the TTS model.

We associate the r and t conformations with the different

conformations of the allosteric core described by Karplus and

coworkers (53, 54). Again, for clarity and simplicity, we only

consider subunit conformations of the T quaternary structure

at alkaline pH where all ionizable salt bridges are broken.

Under these conditions unliganded t contains an unbroken

salt bridge (as in SK and SKL) and a relaxed allosteric core (as

in SKL), liganded t contains a strained but unbroken salt

bridge and a strained allosteric core (as in SKL, but not SK),

unliganded r contains a broken salt bridge and a strained

allosteric core (the least populated species and understandably

not considered by either SK or SKL), and liganded r contains

a broken salt bridge and a relaxed allosteric core (as in SK, but

not SKL). The SKL parameters K and r now take on a

different meaning. The product rS is no longer just the

strength of the strained salt bridge, but collectively measures

the strain in the allosteric core, as well as the strain in the salt

bridge. Furthermore, S reflects both the strength of the salt

bridge and the strain caused by inserting an r subunit into a

structure with inter-ab (a1b2 and a2b1) contacts of the T

quaternary structure (Figs 1 and 4). With this interpretation of

the parameters the correspondence becomes (Fig. 2): Kt¼Kr,Kr¼K, lT¼S. The X-ray study of Dodson and coworkers

showed that the tertiary conformational change of the

oxygenated subunits in the T quaternary structure is in the

direction of the conformation of oxygenated subunits of R (15,

40). Since r5 1, the smaller tertiary equilibrium constant for

liganded subunits (rS) compared to unliganded subunits (S)

(Fig. 2) is consistent with this structural result.

At alkaline pH there is no parameter in the SK or SKL

models corresponding to the tertiary equilibrium constant, lR,

in the R quaternary structure. Since the R quaternary structure

does not permit the inter-subunit salt bridges of T, the

existence of t in R, with the same functional properties as t in

T, implies that the salt bridges play a minor role in

determining the low affinity of T.

ADDITIONAL TEST OF THE TTS MODEL

There is a very important, potentially testable prediction

of the admittedly most speculative part of the TTS model

(Fig. 8), namely that deoxy R contains a t conformation with

the same functional properties as the subunits of deoxy T.

From fitting ligand rebinding and conformational relaxa-

tion kinetic data Henry et al. estimated that the deoxy R

quaternary structure contains 30 – 40% t (in the absence of

strong allosteric effectors) (23). Other evidence suggesting

tertiary conformational equilibria in the R quaternary

structure comes from the oxygen binding measurements of

Yonetani and coworkers under a wide range of conditions

(66). If it were possible to kinetically trap the equilibrium

tertiary conformations of completely deoxygenated R, the

TTS model predicts biphasic bimolecular binding of CO – a

30 – 40% slow phase with the binding rate of t and a much

faster 70 – 60% phase with the r binding rate. The slow-

binding fraction, moreover, is predicted to increase in the

596 EATON ET AL.

presence of strong allosteric effectors. Equilibrium deoxy R

might be prepared by encapsulating CO hemoglobin as R,

completely dissociating the CO by continuous illumination

with a cw laser until tertiary equilibrium is achieved (but prior

to any R to T switching), followed by rapidly switching off the

laser and measuring CO rebinding. The appearance of a slow

phase could of course result from R to T switching, but this

possibility could be eliminated by determining the relative

amplitudes of the two phases as a function of the steady state

desaturation with the cw laser, since the quaternary rate is very

sensitive to the fractional saturation with ligand (23, 59, 60).

Varying the initial fractional saturation with CO of gel-

encapsulated T hemoglobin was used by Viappiani et al. to

rule out the possibility that T to R switching produced a fast

rebinding phase. Experiments based on these ideas are

currently in progress by Viappiani and coworkers.

Interestingly, in the SK and SKL models there is only one

unliganded conformation for the deoxy a subunits, but two

conformations for the unliganded b subunit at neutral pH,

with a broken and an unbroken intra-subunit salt bridge

(Fig. 4), whereas the TTS model postulates two conformations

for both subunits. Consequently, the SK and SKL models also

predict biphasic bimolecular recombination kinetics to gel-

encapsulated deoxy R hemoglobin, but with relaxation rates

(and amplitudes) that differ from the predictions of the TTS

model.

CONCLUSION AND FUTURE DIRECTIONS

It is somewhat surprising that in spite of an enormous effort

over many decades, we do not yet have a fully tested

theoretical model that quantitatively accounts for all of the

structural, equilibrium and kinetic properties of hemoglobin.

The most promising model is the Tertiary Two-State (TTS)

allosteric model of Henry et al. By comparing the TTS model

with the models of Szabo, Karplus, and Lee a structural

interpretation can be given to the TTS parameters. The model

provides a qualitative explanation of the key results on oxygen

binding in solution, gels, and crystals. The TTS model also

quantitatively explains the complex nanosecond to millisecond

ligand rebinding and conformational kinetics of hemoglobin,

and, more impressively, unlike any other model, explains the

unusual CO rebinding kinetics on gel-encapsulated hemoglo-

bin in which both tertiary and quaternary conformations are

kinetically trapped. Its similarity to the SK and SKL models

implies that it will also be capable of fitting oxygen equilibrium

data under different conditions. However, the extensive

structural analysis by Ho and coworkers using NMR

titrations of individual histidine residues to assess their relative

contribution to the Bohr effect indicates that a model which

only considers the salt bridges identified by Perutz will be

somewhat oversimplified (17).

Very basic questions on structure-function relations in

hemoglobin remain unanswered. What is the structural origin

of the difference in affinity for oxygen binding to t and r? More

specifically, what are the relative contributions of the

constraints of the salt bridges suggested by Perutz, and of

the strain in the allosteric core suggested by Karplus? Or as

discussed by Hopfield (70), is the free energy distributed

among so many residues that it will be extremely difficult to

identify specific contributions? Do ligands or just hydroxyl

ions and quaternary switching break the ionizable salt bridges?

What is the mechanism of the tertiary conformational change

(71, 72)? These questions will not be answered definitively until

key structures are solved and their properties investigated in

both equilibrium and kinetic experiments. At present we know

only the structures of deoxy T and liganded R, and liganded T

with unbroken salt bridges. Structures yet to be determined

are liganded T under conditions where protons are released,

and deoxy R. The TTS model predicts that while unliganded T

and liganded R contain essentially 100% of the subunits in the

t and r conformation, respectively, liganded T (in the absence

of strong allosteric effectors) and unliganded R contain

significant populations of both t and r (Fig. 6). Such a

mixture may be difficult to observe in a crystal structure. This

structural problem also becomes difficult for solution NMR

(69, 73, 74), since the tertiary conformations interchange on a

sub-microsecond time scale (60). The most promising

approach would appear to use site-directed mutagenesis to

create stable liganded T structures with nearly 100% of the

subunits in the r conformation, as could be determined by gel-

encapsulation kinetic studies. Creating stable, completely

unliganded R structures with nearly all t subunits is possibly

even more challenging.

ACKNOWLEDGEMENTS

Many of the ideas expressed in this paper are the result of

numerous discussions over the years with Attila Szabo, and we

are grateful to him again for his insights, helpful suggestions, and

careful reading of the manuscript. Work at the NIH was

supported by the Intramural Research Program of NIDDK and

in Parma by a grant to A. M. from the European Union

LSHB.CT-2004-503023 and from COFIN 2004 (MIUR) to C. V.

Figure 8. Proposed test of Tertiary Two State model for R quaternary structure. See text for description.

EVOLUTION OF ALLOSTERIC MODELS FOR HEMOGLOBIN 597

NOTES1 Interestingly, the K40 –H146 salt bridge (Fig. 4) stretches by 0.9 A upon

oxygenation of the T quaternary structure in the crystal (15).

2 The relative thermodynamic weights for a single subunit of the 4

possible species of the T quaternary structure in the SKL model at

neutral pH are (21, 22): 1þmH/SþKr2pþKrpmH/S, where m is the

concentration of hydroxyl ions and H is the hydroxyl ion binding

constant to the broken salt bridge. The second and fourth terms

correspond to the weights of subunits with broken and neutralized salt

bridges (inter-subunit in the case of a subunits and intra-subunit in the

case of b subunits), and the first and third terms are the same as in the

partition function at alkaline pH of equation (7).

REFERENCES1. Brunori, M. (1991) The fascination of hemoglobin – a roman

perspective – a citation-classic commentary on hemoglobin and

myoglobin in their reactions with ligands. Frontiers of Biology,

Volume 21. Edited by Antonini, E., and Brunori, M. Current

Contents/Life Sciences, 8 – 8.

2. Antonini, E., Rossi Fanelli, A., Wyman, J., Brunori, M., Bucci, E., and

Fronticelli, C. (1963) Studies on relations between molecular

and functional properties of hemoglobin .4. Bohr effect in human

hemoglobin measured by proton binding. J. Biol. Chem. 238, 2950 –

2957.

3. Edsall, J. T., and Wyman, J. (1958) Biophysical Chemistry, Academic

Press Inc., New York.

4. Monod, J., Wyman, J., and Changeux, J.-P. (1965) On the nature of

allosteric transitions: a plausible model. J. Mol. Biol. 12, 88 – 118.

5. Brunori, M. (1999) Hemoglobin is an honorary enzyme. Trends

Biochem. Sci. 24, 158 – 161.

6. Antonini, E., and Brunori, M. (1971) Hemoglobin and Myoglobin in

their Reaction with Ligands, North Holland, Amsterdam.

7. Edelstein, S. J. (1975) Cooperative interactions of hemoglobin. Ann.

Rev. Biochem. 44, 209 – 232.

8. Shulman, R. G., Hopfield, J. J., and Ogawa, S. (1975) Allosteric inter-

pretation of haemoglobin properties.Quart. Rev. Biophys. 8, 325 – 420.

9. Imai, K. (1982) Allosteric Effects in Haemoglobin, Cambridge

University Press, Cambridge.

10. Bunn, H. F., and Forget, B. G. (1986)Hemoglobin: Molecular, Genetic

and Clinical Aspects, W. B. Saunders, Co., Philadelphia.

11. Eaton, W. A., and Hofrichter, J. (1987) Hemoglobin-S gelation and

sickle-cell disease. Blood 70, 1245 – 1266.

12. Perutz, M. F. (1989) Mechanisms of cooperativity and allosteric

regulation in proteins. Quart. Rev. Biophys. 22, 138 – 236.

13. Eaton, W. A., and Hofrichter, J. (1990) Sickle cell hemoglobin

polymerization. Adv. Prot. Chem. 40, 263 – 279.

14. Ackers, G. K. (1998) Deciphering the molecular code of hemoglobin

allostery. Adv. Prot. Chem. 51, 185 – 253.

15. Perutz, M. F., Wilkinson, A. J., Paoli, M., and Dodson, G. G. (1998)

The stereochemistry of the cooperative effects in hemoglobin revisited.

Annu. Rev. Biophys. Biomol. Struct. 27, 1 – 34.

16. Shulman, R. G. (2001) Spectroscopic contributions to the under-

standing of hemoglobin function: implications for structural biology.

IUBMB Life 51, 351 – 357.

17. Lukin, J. A., and Ho, C. (2004) The structure-function relationship of

hemoglobin in solution at atomic resolution. Chem. Rev. 104, 1219 –

1230.

18. Bellelli, A., Brunori, M., Miele, A. E., Panetta, G., and Vallone, B.

(2006) The allosteric properties of hemoglobin: insights from natural

and site directed mutants. Curr. Prot. Peptide Sci. 7, 17 – 45.

19. Szabo, A., and Karplus, M. (1972) A mathematical model for

structure-function relations in hemoglobin. J. Mol. Biol. 72, 163 – 197.

20. Perutz, M. F. (1970) Stereochemistry of cooperative effects in

haemoglobin. Nature 228, 726 – 733.

21. Lee, A. W-M., and Karplus, M. (1983) Structure-specific model of

hemoglobin cooperativity. Proc. Natl. Acad. Sci. USA 80, 7055 – 7059.

22. Lee, A.W.-M., Karplus,M., Poyart, C., and Bursaux, E. (1988) Analy-

sis of proton release in oxygen binding by hemoglobin – implications

for the cooperative mechanism. Biochemistry 27, 1285 – 1301.

23. Henry, E. R., Bettati, S., Hofrichter, J., and Eaton, W. A. (2002)

A tertiary two-state allosteric model for hemoglobin. Biophys. Chem.

98, 149 – 164.

24. Herzfeld, J., and Stanley, H. E. (1974) A general approach to co-

operativity and its application to the oxygen equilibrium of

hemoglobin and its effectors. J. Mol. Biol. 82, 231 – 265.

25. Changeux, J. P., and Edelstein, S. J. (2005) Allosteric mechanisms of

signal transduction. Science 308, 1424 – 1428.

26. Buc, H. (2006) In Allosteric Proteins. 40 Years with Monod-Wyman-

Changeux (Brunori, M., Careri, G., Changeux, J.-P., and Schachman,

H. K., eds.), Vol. 17, pp. 31 – 49, Accadaemia Nazionale dei Lincei,

Rome.

27. Muirhead, H., and Perutz, M. F. (1963) Structure of haemoglobin – a

3-Dimensional Fourier synthesis of reduced human haemoglobin at

5.5 angstrom resolution. Nature 199, 633 – 638.

28. Perutz, M. F., Watson, H. C., Muirhead, H., Diamond, R., and

Bolton, W. (1964) Structure of haemoglobin – X-Ray examination of

reduced horse haemoglobin. Nature 203, 687 – 690.

29. Wyman, J. (1964) Linked functions and reciprocal effects in

hemoglobin – a second look. Adv. Prot. Chem. 19, 223 – 286.

30. Perutz, M. F., Rossmann, M. G., Cullis, A. F., Muirhead, H.,

Will, G., and North, A. C. T. (1960) Structure of haemoglobin – 3-

dimensional fourier synthesis at 5.5-angstrom resolution, obtained by

X-ray analysis. Nature 185, 416 – 422.

31. Pauling, L. (1935) The oxygen equilibrium of hemoglobin and its

structural interpretation. Proc. Natl. Acad. Sci. USA 21, 186 – 191.

32. Koshland, D. E., Nemethy, G., and Filmer, D. (1966) Comparison of

experimental binding data and theoretical models in proteins contain-

ing subunits. Biochemistry 5, 365 – 385.

33. Eaton, W. A., Henry, E. R., Hofrichter, J., and Mozzarelli, A. (1999)

Is cooperative oxygen binding by hemoglobin really understood? Nat.

Struct. Biol. 6, 351 – 358.

34. Hopfield, J. J., Shulman, R. G., and Ogawa, S. (1971) Allosteric

model of hemoglobin.1. Kinetics. J. Mol. Biol. 61, 425 – 443.

35. Gibson, Q. H. (1959) Photochemical formation of a quickly reacting

form of haemoglobin. Biochem. J. 71, 293 – 303.

36. Antonini, E., and Brunori, M. (1970) Hemoglobin. Ann. Rev.

Biochem. 39, 977 – 1042.

37. Sawicki, C. A., and Gibson, Q. H. (1976) Quaternary conformational-

changes in human hemoglobin studied by laser photolysis of

carboxyhemoglobin. J. Biol. Chem. 251, 1533 – 1542.

38. Mozzarelli, A., Rivetti, C., Rossi, G. L., Henry, E. R., and

Eaton, W. A. (1991) Crystals of haemoglobin with the T quaternary

structure bind oxygen non-cooperatively with no Bohr effect. Nature

351, 416 – 418.

39. Rivetti, C., Mozzarelli, A., Rossi, G. L., Henry, E. R., and

Eaton, W. A. (1993) Oxygen binding by single crystals of hemoglobin.

Biochemistry 32, 2888 – 2906.

40. Liddington, R., Derewenda, Z., Dodson, G., and Harris, D. (1988)

Structure of the liganded T-state of hemoglobin identifies the origin of

cooperative oxygen binding. Nature 331, 725 – 728.

41. Shibayama, N., and Saigo, S. (1995) Fixation of the quaternary

structures of human adult haemoglobin by encapsulation in trans-

parent porous silica gels. J. Mol. Biol. 251, 203 – 209.

42. Brunori, M., Coletta, M., and Di Cera, E. (1986) A cooperative model

for ligand-binding to biological macromolecules as applied to O2

carriers. Biophys. Chem. 23, 215 – 222.

598 EATON ET AL.

43. Gill, S. J., Robert, C. H., Coletta, M., DiCera, E., and Brunori, M.

(1986) Cooperative free energies for nested allosteric models as

applied to human hemoglobin. Biophys. J. 50, 747 – 752.

44. Smith, F. R., and Ackers, G. K. (1985) Experimental resolution of

cooperative free-energies for the 10 ligation states of human-

hemoglobin. Proc. Natl. Acad. Sci. USA 82, 5347 – 5351.

45. Speros, P. C., Licata, V. J., Yonetani, T., and Ackers, G. K. (1991)

Experimental resolution of cooperative free-energies for the 10

ligation species of cobalt(II) iron(II)-CO hemoglobin. Biochemistry

30, 7254 – 7262.

46. Gelin, B. R., Lee, A. W. M., and Karplus, M. (1983) Hemoglobin

tertiary structural-change on ligand-binding-it’s role in the co-

operative mechanism. J. Mol. Biol. 171, 489 – 559.

47. Yun, K. M., Morimoto, H., and Shibayama, N. (2002) The contri-

bution of the asymmetric alpha 1 beta 1 half-oxygenated intermediate

to human hemoglobin cooperativity. J. Biol. Chem. 277, 1878 – 1883.

48. Bettati, S., Mozzarelli, A., Rossi, G. L., Tsuneshige, A., Yonetani, T.,

Eaton, W. A., and Henry, E. R. (1996) Oxygen binding by single

crystals of hemoglobin: the problem of cooperativity and inequivalence

of alpha and beta subunits. Proteins-Struct. Funct.Gen. 25, 425 – 437.

49. Mozzarelli, A., Rivetti, C., Rossi, G. L., Eaton, W. A., and

Henry, E. R. (1997) Allosteric effectors do not alter the oxygen

affinity of hemoglobin crystals. Prot. Sci. 6, 484 – 489.

50. Perutz, M. F. (1970) The Bohr effect and combination with organic

phosphates. Nature 228, 734 – 739.

51. Shulman, R. G., Ogawa, S., Wuthrich, K., Yamane, T., Peisach, J.,

and Blumberg, W. E. (1969) Absence of heme-heme interactions in

hemoblobin. Science 165, 251 – 257.

52. Szabo, A., and Karplus, M. (1976) Analysis of interaction of organic

phosphates with hemoglobin. Biochemistry 15, 2869 – 2877.

53. Gelin, B. R., and Karplus, M. (1977) Mechanism of tertiary structural-

change in hemoglobin. Proc. Natl. Acad. Sci. USA 74, 801 – 805.

54. Gelin, B. R., Lee, A. W. M., and Karplus, M. (1983) Hemoglobin

tertiary structural-change on ligand-binding – its role in the co-

operative mechanism. J. Mol. Biol. 171, 489 – 559.

55. Bettati, S., and Mozzarelli, A. (1997) T state hemoglobin binds oxygen

noncooperatively with allosteric effects of protons, inositol hexapho-

sphate, and chloride. J. Biol. Chem. 272, 32050 – 32055.

56. Bruno, S., Bonaccio, M., Bettati, S., Rivetti, C., Viappiani, C.,

Abbruzzetti, S., and Mozzarelli, A. (2001) High and low oxygen affinity

conformations of T state hemoglobin. Prot. Sci. 10, 2401 – 2407.

57. Lyons, K. B., Friedman, J. M., and Fleury, P. A. (1978) Nanosecond

transient Raman-spectra of photolysed carboxyhemoglobin. Nature

275, 565 – 566.

58. Hofrichter, J., Sommer, J. H., Henry, E. R., and Eaton, W. A. (1983)

Nanosecond absorption spectroscopy of hemoglobin, elementary

processes in kinetic cooperativity. Proc. Natl. Acad. Sci. USA 80,

2235 – 2239.

59. Jones, C. M., Ansari, A., Henry, E. R., Christoph, G. W.,

Hofrichter, J., and Eaton, W. A. (1992) Speed of intersubunit

communication in proteins. Biochemistry 31, 6692 – 6702.

60. Henry, E. R., Jones, C. M., Hofrichter, J., and Eaton, W. A. (1997)

Can a two-state MWC allosteric model explain hemoglobin kinetics?

Biochemistry 36, 6511 – 6528.

61. Jackson, T. A., Lim, M., and Anfinrud, P. A. (1994) Complex

nonexponential relaxation in myoglobin after photodissociation of

MbCO – Measurement and analysis from 2-ps to 56-mu-s. Chem.

Phys. 180, 131 – 140.

62. Hagen, S. J., and Eaton, W. A. (1996) Nonexponential structural

relaxations in proteins. J. Chem. Phys. 104, 3395 – 3398.

63. Hagen, S. J., Hofrichter, J., and Eaton, W. A. (1996) Geminate

rebinding and conformational dynamics of myoglobin embedded in a

glass at room temperature. J. Phys. Chem. 100, 12008 – 12021.

64. Perrella, M., Colosimo, A., Benazzi, L., Ripamonti, M., and Rossi

Bernardi, L. (1990) What the intermediate compounds in ligand-

binding to hemoglobin tell about the mechanism of cooperativity.

Biophys. Chem. 37, 211 – 223.

65. Perrella, M., and Di Cera, E. (1999) CO ligation intermediates and the

mechanism of hemoglobin cooperativity. J. Biol. Chem. 274, 2605 –

2608.

66. Yonetani, T., Park, S., Tsuneshige, A., Imai, K., and Kanaori, K.

(2002) Global allostery model of hemoglobin – modulation of O-2

affinity, cooperativity, and Bohr effect by heterotropic allosteric

effectors. J. Biol. Chem. 277, 34508 – 34520.

67. Viappiani, C., Bettati, S., Bruno, S., Ronda, L., Abbruzzetti, S.,

Mozzarelli, A., and Eaton, W. A. (2004) New insights into allosteric

mechanisms from trapping unstable protein conformations in silica

gels. Proc. Natl. Acad. Sci. USA 101, 14414 – 14419.

68. Szabo, A. (1978) Kinetics of hemoglobin and transition-state theory.

Proc. Natl. Acad. Sci. USA 75, 2108 – 2111.

69. Lukin, J. A., Kontaxis, G., Simplaceanu, V., Yuan, Y., Bax, A., and

Ho, C. (2003) Quaternary structure of hemoglobin in solution. Proc.

Natl. Acad. Sci. USA 100, 517 – 520.

70. Hopfield, J. J. (1973) Relation between structure, cooperativity

and spectra in a model of hemoglobin action. J. Mol. Biol. 77,

207 – 222.

71. Jayaraman, V., Rodgers, K. R., Mukerji, I., and Spiro, T. G. (1995)

Hemoglobin allostery – resonance Raman-spectroscopy of kinetic

intermediates. Science 269, 1843 – 1848.

72. Balakrishnan, G., Case, M. A., Pevsner, A., Zhao, X. J., Tengroth, C.,

McLendon, G. L., and Spiro, T. G. (2004) Time-resolved absorption

and UV resonance Raman spectra reveal stepwise formation of T

quaternary contacts in the allosteric pathway of hemoglobin. J. Mol.

Biol. 340, 843 – 856.

73. Sahu, S. C., Simplaceanu, V., Gong, Q. G., Ho, N. T., Glushka, J. G.,

Prestegard, J. H., and Ho, C. (2006) Orientation of deoxyhemoglobin

at high magnetic fields: structural insights from RDCs in solution.

J. Am. Chem. Soc. 128, 6290 – 6291.

74. Gong, Q. G., Simplaceanu, V., Lukin, J. A., Giovannelli, J. L., Ho,

N. T., and Ho, C. (2006) Quaternary structure of carbonmonox-

yhemoglobins in solution: structural changes induced by the allosteric

effector inositol hexaphosphate. Biochemistry 45, 5140 – 5148.

75. Dickerson, R. E., and Geis, I. (1983) Hemoglobins: Structure,

Function, Evolution, and Pathology, Benjamin/Cummings, Menlo

Park, CA.

EVOLUTION OF ALLOSTERIC MODELS FOR HEMOGLOBIN 599