transduction of binding energy into hemoglobin cooperativity

TIBS 18 - OCTOBER 1993

Transduction o! binding energy into ; . . . . . I

hemogl6b/in cooperativity TETRAMERIC HUMAN HEMOGLOBIN

(Hb) continues to serve as a model for understanding basic issues of allosteric signal transduction and cooperativity in multisubunit proteins. Long-range interactions between the four oxygen-binding hemesites are classically reflected in the well-known sigmoid shape of the binding curve: initial binding steps pre- condition the molecule for a more energetically favorable reaction at sub- sequent steps so that the final oxygen binds with 200-fold higher affinity than the first.

Such high cooperativity is always accompanied by a suppression of the intermediate species - half-oxygenated Hb never exceeds a few percent of the population of Hb molecules. This energetic effect is commonly seen with intermediates along pathways of protein folding and with 'nucleated polym- erization' of protein filaments. While the low-abundance intermediates carry essential mechanistic secrets they have usually proved frustratingly elusive to capture and study. Researchers have often settled for measuring only average properties over the intermediate species, or formulating models based on the end-state molecules alone. By contrast, the intermediate states of hemoglobin cooperativity have recently been analysed at varying levels of detail with oxygen and with nonlabile oxygen analogs that mimic oxygenated heine- sites (e.g. carbon monoxide, nitric oxide, cyanide or metal-substituted heroes). These results, in combination with single-site mutation studies, have provided new insights into the pathways of cooperative energy transduction that are accessible to the hemoglobin molecule. The ways in which these pathways may be utilized in oxygen binding remains an open question that will be discussed.

The classical allosteric theories of Monod e ta l . ~ and of Koshland et aL 2 in- itially described how multisubunit proteins may act as molecular switches to control metabolic pathways. These models of functional regulation were formulated at the level of generalized conformational changes coupled to the local-site binding of substrates and other small 'effector' molecules. The

G. K. Ackers and J. H. Hazzard are at the Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St Louis, MO 63110, USA.

Hemoglobin is a tetrameric molecule consisting of two identical (~l~ dimers which assemble into either of two quaternary structures, T or R. Recent studies on mutant and partially ligated hemoglobins have revealed that cooperativity exists between the e~ and the I} heroes of each dimeric half-molecule and have led to asymmetry rule for quaternary T--)R switching: the quaternary R structure is energetically favored over the T structure when each dimeric half-molecule contains at least one ligated subunit.

major structural elements of hemoglobin allostery were defined by the pioneering X-ray studies of Perutz'~,4: two quaternary structures (T and R) dif- fer in the orientations of their assembled dimeric half-molecules (Fig. la, b). A global shift of this dimer-dimer

interface accompanies complete heine- site ligation. Early structural work also showed that the inter-heine dis- tances (25-40 A) preclude any direct heme-heme interactions, so that cooperativity must be mediated through protein-protein contacts of the subunits.

.- . . . . . , ,-~." .... ~-. -.,

i L t :b t

( b ) o !k-~-~ ~-.,

%, ; / . t,~

Figure 1 Subunit interactions in the hemoglobin tetramer. (a) Front view showing the c~ 1 subunit (lower right, solid) and the 132 subunit (upper left, dashed). At the center lies the (xll} 2 con- tact region, which, along with c~1~ 2, forms half of the dimer-dimer interface (designated 'lxll} 2 interface' herein). The remaining half of the interfacial region includes the ~21~1 and (~2(xl contacts, not visible from this view. (b) Side view illustrating c~l~ dimer movement in the quaternary transition from deoxy (solid) to oxy (dashed) hemoglobin. Reproduced, with permission, from Ref. 34. (c) Expanded view of the c~J] 2 and (x~ 2 contacts indicating salt bridges and hydrogen bonds (dotted) and nonbonding packing contacts (dashed). Reproduced, with permission, from Ref. 35.

© 1993, Elsevier Science Publishers, (UK) 0968-0004/93/$06.00 385

TIBS 1 8 - OCTOBER 1993

(a)

1,0-

0.8 J

0.6. /

0.4-

o.2./ } 0

o 014 o'.s 1:2 2'.o £4 216 [02] x 10 ~

(b) -14.3 kcal 2D m T

2(--8.3) -11.4 kcal ~ TX

-5.7 2DX -8.8 kcal TX2

2(-8.3) -7.2 kcal ~ TX 3 l

--8.0 kcal ¥ 2DX2 ~ TX4

Cooperative free energy

2.9

2.6

1.6

-0.8

Totals -33.2 - -26.9 6.3

Cost of structure rearrangement = 6.3 kcal

Rgure 2 Energetic penalties of stepwise cooperativity. (a) Effect of a decreasing hemoglobin concentration on oxygen binding isotherms, illustrating the increased affinity and loss of cooperativity upon dissociation of the tetramer to (xl~ dimers in dilute solutions. Curves D and T are for pure dimers and tetramers, respectively. The interior curves, from right to left, represent decreasing Hb concentrations from 380 pM to 0.04 pM. (b) Thermodynamic linkage scheme for oxygen binding, where X is oxygen. The cooperative free energy at each stage of binding is the energy difference between binding oxygen to the tetramer (T) and to the dissociated (x~ dimers (D). The dimer binds oxygen noncooperatively with an affinity equal to the average affinity of the constituent (x and ~ subunits 13 and thus serves as a ref- erence species for analysis of cooperativity effects. Formation of the dimer-dimer interface pre- conditions the hemesites for altered affinities and cooperative behavior. Adapted from Ref. 13.

Of particular interest has been the ~t[32 interlace (Fig. lc), which separates c([~ dimeric half-molecules and mediates the quaternary T~R structural transition.

These classical contributions of Monod, Koshland and Perutz provided a framework for dissecting the energetics of the hemoglobin allosteric mechanism. The next logical step was to determine the energetics of forming the subunit i~;terfaces at all combinations of bound and empty hemesites s-7, which was made possible by several additional discoveries and tech. niques 8-12. High-precision oxygen binding curves were measured at a series of decreasing hemoglobin concentrations that reflected increasing dimer popu- lations 13 (Fig. 2a). These data, in combination with independently determined energies of the dimer-tetramer assembly reactions, yielded the free ener. gies of the ! 1 coupled reactions shown (Fig. 2b).

Stepwise control of dimer-dlmer interaction

Relationships between the free energies in Fig. 2b can be used to deduce mechanistic features of the hemoglobin system. In particular they show how the number of ligated hemesites con- trois the 'strength' of the dimer-dimer interface, i.e. how much free energy is transduced at each binding step into alterations in the energy of dimer--dimer

386

interaction. Due to the path independence of AG the change in assembly energy at each ligation step measures the 'extra cost' of binding to subunits that are constrained within the tetrameric structure, relative to the same sites in dissociated dimers. For example, the tetramer binding energies at the first two steps reflect essentially equal energy costs for their ligand- induced structural changes within the tetramer (i.e. 2.9 and 2.6 kcal). A knowl- edge of the tetramer constants alone would not convey this important aspect of the energetics. The energy costs on the right of Fig. 2b are termed 'cooperative free energies' - AGc. The distribution of AG: values over all the ligation steps determines how the tetrameric binding curve differs from that of a noninteracting set of the same binding sites. The AGc values determine the Hill coefficient and other traditional measures of overall cooperativity 14, Figure 2b illustrates the fundamental point that energy-generating structure changes at any location within the tetrameric molecule will contribute fully to AG c, independent of the experimental method used in its determination. Most often AGe opposes the (negative) free energy of binding, thus acting as an 'energy penalty'. However, the opposite order is seen at the fourth binding step where the system enjoys an 'energy dividend'. This latter effect, where quaternary assembly causes

enhanced binding affinity ('quaternary enhancement') is a widespread feature of human hemoglobins ~5,16.

Dissecting the microstate energy penalties

The approach shown in Fig. 2b of dissecting the overall cooperativity into stepwise AGc values has been extended to mutant hemoglobins 17-~9, and to the effects of allosteric regulators 2°. These results have advanced our understanding of the energetic driving forces and the structural locations of residues that control cooperativity z9,21. However, the further dissection of these stepwise values into contributions from the specific 'microstate' isomers at each ligation stoichiometry (Table I) is essential to a

complete understanding of the pathways of cooperative ener~y transduction. For example, what are the individual contributions of the four doubly ligated species (i.e. [21], [22], [23] and [24]) to the AGe of 2.6 kcai tool -~ that was determined for the (overall) second oxygen-binding step (Fig. 2)?

This goal has posed an even more formidable challenge than that of the stepwise dissection shown in Fig. 2. In addition to the low relative abundances noted earlier for the eight partially oxygenated tetramers, their cooperative free energies were not resolvable because: (1~ heine-bound oxygen is extremely labile - even if it were possible to isolate tetramers with a particular configuration of oxygenated sites (Table I) they would quickly rearrange to a mixture of configurations through rapid dissociation and rebinding; and (2) the tetramers themselves dissociate readily into dimers and their re- assembly leads to rearranged site configurations.

Despite these barriers it has been feasible to determine AG~ values for all eight intermediate states of hemesite ligation by using nonlabile oxygen analogs such as cyanomet and carbon monoxide, and with heroes containing metals to replace the iron (such as manganese or cobalt). These analogs mimic the behavior of oxygenated heroes in terms of their general functional and structural properties (in fact


the quaternary R structure was first defined crystallographically using horse methemoglobin rather than oxyhemoglobin). As with enzyme suh- strate analogs, the various aspects of functional behavior may be amplified or diminished compared with the natural substrate. It may be expected, however, that these 'oxygen analogs' will trigger the same basic modes of intersubunit coupling and conformation change that normally generate cooperativity. Thus an overall strategy has been to determine the cooperative free energies over a range of different ligation systems and ask whether they exhibit a common qualitative pattern. If so, can the common pattern for the explicitly resolved systems also predict the properties of oxygen binding?

Since the stable oxygen analogs are not amenable to direct binding techniques, an extension of the previous strategy for using energetic linkages between binding and assembly was developed ~ for each microstate tetramer of Table I. For example, foot- note c in Table I shows these linkages for the half-ligated molecule, designated species [21].

Linkage relationships analogous to this were used for other ligation intermediates as shown in Table I. For six species ([II], [12], [21], [22], [31] and [32]), dissociation of tetramers into dimers leads to disproportionation reactions where the dimers reassemble to form other tetramers. Thus the assembly energies of these species must be resolved in the presence of their 'accompanying parents'. A variety of kinetic and equilibrium techniques were adapted for analysing these hybridizing systems zL2~. Especially use- ful have been the cryogenic isoelectric focusing methods of Perrella '~-~s in which the hybrid equilibrium mixture is quenched at low temperature into a cryosolvent.

Combinatodal distribution of cooperative bee energies

Init ial studies ~ with cyanomet-[-Ib revealed that the ten microstate species distribute into three discrete levels of cooperative free energy (Table D. Particularly unexpected was the find- ing of 'combinatorial switching' in the distribution: one of the doubly ligated species (species [21]) and both singly ligated species (species [11] and [12D occupy an intermediate level between the unligated species [01] and the fully ligated species [41]. By contrast, the

Table I. Cooperative bee energies for the ten Iigation microstates

tLi~a~, ~¢:r-~-te ~ Parent Assembly Cooperative [i[I species free energy ~ free energy ~

[~9-~ ~ None -:14.3 0

I23r ~ None ~ .4 5.9

[24~ ~ None -8.0 6.3

[3t~ ~ ~ + I ~ -8.0 6.3

[4T.: ~ NDne -8.2' 6.0

~lThe m~. @ @r=~'~es the particular species j among those with i ligands bound (i = O, :1, 2, 3, 4). O r ~ ~, ~ .w~h respe~I to j values is arbitrary. Subunit orientation within the tetramer is shown in, soeci~ !011 ~. ~'V~t~ a~ ~ ~ -+ 0.2 kcal. :Fro=5 ~.~er~ ~ i ~ f~T placir~ i li~,ands (X) on hemesites in configuration [ij] compared to ligating the same ~,~.es i~ ~.~i~--tecl ~iimers. Calculated from:

age Jl

AG# 1

+ ~ . ~AGz ~

] z~AG 2 ~ , ~

The reaction process of binding two ligands to form species [21] includes the free energies of binding to an u-subunit and a 13-subunit (as defined by dimer values on the left) plus an additional free energy 2~AG: that accompanies these steps (i.e. the co-

~, operative free energy 'penalty'). Even when such binding reactions cannot be measured per se, the determination of dimer to tetramer assembly values °~AG~ and 2lAG, provides immediate evaluation of ~AG, by the path independence of free energy. The Dower of linkage thermodynamics is illustrated by the fact that a AG: value determined solely by measure- ments of subunit assembly reflects not only the contributions from the dimer-dimer interface but also from all other structural regions of the molecules, including those regions distant from the interface.

other three doubly ligated species occupy a dislinctly different level along with the triply ligated species [31] and [321, and the fully ligated species [41!"~. This "combinatorial" behavior at the doubly ligated stage is incompat- ible with the traditional two-state MWC allusteric mechanism '~. where cooperative ~ree energies are determined solely by the number of ligands bound and are independent of their site con- figmrations. '~olalion of this MWC rule does not preclude a major role of the quaternary, transitinns that are known

to occur upon complete ligation. It simply means that additional features must also be involved.

Recent work on other ligation systems (Table llA), has demonstrated that the combinatorial distribution of AGc values is a common feature and not just a special effect of cyanomet lig~ion. These diverse ligation analogs exhibit a common pattern of AGc values that is qualitatively similar to cyanomet-Hb (including nonidentical AG values for doubly ligated species) but with vari- ations in the energy-level spacings. The

387


Table II. is combinatorial switching a general feature of the Hb mechanism?

A Ligated Unligated Combinatorial hemesite hemesite Species resolved switching? Ref(s)

Fellll) CN Fe(ll) 10 Microstates, Yes 22,26 pH 7.4-9.5

Mn(lll) Fe(ll) 10 Microstates, pH 7.4 Yes 27,30

Fe(ll) CO Mn(ll) 5 Microstates, pH 7.4 Yes 30

Fe(ll) CO CoOl) 10 Microstates, Yes 24 pH 7.4, 6.5

Co(ll) 02 CoOl) 5 Stepwise reactions, Consistent 28 pH 7,4, 6.5

Fe(ll) CO Fe(ll) [21] + [22] v. [23] + [24], Consistent 29 pH 7

Fe(ll) NO Fe(ll) 121] v. [22] Yes 29

Fe(ll) O~ Fe(ll) 5 Stepwise reactions, Consistent 14,16 pH 7.4-9.5

B Consensus partition function ( E )

E.(X) = 1 + 2Ktc (K + KI,) X + (2K KI~K~e t + 2K,,KI,KcK',c + K2~KcK',: + K2~KcK',c) X 2 + 2KcK',:(K,,K~, + K~Kp)X 3 + K,,2K~Kc X'

K and K are intrinsic binding constants for the ~ and ~ subunits. Kte is a 'tertiary constraint' interaction constant for the first hgabon event. K~ denotes the tertmry constra nt for the format on of speo es 21] within the T structure. K't: is a tertiary constraint constant for quaternary enhancement.

Cq

4 -

3

2-

H i[ I H , ,

i i I, IV II II, Ill

[01] [21] [41]

11 U "

III V Vl' Vl

Subunit contacts at the ~1[32 interface

Figure 3 Effects of single-residue modifications on AG 2, the free energy of assembling c(~ dimers into tetramers in each of three cyanomet ligation states. Black: unligated species [0t]. Grey: half-ligated species [21]. Open: fully-ligated species [41]. At~G 2 is equal to AG 2 for normal hemoglobin minus AG 2 for the mutant hemoglobin. Hemoglobins are ordered by Roman numeral according to structural regions within the cd~ 2 interface (Fig. lc): I, c~ZFG-[3~C (flexible joint); II, (~C-[~2FG (switch); III, FG corners; IV, C helices; V, carboxyl termini of c~ subunits; VI and VI', carboxyl termini of [~ suhunits. Adapted from Ref. 32.

388

cyanomet system behaves as a simpli- fied version of a more general distribution exemplified by the cobalt-substituted Hbs where additional features such as quaternary enhancement are also present. For the general case: (1) the ten ligation species distribute into five discrete levels of cooperative free energy (for example, species [01], [ 11 ], [21], [22], and [41]); (2) species [11] and [21] occupy separate levels; and (3) five species (species [22], [23], [24], [31], and [32]) exhibit quaternary enhancement and are more weakly assembled than the fully ligated species [411.

The various ligation systems of Table IIA thus show a common set of qualitative relationships between the configurations of ligated sites and the ordered distribution of cooperative free energies. The premise of a common thermodynamic mechanism for cooperative energetics requires that the various ligation systems conform to a common formula for their molecular partition function 14,1~. Such a 'consensus partition function' (Table liB) embodies rules of the hemoglobin mechanism by prescribing exact relationships between the various energetic contributions. It is these relationships that must be constant among the various heine- site ligands, not the numerical values of the terms. In this way the consensus partition function reflects the common pattern of experimental results from the explicitly resolved ligation systems obtained over a range of conditions.

Comparison with oxygen Using known values of K. and Kp

(the intrinsic binding constants for the c( and [~ subunits), the consensus partition function given in Table lIB is ca- pable of predicting the tetramer oxygen- binding curve in Fig. 2 to within the accuracy of its experimental determination 14. The stepwise AGc values for oxygen binding to normal hemoglobin [Fe(ll')/Fe(ll)-O2] are found to be entirely consistent with results on the other ligation systems of Table IIA. Thus the common energetic mechanism determined for these explicitly resolved 'oxygen analog' systems is indeed ca- pable of predicting the quantitative behavior of normal hemoglobin binding oxygen.

quatemary assignment of the intermediates Discovery of the combinatorial

responses to hemesite ligation led to the question of what types of structures


are adopted by the intermediate lig. ation species. Do the intermediates utilize an entirely different quaternary structure from the well-known T and R forms represented by species [01] and [41]? By contrast, are the intermediates allosterically distinct only in the 'sequential' KNF sense, while maintain- ing one of the two classical dimer- dimer orientations R or T?

The answer to this question for cyanomet-Hb came from measuring the effects of single-site mutations on assembly of the dimer--dimer interface 3u,32 (Fig. 3). When the interface shifts globally to a new dimer-dimer orientation, each interface residue will experience a new local environment at the adjacent dimer. The strategy was to measure the energetic perturbations of dimer to tetramer assembly by a series of single-residue interface mutations o n

the unligated species [01L the half- ligated species [21], and the fully ligated species [41]. It was found (Fig. 3) that the single-site perturbations to assembly of species [41] (quaternary R) did not correlate with those of the unligated species [01] (quaternary 1"). By sharp contrast, however, the pertur- bation to the species [21] tetramer from each of the single-site modifications was quantitatively identical to that produced by the same modification in the deoxy species [01] tetramer. These results indi- cate identity between species [01] and [21] in the spatial distribution of local interactions contributed by residues of the unligated dimers. Species [21] was therefore assigned to the quaternary T structure. Other techniques have also led to the assignment of species [21] and species [II] and [12] to quaternary T 14,16. The remaining doubly ligated species [22], [23], and [24], and both triply ligated molecules were found to be in quaternary R.

Pathways of cooperative energy transduction

An immediate consequence of these quaternary assignments was to reveal a 'symmetry rule' (Fig. 4) which specifies the relationship between hemesite ligand binding and quaternary transition: T-->R quaternary switching occurs when hemesite binding yields at least one ligated subunit on each side of the dimer--dimer interface 31.

Molecular origins of the symmetry rule arise from the propagation of tertiary structure change within the dimeric half- molecule in response to ligation of the first site. Cyanomet-Hb species

T

21-

I I I I I I I 0 1 , I I I I I I I I I

11 12 ,, II m = =

!

I

' 22 23 24 I I I

R

I , 31 32 I I I

I | I ! I ! , 4 1

Rgure 4 Diagrammatic illustration of the symmetry rule and allosteric mechanism found in cyanomet-Hb. The tertiary structure of the individual ~ and j] subunits is either 't' (squared) or "r' (rounded). Ligand binding to either th~ ~ or ~ subunit of species [01] is communicated across the czt~ ~ interface to the remaining subunit within the cx[~ dimer, denoted by the grey dashed line in species [11], [12] and [21]. Quaternary switching from T (black) to R (cyan) follows a 'symmetry rule' (indicated by black dashed line): the R quaternary structure is energetically favored in a tetramer with at least one ligated subunit on each dimeric half-molecule.

[21] and the singly ligated species have the same cooperative free energy so that only the first binding step includes the 3 kcal energy penalty. Hence, the second binding step within a dimeric half- molecule is accompanied solely by the intrinsic free energy AG~ or AG~. The net energy of binding the second ligand with- ~n the dimer is thus 3 kcal more favorable than for the first binding step. This trans- lates into a 200-fold increase in affinity for the second binding step leading to species [21]. The free energy of initial binding is thus transduced into 'confor- mationai energy' of the ligated subunit

which is also propagated into the other subunit of a dimeric half tetramer. If no ligands are bound on the adjacent dimer the quaternary T interface is maintained. However, when the first subunit of the adjacent dimer is ligated the T~R switch is triggered. This quaternary transition provides relief from the energetically un- favorable tertiary constraints. In terms of classical concerted versus sequential aUosteric models, the hemoglobin tetramer is seen to exhibit both mechanisms of generating cooperativity with the distribution between them governed by the symmetry rule.

389

TIBS 1 8 - OCTOBER 1 9 9 3

Since these modes of cooperative energy transduction have been dis- covered using cyanomet-Hb and other 'oxygen analogs', the extent to which they are utilized with oxygen as the ligand remains an open question. Recent experiments with mixed ligands (oxygen and cyanomet) ~ and with combinations of nitric oxide and carbon monoxide ~3 have provided further support for the symmetry rule. It seems unlikely that the specific modes of cooperative energy transduction revealed by these oxygen analogs would have evolved adven- titiously, i.e. that hemoglobin's tertiary and quaternary switches are being made to couple with a remarkable set of new rules just by changing the hemesite ligand.

As the known repertoire of protein 'molecular switches' and energy trans- ducers grows, so does the need for an increased understanding of |undamen- tal mechanisms in multisubunit protein assemblies. The recent studies with hemoglobin provide new insights into the nature of intramolecular communi- cation between binding sites that are separated by subunit interlaces and of the energy costs that dictate their 'molecular choreography.'

Acknowledgements We thank members of our research

group, including Paula Dalessio, Peggy Daugherty, Michael Doyle, Yingwen Huang and George Lew for valuable discussions. This work has been supported by NIH Grant R37-GM24486 and by NSF Grant DMB9107244.

References 1 Monod, J., Wyman, J. and Chan~eux, J-P. (1965)

1 Mol. Biol. 12, 88-.-118 2 Koshland, D. E., Nemethy, G. and Rimer, D.

(1966) Biochemistry 5, 364-385 3 Perutz, M. F. (1989) quart. Rev. Biophys. 22,

139-236 4 Perutz, M. F. (1970) Nature 228, 726-734 5 Noble, R. W. (1969) J. MoL Biol. 39, 479-491 6 Weber, G. (1972) Biochemistry11, 864-8~8 7 Ackers, G. K. and Halvorson, H. R. (1974) Prec.

Natl Acad. Sci. USA 71, 4312-4316 8 Rosemeyer, M. A. and Huehns, E. R. (1967)

J. MoI. Biol. 25, 253-273 9 Nagel, R. L. and Gibson, Q. H. (1971) J. Biol.

Chem. 246, 69-73 10 Kellett, G. L. and Gutfreund, H. (1970) Nature

227,921-926 11 Imai, K. et al. (1970) Biochim. Biophys. Acta

200, 189-196 12 Johnson, M. L., Halvorson, H. R. and Ackers,

G. K. (1976) Biochemistry 15, 5363-5371 13 Mills, F. C., Johnson, M. L. and Ackers, G. K.

(1976) Biochemistry 15, 5350-5362 14 Ackers, G. K., Doyle, M. L., Myers, D. and

Daugherty, M. A. (1992) Science 255, 54-63 15 Ackers, G. K. and Johnson, M. L. (1990)

Biophys. Chem. 37,265-279 16 Doyle, M. L. and Ackers, G. K. (1992)

Biochemistry 31, 11182-11195 17 Atha, D., Johnson, M. L. and Riggs, A. F. (1979)

J. Biol. Chem. 254, 12390-12398 18 Doyle, M. L. etaL (1992) Biochemistry31,

8629-8639 19 Turner, G. J. et aL (1992) Proteins 14, 333-350 20 Chu, A, H., Turner, B. W. and Ackers, G, K.

(1984) Biochemistry 23, 604-617 21 Ackers, G. K. (1980) Biophys, J. 32, 331-343 22 Smith, F. R. and Ackers, G. K. (1985) Proc. Natl

Acad. Sci. USA 82, 5347-5351 23 UCata, V. J., Spores, P. C., Rovida, E. and

Ackers, G. K. (1990) BiochPmistry 29, 9771-9783

24 Speros, P. C., LiCata, V. J., Yonetani, T. and Ackers, G. K. (1991) Biochemistry30, 7254-7262

25 Perrella, M. and Rossi-Bernardi, L. (1981) Methods EnzymoL 76, 133-143

26 Perretla, M., Benazzi, L., Shea, M. A. and Ackers, G. K. (1990) Biophys. Chem. 35, 97-103

27 Ackers, G. K. (1990) Biophys. Chem. 37, 371-382

28 Doyle, M. L. et eL (1991) Biochemistry30, 7263-7271

29 Perrella, M. et al. (1990) Biophys. Chem. 37, 211-223

30 Smith, F. R,, Gingrich, D., Hoffman, B, and Ackers, G, K. (1982) Prec. Natl Acad. Sci. USA 84, 7089-7093

31 Daugherty, M, A. et aL (1991) Proc. Nat/Acad. Sci. USA 88, 1110-1114

32 LiCata, V. J,, Dalessio, P, M. and Ackers, G. K. Proteins (in press)

33 KliEer, L., Poyart, C. and Marden, M. C. Biophys. J. (in press)

34 Baldwin, J. M. and Chothia, C. (1979) J. Mol. BioL 129, 175-193

35 Dickerson, R. E. and Gels, I. (1983) Hemoglobin: Structure, Function and Evolution, Benjamin/Cummings

What are the intermediate states?

' / f ' ~ ' I

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390

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Hamlet Act I Hamlet Final Scene

transduction of binding energy into hemoglobin cooperativity

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