Experimental basis for a new allosteric model for multisubunit proteins

Significance

Although the theoretical model of Monod, Wyman, and Changeux (MWC) is one of the most influential and highly cited theoretical models in bioscience, it fails to explain allosteric effects in hemoglobin, the paradigm of allostery, because their model considers only quaternary preequilibria. By using a new kind of laser photolysis experiment, measurements of ligand rebinding kinetics for transient hemoglobin conformations trapped by encapsulation in silica gels support the simplest possible extension of the MWC allosteric model to include tertiary in addition to quaternary conformational preequilibria. While the MWC model provides a qualitative explanation for allostery in many multisubunit proteins, quantitative analysis will most probably require the extension used here to explain our new results.

Abstract

Monod, Wyman, and Changeux (MWC) explained allostery in multisubunit proteins with a widely applied theoretical model in which binding of small molecules, so-called allosteric effectors, affects reactivity by altering the equilibrium between more reactive (R) and less reactive (T) quaternary structures. In their model, each quaternary structure has a single reactivity. Here, we use silica gels to trap protein conformations and a new kind of laser photolysis experiment to show that hemoglobin, the paradigm of allostery, exhibits two ligand binding phases with the same fast and slow rates in both R and T quaternary structures. Allosteric effectors change the fraction of each phase but not the rates. These surprising results are readily explained by the simplest possible extension of the MWC model to include a preequilibrium between two tertiary conformations that have the same functional properties within each quaternary structure. They also have important implications for the long-standing question of a structural explanation for the difference in hemoglobin oxygen affinity of the two quaternary structures.

Small molecules can regulate protein reactivity by binding to residues distant from the active site, a phenomenon known as allostery. The classic theoretical model proposed by Monod, Wyman, and Changeux (MWC) (1, 2) for explaining this phenomenon considered only proteins with multiple subunits, and the two-state allosteric model of MWC was originally used by them to explain the functional properties of the hemoglobin tetramer, the “honorary enzyme” (1, 3). This famous model has since been applied to a wide variety of other systems in biology, including ligand-gated ion channels, G-protein–coupled receptors, nuclear receptors, and supramolecular assemblies such as chaperonins (4–7). In the case of hemoglobin, the paradigm of allostery, MWC makes two key postulates that have been extensively tested by experiments. Oxygen binding to the deoxy quaternary structure (T) is noncooperative; cooperativity arises from a shift in the population from the low-affinity T quaternary structure to the high-affinity R quaternary structure as the oxygen concentration is increased. The second postulate is that allosteric effectors regulate oxygen affinity by altering only the R ⇄ T preequilibrium. Investigations of hemoglobin focused primarily on the first postulate, which was finally confirmed by single-crystal oxygen-binding measurements that ruled out a sequential model (8) and ended a 25-y controversy (9–12). The second is of more general interest because it applies to all multisubunit proteins exhibiting allosteric behavior and has been known for many years to be inconsistent with the fact that allosteric effectors markedly affect oxygen affinity without changing the quaternary preequilibrium [see data summaries by Imai, Yonetani, and coworkers (13, 14)]. The change in oxygen affinity constants, K_T and K_R, with conditions was interpreted as indicating that tertiary conformations must be affected or that more than two quaternary states exist. Consequently, many variations of the MWC model have appeared over the years to explain this result, as well as a wide range of equilibrium, kinetic, and spectroscopic data for hemoglobin (see, for example, refs. 11, 12, and 15–20).

Now that regulating protein reactivity by altering tertiary conformations is recognized as widespread in the protein world (21–26), there has been a need to extend the MWC model for multisubunit proteins to include tertiary as well as quaternary conformational changes. The tertiary two-state (TTS) model of Henry et al. (27) is the simplest possible extension and is capable of providing a quantitative explanation for a vast array of experimental data for hemoglobin. In this work, we test a key prediction of the TTS model by using a new kind of kinetic measurement in which carbon monoxide rebinding to R-state hemoglobin is measured following millisecond-to-kilosecond continuous-wave (cw) photodissociation of silica gel-encapsulated hemoglobin.

Silica gels slow conformational changes in hemoglobin by many orders of magnitude without altering equilibria (28–30), as shown by identical oxygen binding curves in the gel and in solution (Fig. 1). Consequently, it is possible to interrogate properties of protein conformations that are undetectable in both kinetic and equilibrium experiments in solution, but are key for testing theoretical models. In a previous study, we carried out nanosecond pulsed laser photolysis experiments on HbCO encapsulated and thereby trapped in either the T or R quaternary structures, corresponding to the arrangement of the four subunits in fully unliganded and fully liganded hemoglobin, respectively (Fig. 2B) (34). We discovered that, although the R and T quaternary structures show a single fast and slow CO rebinding phase in the presence of allosteric effectors, respectively, in the absence of allosteric effectors the T quaternary structure exhibits two phases—the expected slow phase and, surprisingly, a much faster phase with a rate identical to that found in R (Fig. 2B). This fast rate was interpreted in terms of the TTS model (Fig. 3) as arising from subunit conformations of liganded T trapped by the gel in the r tertiary conformation that is functionally identical to unliganded r subunits in the R quaternary structure. Because there is no exchange of tertiary conformations during ligand rebinding, the experiment measures the equilibrium fraction of r subunits in liganded T.

Fig. 1.

Hill plots for oxygen binding to hemoglobin in solution, gel, crystal, and sickle fiber (y is fractional saturation with oxygen and p is oxygen pressure). (Inset) Comparison of p50 (the oxygen pressure at half fractional saturation of the four hemes) in the absence of allosteric effectors in solution and gel. T⁺, R⁺ and T⁻, R⁻ refer to the T, R quaternary structures in the presence and absence of the allosteric effectors, inositol hexaphosphate (IHP) and bezafibrate (Bzf). The striking identity of the oxygen affinities in solution, gel, and crystal show that both the gel and the crystal trap unstable tertiary and quaternary structures, but do not alter their equilibrium properties. The extreme low affinity (highest p50) occurs because the liganded molecule (in the sickle fiber also) remains in the t tertiary conformation of the tertiary two-state model. Detailed solvent conditions: gray circles (R⁻ gel): Hb encapsulated in gel as R from Shibayama: 100 mM phosphate, pH 7, 20 °C, p50 = 0.16 torr, n = 0.86 (28). Violet circles (R⁻ crystal): Hb C crystals in R quaternary structure, 0.8 M NaH₂PO₄, 1.7 M K₂HPO₄, pH 7.2, 21–22 °C, p50 = 0.32 torr, n = 1.03 (31). Magenta dashed line [R⁻ solution (soln)]: binding of fourth oxygen, K₄, in solution, 100 mM Hepes, pH 7.0, 15 °C, 1/K₄ = 0.18 (14). Orange continuous line (T⁻ soln): binding of first oxygen, K₁, in solution, 20 mM Bis-Tris, 5 mM Cl⁻, 1 μM EDTA, pH 7.6, 25 °C, 1/K₁ = 7.6 torr (32) [data normalized to 15 °C through correction factor from Imai (13)]. Dark blue dashed line (T⁻ gel): Hb encapsulated in gel in the absence of allosteric effectors, 100 mM Hepes, pH 7.6, 15 °C, p50 = 7.9 torr, n = 1 (33). Green dashed line (T⁺ gel): Hb encapsulated in gel as T in the presence of allosteric effectors, 100 mM Hepes, 10 mM IHP, 2 mM Bzf, 200 mM Cl⁻, 1 mM EDTA, pH 7.0, 15 °C (34). Red dashed line (T crystal): Hb crystals in 10 mM potassium phosphate, 54% (wt/vol) PEG 1000, 2 mM IHP, 1 mM EDTA, 15 °C, pH 7.0, p50 = 135 torr, n = 0.97 (35). Open circles (T sickle fiber): sickle cell fibers, 23.5 °C (36). Light blue continuous line (T⁺ soln): binding of first oxygen in solution in the presence of allosteric effectors, 100 mM Hepes, 2 mM IHP, 10 mM Bzf, 100 mM M Cl⁻, pH 7.0, 15 °C, 1/K₁ = 139 torr (14). (Inset) p50 dependence on pH. T⁻ gel, dark blue circles (33); T⁻ soln, orange circles (32).

Fig. 2.

Nanosecond pulsed laser photolysis experiments of CO rebinding with cartoon explanation. (A) CO rebinding in solution. Ligand rebinding is characterized by three phases—unimolecular geminate rebinding, bimolecular rebinding to the R quaternary structure, and a slower bimolecular phase corresponding to rebinding to molecules that have switched from the R to the T quaternary structure (37). (B) CO rebinding in gel to hemoglobin in the R quaternary structure (red curve; labeled R⁻), to the T quaternary structure in the absence of allosteric effectors (cyan curve; labeled T⁻), to the T quaternary structure in the presence of the allosteric effectors IHP and BZF (blue curve; labeled T⁺). Solution and gel experiments were performed at 20 °C and at 0.2 and 1 atm CO, respectively. The black curve is a linear combination of the CO rebinding curves for the T⁺ and R gels that optimally superimposes on the T⁻ curve. (C) Cartoon interpretation of experiments in gels, where squares represent slow binding (t) subunit conformations, and circles, fast binding (r) subunits. The open symbols signify unliganded, and closed symbols, liganded. The gel traps both tertiary and quaternary structures for the duration of the experiment. The fast rebinding r conformation is not observed in pulsed laser photolysis of HbCO in the T quaternary structure in solution (38), because it relaxes too fast to the slow rebinding (t) conformation characteristic of the fully unliganded T quaternary structure before any significant geminate rebinding occurs (27).

Fig. 3.

Schematic structures of the MWC and TTS models for a dimer with equivalent subunits. The subset of MWC is enclosed with a green dashed line. In both T and R quaternary structures, the empty and filled symbols correspond to unliganded and liganded subunits; squares, to less reactive (t) tertiary conformations; and circles, to more reactive (r) tertiary conformations of the TTS model. For clarity, degenerate states (which introduce statistical factors in the partition function) are not shown. The relative lengths of the arrows indicate that r has a higher reactivity than t, that the reactivity of t is the same in both quaternary structures, as is the case for r, that the T quaternary structure biases the tertiary equilibrium toward t, and that the R quaternary structure biases the tertiary conformational equilibrium toward r. Although the partition function for a tetramer can be as mathematically compact as that of a dimer (SI Text), a similar diagram for a tetramer is much too complex.

The TTS model is the simplest extension of the MWC model that includes a tertiary as well as a quaternary preequilibrium (27) (Fig. 3). The model had previously explained the appearance of a T-like optical absorption spectrum as a tertiary conformational relaxation from r to t within unliganded R before the R → T transition following nanosecond photodissociation of R-HbCO in solution (27). The TTS model has also been used by Spiro and coworkers (39) to explain the kinetics of structural changes observed by time-resolved resonance Raman experiments. To distinguish between the TTS model and other theoretical models for hemoglobin allostery (12), it became essential to determine the functional properties of the t subunits of unliganded R. We therefore designed a new kind of laser photolysis experiment that consists of extended cw illumination of HbCO encapsulated in the R quaternary structure to create an equilibrium population of unliganded subunits. It was expected that the gel would also prevent tertiary conformational exchange during ligand rebinding, so that the rebinding kinetics of individual conformations could be measured in the absence of any tertiary conformational exchange dynamics.

Results

Confirmation of Tertiary r in Liganded Quaternary T.

As a control and to confirm our interpretation of r tertiary in T quaternary in the pulsed laser photolysis experiments of Viappiani et al. (34) (Fig. 2), we first carried out cw photolysis experiments on the T quaternary structure in the absence of allosteric effectors (T⁻) (Fig. 4). In these experiments, the sample is exposed to the cw laser for various times, suddenly turned off, and the kinetics of CO rebinding to unliganded subunits is measured by optical absorption. Because the gel traps partially liganded T for many minutes, all of the tetramers are in the T quaternary structure during the experiment, as shown previously (34). Fig. 4A shows that there is initially a fast and a slow rebinding phase, but by 10 ms of continuous laser photolysis all of the subunits rebind with the single characteristic slow (t) rate (Fig. 4 A and B). The fast rebinding phase, corresponding to r rebinding, disappears with a stretched exponential time course having a half-time of ∼100 μs, slowed by encapsulation by a factor of ∼10⁴. The overlap of the timescales for bimolecular rebinding and the r → t relaxation explains the lack of a more perfect overlap of the T⁻ gel bimolecular kinetics and the linear combination of the R and T⁺ bimolecular kinetics in the pulsed laser photolysis experiments (Fig. 2B). Whereas the gel traps r in T on the nanosecond–microsecond timescale, the r ⇄ t conformational equilibrium is fully established on the minutes timescale, allowing true equilibrium oxygen binding curves to be determined for the T quaternary structure (Fig. 1) (28, 29).

Fig. 4.

cw laser photolysis experiments on T⁻ gels. (A) Normalized rebinding curves upon turning off cw laser following continuous photodissociation of T encapsulated HbCO in the absence of allosteric effectors for 500 μs (green curve; 1% of CO hemes photolyzed) and 100 ms (magenta curve; 8% of hemes photolyzed) at 20 °C and 1 atm CO. The black dashed curves are the fits to a sum of two slightly stretched exponentials, i.e., f(t) = Aexp[−(t/τ_f)^β] + (1 − A)exp[−(t/τ_s)^β], where A and (1 − A) are the fractions of the optical changes at 532 nm for each phase, respectively, τ_f (=220 ± 50 µs) is the time constant for the fast rebinding phase, τ_s (=5.2 ± 0.5 ms) is the time constant for the slow rebinding phase, and β is 0.8. (A, Inset) Rate distributions from maximum entropy method (40). (B) Fraction of slow and fast rebinding phases as a function of exposure time to cw laser. The time course is fit with a stretched exponential, f(t) = (1 − exp[−(t/τ)^β]), with τ = 200 ± 20 μs and β = 0.39 ± 0.03. (C) Time constants for slow and fast rebinding phases as a function of exposure time. (D) Cartoon of interpretation of experiment: before continuous photodissociation of CO, subunits in both t and the r conformations are populated. In the steady state, unliganded r subunits in T⁻ gels convert completely to t within 10 ms. For clarity, the cartoon shows 100% photolysis.

Discovery of Tertiary t in Unliganded Quaternary R.

Fig. 5 shows the results for cw photolysis experiments carried out on hemoglobin trapped in the R quaternary structure by encapsulation in the gel as the CO complex in the absence of allosteric effectors. As the exposure time is increased, a slow rebinding phase appears that increases with a highly stretched exponential time course and extends to >1,000 s. There is a small increase in bimolecular rate with exposure time, asymptotically approaching the same bimolecular rate observed for the slow rebinding phase observed for the T quaternary structure (Fig. 5C) and a rebinding amplitude of ∼20% (Fig. 5B and Table S1).

Fig. 5.

cw laser photolysis experiments on R⁻ gels. (A) Normalized rebinding curves upon turning off cw laser following continuous photodissociation of R encapsulated HbCO for 1 ms in the absence of allosteric effectors (1% of hemes photolyzed) and 1,000 s (12% of hemes photolyzed) at 20 °C and 0.2 atm CO. The black dashed curves are the fits to a sum of two slightly stretched exponentials, i.e., f(t) = Aexp[−(t/τ_f)^β] + (1 − A)exp[−(t/τ_s)^β], where A and (1 − A) are the fractions of the optical changes at 532 nm for each phase, respectively, τ_f (average = 0.98 ± 0.07 ms) is the time constant for the fast rebinding phase, τ_s (=25 ± 1 ms) is the time constant for the slow rebinding phase after 1,000 s exposure, and β is 0.8. This slight stretching most probably reflects either a small α−β inequivalence or lack of sufficiently fast interconversion of conformational substates. (A, Inset) Rate distributions from maximum entropy method. (B) Fraction of slow and fast rebinding phases as a function of exposure time to cw laser. The time courses for the fraction of slow rebinding and fast rebinding phases are well fit with stretched exponentials with τ = 4 ± 2 s and β = 0.20 ± 0.07, and f(∞) = 0.17 ± 0.02. (C) Time constants, τ_f = 0.98 ± 0.07 ms, and τ_s, as a function of exposure time, and fit of τ_s with a stretched exponential function [τ_s (∞) = 25 ± 2 ms], with β = 0.2 ± 0.1, τ = 4 ± 3 s. The ligand rebinding rate decreases slightly with exposure time because the ensemble of substates of t in R require the longer exposure times to fully equilibrate. (D) Cartoon of interpretation of experiment for R⁻ gel: before continuous photodissociation of CO, all subunits are in the r conformation. In the steady state, a fraction of the unliganded subunits converts from r to t, which requires more than 1,000 s to reach equilibrium. For clarity, cartoon shows 100% photolysis.

It is of course essential to demonstrate that the appearance of a slow rebinding phase is not due to R-to-T conversion. There are several lines of evidence to show that this is not the case, particularly for the R⁻ gel with the long exposure times to the cw laser (SI Text). Most convincingly, the fraction of slow rebinding is independent of the degree of photolysis and therefore the number of ligands bound (Fig. 6). This is the classic test for distinguishing tertiary and quaternary kinetics, because the amplitude of the R-to-T quaternary transition is highly dependent on the fraction of subunits with ligand bound (41).

Fig. 6.

Lack of dependence of slow bimolecular rebinding to R⁻ on degree of photolysis. Fraction slow rebinding after 1 s (red symbols), 10 s (green symbols), or 100 s (blue symbols) of exposure to cw photolysis. Correlation coefficients are R = −0.032 (P = 0.94) after 1 s, R = 0.071 (P = 0.87) after 10 s, and R = 0.378 (P = 0.32) after 100 s.

These results are remarkably consistent with the prediction of the TTS model (Fig. 3) (27). When the laser is first turned on, all of the unliganded subunits are in the r conformation. With time, r converts to t within R with a highly stretched exponential time course as observed in solution, and the rebinding rate to t in R asymptotically approaches the same rate as t in T. The fractional population of 20% for the t subunits, moreover, is very close to the 30–40% predicted from fitting the kinetics in solution with the TTS model under conditions that would be expected to favor more t (27). A result that strongly supports our interpretation of these experiments is that the stretching exponent of ∼0.2 is nearly identical to the exponent of ∼0.3 observed in solution for the unliganded heme spectral changes that were interpreted as corresponding to the r → t relaxation (27, 42), but with a half-time that is ∼10⁶-fold larger due to slowing by the gel. The highly stretched exponential time course for the r → t tertiary conformational relaxation was previously explained by a theoretical model (43) that takes into account the dynamics of interconversion within the ensemble of conformational substates (21, 44).

The addition of allosteric effectors shifts the r ⇄ t equilibrium of unliganded subunits toward t, explaining the larger slow rebinding phase in R⁺ gels (Fig. 7), as expected from the decrease in oxygen affinity of R-state hemoglobin upon addition of the same allosteric effectors (14). The half-time for the r → t relaxation in R⁺ decreases compared with R⁻ as a result of stabilization of t upon addition of allosteric effectors, but the 100-fold decrease results from only a fourfold increase in the apparent t/r equilibrium constant (from ∼0.25 to ∼1.0 based on the infinite-time t populations in Fig. 5B). The much higher than first-power dependence of half-times versus equilibrium constants is very different from what is observed in the linear free-energy relations of exponential kinetics, but such relationships have not yet been investigated for systems with highly stretched exponential kinetics. The increase in the stretching exponent from 0.2 to 0.3 in the presence of allosteric effectors indicates more rapid equilibration of conformational substates (43) and could account for at least part of the large half-time decrease. An alternative explanation is that either primarily α or primarily β deoxy subunits switch from r to t upon addition of allosteric effectors, in which case the change in rate would scale more closely with the change in equilibrium constant. This explanation is suggested by very recent work using resonance Raman spectroscopy carried out by Spiro and coworkers (45).

Fig. 7.

cw laser photolysis experiments on R⁺ gels at 20 °C. (A) Normalized rebinding curves upon turning off cw laser following continuous photodissociation of R encapsulated HbCO in the presence of allosteric effectors for 100 μs (1% of hemes photolyzed) and 100 ms (13% of hemes photolyzed) at 0.2 atm CO. The black dashed curves are the fits to a sum of two slightly stretched exponentials, i.e., f(t) = Aexp[−(t/τ_f)^β] + (1 − A)exp[−(t/τ_s)^β], where A and (1 − A) are the fractions of the optical changes at 532 nm for each phase, respectively, τ_f is the time constant for the fast rebinding phase, τ_s is the time constant for the slow rebinding phase, and the stretching exponent β is 0.8. This slight stretching most probably reflects either a small α−β inequivalence or lack of sufficiently fast interconversion of conformational substates. (A, Inset) Rate distributions from maximum entropy method. (B) Fraction of slow and fast rebinding phases as a function of exposure time to cw laser. The time courses for the appearance of the fraction of slow rebinding and decrease of the fast rebinding phases are well fit with a stretched exponential, f(t) = (1 − exp[−(t/τ)^β]), with τ = 11 ± 4 ms and β = 0.27 ± 0.04, and f(∞) = 0.45 ± 0.04. (C) Time constants τ_f (average = 1.04 ± 0.08 ms) and τ_s, as a function of exposure time, and fit of τ_s with a stretched exponential function [τ_s (∞) = 22 ± 4 ms], with β = 0.3 ± 0.1, τ = 10 ± 7 ms. (D) Cartoon of interpretation of experiment for R⁺ gel: before continuous photodissociation of CO, all subunits are in the r conformation. In the steady state, a fraction of the unliganded subunits convert from r to t. For clarity, photodissociation in cartoon is 100%.

Discussion

Interpretation of Results Using TTS Model.

By measuring the kinetics of CO binding to hemoglobin encapsulated in silica gels, which enormously slows both tertiary and quaternary conformational changes, we have discovered that both R and T quaternary structures contain subunits that exhibit fast and slow binding rates. The striking result is that, although the fraction of each depends on the quaternary structure and the presence or absence of allosteric effectors (Fig. 8 B and C), the rates are almost identical (Fig. 8A).

Fig. 8.

Summary of CO binding kinetics in R and T quaternary structures under varying solution conditions at 20 °C. (A) Rebinding times, τ_f and τ_s, at 0.2 atm CO for fast and slow rebinding phases extrapolated to infinite exposure time using stretched exponential fits in Figs. 4C, 5C, and 7C. (B) Equilibrium fractional population of t and r in unliganded quaternary structures based on cw laser experiments (R⁻ and R⁺). (C) Equilibrium fractional population of t and r in liganded quaternary structures based on pulsed laser experiments (T⁻ and T⁺). Numbers labeling the x axis are pH values.

Our finding of two functional conformations for the subunits of hemoglobin in each quaternary structure is readily explained by the simplest possible extension of the allosteric model of MWC to include tertiary equilibria, and is inconsistent with all other theoretical models proposed for hemoglobin (12). In this TTS allosteric model (Fig. 3), there are only two functionally significant conformations of the subunits, called t and r, which exist in a preequilibrium in both unliganded and liganded states and in both R and T quaternary structures. The relative populations of r and t are determined by the quaternary structure, the ligation state, and allosteric effectors. In unliganded T and liganded R, the subunit conformations are almost entirely t and r, respectively, whereas in liganded T and unliganded R the r ⇄ t equilibrium is observable with relative populations that are altered by allosteric effectors (Fig. 8 B and C). As was done for the MWC model by Edelstein (46), the TTS model can be readily extended to recognize that the α- and β-chains of the hemoglobin tetramer do not have functionally identical structures.

In the MWC model, the subunit conformations are implicitly considered to be completely coupled to the quaternary structure, whereas in the TTS model the subunit conformations are only partially coupled (Fig. 3) (39). The TTS model maintains the key MWC concept that allosteric effectors regulate protein reactivity by altering conformational preequilibria, but extends their theoretical model to include tertiary (r ⇄ t) in addition to quaternary (R ⇄ T) preequilibria (27). Although the MWC model provides a qualitative explanation for allostery in a number of multisubunit proteins, quantitative analysis will most probably require models that include tertiary conformational equilibria within quaternary structures, as we have done here for hemoglobin.

Implications for Structural Origin of Low Affinity of t.

These results have important implications for solving the long-standing question in hemoglobin of the structural explanation for the difference in oxygen affinity of the two quaternary structures (45). According to Perutz, salt bridges between subunits and within the β-subunit are the quaternary constraints envisaged by MWC that are responsible for the low affinity of T (47, 48) (Fig. S1). So one possibility for the structural origin of the slow (t) rebinding rate in R is the presence of the intra–β-subunit salt bridge that contributes most to the Bohr effect (49) (Fig. S1). However, it is not present in the crystal structure of either oxy R (Fig. S1) or deoxy R (50), and there is no Bohr effect for oxygen binding to the R quaternary structure in solution (51–53). There are caveats to both of these results, because the hemoglobin in these studies was chemically modified to maintain the R quaternary structure when completely deoxygenated, and the modified hemoglobin was crystallized in the ferric form and then chemically reduced to ferrous deoxy, with the possibility that the lattice prevents the conformational change necessary to form the intra–β-subunit salt bridge. However, our measurements show no dependence of the fraction of slow rebinding on pH (Fig. 8B and Table S1), also indicating that the salt bridge involving His146β is not present and is therefore not a source of the observed slow (t) rebinding rate in R. [No pH dependence of the oxygen affinity was observed in T crystals because the salt bridges were present but did not break upon oxygenation (9, 10).] These results further suggest that the Perutz salt bridges are not the sole source of the low oxygen affinity of T, as suggested earlier (48, 54, 55).

It appears that understanding the structural basis of oxygen affinity in hemoglobin still remains a major unsolved problem (45). We know the structures of unliganded and liganded t in T, and unliganded and liganded r in R (48), but not liganded r in T and unliganded t in R discovered in this and our previous work (34). These two missing structures may provide important clues. However, determining them by X-ray crystallography will be challenging. The lack of detection of two tertiary conformations in a single quaternary structure, despite a large number of hemoglobin X-ray structures, suggests that the difference in overall tertiary conformation is sufficiently large that only one of the two conformations can be accommodated by the crystal lattice, namely r in R and t in T. A more profitable route for determining the structure of liganded r in T might be by solution NMR. Determining the structure of unliganded t in R will be much more problematic because of line broadening due to the large paramagnetic susceptibility of deoxyhemes.

Materials and Methods

Sample preparation and measurements are described in SI Text. Pulsed photolysis instrumentation is described in ref. 34. The cw photolysis instrumentation is described in SI Text and Fig. S2.