The Monod-Wyman-Changeux allosteric model accounts for the quaternary transition dynamics in wild type and a recombinant mutant human hemoglobin

Abstract

The acknowledged success of the Monod-Wyman-Changeux (MWC) allosteric model stems from its efficacy in accounting for the functional behavior of many complex proteins starting with hemoglobin (the paradigmatic case) and extending to channels and receptors. The kinetic aspects of the allosteric model, however, have been often neglected, with the exception of hemoglobin and a few other proteins where conformational relaxations can be triggered by a short and intense laser pulse, and monitored by time-resolved optical spectroscopy. Only recently the application of time-resolved wide-angle X-ray scattering (TR-WAXS), a direct structurally sensitive technique, unveiled the time scale of hemoglobin quaternary structural transition. In order to test the generality of the MWC kinetic model, we carried out a TR-WAXS investigation in parallel on adult human hemoglobin and on a recombinant protein (HbYQ) carrying two mutations at the active site [Leu(B10)Tyr and His(E7)Gln]. HbYQ seemed an ideal test because, although exhibiting allosteric properties, its kinetic and structural properties are different from adult human hemoglobin. The structural dynamics of HbYQ unveiled by TR-WAXS can be quantitatively accounted for by the MWC kinetic model. Interestingly, the main structural change associated with the R–T allosteric transition (i.e., the relative rotation and translation of the dimers) is approximately 10-fold slower in HbYQ, and the drop in the allosteric transition rate with ligand saturation is steeper. Our results extend the general validity of the MWC kinetic model and reveal peculiar thermodynamic properties of HbYQ. A possible structural interpretation of the characteristic kinetic behavior of HbYQ is also discussed.

Ever since the publication of the Monod-Wyman-Changeux paper on allostery (1), hemoglobin (Hb) has been considered the prototype of an allosteric protein; the molecular basis of positive cooperativity in O₂ binding involving a ligand-linked shift between two different quaternary states. The dynamics of ligand rebinding and of the tertiary and quaternary allosteric changes of tetrameric human Hb have been investigated, by-and-large, using transient spectroscopy in the picosecond to millisecond time range, following laser-induced photolysis of the ligand-heme iron bond. Starting with the carbon monoxide adduct HbCO in the allosteric quaternary state called R₄, complete photolysis yields the unliganded R₀ state; the destiny of this photoproduct is a complex time-dependent process involving competing events such as ligand rebinding and (tertiary and quaternary) conformational decays. Changes in the optical and resonance Raman spectra of the different states have provided, over the last four decades, a quantitative estimate of the rates of the competing events (2–5). For a review on time-resolved optical absorption (TR-OA) data describing conformational decays as well as rebinding in the dark of a ligand escaped into the solvent (bimolecular) or trapped within the protein matrix (geminate), see Eaton et al. (6).

It is generally accepted that tertiary structural changes within the α and β subunits occur in the nanosecond time regime and follow a complex time course. The much larger structural changes of the quaternary allosteric transition (involving shifts in the inter-subunit contacts and relative motions of the two symmetric dimers α₁β₁/α₂β₂) occur in the microsecond time range; the single time constant estimated from optical changes of the deoxy photoproduct is about 20 μs for human HbA at neutral pH and 20 °C (2, 3, 6, 7). The dynamics of the structural changes followed by ultraviolet resonance Raman (UVRR) spectroscopy after laser photolysis showed, however, the quaternary conformational transition involving contacts at the α₁β₂ and α₂β₁ interfaces (8, 9) to be more complex. Since the UVRR spectra of Trp37β and Tyr42α are distinct, it was possible to show that upon population of the T state (i) Trp37β forms a H-bond with Asp94α at the “hinge” region of the α₁β₂ interface, and (ii) Tyr42α forms an H-bond with Asp99β at the switch region (5, 10), the former T state contact being established in 2 μs while the latter forms in 20 μs. A similar 2 μs phase has also been detected by time-resolved magnetic circular dichroism associated with Trp (11).

All spectroscopic probes, valuable as they are, provide limited information on the global structure of the protein and therefore on the dynamic profile of the major allosteric transition. However recently Cammarata et al. (12, 13) published the first experiments using time-resolved wide-angle X-ray scattering (TR-WAXS) on Hb and unveiled the protein motions related to the tertiary and quaternary conformational changes. Following laser photodissociation of CO, the early (147 ns) post-photolysis signal evolved toward the well defined deoxyHb vs. HbCO scattering difference pattern in about 2 μs. This estimate implies that dimer rotation—the largest structural change in the R–T allosteric transition—is much faster than 20 μs, the time constant detected by optical spectroscopy (2, 3). Quite recently Fischer et al. (14) published a computational analysis of Hb dynamics which revealed distinct tertiary and quaternary conformational events; in particular, they reported two sequential quaternary changes (called Q₁ and Q₂), which they assumed to be consistent with the time constants at 2 μs (for Q₂) and 20 μs (for Q₁) reported by Balakrishnan et al. (10).

We have repeated the TR-WAXS experiment on wild-type human HbA employing a different laser pulse, and in parallel analyzed a recombinant mutant called HbYQ (15, 16) with the α and β chains containing two mutations in the distal heme pocket—i.e., His(E7)Gln and Leu(B10)Tyr—which was characterized (15–17) by crystallography, transient spectroscopy, and ligand binding experiments. The main motivation to undertake the TR-WAXS experiment on HbYQ was to test the general validity of this approach to follow the time evolution of the global structure of the protein in solution. HbYQ seemed a promising case because this variant undergoes a ligand-linked allosteric transition and binds O₂ cooperatively, albeit with much reduced affinity and a smaller Hill’s coefficient (n = 1.8 vs. 2.9 for HbA). The structure of the deoxy T₀-state, identical to that of HbA, when exposed to CO yields an intermediate with the ligand bound only at the β chains. Assuming L₀ (the population ratio of the T₀ to R₀ states) to be the same for HbA and HbYQ, O₂ binding was fitted to the MWC model with a switch-over point ≥3; this parameter, which indicates the average number of bound ligands at which the two quaternary states are equally populated, is reported to be about 2 for HbA (2, 9). Relative to HbA, in HbYQ the CO bimolecular rate constant is much smaller and no significant geminate rebinding is detected because of steric hindrance by TyrB10 (as seen for a similar mutant of sperm whale myoglobin) (18, 19). This is of considerable advantage because (i) essentially no CO rebinding will take place in the nanosecond time scale, and (ii) a large fraction of tetramers will undergo the R–T transition even with a 3-ns-long photolysis pulse, at variance with HbA. The results reported below are very satisfactory insofar as the TR-WAXS data on HbA and HbYQ can be fitted within the canonical kinetic allosteric model in spite of the significant differences; thus the new data support the general validity of the model and of the experimental approach alike. Unexpectedly, however, the time constant of the R₀ → T₀ quaternary transition for HbYQ is 12.4 μs, and therefore clearly slower than the value of 1–2 μs previously reported for HbA by Cammarata et al. (12, 13). Based on the crystallographic data of Miele et al. (15, 17), we propose a possible structural mechanism for the slow down of the quaternary allosteric transition observed in HbYQ.

Results

Time-Resolved Scattering.

In order to track and compare the structural dynamics of HbA and HbYQ, we have collected TR-WAXS difference patterns, ΔS(q), of both proteins at several time delays after photolysis (Fig. 1). The overall shape of the HbYQ difference patterns is analogous to that of HbA, indicating that the structural intermediates involved in the R–T transition of the two variants are similar. Nevertheless, differences in the time evolution of the patterns are evident. In the nanosecond time scale, TR-WAXS patterns (due to tertiary structural changes) are similar both in shape and amplitude. Note that the 3.16 ns and 316 ns patterns have different shapes, both in the case of HbA and HbYQ, reflecting the complex nature of the tertiary transition, as documented for myoglobin (18, 20). The 100 μs TR-WAXS patterns (due to quaternary structural changes) (12, 13) are very similar in shape, but the amplitude of the HbA signal is significantly smaller; at longer time delays (when CO bimolecular rebinding dominates), the HbA signal decays much more rapidly, becoming negligible at 100 ms. The clear cut amplitude difference of the 100 μs TR-WAXS patterns reveals a larger fraction of tetramers undergoing the R–T transition in HbYQ, as expected since geminate rebinding is essentially absent (17). Moreover, the observed signal evolution in the microsecond time scale agrees with a much smaller CO bimolecular rebinding rate to T state HbYQ (15), consistently with the 3D structure (SI Discussion and Figs. S1–S3).

Fig. 1.

TR-WAXS difference patterns of HbA (A) and HbYQ (B) measured at different time delays from a 3-ns-long photolysis pulse. Continuous lines are fitting curves obtained from a global analysis of the experimental patterns at time delays longer than 250 ns as described in the text. A fast local structural change is detected at 3.16 ns in both HbA and HbYQ. At 100 μs the typical pattern assigned to the αβ dimers relative rotation and translation is observed (12, 13); its amplitude is larger for HbYQ than for HbA due to the large difference in geminate rebinding. At 100 ms, while HbA has already recombined with CO, HbYQ is still mostly in the deoxy state due to the smaller bimolecular rebinding rate.

As reported by Cammarata et al. (13), the peak at about 0.19 Å^-1 in the TR-WAXS difference patterns can be used to monitor the kinetics of the overall structural changes of the globin after photolysis. Fig. 2A reports the time evolution of the amplitude of this peak for both proteins: the signal initially increases due to both tertiary and quaternary structural changes, then reaches a maximum mostly determined by the number of tetramers undergoing the R–T transition, and finally decreases to zero due to bimolecular rebinding of CO to deoxyHb, leading back to fully saturated R state. The number of Hb molecules undergoing the R–T transition (as judged by the approximate maximum of the 0.19 Å^-1 peak) is greater in HbYQ than in HbA. In view of the various physical processes (geminate and bimolecular rebinding, tertiary and quaternary relaxations) underlying the observed signal time evolution, it is not easy to estimate quantitatively the R–T transition rates for the two variants from the data reported in Fig. 2A. The different population of R state Hb tetramers partially bound to CO due to geminate rebinding, which is relevant for HbA but negligible for HbYQ, is crucial because partially bound R state molecules relax to the corresponding T states more slowly than R₀ (2). A more appropriate comparison of raw data time evolution demands a similar initial population of R_i species; this was obtained in a previous experiment on HbA using a 230-ns photolysis pulse (13), long enough to rephotolyze geminate states, thus pumping the system towards R₀ (2, 3, 6). Once the initial distribution of the R_i populations is quite similar, the comparison highlights that the R–T transition of HbYQ is significantly slower than that of HbA (Fig. 2B).

Fig. 2.

(A) Time dependence of the TR-WAXS signal at ∼0.19 Å^-1. For HbA (open squares) the maximum value of the signal is smaller than for HbYQ (closed circles); both sets of data have been obtained using a 3-ns-long photolysis pulse. (B) HbYQ signal obtained with a 3-ns-long photolysis pulse (closed circles) compared with the HbA signal obtained with a 230-ns photolysis pulse (open triangles, data from ref. 13); both signals have been normalized to their maximum. Error bars have been estimated from the noise of the difference patterns.

MWC Allosteric Kinetic Model.

In order to estimate the kinetic parameters characterizing the dynamics of the two variants of Hb, the TR-WAXS data were analyzed with a kinetic model describing the various physical processes occurring after photolysis. However, developing a kinetic model including both faster (geminate rebinding and tertiary relaxations) and slower (quaternary relaxations and bimolecular rebinding) processes would require the introduction of too many different species (21, 22), and the number of kinetic parameters would exceed the accuracy of present day TR-WAXS data. A great simplification is obtained if only data at time delays longer than about 250 ns are considered given that both geminate rebinding and tertiary relaxations are expected to be over (10, 23). This enables the use of the canonical MWC kinetic model previously employed to analyze the dynamics of the allosteric transition of HbA as followed by TR-OA (2, 3), and recently applied to TR-WAXS data (12, 13) (Materials and Methods, Fig. S4). The entire data set has been reconstructed as a linear combination of a ΔS_R-like(q) basis pattern corresponding to unrelaxed R state Hb, and a ΔS_T-like(q) pattern corresponding to T state Hb,

[1]

where R-like(t) and T-like(t) are weighted sums of the R_i(t) and T_i(t) populations, respectively. A fit of the experimental data allows a reliable determination of basis patterns and kinetic parameters such as the R₀–T₀ transition rate constant (k₀) and the fraction of deoxy-hemes at 250 ns from photolysis (N₀). Fig. 3 A and B reports the basis patterns obtained for HbA and HbYQ, respectively; the corresponding R-like(t) and T-like(t) populations are shown in Fig. 3 C and D and best fit values of kinetic parameters are given in Table 1. It may be seen that in spite of the mutations and their effect on the geminate rebinding yield, the basis patterns obtained for HbA and HbYQ are very similar, supporting the conclusion that the structural changes involved in the R–T transition are essentially the same for the two Hb variants, in agreement with crystallographic data on deoxygenated T state HbYQ (15, 17). The time course of the intermediate species populations has a similar overall shape (Fig. 3 C and D). At 250 ns the fraction of Hb tetramers in the R state is quite different in the two variants (81% vs. 52%) because of the large difference in geminate rebinding extent. Thereafter the R-like population decreases due to quaternary transition and bimolecular rebinding. In turn, the T-like population initially increases due to the R_i–T_i quaternary transition and finally disappears due to bimolecular rebinding of CO.

Fig. 3.

Results of the global analysis of TR-WAXS patterns according to the MWC allosteric kinetic model for HbA and HbYQ based on data obtained with a 3-ns laser pulse for both proteins. Tops: normalized basis patterns obtained for HbA (A) and HbYQ (B). Bottoms: relative R-like and T-like populations for HbA (C) and HbYQ (D) as obtained from the decomposition of experimental patterns in terms of a linear combination of the basis patterns reported in A and B (symbols), and from the kinetic model (lines).

Table 1.

Kinetic parameters obtained by the fitting procedure described in the text

Sample	N0	τ0 = 1/k0 (μs)	s	L0 × 10-3	c × 103	* (μM-1 s-1)	* (mM-1 s-1)
HbYQ	0.81	12.4	23	20	21	1	0.75
	(±0.01)	(±0.6)	(±1)	(±8)	(±8)
HbA	0.518	0.96	8.6	17	1.4	5	32.5
	(±0.004)	(±0.05)	(±0.4)	(±2)	(±0.1)

^*Parameters and have been fixed to values derived from partial photolysis and stopped-flow experiments, respectively (17).

In the case of HbA the kinetic parameters resulting from the new data obtained using a 3-ns laser pulse are in good agreement with those previously obtained (13) using a 230-ns laser pulse at three different protein concentrations (0.25, 0.5, and 1 mM). As already outlined, in the latter experiments the longer laser pulse rephotolyzed the partially bound R states populated via geminate rebinding, increasing the fraction of deoxy-hemes at 250 ns from photolysis (72–80% vs. about 50%). The R₀–T₀ transition time (i.e., τ₀ = 1/k₀) is slightly shorter (1.0 μs vs. 1.2–1.9 μs) and the parameter s (2, 3), which defines the increase of the quaternary transition time as the ligands bound to R increase from 1 to 4 (e.g., τ₁ = τ₀ × s in the case of the R₁–T₁ transition), is smaller than that previously reported (9 vs. 14–26). Note that, in view of the much higher fraction of tetramers that undergo the R₁–T₁ transition in the present experiment, the new s value is better determined than the previous one. The value of L₀ = 1.7 × 10⁴ obtained from the present experiment is similar to that reported by Cammarata et al. (13), although smaller than that generally accepted for HbA (see Structural Interpretation for further comments). Finally, the value 1.4 × 10^-3 obtained for the affinity ratio c is within the range of values previously obtained (i.e., 0.8–6.1 × 10^-3), and close to that obtained from the equilibrium CO binding data of Perrella et al. (24, 25). In a nutshell, present analysis confirms that in HbA the largest structural rearrangement associated to the R–T transition (i.e., the relative αβ dimers rotation and translation) is faster than what has been obtained by TR-OA data (2, 3, 23, 26), though consistent with the faster step seen by UVRR and assigned to the relaxation of Trp37β (5, 10).

In the case of HbYQ, the kinetic parameters (Table 1) show significant differences with respect to HbA. In agreement with the lack of geminate rebinding, the N₀ value is higher than that obtained for HbA using a 3-ns laser pulse and falls within the range obtained with the latter protein using a 230-ns photolysis pulse. The R₀–T₀ transition time, however, is significantly longer than that of HbA (12.4 μs vs. 1.0 μs), and the s value is higher. Although no equilibrium CO binding data is available for HbYQ, the c value of 0.021 is not inconsistent with that calculated from the O₂ binding data on the same mutant (15) assuming L₀ = 2 × 10⁴.

Discussion

We have documented above that in the double mutant HbYQ, the R₀–T₀ transition, which involves the relative rotation and translation of the two αβ dimers, is about an order of magnitude slower than in HbA, while the overall structural states detected by TR-WAXS are fairly similar. We conclude that the two mutations at the active site [His(E7)Gln and Leu(B10)Tyr] not only abolish CO geminate yield, reduce the rate of bimolecular rebinding, and cause αβ chain heterogeneity, but also increase the activation barrier for the large conformational transition basic to the Hb allosteric behavior. This feature would not have been discovered without TR-WAXS that, being directly sensitive to the overall structure of the protein, is the most suitable technique to follow the dynamics of the overall conformational changes of a protein in solution.

Thermodynamic Properties of the R–T Transition State.

Relevant information on the activation free energy for the R_i–T_i dimers rotation and translation () can be obtained following Eaton and coworkers (23) who applied the linear free energy relationship between the activation energy of the R_i–T_i transition and the equilibrium free energy difference between R_i and T_i states:

[2]

The parameter α, with values between 0 and 1, may be interpreted as a measure of the thermodynamic properties of the transition state, that for α = 0 would be R-like and conversely for α = 1 would be T-like. The allosteric kinetic model used to fit our TR-WAXS data implicitly assumes the validity of Eq. 2 with α = - log(s)/ log(c); the values reported in Table 1 yield α = 0.33 and 0.81 for HbA and HbYQ, respectively. In the case of HbA, the difference between our estimate and the value of α = 0.17 determined by TR-OA data (23) may be traced to the proposed stepwise character of the R–T allosteric transition (10, 14, 26). Following this idea, Cammarata et al. (13) proposed that TR-WAXS essentially monitors a first step of the R–T transition of HbA (namely the αβ dimers rotation and translation), while TR-OA monitors a second slower step associated with a more localized reorganization around the active site; accordingly, the transition states explored by TR-WAXS and TR-OA spectroscopy are not the same (Fig. S5). This interpretation is consistent with recent conjugate peak refinement calculations (14) presenting a stepwise allosteric transition that, seen along the R to T pathway, consists of a larger quaternary transition (Q₂ in their terminology) followed by a smaller quaternary step (Q₁) coupled to a residual tertiary change. In light of the above scenario, the value α = 0.33 obtained for HbA by TR-WAXS implies that the transition state associated to the αβ dimers rotation has thermodynamic properties closer to the R state than to the T state; while in the case of HbYQ, the transition state has thermodynamic properties considerably more similar to those of the T state, given that α = 0.81. It is not easy to propose a structural interpretation for this observation since it may involve differences in the shape of the free energy profile along the reaction coordinate, as suggested by Edelstein and Changeux (27). Moreover, in view of the complexity of the R–T transition, we cannot exclude that the higher value of α observed for HbYQ simply reflects the merging of the two quaternary steps in the mutant.

Structural Interpretation.

Miele et al. (15, 17) demonstrated that HbYQ in solution undergoes a ligand-linked structural change recalling that of HbA (8, 9, 28). The 3D structure of deoxy T state HbYQ is identical to that of T state HbA to high resolution, apart for the two mutations introduced in the distal heme pocket. To fit the O₂ binding data, Miele et al. (15) boldly assumed that L₀ = 1.4 × 10⁶ would be the same for both proteins. Likewise the values of L₀ obtained from the fit of the TR-WAXS data (Table 1), though much smaller (L₀ = 1.7 or 2.0 × 10⁴), are pretty much the same for the two variants; therefore it is unlikely that the slowdown of the R₀–T₀ transition rate observed in HbYQ could be accounted for by a significant stabilization of the R₀ state. Note that, given the stepwise character of the Hb quaternary transition, the overall L₀ value estimated by equilibrium O₂ binding data may not be directly comparable to the value obtained by TR-WAXS, which is sensitive to the fastest and structurally most prominent kinetic step.

Can we identify in HbYQ some perturbation of the α₁β₂ interface correlated to the active site motions and possibly affecting the quaternary transition barrier? The high-resolution crystal structures of deoxy and CO-bound HbA (29) were compared with data available for deoxy T state HbYQ and those of the same crystals exposed to CO, which was found to bind only to the β chains (15–17, 30). We focus in this discussion on two crucial residues—i.e., Trp37(C3)β and His97(FG4)β—both located at the α₁β₂ interface contributed by residues of the C helix and FG corner of the α and β chains (Fig. 4). Spectroscopic and crystallographic studies have shown that the αβ dimers rotation is associated with a rearrangement around Trp37(C3)β, located in the so-called “hinge” region. In discussing their conjugate peak refinement calculations, Fischer et al. (14) pointed out that the transition of His97(FG4)β gliding over Thr41(C6)α at the switch interface occurred in the main Q₂ phase of the allosteric conformational change. How do the distal side mutations introduced in HbYQ affect the α₁β₂ interface, where the quaternary transition is associated to the largest changes?

Fig. 4.

Close-up view of T state HbYQ α chain (A) and β chain (B) in the proximity of the heme; notice that CO is bound to the β chains only. The contacts that could allow distal tertiary changes to be transmitted from the heme pocket to the hinge and the switch regions of the α₁β₂ interface are indicated by orange arrows.

The prominent feature upon CO binding to the β chains of T state HbYQ is the swinging of Tyr28(B10)β, resulting in a contact with Phe42(CD1)β that is displaced from the position occupied in HbA (Fig. 4B). This pressure can be transmitted via Phe41(C7)β to both the hinge residue Trp37(C3)β and the switch residue His97(FG4)β. In the α chains, Pro44(CD2)α, Thr41(C6)α and Thr38(C3)α could also be affected by the motion of Tyr29(B10)α via Phe43(CD1)α and Tyr42(C7)α, similarly to that illustrated above for the β subunits (Fig. 4A). This chain of contacts would allow distal tertiary changes to be transmitted from the heme-binding pocket to the hinge and the switch contacts of the α₁β₂ interface (Fig. S6). We may therefore hypothesize that in the CO-bound R state of HbYQ, the distal Tyr(B10) push-up, and the subsequent strain transmitted to several other side chains (Fig. 4 A and B) may interfere with the sliding motion of His97(FG4)β over Thr41(C6)α in the α₁β₂ interface, increasing the energy barrier and slowing down the R₀–T₀ transition.

Concluding Remarks

The MWC allosteric kinetic model, previously employed to fit the TR-WAXS data on HbA after photolysis with a 230-ns-long laser pulse (12, 13), describes the time evolution of WAXS signals also when a shorter (3-ns-long) laser pulse is used to photolyze the CO adducts of either HbA or of the functionally relevant HbYQ double mutant. Although the model is oversimplified in that it does not explicitly take into account the recently proposed tertiary contributions to the kinetics of the R–T allosteric transition (6), it is able to reproduce the observed kinetics with satisfactory fidelity.

The new set of TR-WAXS experiments on HbA and HbYQ provide a test for the validity of the canonical MWC kinetic model. Indeed, the structural and functional properties of this double mutant of human Hb, with substitutions Leu(B10) → Tyr and His(E7) → Gln on both the α and β chains, are sufficiently consistent with a cooperative allosteric tetramer to attempt a quantitative comparison with HbA, yet they are different enough to make it a valid test of generality. The unexpected difference between the two variants is the rate of the R₀ → T₀ quaternary transition that in HbYQ is slower by a factor of about 10 relative to that previously estimated for HbA (13) and confirmed with the new data reported here. From a comparative analysis of the available 3D structures of HbA and HbYQ we tentatively propose a structural interpretation for a mechanism whereby ligand binding to the mutated site perturbs the critical α₁β₂ interface and possibly accounts for an increase in the transition state barrier; this, however, should be taken as a working hypothesis.

In order to reliably test more sophisticated models including two different transition states along the kinetic pathway connecting the R and T states, a combined approach using TR-WAXS, UVRR, and TR-OA on the same sample may be needed. A global fit of data obtained from different techniques could yield well-determined kinetic parameters and constitute a more advanced test for the MWC kinetic model.

Materials and Methods

Hb Purification.

HbA was purified from freshly collected human blood with standard techniques (31), while the mutant HbYQ was expressed in E. coli and purified as previously reported (15).

Data Acquisition Protocol.

TR-WAXS patterns were acquired at beamline ID9B of the European Synchrotron Radiation Facility (ESRF) while the machine was running in four-bunch mode. HbCO samples were photolyzed with circularly polarized laser pulses at 532 nm incident on the bottom of the capillary. Delayed quasi-monochromatic X-ray pulses (100 ps, full width at half maximum) penetrated the capillary 0.2 mm above its bottom edge yielding an orthogonal geometry between superimposed X-ray and photolysis pulses. The photolysis energy density at the capillary surface was approximately 2 mJ/mm². Taking into account the bimolecular rebinding rates, X-ray scattering patterns were acquired between 3 ns and 0.1 s (six time delays per decade) for HbA, and between 3 ns and 0.32 s (two time delays per decade) for HbYQ. To dilute any X-ray radiation damage over a large sample volume, the capillary was translated back and forth over a 25-mm range, ensuring that each laser pulse excited adjacent but spatially separated sample volumes. Scattered X-rays were recorded in the forward direction by a sensitive CCD FReLoN camera. Each image was azimuthally averaged and converted into a one-dimensional q-curve using a wavelength of 0.6793 Å corresponding to the peak of the X-ray spectrum. After normalization (in the 2–2.2 Å^-1 q-region), a reference scattering pattern (“laser off” image), which probed the unexcited sample, was subtracted from the scattering pattern at a given time delay (“laser on” image). Difference patterns at the same time delay were averaged. Structural changes occurring at different time delays leave their “fingerprints” in the “laser on—laser off” differences.

MWC Allosteric Kinetic Model.

The kinetic model used to analyze the TR-WAXS difference patterns is similar to that originally introduced by Sawicki and Gibson (2). It assumes Hb to populate two quaternary conformations, R and T, and five ligation states (R_i and T_i, where i = 0–4). A single bimolecular ligand-rebinding rate constant (apart from statistical factors) is introduced in the model for each quaternary state (the microscopic bimolecular association rates being indicated as and , respectively). It is well established (32) that, in the case of CO binding, cooperativity is fully expressed in the association rate constants; since the dissociation rate constants ( and ) are not only independent of state, but are also extremely small, they have been neglected in the model. The R_i–T_i transition rates are assumed to be proportional to the R₀–T₀ one and to scale down with the number of ligands bound through the parameter s (2, 23). The reverse T–R transition rates are linked to the forward R–T rates through thermodynamic equilibrium relations that make use of the allosteric constant L₀ = [T₀]/[R₀] and the affinity ratio c = ^TK/^RK, where ^TK and ^RK are the equilibrium association constants to the T and R states, respectively.

Further details on sample preparation and handling, data refinement, and best fit of the data in terms of the MWC kinetic model are given in SI Materials and Methods.