Experimental basis for a new allosteric model for multisubunit proteins

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.

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.

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.

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.

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.

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%.

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.