Protein dynamics explain the allosteric behaviors of hemoglobin

Abstract

Bohr, Hasselbalch, and Krogh discovered homotropic and heterotropic allosteric behaviors of hemoglobin (Hb) in 1903/1904. A chronological description since then of selected principal models of the allosteric mechanism of Hb, such as the Adair scheme, the MWC two-state concerted model, the KNF induced-fit sequential model, the Perutz stereochemical model, the tertiary two-state model, and the global allostery model (an expanded MWC models), is concisely presented, followed by analysis and discussion of their limitations and deficiencies. The determination of X-ray crystallographic structures of deoxy- and ligated-Hb and the structure-based stereochemical model by Perutz are an epoch-making event in this history. However, his assignment of low-affinity deoxy- and high-affinity oxy-quaternary structures of Hb to the T- and R-states, respectively, though apparently reasonable, and as well as his hypothesis that the T-/R-quaternary structural transition regulates the oxygen-affinity, have created confusions and side-tracked studies of Hb on the structure-function relationship. The differences in static molecular structures of Hb between T(deoxy)- and R(oxy)-quaternary states reported in detail by Perutz and others are ligation-linked structural changes, but not related to the control/regulation of the oxygen-affinity. The oxygen-affinity (K(T) and K(R)) of Hb has been shown to be regulated by the heterotropic effector-linked tertiary structural changes without involving the T/R-quaternary changes. However, a recent high-resolution crystallographic analysis of Hb with different oxygen-affinities shows that static molecular structures of Hb determined by crystallography can neither identify the nature of the T(low-affinity) functional state nor decipher the mechanism by which Hb stores free energy in the T(low-affinity) functional state. Molecular dynamics simulations show that fluctuations of helices of oxy-Hb are increased upon de-oxygenation and/or binding 2,3-biphosphoglycerate. These are known to lower the oxygen-affinity of Hb. It is proposed that the coordination mode of the heme Fe with proximal and distal His is modulated by these helical fluctuations, resulting in the modulation of the oxygen-affinity of Hb. Therefore, it is proposed that the oxygen-affinity of Hb is regulated by pentanary (the 5th-order time-dependent or dynamic) tertiary structural changes rather than the T-/R-quaternary structural transitions in Hb. Homotropic and heterotropic allosteric effects of Hb are oxygen- and effector-linked, conformational entropy-driven entropy-enthalpy compensation phenomena and not much to do with static structural changes. The dynamic allostery model, which integrates these observations, provides the structural basis for the global allostery model (an expanded MWC model).

Fig. 1

Original oxygen-binding curves of Hb as a function of P_CO2 (mmHg) by Bohr, Hasselbalch, and Krogh (1904). The sigmoidicity (or cooperativity) and P_CO2-dependence (or the Bohr effect) represent the first quantitative observations of homotropic and heterotropic allostery of Hb, respectively.

Fig. 2

Models of the oxygen-binding equilibria of Hb. (A) Adair scheme in 1925, (B) MWC model in 1965, and (C) Perutz model in 1970. It should be noted that the full set of ligation states [Hb(O₂)_{n (n = 0→4)}] are assigned to either the T(low-affinity)- and R(high-affnity)-functional states (the blue and red shaded regions, respectively) in the MWC model (B). On the other hands, (III) Hb(O₂)₀ and (II) Hb(O₂)₄, the two end-products of the oxygen-binding equilibrium, which are equivalent to “E” and “ES” of an enzyme system, are assigned to T(deoxy)- and R (oxy)-quaternary states (the blue and red shaded circles), respectively, in the Perutz model (C).

Fig. 3

Global allostery model of allostery of Hb, describing the relationship among the oxygen-affinity, homotropic and heterotropic allostery. The oxygen-affinities (K_T and K_R) of T(low-affinity)- and R(high-affinity)-functional states are regulated by effector-linked tertiary structural changes, but not by the T/R-quaternary structural changes. The K_T and K_R values reach the lowest value of 0.005 torr^-1 under the maximal allosteric potency (the low-affinity-extreme state), which is considered as the (lowest-afinity)-functional-state of Hb (Condition G) in the global allostery model, an expanded MWC model. The original T(low-affinity)-functional state with K_T = 0.3 torr^-1(Condition A) is that in the absence of the heterotropic effect (stripped Hb). Under each of these well-defined conditions, the oxygen-binding equilibrium strictly follows the MWC model, determining K_T, K_R and L₀ under such a defined condition. Thus, K_T and K_R values are floating as a function of allosteric potencies ([effector]* ^TK_effector and [effector]* ^RK_effector) according to Equations 3 and 4, respectively.

Fig. 4

Allosteric plot describing the ranges of K_T, K_R, L₀, and L₄ as a function of heterotropic allosteric effects (at pH 6.6 to 9.0) in the global allostery model. The lowest-affinity-state (the yellow circle) has K_T ≈K_R ≈ 0.005 torr^-1 and L₀ ≈ L₄ ≈ 1, whereas the highest-affinity state (the red circle) has K_T ≈ K_R ≈ 10 torr^-1 and L₀ ≈ L₄ ≈1.

Fig. 5

X-ray crystallographic comparison of the α₁-heme environments of (A) human (III) T(deoxy)-Hb and (B) horse (II) R(CO)-Hb in absence (yellow-shaded) and presence (grey-shaded) of L35, (IV) and (V), respectively. (C) The oxygen-affinities of (III) T(deoxy)-Hb and (II) R(oxy)-Hb are reduced as much as ~60- and 2,000-folds in the presence of L35, (IV) and (V), respectively. However, there is no detectable difference of the tertiary heme environments and the quaternary structures in the presence and absence of L35.

Fig. 6

Effector-linked E- and F-helical fluctuations of (III) T(deoxy)-Hb, (II) R(oxy)-Hb, (IV) T(deoxy)-Hb-BPG, and (V) R(oxy)-Hb-BPG, determined by MD simulations. (II) R(oxy)-Hb is dynamically relatively rigid, whereas the amplitude of helical fluctuations increases upon de-oxygenation and/or binding BPG, which reduce the oxygen-affinity.

Fig. 7

Possible modes of the heme Fe coordination of Hb during cycles of helical fluctuations. During the cycles of helical fluctuations these different modes are time-shared, modulating the oxygen-affinity of the heme Fe in a wide range of >10³-folds from 10 torr^-1 (P₅₀ = 0.1 torr) to 0.005 torr^-1 (P₅₀ = 200 torr) in both deoxy- and oxy-Hb.

Fig. 8

Elevator-expression of the dynamic allostery model, indicating the correlation between the effector-linked changes in the oxygen affinity and the effector-linked dynamic tertiary structural fluctuations. (A) The effector-linked tertiary structural changes (varying amplitudes of the helical fluctuations) not only regulate the floor level [the oxygen-affinities (K_T and K_R)] of the allosteric equilibrium system, but also control the cabin height (the cooperativity). The ligation process (the T- to R-quaternary structural transition) is responsible for the switch of the allosteric equilibrium from K_T-dominant to K_R-dominant states, resulted in an apparent increase in the oxygen-affinity (K_T →K_R) of the allosteric system. (B) The effector-linked helical fluctuations modulate the coordination structure of the heme Fe, resulting in the continuous modulations of the oxygen-affinity of the heme Fe.

Fig. 9

Dynamic allostery model: Integrated relationship of structure, function, homotropic and heterotropic allostery, dynamics, and energetics of Hb. The difference in the definition of “T” and “R” between the MWC and Perutz models is explicitly indicated.