Biochemistry & Analytical Biochemistry

De-Constructing the ^TState/^RState Structure Change of Human Hemoglobin

Francis Knowles^* and Douglas Magde Department of Chemistry and Biochemistry, University of California, San Diego, USA
^*Correspondence: Francis Knowles, Department of Chemistry and Biochemistry, University of California, San Diego, USA, Email:

Received: 29-Dec-2022, Manuscript No. BABCR-23-19474; Editor assigned: 02-Jan-2023, Pre QC No. BABCR-23-19474 (PQ); Reviewed: 17-Jan-2023, QC No. BABCR-23-19474; Revised: 25-Jan-2023, Manuscript No. BABCR-23-19474 (R); Published: 01-Feb-2023, DOI: 10.35248/2161-1009.23.12.479

Introduction

ΔGo for reaction of a pair of equivalent ^Rstate α-chains with O₂, ΔG°(^RαO₂), was estimated from the known affinity of myoglobin for O₂ at 37°C. (Biochem. Z., 268, 73-81),-63.4 kJ/mol. The unknown quantity, ΔG°(^R(HbO₂)₄/BPG), was obtained by solving Equation (1), being-10.5 kJ/mol, K (HbO₂)₄/BPG)=58.4 L/mol. The value of the equilibrium constant for binding BPG to the R-state structure represents 0.0073% of the value of the binding constant of BPG to the ^Tstate structure: 800,000 L/mol. The value of K_Δ; (i) Accounts for the ability of O₂ to escape, virtually unhindered from red blood cells and (ii) Provides a biophysical basis for manifestation of high resting rates of metabolism in warm blooded species. The Perutz/ Adair equation of state, Equation (1), imposes the elements of the Perutz stereochemical model on the Adair equation. The Perutz/ Adair equation, comprised of only three unknown quantities, accurately predicts equilibrium binding curves of whole blood with both O₂ and CO.

These observations are particularly relevant insofar as they define the properties of haemoglobin in human RBCs in vivo, in the presence of the naturally occurring E-molecule, BPG. The result obtained with the Perutz/Adair equation permits unambiguous assignment of structural states, R and T, to the subunits in each intermediate species in the reaction sequence, Equation (a). Species I and II, as encountered in rbcs of whole blood, are ^Tstate. Species III and IV, as encountered in red blood cells of whole blood, are ^Rstate. Species l is in a special category insofar as it does not exist in vivo. Species I, however, is readily prepared in the laboratory [1,2].

The value of the equilibrium constant for the structural change, K_Δ=0.02602, is of particular interest. It accounts for the ability of molecules of O₂ to escape, virtually unhindered, from RBCs. This single insight, by itself, provides strong justification for the model underlying the Perutz-Adair equation. Upon release of O₂ atoms from β-chains, species III and IV, 98% of species III revert to species II. Species II is unable to bind O₂ molecules to ^Tstate β-chains, precisely defining the boundary condition of the molecular mechanism releasing O₂ from arterial blood into the systemic circulation. The value of K_Δ provides a biophysical basis for manifestation of high resting rates of metabolism in warm blooded species.

The endothermic ^Tstate → ^Rstate structure change is coupled with: (i) exothermic conversion of ^TαO₂-chains (species II, Equation (a)) to ^RαO₂-chains (species III, Equation (a)) and (ii) marked decrease in affinity of the ^Rstate for BPG. ΔG° for formation of ^THb₄/BPG is- 33.7 kJ/mol at 25°C. The ^Rstate structure forms a less stable binary complex with BPG. The Perutz/Adair equation is based on the assumption that: (i) ^Tstate protein structures, species I and II Equation (a), bind BPG with the exactly the same high affinity and (ii) ^Rstate protein conformations, species III and IV Equation (a), bind BPG with exactly the same relativity low affinity, in comparison with ^Tstate structure. Nevertheless, the diminished affinity of ^Rstate structures for BPG is large enough to be exothermic, estimated to be-10.5 kJ/ mol. These reactions, endothermic and exothermic, taken together, account for the observed value of KC, 0.02602. Equation (2) and (3) define the reactions predicted to account for the observed value of the equilibrium constant for the ^Tstate to ^Rstate structure change [3,4].

Literature Review

Determination of Unknown Quantities in Eq. (3): Calculation of the Values of ΔG° (K_ΔC) and ΔG° (^Tα*O₂) at 37°C

These values are returned by curve fitting of O₂-binding date of whole blood, under standard conditions, to the Perutz/Adair equation:

ΔG°(K_ΔC)=9.41 kJ/mol; ΔG°(^Tα*O₂)=-49.6 kJ/mol. Results are summarized in Table 1.

Table 1: Equilibrium Constants and ΔG° for the Sequence of Reactions Comprising the Perutz-Adair Equation, 37°C.

Estimation of the Value of ΔG°(^Rα*O₂) at 37°C. The model described in Equation (a) does not permit determination of ΔG° for binding of a molecule of O₂ to equivalent ^Rstate (^Rα*)-chains. Molecules of O₂ have only equivalent ^Tstate deoxy-(^Tα*) chains to form equivalent (^Tα*O₂) chains. (^Rα*O₂) chains are formed directly from ^T(α* O₂) when the ^Tstate → ^Rstate structure change relaxes proximal strain. One can estimate ΔG° for formation of ^RαO₂ in two ways: (i) assume that ΔG° (MbO₂) is similar to ΔG° (^RαO₂); (ii) assume that ΔG° (^RαO₂) for E-free hemoglobin is an upper limit [5-7]. Theorell elaborated O₂-binding data for horse heart myoglobin at 37O, with half-saturation of myoglobin occurring at a partial pressure of O₂ in the gas phase of approximately 3.5 Torr, corresponding to a concentration of O₂ of 4.60 µmol/L. This allows an assignment of 2.2 x 105 L/mol as the O₂-binding equilibrium constant of ^Rstate (^Rα*O₂) chains: ΔG°=-63.4 kJ/mol. Using equilibrium constants obtained for E-free hemoglobin at 20°C Results are summarized in Table 1.

Assignment of the value of ΔG°(THbO₂)₄/BPG) for the endothermic change, ^Tstate to ^Rstate, in protein structure

BPG, a potent E-molecule, binds avidly to ^RHb₄. In the process of forming the binary complex, the structure of ^RHb₄ changes to that of ^T(Hb₄/BPG). In contrast to the great stability of ^THb₄/ BPG, the equilibrium constant for the binary complex of BPG, yielding the ^Rstate binary complex, ^R(HbO₂)₄/BPG, is low. ΔG° for reversing the binding of BPG to ^RHb₄, ΔG° (^R(Hb)₄, BPG), is +33.7 kJ/mol at 25°C. A correction due to the increase in temperature was not applied. ΔG° for binding of BPG by ^Rstate conformations, ΔG°(^R(HbO₂)₄/BPG), can be calculated directly from Equation (3) since all other values are known, estimated, or assigned. This procedure computes a value of ΔG° for binding of BPG to an ^Rstate structure, ΔG°(^Rstate/BPG)=-10.5 kJ/mol, corresponding to an equilibrium constant for binding of BPG to R-state conformations, K(^R(HbO₂)₄/BPG)=58.9 L/mol. O₂-Equilibrium binding curves at pH 9.1 demonstrate binding of IHP to R-state conformations.

Discussion

^RHb₄, free of E-molecules, such as BPG or 0.10 M chloride ions demonstrates a high affinity for O₂, being half saturated with O₂ in 2 μM O₂/L. Addition of stoichiometric amounts of BPG to solutions of ^RHb₄ results in formation of a binary complex with markedly diminished affinity for O₂. The product is a ^Tstate binary complex. The reaction can be written as follows, where BPG is indicated by a bullet: and superscript * indicates equivalent binding by a pair of subunits.

The reaction of BPG with ^RHb₄ is exothermic: ΔG°=-33.7 kJ/ mol. The history of observations of the properties of human hemoglobin, until approximately 1967, were conducted without knowledge of the effect of BPG on the properties of hemoglobin. Analysis of the O₂ equilibrium binding curve of E-free preparations of human Hb₄ reveals a pair of equivalent cooperative dimers: (α₁β₂) and (α₂β₁). It may be incorrect to describe these cooperative dimers as being ^Rstate. An ^Rstate β-chain regulates an α-chain of diminished affinity. α-Chains in cooperative dimers of ^RHb₄, then, are not ^Rstate until an Rβ-chain binds O₂. The cooperative dimer, nevertheless, demonstrates a much higher affinity for O₂ than does T(α*●β*), requiring 35 μmol O₂/L for half saturation. Significant allosteric structure is present in ^RHb₄. Addition of BPG to ^RHb₄ results in: (i) formation of ^T(Hb₄)/BPG; (ii) increased proximal strain in Tα-chains; (iii) imposition of steric hindrance to O₂-binding by β-chain heme moieties. β-chain heme moieties in ^T(Hb₄/BPG) may be ^Rstate in reactivity and simply unable to gain access to an O₂ molecule due to distal side steric hindrance. If it was not possible to reverse the effects of binding BPG on Tβ-chain reactivity, the O₂ equilibrium binding curve would be described by a simple equation of state accounting only for species I and II of Equation (a).

Imposition of the stereochemical model on the Adair (1925) sequence of four O₂-binding reactions results in an equation of state acknowledging the existence of a ^Tstate → ^Rstate structure change. The discussion concerning binding of BPG to ^RHb₄ suggests that an exothermic input of as much as-33.7 kJ/mol would be required. It is unlikely that BPG actually separates from the globin moiety in the ^Tstate → ^Rstate structure change. Our procedure is viewed from the perspective of thermodynamics: assuming release of BPG from a ^Tstate intermediate and rebinding to form an ^Rstate intermediate. The molecule of BPG bound to ^Tstate conformation remains, in all likelihood, attached to the globin moiety throughout the ^Tstate → ^Rstate transition. The physical realty of an equilibrium constant for a ^Tstate → ^Rstate change is supported by the virtual identity of the values for K_Δ returned by equilibrium binding curves for both CO and O₂, in whole blood, as well as purified human hemoglobin for O₂ in the presence of 0.1 M NaCl: 0.0574; 0.02602; 0.03252; respectively Following the ^Tstate → ^Rstate change, step II to step III, there are only equivalent O₂-binding reactions by ^Rstate β-chains, these reactions further stabilizing the ^Rstate conformation. Binding of O₂ to Rβ-chains and release of O₂ from ^RβO₂-chains is free of changes in elements of allosteric structure. A ^Tstate structure is entirely different than an ^Rstate. ^Tstate and ^Rstate structures are, in fact, different molecules [8-14].

Since the curve fitting procedure is based on a model in which a pair of α-chains are equivalent and a pair of β-chains are equivalent, there can only be only be one ^Tstate → ^Rstate change and, therefore, only two structures: ^Rstate and ^Tstate. That single ^Tstate → ^Rstate transition occurs between species II and species III, Equation (a). Although there are two structural states, the model which underlies the Perutz/Adair equation is incompatible with the two state models in which the reactant, product, and all intermediate species are capable of being in either of the two states. These conclusions do extend to hemoglobin in whole blood from other species. These conclusions, however, do not address the validity of the two state models in other systems.

The value of K_Δ, 0.02602, establishes the ability of the binary complex of hemoglobin and DPG in red blood cell to release O₂ from arterial blood. The release of O₂ from the equivalent ^Rstate βO₂-chains is, kinetically, first order. Recapture of O₂ by species III is extinguished by the thermodynamically favoured conversion of species III to species II, which is not capable of binding O₂ to β-chains. If O₂ depleted β-chains remained as ^Rstate haemoglobin molecules, the ability of the red blood cell to release O₂ would be dramatically impaired, O₂ molecules being subject to recapture before diffusing through the red blood cell membrane, thereby escaping from the RBC. The efficiency of O₂ transport to mitochondria of the components of the systemic circulation from arterial blood is dependent upon the conversion of species III to species II. Using the Perutz/Adair equation to fit equilibrium binding date, the value of ΔG°(K_Δ) is revealed to be remarkably well fitted to the purpose of O₂ transport from arterial blood to mitochondria.

Conclusion

Variation in values of K_Δ across the spectrum of mammals, birds and lizards offers new insights into comparative respiratory physiology. A significant increase in the value of K_Δ would lower the rate at which rbcs could deliver O₂ to mitochondria. The Perutz/Adair equation of state is the first probe of respiratory function to reveal insight into the mechanism of enhanced transport of O₂ from the lungs to the respiratory tissues. The picture, however, is incomplete without consideration of the consequences of the cyclic variation in the pH of the interior of red blood cells. Doing so is the subject of another communication.

Acknowledgement

Francis Knowles would like to acknowledge the help of Professor Glen Lo at Nicholls State University in providing assistance with curve fitting procedures and providing copies of XYCALC. Francis Knowles would to thank Professor Quentin Gibson and the Department of Biochemistry at Cornell University for their hospitality and assistance in elaborating instrumentation for determination of equilibrium binding curves of hemoglobin for O₂ (1972-1977). Francis Knowles would like to thank the Department of Chemistry and Biochemistry at UCSD for continuing appointments as a Lecturer and Professors Douglas Magde and Michael Tauber for hosting the author as a Visiting Scholar.

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