Biochemistry & Analytical Biochemistry

Allosteric Structure of Effector-free Human Hemoglobin

Francis Knowles^* 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-23-19477; Editor assigned: 02-Jan-2023, Pre QC No. BABCR-23-19477 (PQ); Reviewed: 17-Jan-2023, QC No. BABCR-23-19477; Revised: 25-Jan-2023, Manuscript No. BABCR-23-19477 (R); Published: 01-Feb-2023, DOI: 10.35248/2161-1009.23.12.471

INTRODUCTION

O₂-Binding constants are not expected to be identical for each of the dimeric cooperative subunits: (¹α,²β) and (²α,¹β). The first cooperative subunit, (^T,1α, ^R,2β), binds O₂ while bound to an O₂- free cooperative dimer, (^T,2α,^R,1β). The second cooperative dimer, (^T,2α, ^R,1β), binds O₂ while bound to R(¹αO₂,²βO₂). The best fitting values obtained in fitting O₂-binding data in an E-free supporting electrolyte to the equation of state, in units of L/μmol are: K₁=0.2913; K₂=1.112; K₃=0.4912; K₄=0.3185. A plot of predicted values of F versus observed values of F is linear: F_PRE=0.9995 F_OBS+0.0007 with a correlation coefficient of 0.9995. In the instance of each cooperative dimer, K_α exceeds K_β. An equilibrium constant describing structural changes such as K_Δ=[^Rstate]/[^Tstate] does not appear in E-free supporting electrolytes [1].

O₂-Binding constants are not expected to be identical for each of the dimeric cooperative subunits: (¹α,²β) and (²α,¹β). The first cooperative subunit, (^T,1α, ^R,2β), binds O₂ while bound to an O₂- free cooperative dimer, (^T,2α,^R,1β). The second cooperative dimer, (^T,2α, ^R,1β), binds O₂ while bound to R(¹αO₂,²βO₂). The best fitting values obtained in fitting O₂-binding data in an E-free supporting electrolyte to the equation of state, in units of L/μmol are: K₁=0.2913; K₂=1.112; K₃=0.4912; K₄=0.3185. A plot of predicted values of F versus observed values of F is linear: F_PRE=0.9995 F_OBS+0.0007 with a correlation coefficient of 0.9995. In the instance of each cooperative dimer, K_α exceeds K_β. An equilibrium constant describing structural changes such as K_Δ=[^Rstate]/[^Tstate] does not appear in E-free supporting electrolytes [2].

Addition of 0.1 M NaCl to the supporting electrolyte results in an approximately 4-fold increase in the concentration of O₂ required for half saturation of hemoglobin: 1.9 μmol/L in 0.05 M Bis-Tris, pH 7, 20°C and 8.1 μmol/L in the presence of 0.10 M NaCl. O₂- Equilibrium binding data obtained in the presence of 0.10 M NaCl cannot be fitted by the equation of state described above for the E-free solution. O₂-Equilibrium binding data obtained in the presence of 0.100 M NaCl can, however, be fitted by the Perutz- Adair equation: K_α=5.3 × 104 L/mol; K_c=0.0325; K_β=1.8 × 106 L/ mol [3,4].

Supplementing 0.050 M Bis-Tris, pH 7.0 with HCl with 0.100 M NaCl results in a supporting electrolyte that induces a T-state of relatively high affinity in Hb₄ compared to the T-state obtained in the binary complex of Hb₄/BPG. Hb₄ appears to respond to the presence of chloride ions in the central cavity. The mechanism of the response to chloride ions is attributed to neutralization of positively charged residues in the central cavity of Hb₄ by the relatively high concentration of chloride ions.

It is of interest to consider the effect on the O₂-equilibrium binding properties of human rbc-lysates, brought about by quantitative removal of E-molecules. BPG, as well as many other E-molecules, stabilize a ^Tstate structural configuration (described as a conformation in earlier literature) of Hb₄ (Accession Code: UniProtKB-P69905 (HbA_Human)) resulting in markedly diminished affinity for O₂. Hb₄, in supporting electrolytes free of any E-molecules, is not in the structural configuration characteristic of Hb₄/BPG. Hb₄/BPG only exists in vitro, not being presented in vivo under normal conditions. E-free Hb₄ contains elements of structure which respond to the presence of BPG. Information concerning these incomplete unit(s) of allosteric structure is reflected in the O₂-equilibrium binding data obtained in E-free supporting electrolytes. O₂-Equilibrium binding data (Knowles)¹ and 19F-nmr data (Knowles)² identify cooperative dimeric subunits in the hemoglobin tetramer. Equation a, a model describing structural changes as E-free α²β² is converted to E-free (αO₂)²(βO₂)², by a sequence of four O₂-binding reactions, is supported by the experimental results described herein. This model can be viewed as a variant of the Adair model insofar as it is comprised of a sequence of O₂-binding reactions³.

Equation a is a model for the reaction sequence from E-free Hb₄, species I, to (HbO₂)₄, species V. Hemoglobin subunits are represented as α and β. Parenthetical inclusions describe cooperative dimeric subunits. Superscript integers to the upper left describe: the position of subunits in the hemoglobin tetramer and the conformational state, R or T.

In this communication, an equation of state for E-free Hb₄ is presented for O₂-equilibrium binding curves and tested for its ability to account for equilibrium binding data. Fractional saturation, F, is defined in Equation (1), with integers representing the number of occupied O₂-binding sites on each of the species defined in Equation a.

The allosteric architecture of species I through V is assigned in Equation a, cooperative units of structure being enclosed within brackets, as in (¹α ²β) and (²α ¹β). Substitution of analytical expressions for species I through V, obtained from individual mass action expressions, into (1) leads to the equation of state, (2), relating F to [O₂]

Equation (2), based on binding constants intrinsic to α-chains and β-chains, Equation a, requires four variables to describe the O₂-equilibrium binding curve modeled in Equation a. Equation (2), presented in a form compressed by repeated algebraic factoring, is found to describe the E-free O₂-equilibrium binding curve. O₂- Equilibrium binding constants are expected to be related to intrinsic binding constants for a- and b-chains, K_α and K_β, respectively, by statistical factors: K₁=2 K_β, K₂=K_α, K₃=K_β, K₄=0.5 K_α. Statistical factors suggest that the equation of state can be expressed with only 2 unknown quantities: K_β and K_α.

Efforts to establish an E-Free supporting electrolyte demand an amine buffer. Amine buffers, such as Bis-Tris, require neutralization with an acid to obtain a pH-value of 7. The conjugate base of any acid that might be utilized to neutralize a solution of Bis-Tris is likely to be an E-molecule. Therefore, it is necessary to use as low a concentration of buffering amine as possible. Use of a strong acid ensures that un-dissociated acids will not be present in the supporting electrolyte. HCl was chosen to adjust the pH of 0.05 M Bis-Tris. The pK-value of Bis-Tris suggests that the concentration of chloride ion in solutions used to establish binding data was 0.012 M. O₂-Equilibrium binding curves in 0.025 M Bis-Tris, pH 7 and 0.05 M Bis-Tris, pH 7 are identical, establishing that chloride ion, at the concentrations used in these experiments, does not act as an E-molecule. A response to chloride ions requires concentrations as high as 0.10 M [5,6].

Materials and Methods

Stock solutions of human hemoglobin were prepared from whole blood obtained from a single donor. These stock solutions of hemoglobin were subjected to buffer exchange operations on a column of Sephadex G-25 equilibrated witheither (i) 0.050 M Bis-Tris, pH 7.0 or (ii) 0.050 M Bis-Tris, 0.100 M NaCl, pH 7.0. The hemoglobin solutions were further diluted with either (i) 0.050 M Bis-Tris, pH 7.0 or (ii) 0.050 M Bis-Tris, 0.100 M NaCl, pH 7.0 to provide approximately 200 mL of a hemoglobin solution suitable for use in the gas-liquid equilibration apparatus [7]. The details of the procedure for purification of stock solutions of hemoglobin, generation of gas mixtures of known composition, equilibration of hemoglobin solutions with gas mixtures, and spectroscopic analysis of Hb₄ solutions partially saturated with O₂ have previously been described (Knowles and Gibson)⁹. Bis-Tris, obtained from Aldrich Chemical Company, was crystallized from ethanol. The heme concentration of samples of hemoglobin used for elaboration of O₂-binding curves was 300-400 μM. Binding data were fitted to the appropriate equation of state using XYCALC, Version 3.0. XYCALC determined best fitting values of non-linear parameters by an iterative procedure based on Nelder and Mead’s downhill simplex method. These results have been confirmed by use of the curve fitting tool in MatLab [8,9].

Results and Discussion

The affinity of Hb₄ for O₂ in 0.050 M Bis-Tris, pH 7.0 with HCl, 20.0°C

Equilibrium binding data are presented in Table 1, O₂ concentrations being expressed in units of μmoles/L. The concentration of O₂ in the liquid phase, required for half-saturation of Hb₄, is 1.90 μmol/L (corresponding to a partial pressure of 1.07 torr O₂ in the gas phase). The O₂-equilibrium binding curve is presented in Figure 1.

Table 1: Binding data for Hb₄ in 0.050 M BisTris, pH 7.0, 20.0°C.

Figure 1: O₂ Equilibrium binding curve of E-free purified human hemoglobin. Data obtained in 0.050 M BisTris, pH 7.00 with HCl, 20.0°C.

A hill plot of O₂ binding data is presented in Figure 2. The shape of the hill plot deviates from the expected sigmoid-shape in several respects: (i) the limiting n-value, as the concentration of O₂ approaches zero, is 2 rather than 1; (ii) an upward inflection is not observed; (iii) the n-value decreased from 2.0 to values approaching unity at concentrations of O₂ supporting values of F greater than 0.75.

Figure 2: Hill plot of O₂ equilibrium binding data. The supporting electrolyte is 0.050 M BisTris, pH 7.00 with HCl, 20.0°C.

The best fitting values obtained in fitting O₂-binding data in an E-free supporting electrolyte to the equation of state, in units of L/μmol are: K₁=0.2913; K₂=1.112; K₃=0.4912; K₄=0.3185. The correlation coefficient for fitting of binding data to the equation of state is 0.9995. Assigning equilibrium constants to individual chains in the first cooperative subunit yields: K_β=0.146 and K_α=1.112. Equilibrium constants for the second cooperative subunit are K_β’=0.4912 and K_α’=0.637. A plot of predicted values of F versus observed values of F, (Figure 3), is linear, F_PRE=0.9995 F_OBS+0.0007, a straight line being F_PRE=F_OBS. The correlation coefficient is 0.9995. In each cooperative dimer, K_α exceeds K_β. Predicted values of F, F_PRE, were obtained using the best fitting values for the equilibrium constants together with Equation (2), and the experimentally determined values for concentration of O₂. The graph of F_PRE versus F_OBS is given in Figure 4.

Figure 3: Evaluation of the ability of the equation of state to predict F of Hb₄ in E-free electrolytes. Comparison of observed values of F in 0.050 M BisTris, pH 7.0, 20.0°C with values of F predicted by the equation of state, Eq. (1.3) and the best fitting values of K.

Figure 4: O₂ equilibrium binding curve of human hemoglobin in 0.050 M BisTris, 0.100 M NaCl, pH 7.0, 20.0°C. Half saturation was obtained at 8.1 μmol /L in the liquid phase.

The value of K_β, the first subunit to bind O₂, is small in comparison with the value of K_α=7.62. Binding of O₂ to the α-chain in each cooperative subunit is regulated by reaction of the β-chain with O₂. The value of K_α\K_β for the second cooperative dimeric subunit is significantly less: 1.30, due to a decrease in the value of K_α and an increase in the value of K_β.

Affinity of Hb₄ for O₂ in 0.050 M Bis-Tris, 0.100 M NaCl, pH 7.0, 20.0°C

O₂-affinity of Hb₄ in 0.050 M Bis-Tris, pH 7.00, 20.0°C responds to the addition of NaCl to a final concentration of 0.100 M, binding data being presented in Table 2. The effect of addition of 0.100 M NaCl to 0.050 M Bis-Tris, pH 7.0, 20.0°C is: (i) to increase the O₂ concentration in the liquid phase at which Hb₄ is half-saturated with O₂ from 1.9 μmol/L to 8.1 μmol/L, and (ii) to change, dramatically, the shape of the Hill plot, (Figure 5). The equilibrium binding curve is markedly S-shaped. Fitting of O₂-equilibrium binding data to the Perutz/Adair equation yields: K_α=5.3 × 104 L/μmol; K_Δ=0.0325; K_β=1.8 × 105 L/μmol. The correlation coefficient for the curve fitting procedure is 0.9997 A graph of predicted values of F versus observed values of F should be linear: F_PRE=F_OBS. A graph of F_PRE versus F_OBS yields: F_PRE=0.995 F_OBS+0.0007, (Figure 6).

Table 2: Binding data for Hb₄/(Cl-)n in 0.050 M BisTris, 0.100 M NaCl, pH 7.00 20.0°C.

Figure 5: Hill plot of O₂ equilibrium binding data. The supporting electrolyte is 0.050 M BisTris, 0.100 M NaCl, pH 7.00 with HCl, 20.0°C.

Figure 6: Observed and predicted values of F of the O₂ equilibrium binding curve of purified Hb₄ in 0.100 M NaCl, 0.05 M BisTris, pH 7.00 with HCl, 20.0°C. Predicted values of F, F_PRE, were calculated with the Perutz/Adair equation using the best fitting values of K_α, K_β, and K_Δ and the corresponding O₂-values.

The Hill plot of O₂-equilibrium binding date is similar to the majority of Hill plots obtained for human hemoglobin and described in the voluminous hemoglobin literature: (i) The n-value approaches unity as [O₂] approaches zero; (ii) The Hill plot demonstrates an inflection point with n-value of approximately 2.6: the n-value decreases beyond the inflection point. The concentration of O₂ required to attain F=0.5, however, is much lower than that required by BPG.

The results shown in Table 1 and Figures 1-3 represents the properties of Hb₄ tetramers free of the influence of E-molecules. The results shown in Table 2 and Figures 4-6 are representative of the properties of a Hb₄/E complex: Hb₄/(Cl-1)n.

Hb₄, in 0.050 M Bis-Tris, pH 7.0 with HCl, is, effectively, free of E-molecules. The O₂-equilibrium binding properties of Hb₄ differ markedly from the equilibrium binding properties of binary complexes of Hb₄ with E-molecules. In O₂-equilibrium binding experiments, E-free Hb₄ behaves as a pair of cooperative dimeric elements of allosteric structure. These elements of allosteric structure come into existence when a pair of identical αβ dimers reacts to form E-free Hb₄. The structural states assigned to each chain in Hb₄ are established by the results of O₂-equilibrium binding constants.

The interface between the α- and β-subunits of physical dimers, ¹α, ¹β (MW=32 kD), remaining when an Hb₄ molecule dissociates into a pair of dimers, is not (cannot be) identical to the αβ interface formed when a pair of identical physical dimers associate to form tetrameric Hb₄ (MW=64 kD). Physical dimers are R-state and fail to demonstrate allosteric properties (Anderson et al., Edelstein et al., Edelstein and Gibson). The integral n-value of 2.0 for the Hill plot of E-free Hb₄ as F approaches zero, (Figure 3), defines a functional unit of co-operativity as being comprised of two O₂-binding sites. 19F-NMR experiments with E-free Hb₄ labeled at Cys-β93 by a disulfide linkage to the trifluoroethyl residue does not reveal chain heterogeneity while the same experiment in the presence of IHP demonstrates chain heterogeneity (Knowles). Strong binding of O₂ to a α-chain, following week binding of O₂ to a β-chain of E-free Hb₄ accounts for the absence of chain heterogeneity.

O₂-Binding constants are not necessarily identical for each of the dimeric cooperative subunits (^T,1α, ^R,2β) and (^T,2α, ^R,1β). The first cooperative subunit, (^T,1α, ^R,2β), binds O₂ while in combination with a second O₂-free cooperative dimer, (^T,2α,^R,1β). The second cooperative dimer, (^T,2α, ^R,1β), binds O₂ while bound to an R-state oxy-dimer, R(¹αO₂,²βO₂). Clearly, (^T,2α, ^R,1β) and R(¹αO₂, ²βO₂) are different structures. It is likely that may not be identical in each of the two cooperative subunits of E-free Hb₄.

The O₂-binding constants of β-and α-chains of the first cooperative dimeric subunit to bind O₂, in the E-free supporting electrolyte, in order of binding, are: K_β=1.45 × 105 L/mol; K_α=1.11 × 106 L/ mol. They may be compared with the O₂-binding constants in the presence of the weakest of E-molecules, 0.100 M NaCl, in order of binding: K_α=5.34 × 104 L/mol; K_β=1.81 × 106 L/mol. E-molecule effects the values of both K_α and K_β E-molecules reduce the affinity of β-chains below that of Tstate α-chains.

The first cooperative subunit of Hb₄ undergoes the following sequence of reactions:

The ^Tstate in α-chains is established by proximal strain in the imidazole bond to the ferrous atom of the heme moiety (Perutz 1970 Perutz 1987). The ^Tstate α-chain is converted to the ^Rstate α-chain upon reaction of the ^Rstate β-chain with O₂.

The ^Tstate in the presence of chloride ions, Hb₄/(Cl-1)n, enhances pre-existing proximal strain in α-chains as well as establishing distal side steric hindrance to O₂-binding by the β-chain. Distal side steric hindrance of β-chain heme moieties is a unique characteristic of all binary complexes of Hb₄ and E-molecules, Hb₄/(Cl-1)n in this instance. The order of binding of O₂ to chains in E-free Hb₄ is: The order of binding of O₂ in Hb₄/(Cl-1)n is: α,α, β,β.

An alternative model for O₂-binding by Hb₄, expressed in terms of the statistical assigned equilibrium constants, yields close agreement of predicted and observed values with the four-step ordered sequence cited above.

The equation of state for the model in Equation b, Equation 3, can be expressed in terms of only two unknown quantities.

The correlation coefficient for the equation of state, Equation (3), for the alternative model, Equation b, is 0.9992. These values are reasonably close to those presented for the model based on a sequence of four steps.

Conclusion

It is likely that a significant step in the evolution of the fully cooperative tetrameric hemoglobin molecule we know today occurred when (¹α ¹β) dimers underwent mutations leading to formation of tetramers resulting in (¹α ²β) and (²α ¹β) interfaces potentially supporting cooperative properties. Such a step may precede (i) Development of an E-molecule contributing to proximal strain in ^Tstate α-chains, (ii) Establishing steric hindrance to O₂- binding by β-chains, and (iii) Sensitivity of O₂-binding to the pH of the supporting electrolyte (Bohr Effect).

E-free Hb₄ possesses a fundamental element of allosteric structure: identified as a pair of cooperative dimers that exist in Hb₄ and do not exist in the dimeric molecules obtained upon dissociation of Hb₄ into dimers. The O₂-affinity of E-free Hb₄ is too high to be useful as an O₂ transport protein, being half saturated with O₂ at less than 2 µmol/L. E-free (HbO₂)₄ generates an insufficient concentration gradient to move O₂ from rbcs to mitochondria by the process of diffusion. BPG is a non-competitive inhibitor of O₂ binding to Hb₄, the resulting Hb₄-inhibitor complex, Hb₄/ BPG, possessing lower affinity for O₂, being half saturated with O₂ at approximately 60 µmol/L at pH 7.4 and 37°C. The role of Hb₄ as an O₂-transpsort protein is best managed as follows: (i) Hb₄ should possess a high O₂-affinity in the pulmonary circulation (the lung) and a low affinity for O₂ in the systemic circulation (muscles, kidney, etc.). E-Free Hb₄ possesses a pair of cooperative dimers: (^T1α, ^R2β) and (^T2α, ^R1β). These cooperative dimers are an underlying element of allosteric structure upon which other elements of allosteric structure are constructed. These other elements of allosteric structure can be summarized as follows: (i) Enhancement of proximal strain in α-chains; (ii) Introducing steric hindrance to O₂-binding by β-chains; (iii) A high affinity of ^Tstate structures for BPG and a low affinity of Rstate structures for BPG; (iv) Introduction of pH-sensitivity to O₂-binding (Bohr Effect): (v) Packaging these elements of structure in a manner supporting respiration in mammals.

The following linked manuscripts address the role of the BPG mediated R to T structural change, a second element of allosteric structure diminishing the O₂-affinity of ^Tstate α-chains and regulating access of O₂ to ^Rstate β-chains. A third element of allosteric structure converts ^Tstate/BPG complexes to ^Rstate/BPG complexes in conjunction with conversion of ^Tstate αO₂ chains to ^Rstate αO₂-chains. These elements of allosteric structure by BPG can be shown to account for the characteristic shape of O₂-equilibrium binding curves of the binary complex of Hb₄ and BPG obtained under conditions of constant pH. A fourth element of allosteric structure, not addressed in experiments conducted at constant pH-values, concerns the rise in pH in the pulmonary circulation and the decrease in pH in the systemic circulation.

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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