Allosteric control of hemoglobin S fiber formation by oxygen and its relation to the pathophysiology of sickle cell disease

Abstract

The pathology of sickle cell disease is caused by polymerization of the abnormal hemoglobin S upon deoxygenation in the tissues to form fibers in red cells, causing them to deform and occlude the circulation. Drugs that allosterically shift the quaternary equilibrium from the polymerizing T quaternary structure to the nonpolymerizing R quaternary structure are now being developed. Here we update our understanding on the allosteric control of fiber formation at equilibrium by showing how the simplest extension of the classic quaternary two-state allosteric model of Monod, Wyman, and Changeux to include tertiary conformational changes provides a better quantitative description. We also show that if fiber formation is at equilibrium in vivo, the vast majority of cells in most tissues would contain fibers, indicating that it is unlikely that the disease would be survivable once the nonpolymerizing fetal hemoglobin has been replaced by adult hemoglobin S at about 1 y after birth. Calculations of sickling times, based on a recently discovered universal relation between the delay time prior to fiber formation and supersaturation, show that in vivo fiber formation is very far from equilibrium. Our analysis indicates that patients survive because the delay period allows the majority of cells to escape the small vessels of the tissues before fibers form. The enormous sensitivity of the duration of the delay period to intracellular hemoglobin composition also explains why sickle trait, the heterozygous condition, and the compound heterozygous condition of hemoglobin S with pancellular hereditary persistence of fetal hemoglobin are both relatively benign conditions.

Keywords: polymerization; protein fibers; sickle cell.

Fig. 1.

Cartoons of hemoglobin structure. (Top) The schematic structure shows the location of the amino acid replacement of glutamate with valine on the molecular surface at the sixth position in the sequence from the N terminus of the β chains (yellow dots). (Bottom) Cartoons show that the difference in quaternary structure between oxyhemoglobin and deoxyhemoglobin consists primarily of a 15° relative rotation of the two αβ dimers related by a twofold rotation axis. Adapted with permission from ref. .

Fig. 2.

Schematic structure of gel with HbS partially saturated with oxygen showing that only the T quaternary structure enters the fiber. The total concentration of free HbS tetramers (Left) is the solubility, which is an accurate measure of the thermodynamic stability of the fiber (Right).

Fig. 3.

Measured solubility of HbS as a function of the fractional saturation with oxygen of the tetramers in the liquid phase with oxygen and theoretically predicted values based on oxygen binding curves. The filled cyan circles are the measured solubilities. Dashed gray (fiber) curve is solubility calculated from the free tetramer cooperative binding curve (Eq. 3) and the measured noncooperative fiber binding curve (30) (K_P = 0.0059 torr⁻¹) using Eq. 1. The free tetramer cooperative binding curve is taken from the measurements of Gill et al. (51) at 25 °C using the MWC saturation function (43) (Eq. 3) with L = 60,500, K_R = 1.47 torr⁻¹, and K_T = 0.016 torr⁻¹. Dark blue (crystal) curve is solubility calculated from the free tetramer cooperative binding curve (Eq. 3) and the binding curve of the HbA single crystal in T quaternary structure (Eq. 4) at 25 °C (52) (K_P = K_crystal = 0.0036 torr⁻¹) using Eq. 1. Green (MWC) curve is solubility calculated from the free tetramer cooperative binding curve (Eq. 3) and the noncooperative binding curve of the fiber assumed to have the same affinity as the free tetramer in the T quaternary structure in the liquid phase with affinity K_T = 0.016 torr⁻¹ (Eq. 5). Red (TTS) curve is solubility calculated from the free tetramer cooperative binding curve (Eq. 3) and the best least squares fit to the data points using Eq. 6 of the TTS model [with the known 25 °C parameters of K_t = 0.0036 torr⁻¹ (52), K_r = 3.7 torr⁻¹ (47)] with one adjustable parameter, l_t = 840. In this fit, the points at saturations greater than 0.85 are the most uncertain and were downweighted by a factor 10 relative to the points at lower saturation. Black curve is an empirical fit to the data points.

Fig. 4.

Physiological concentration–saturation phase diagram at 37 °C for Hb in red cells from homozygous sickle cell patients calculated from the average hemoglobin composition of 88% HbS and 12% (HbF + HbA2) for 29 patients. Given the absence of information on the heterogeneity in the HbF + HbA2 composition, which is certainly present, we have assigned a fixed composition of 12% to all cells. The solubility (black curves at intervals of 50 mg/cc, from 250 to 500 mg/cc) increases with increasing total Hb concentration because the species α₂γ₂ and α₂β^Sγ build up in the liquid phase as the total Hb concentration increases due to lack of copolymerization of α₂γ₂ and only partial copolymerization of α₂β^Sγ.The solution contains fibers at equilibrium for all values of the Hb concentration and fractional saturation of the Hb tetramers in the liquid phase above the solubility lines and no fibers below the lines. In vivo, the distribution of intracellular HbS concentrations vary from 250 to 500 mg/cc, while the oxygen pressure is less than 40 torr in most tissues (60, 61), corresponding to a hemoglobin saturation with oxygen in the liquid phase of about 75%. Solubilities were calculated from Eq. 7 with e₂ = 0.1 and with K_T = 0.0093 torr⁻¹, K_R = 1.04 torr⁻¹, K_P = 0.006 torr⁻¹, and L = 5.6 × 10⁵ in Eq. 8. The concentration distribution on the right-hand y axis is the same as in Fig. 5 and is the average of the distributions for cells from 29 homozygous SS patients not being treated with hydroxyurea or transfused. The red shaded area of the concentration distribution shows that at equilibrium and 75% saturation of hemoglobin in the liquid phase the vast majority of cells would contain fibers in the tissues, while for oxygen pressures at the p50, almost every cell would contain fibers.

Fig. 5.

Intracellular hemoglobin concentration distributions. Blue curve shows average of 61 determinations of concentration distributions measured with the Advia 2120 for red cells from six individuals with sickle trait, which is very close to the average for 22 individuals with only normal hemoglobin (62). Red curve shows concentration distribution that is average of concentration distributions derived from density distributions for cells from 29 homozygous SS patients not treated with hydroxyurea. The derivation of concentration distributions from density distribution is described in Methods. Green curve shows concentration distribution determined measured with the Advia 2120 for cells from 16 homozygous SS patients being treated with hydroxyurea.

Fig. 6.

Physiological concentration–saturation phase diagram at 37 °C for Hb in red cells from sickle trait donors calculated from the average hemoglobin composition of 38% HbS and 58% HbA and 4% HbA2. The solution contains fibers at equilibrium for all values of the Hb concentration and fractional saturation of the Hb tetramers in the liquid phase above the solubility lines and no fibers below the lines. In vivo, the distribution of intracellular HbS concentrations vary from 250 to 450 mg/cc, while the oxygen pressure is less than 40 torr in most tissues (60, 61), corresponding to a hemoglobin saturation with oxygen in the liquid phase of about 75%. Solubilities were calculated from Eq. 7 with e₂ = 0.37 and with K_T = 0.0093 torr⁻¹, K_R = 1.04 torr⁻¹, K_P = 0.006 torr⁻¹, and L = 5.6 × 10⁵ in Eq. 8. The solubility (black curves at intervals of 50 mg/cc, from 250 to 500 mg/cc) increases with increasing total Hb concentration because the species α₂β^A₂ and α₂β^Sβ^A build up in the liquid phase as the total Hb concentration increases due to lack of copolymerization of α₂β^A₂ and only partial copolymerization of α₂β^Sβ^A. The red shaded area in the concentration distribution on the right y axis shows the fraction of trait cells containing fibers at equilibrium when the liquid phase is 75% saturated with oxygen, while the pink plus red shaded areas show the fraction of trait cells containing fibers when the liquid phase is 50% saturated with oxygen. The concentration distribution is the average of 61 determinations for red cells from six individuals with sickle trait.

Fig. 7.

Physiological concentration–saturation phase diagram at 37 °C for a 30/70 HbF/HbS mixture as is found in S/HPFH. Solubilities were calculated from Eq. 7 with e₂ = 0.1 and with K_T = 0.0093 torr⁻¹, K_R = 1.04 torr⁻¹, K_P = 0.006 torr⁻¹, and L = 5.6 × 10⁵ in Eq. 8. A value of 0.1 is more in keeping with composition studies, which found γ subunits in the HbS fibers (69, 70) (table 3.3 in ref. 54). The solubility (black curves at intervals of 50 mg/cc, from 250 to 450 mg/cc) increases with increasing total Hb concentration because the nonpolymerizing α₂γ₂ tetramer and the weakly polymerizing α₂β^Sγ tetramer build up in the liquid phase as the total Hb concentration increases. The solution contains fibers at equilibrium for all values of the total Hb concentration and fractional saturation of the free Hb tetramers in the liquid phase above the lowest black curve. In vivo, the distributions of intracellular HbS concentrations vary from 250 to 500 mg/cc, while the oxygen pressure is less than 40 torr in most tissues (60, 61), corresponding to a hemoglobin saturation with oxygen in the liquid phase of about 75%. The red shaded area in the concentration distribution on the right y axis shows the fraction of S/HPFH cells containing fibers at equilibrium when the liquid phase is 75% saturated with oxygen, while the pink plus red shaded areas show the fraction of S/HPFH cells containing fibers when the liquid phase is 50% saturated with oxygen. The concentration distribution is the average of 61 determinations for red cells from six individuals with sickle trait.

Fig. 8.

The double nucleation mechanism for HbS polymerization (, , –73). There are two nucleated polymerization processes to HbS fiber formation, hence the name double nucleation mechanism. The first fiber in any given volume forms by the classical Oosawa nucleation growth model (74), called homogeneous because it occurs without any contact to other fibers or surfaces. The initial aggregation steps are thermodynamically unfavorable (as indicated by the relative lengths of the arrows) because the loss of translation and rotational entropy is greater than the stabilization from intermolecular contacts and the compensatory increased entropy due to low frequency intertetramer vibrations of the polymerized molecules. So the overall reaction is uphill in free energy until a critical nucleus (asterisk) is formed. Addition of molecules to the critical nucleus and all subsequent fiber growth is downhill in free energy. Except at the very highest concentrations, homogeneously nucleated fiber formation is quickly superseded by a secondary nucleation process, called heterogeneous nucleation, because fibers are nucleated on the surface of existing ones. Secondary nucleation becomes much more favorable than homogeneous nucleation from two effects. First, the free energy barrier to heterogeneous nucleation is lowered as a result of the additional stability from contacts with a fiber surface. Second, even a small reduction in the free HbS concentration from fiber formation shuts down homogeneous nucleation because of the enormous dependence of the homogeneous nucleation rate on concentration (50th to 80th powers) (34, 35). As more fibers form, there is increasing surface area for heterogeneous nucleation, providing an autocatalytic mechanism that explains the exponential growth of polymerized HbS. The exponential growth results in an apparent delay or what is often called a lag phase. Therefore, the duration of the delay period, the delay time, depends on the sensitivity of the method used to detect fiber formation.

Fig. 9.

Comparison of average measured and theoretically calculated fraction SS cells sickled vs. time for slow deoxygenation to a final gas mixture of 95% nitrogen and 5% oxygen. Cells are from 16 homozygous SS patients on hydroxyurea (see SI Appendix, Table S1, for Hb compositions). The average composition is 79% HbS and 21% (Hb F + HbA2). The average concentration distribution is the green curve shown in Fig. 5. The measured fraction sickled vs. time shows the average fraction at each time point for 16 samples. The error bars correspond to 1 SD from the mean, which are large due to patient-to-patient differences in sickling curves that result from differences in hemoglobin composition (mainly HbF) and intracellular concentration distributions. The calculated fraction sickled vs. time was performed for each blood sample using its measured composition and total intracellular hemoglobin concentration. The pink shaded area represents the patient-to-patient variation in the calculation. SI Appendix, Fig. S4, shows the individual steps in the calculation of the theoretical curve.

Fig. 10.

Fraction sickled as a function of final oxygen pressure after 1-, 2-, 3-, and 4-s linear decreases (ramps) for the average composition and average concentration distribution for the red cells from 29 SS patients not on hydroxyurea therapy.

Fig. 11.

Comparison of calculated in vivo SS (red), S/HPFH (green), and AS (blue) sickling kinetics together with fraction sickled at equilibrium. Fraction sickled at the end of a 1-, 2-, 3-, and 4-s linear decrease of the oxygen pressure to pressures between 0 and 50 torr (continuous curves) and the fraction sickled at equilibrium at each pressure for cells from SS patients not being treated with hydroxyurea, sickle trait donors with average composition of 38% HbS, 58% HbA, and 4% HbA2 and for red cells having a hemoglobin composition of 30% HbF and 70% HbS as found in the compound heterozygous condition of S/HPFH. SI Appendix, Fig. S8, shows the fraction sickled vs. time induced by a 1-s linear decrease in oxygen pressure.

Fig. 12.

Relation between fiber formation kinetics and pathophysiology of sickle cell disease. (Left) Schematic of kinetic progress curve for fiber formation. The delay time is extraordinarily sensitive to HbS concentration, depending on up to 40th power of the concentration, most probably the largest concentration dependence ever observed for a chemical reaction. Thus, for example, an 8% decrease in the Hb concentration will result in a 10-fold increase in the delay time (recall for a bimolecular reaction, an 8% decrease in reactants will produce an 8% increase in the half-time for the reaction). (Right) Schematic of microcirculation showing an arteriole, capillary, and venule and various sickling scenarios. (A) The delay time is so long that the red cell squeezes through the narrow capillary before any fibers form to produce cellular distortion (sickling) and may even return without sickling all the way to the lungs, where it is reoxygenated. (B) Sickling occurs in larger vessel and returns to the lungs where the fibers melt and the cell unsickles. (C) Fibers form while the cell is in the capillary and becomes stuck, causing a log jam effect and decreased oxygen delivery to the surrounding tissue (hypoxia). (D) Unsickled cell escapes the both the capillary and the postcapillary venule where sickled cells are adherent to the venule endothelium. (E) Cell sickles and cannot escape the postcapillary venule, where sickled cells are adherent, causing a log jam (50, 81, 87). (F) Cell sickles in capillary but nevertheless squeezes through to the larger vessels. (G) Cell sickles before or within the precapillary arteriole because the concentration of intracellular hemoglobin is very high or nuclei are already present because fibers have not completely melted upon oxygenation in the lungs, enormously decreasing the delay time (88, 89).