Two-step mechanism of homogeneous nucleation of sickle cell hemoglobin polymers

Abstract

Sickle cell anemia is a debilitating genetic disease that affects hundreds of thousands of babies born each year worldwide. Its primary pathogenic event is the polymerization of a mutant, sickle cell, hemoglobin (HbS); and this is one of a line of diseases (Alzheimer's, Huntington's, prion, etc.) in which nucleation initiates pathophysiology. We show that the homogeneous nucleation of HbS polymers follows a two-step mechanism with metastable dense liquid clusters serving as precursor to the ordered nuclei of the HbS polymer. The evidence comes from data on the rates of fiber nucleation and growth and nucleation delay times, the interaction of fibers with polarized light, and mesoscopic metastable HbS clusters in solution. The presence of a precursor in the HbS nucleation mechanism potentially allows low-concentration solution components to strongly affect the nucleation kinetics. The variations of these concentrations in patients might account for the high variability of the disease in genetically identical patients. In addition, these components can potentially be utilized for control of HbS polymerization and treatment of the disease.

FIGURE 1

Schematic representation of the two-step nucleation mechanism of HbS polymers. (a) The nucleation pathway in the space of order parameters. Horizontal axis is HbS concentration, along which dilute solution and dense liquid can be distinguished. Axes of evolution of ordered structures are orthogonal to concentration axis, only two leading to polymers and crystals, respectively, are shown. Other possible structure axes include other crystal polymorphs, disordered aggregates, and gels. Thin dashed arrow along the diagonal indicates pathway of the one-step nucleation mechanism. Thick short-dashed lines indicate pathways of the two-step mechanism leading to polymers or crystals, respectively. (b) Free energy G landscape for different phases possible in HbS solutions. The abscissa is a one-dimensional projection of the full set of order parameters characterizing the phases in the hemoglobin plus solvent system. This coordinate can be approximately thought of as HbS density plus degree of ordering of the HbS molecules. Lower G corresponds to higher stability; thus, the dense liquid is metastable with respect to the solution in HbS solutions and becomes stable upon the addition of PEG (60) or concentrated phosphate (84).

FIGURE 2

Evolution of HbS polymerization. (a–f) DIC images of a 25-μm-thick slide of polymerizing HbS solution. Times for (a–e) indicated on panels, image in f corresponds to equilibrium between polymers and solution reached after ∼1 min of polymerization. Elongated spherulites in b–e evolve into isometric spherulites in f. Width of panels (a–e) is shown in a. Determinations of fiber length, l, and orientation angle, φ, are illustrated in b. Individual fiber spherulites traced through (b–e) are labeled with numbers. (g) Evolution of the mean number of polymer spherulites determined from 85 series of images similar to those in (a–f). Determination of delay time, θ, and slope of dependence tanα = J V_total (V_total, volume in which polymerization occurs; J, nucleation rate) is illustrated. At long times the spherulites compete for supply and the nucleation of new fibers is hampered in the regions between them; for details, see Galkin and Vekilov (42).

FIGURE 3

Correlation between reciprocal fiber growth rate 1/R and delay time for nucleation θ at four HbS concentrations and different temperatures. (Circles) C_HbS = 201 mg ml⁻¹, (triangles) C_HbS = 210 mg ml⁻¹, (diamonds) C_HbS = 220 mg ml⁻¹, and (squares) C_HbS = 230 mg ml⁻¹, different fills correspond to different runs in the same solution; within a run, different data points are taken at different temperatures, which vary within ΔT = 5°C for each run. Solid line represents a linear fit through all points with an intercept A = 0.254 ± 0.027. Dashed lines show 95% confidence interval for this fit (i.e., in 95% of experiments the fit line is expected to lie inside the confidence interval). A t-test for the hypothesis that A = 0, i.e., 1/R is proportional to θ, gives a probability p < 0.0001.

FIGURE 4

Distributions of the angles of orientation of the HbS polymer spherulites defined in Fig. 2 b. (a and b) Illumination with linearly polarized light, the orientation of plane of polarization φ′ is indicated and marked with a solid arrow; the direction at 90° from that of the plane of polarization is marked with a shaded arrow. (c) Illumination with elliptically polarized light, ratio between axes of ellipse is shown; halfwidth of distribution is indicated with double-sided arrow. (d) Fiber nucleation in solution deoxy-HbS by temperature jump without illumination. C_deoxy-HbS = 261 mg ml⁻¹, horizontal dashed line indicates mean value of distribution. Total number of analyzed spherulites: (a) 470, (b) 586, (c) 398, and (d) 162. (e) The nucleation rate, J (diamonds), and delay times, θ (circles), at three temperatures during illumination by linearly (solid symbols) and elliptically (open symbols) polarized light. (f) Schematic of light polarization states used in experiments: linearly polarized light has ratio of intensities of the two perpendicular directions of 1:68; elliptically polarize light: 1:1.6. Circularly polarized or nonpolarized light, not used in experiments discussed here, would have a ratio of 1:1.

FIGURE 5

Light scattering characterization of dense liquid clusters. (a) Examples of correlation function (diamonds) and its delay time density function (open circles) of a deoxy-HbS solution with C_HbS = 67 mg ml⁻¹. (b) Time dependence of the radii of dense liquid droplets in deoxy-HbS with C_HbS = 67 mg ml⁻¹ (squares) and C_HbS = 131 mg ml⁻¹ (circles). From Pan et al. (68).

FIGURE 6

Evolution of the distribution of fiber orientations Ψ at three energies of interaction with external electric field, indicated in the plots. φ, angle between fiber dipole moment and direction of electric vector of optical field. Since fiber dipole moment is perpendicular to fiber axis, the fiber orientation is shifted by π/2 with respect to those shown here. Fiber growth with rate R = 1 μm s⁻¹ increases dipole moment, μ, and length, L, and changes rotational diffusion coefficient according to the expression in the text.

FIGURE 7

Randomization of fiber orientation due to thermal motion. φ is an angle between a fiber and an arbitrarily chosen direction. A highly nonuniform initial distribution is assumed. Solutions of viscosity, η, are shown in the plots; rate of growth of fibers is the same as in Fig. 6.

FIGURE 8

Evolution of the distribution of orientations of spherical objects with radii, R, indicated in the plots.