Mechanisms of homogeneous nucleation of polymers of sickle cell anemia hemoglobin in deoxy state

The primary pathogenic event of sickle cell anemia is the polymerization of the mutant hemoglobin (Hb) S within the red blood cells, occurring when HbS is in deoxy state in the venous circulation. Polymerization is known to start with nucleation of individual polymer fibers, followed by growth and branching via secondary nucleation, yet the mechanisms of nucleation of the primary fibers have never been subjected to dedicated tests. We implement a technique for direct determination of rates and induction times of primary nucleation of HbS fibers, based on detection of emerging HbS polymers using optical differential interference contrast microscopy after laser photolysis of CO-HbS. We show that: (i). nucleation throughout these determinations occurs homogeneously and not on foreign substrates; (ii). individual nucleation events are independent of each other; (iii). the nucleation rates are of the order of 10(6)-10(8)cm(-3)s(-1); (iv). nucleation induction times agree with an a priori prediction based on Zeldovich's theory; (v). in the probed parameter space, the nucleus contains 11 or 12 molecules. The nucleation rate values are comparable to those leading to erythrocyte sickling in vivo and suggest that the mechanisms deduced from in vitro experiments might provide physiologically relevant insights. While the statistics and dynamics of nucleation suggest mechanisms akin to those for small-molecule and protein crystals, the nucleation rate values are nine to ten orders of magnitude higher than those known for protein crystals. These high values cannot be rationalized within the current understanding of the nucleation processes.     

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

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.     

Polymerization of deoxy-sickle cell hemoglobin in high-phosphate buffer

Deoxy-sicklecell hemoglobin (HbS) polymerizes in 0.05 M phosphate buffer to form long helical fibers. The reaction typically occurs when the concentration of HbS is about 165 mg/ml. Polymerization produces a variety of polymorphic forms. The structure of the fibers can be probed by using site-directed mutants to examine the effect of altering the residues involved in intermolecular interactions. Polymerization can also be induced in the presence of 1.5 M phosphate buffer. Under these conditions polymerization occurs at much lower concentrations (ca. 5 mg/ml), which is advantageous when site-directed mutants are being used because only small quantities of the mutants are available. We have characterized the structure of HbS polymers formed in 1.5 M phosphate to determine how their structures are related to the polymers formed under more physiological conditions. Under both sets of conditions fibers are the first species to form. At pHs between 6.7 and 7.3 fibers initially form bundles and then crystals. At lower pHs fibers form macrofibers and then crystals. Fourier transforms of micrographs of the polymers formed in 1.5 M phosphate display the 32- and 64-A(-1) periodicity characteristic of fibers formed in 0.05 M phosphate buffer. The 64-A(-1) layer line is less prominent in Fourier transforms of negatively stained fibers formed in 1.5 M phosphate possibly because salt interferes with staining of the fibers. However, micrographs and Fourier transforms of frozen hydrated fibers formed in high and low phosphate display the same periodicities. Under both sets of reaction conditions HbS polymers form crystals with the same unit cell parameters as Wishner-Love crystals (a = 64 A, b = 185 A, c = 53 A). Some of the polymerization intermediates were examined in the frozen-hydrated state in order to determine whether their structures were significantly perturbed by negative staining. We have also carried out reconstructions of the frozen-hydrated fibers in high and low phosphate to compare their molecular coordinates. The helical projection of the reconstructions in low phosphate shows the expected 14-strand structure. In high phosphate the 14-strand fibers are also formed and their molecular coordinates are the same (within experimental error) as those of fibers formed in 0.05 M phosphate. In addition, the reconstructions of high-phosphate fibers reveal a new minor variant of fiber containing 10 strands. The polymerization products in 1.5 M phosphate buffer were generally indistinguishable from those formed in 0.05 M phosphate buffer. Micrographs of frozen hydrated specimens have facilitated the interpretation of previously published micrographs using negative staining.     

The kinetics of nucleation and growth of sickle cell hemoglobin fibers

Polymerization of sickle cell hemoglobin (HbS) in deoxy state is one of the basic events in the pathophysiology of sickle cell anemia. For insight into the polymerization process, we monitor the kinetics of nucleation and growth of the HbS polymer fibers. We define a technique for the determination of the rates J and delay times theta of nucleation and the fiber growth rates R of deoxy-HbS fibers, based on photolysis of CO-HbS by laser illumination. We solve numerically time-dependent equations of heat conductance and CO transport, coupled with respective photo-chemical processes, during kinetics experiments under continuous illumination. After calibration with experimentally determined values, we define a regime of illumination ensuring uniform temperature and deoxy-HbS concentration, and fast (within <1 s) egress to steady conditions. With these procedures, data on the nucleation and growth kinetics have relative errors of <5% and are reproducible within 10% in independent experiments. The nucleation rates and delay times have steep, exponential dependencies on temperature. In contrast, the average fiber growth rates only weakly depend on temperature. The individual growth rates vary by up to 40% under identical conditions. These variations are attributed to instability of the coupled kinetics and diffusion towards the growing end of a fiber. The activation energy for incorporation of HbS molecules into a polymer is E(A)=50 kJ mol(-1), a low value indicating the significance of the hydrophobic contacts in the HbS polymer. More importantly, the contrast between the strong theta(T) and weak R(T) dependencies suggests that the homogenous nucleation of HbS polymers occurs within clusters of a precursor phase. This conclusion may have significant consequences for the understanding of the pathophysiology of sickle cell anemia and should be tested in further work.     

Molecular crowding limits the role of fetal hemoglobin in therapy for sickle cell disease

The dominant assumption central to most treatments for sickle cell anemia has been that replacement of sickle hemoglobin (HbS) by fetal hemoglobin (HbF) would have major clinical benefit. Using laser photolysis, we have measured polymerization kinetics including rates of homogeneous and heterogeneous nucleation on mixtures of 20% and 30% HbF with HbS. We find that the present model for polymerization, including molecular crowding, can accurately predict the rates of such mixtures, by using the single assumption that no significant amount of HbF enters the polymer. The effects of replacing HbS by HbF on the rates of polymer formation are found to be significantly lower than previous measurements appeared to indicate because the impact of the replacement is also highly dependent on the total hemoglobin concentration. This is because the molecular crowding of non-polymerizing HbF offsets substantially the effects of decreasing the concentration of HbS concentration, an effect that increases with concentration. Most strikingly, the demonstrated benefit of hydroxyurea therapy in slowing the kinetics of intracellular polymerization cannot be primarily due to enhanced HbF, but must have some other origin, which could itself represent a promising therapeutic approach.     

Determination of the transition-state entropy for aggregation suggests how the growth of sickle cell hemoglobin polymers can be slowed

Sickle cell anemia is associated with the mutant hemoglobin HbS, which forms polymers in red blood cells of patients. The growth rate of the polymers is several micrometers per second, ensuring that a polymer fiber reaches the walls of an erythrocyte (which has a 7-μm diameter) within a few seconds after its nucleation. To understand the factors that determine this unusually fast rate, we analyze data on the growth rate of the polymer fibers. We show that the fiber growth follows a first-order Kramers-type kinetics model. The entropy of the transition state for incorporation into a fiber is 95 J mol^− 1 K^− 1, very close to the known entropy of polymerization. This agrees with a recent theoretical estimate for the hydrophobic interaction and suggests that the gain of entropy in the transition state is due to the release of the last layer of water molecules structured around contact sites on the surface of the HbS molecules. As a result of this entropy gain, the free-energy barrier for incorporation of HbS molecules into a fiber is negligible and fiber growth is unprecedentedly fast. This finding suggests that fiber growth can be slowed by components of the red cell cytosol, native or intentionally introduced, which restructure the hydration layer around the HbS molecules and thus lower the transition state entropy for incorporation of an incoming molecule into the growing fiber.     

Metastable mesoscopic clusters in solutions of sickle-cell hemoglobin

Sickle cell hemoglobin (HbS) is a mutant, whose polymerization while in deoxy state in the venous circulation underlies the debilitating sickle cell anemia. It has been suggested that the nucleation of the HbS polymers occurs within clusters of dense liquid, existing in HbS solutions. We use dynamic light scattering with solutions of deoxy-HbS, and, for comparison, of oxy-HbS and oxy-normal adult hemoglobin, HbA. We show that solutions of all three Hb variants contain clusters of dense liquid, several hundred nanometers in size, which are metastable with respect to the Hb solutions. The clusters form within a few seconds after solution preparation and their sizes and numbers remain relatively steady for up to 3 h. The lower bound of the cluster lifetime is 15 ms. The clusters exist in broad temperature and Hb concentration ranges, and occupy 10(-5)-10(-2) of the solution volume. The results on the cluster properties can serve as test data for a potential future microscopic theory of cluster stability and kinetics. More importantly, if the clusters are a part of the nucleation mechanism of HbS polymers, the rate of HbS polymerization can be controlled by varying the cluster properties.     

Sickle hemoglobin fibers: mechanisms of depolymerization

We examined the depolymerization of hemoglobin (Hb) S fibers in the presence of CO by using photolysis of COHbS to create and isolate individual fibers, then removing photolysis to induce depolymerization. Depolymerization occurs at two sites, fiber ends and fiber sides, with different kinetics and by different mechanisms. At low partial pressure of CO (pCO), end-depolymerization is dominant, proceeding at approximately 1 microm s(-1), whereas at high pCO fibers vanish very rapidly, in much less than one second, by side-depolymerization. Each kind of depolymerization could occur by a ligand-independent path, in which deoxyHb depolymerizes and then is prevented from returning to the polymer by liganding with CO, or by a ligand-dependent path in which CO binds to the polymer inducing dissociation of the newly liganded molecules from it. We find that ligand-independent depolymerization is the dominant path for end-depolymerization and ligand-dependent depolymerization dominates, at least at high pCO, for side-depolymerization. On the basis of our kinetic results and electron micrographs of depolymerizing fibers, we propose a model for side-depolymerization in which a hole is nucleated by cooperative loss of a few molecules from fiber sides, followed by rapid depolymerization from the newly created fiber ends abutting the hole. Potential significance of these results for the pathophysiology of sickle cell disease is discussed.     

Modeling sickle hemoglobin fibers as one chain of coarse-grained particles

Sickle cell disease (SCD) is caused by a single point mutation in the beta-chain hemoglobin gene, resulting in the presence of abnormal hemoglobin S (HbS) in the patients' red blood cells (RBCs). In the deoxygenated state, the defective hemoglobin tetramers polymerize forming stiff fibers which distort the cell and contribute to changes in its biomechanical properties. Because the HbS fibers are essential in the formation of the sickle RBC, their material properties draw significant research interests. Here, a solvent-free coarse-grain molecular dynamics (CGMD) model is introduced to simulate single HbS fibers as a chain of particles. First, we show that the proposed model is able to efficiently simulate the mechanical behavior of single HbS fibers. Then, the zippering process between two HbS fibers is studied and the effect of depletion forces is investigated. Simulation results illustrate that depletion forces play a role comparable to direct fiber-fiber interaction via Van der Waals forces. This proposed model can greatly facilitate studies on HbS polymerization, fiber bundle and gel formation as well as interaction between HbS fiber bundles and the RBC membrane.     

Characterization of Caulobacter crescentus FtsZ protein using dynamic light scattering

The self-assembly of the tubulin homologue FtsZ at the mid-cell is a critical step in bacterial cell division. We introduce dynamic light scattering (DLS) spectroscopy as a new method to study the polymerization kinetics of FtsZ in solution. Analysis of the DLS data indicates that the FtsZ polymers are remarkably monodisperse in length, independent of the concentrations of GTP, GDP, and FtsZ monomers. Measurements of the diffusion coefficient of the polymers demonstrate that their length is remarkably stable until the free GTP is consumed. We estimated the mean size of the FtsZ polymers within this interval of stable length to be between 9 and 18 monomers. The rates of FtsZ polymerization and depolymerization are likely influenced by the concentration of GDP, as the repeated addition of GTP to FtsZ increased the rate of polymerization and slowed down depolymerization. Increasing the FtsZ concentration did not change the size of FtsZ polymers; however, it increased the rate of the depolymerization reaction by depleting free GTP. Using transmission electron microscopy we observed that FtsZ forms linear polymers in solutions which rapidly convert to large bundles upon contact with surfaces at time scales as short as several seconds. Finally, the best studied small molecule that binds to FtsZ, PC190723, had no stabilizing effect on Caulobacter crescentus FtsZ filaments in vitro, which complements previous studies with Escherichia coli FtsZ and confirms that this class of small molecules binds Gram-negative FtsZ weakly.     

Cooperative polymerization reactions. Analytical approximations, numerical examples, and experimental strategy

How does one obtain kinetic rate constants from the time course of a reversible and cooperative polymerization reaction? We examine a simple version of the homogeneous nucleation-elongation model with both analytical and numerical techniques to test some common assumptions and develop an experimental strategy. The assumption of irreversible polymer formation is found to be a useful and adequate approximation for the numerical determination of monomer disappearance. The assumption of early "pre-equilibrium" between monomer and seed, however, is shown numerically and analytically to produce significant errors over a wide range of parameters, particularly for small seed lengths. We exhibit numerical solutions for many different parameters, and also discuss analytical techniques that allow approximate solutions for several conditions: the high-concentration limit; the long-time limit; and the long-seed-length, lows concentration limit. The overall reaction simplifies when the monomer concentration is large. An experimental strategy for elucidating the seed size and the rate constants for polymerization and depolymerization is presented.     

O2 dependence of K+ transport in sickle cells: the effect of different cell populations and the substituted benzaldehyde 12C79.

The molecular basis of sickle cell disease (SCD) is well known but the pathophysiology is poorly understood. It remains intractable to therapy. Hyperactivity of several membrane transport systems, including the K+-Cl- cotransporter (termed KCC), cause HbS-containing red cells (termed HbS cells) to dehydrate and sickle, leading to the development of sickle cell crises (SCCs). Contrary to normal red cells (HbA cells), KCC in HbS cells is active at low O2 tensions (PO2s), remaining responsive to low pH or urea. Since these stimuli are usually encountered in hypoxic regions, the abnormal O2 dependence increases the contribution of KCC to dehydration, and hence development of SCCs. These differences with HbA cells may be due to the younger population of cells or to polymerization of HbS. We used 86Rb+ as a K+ congener to investigate the activity of KCC at different PO2s, and density gradient separation to investigate different red cell fractions. We found no correlation of O2 dependence with cell fractions. We also used the substituted benzaldehyde 12C79 to increase the O2 affinity of HbS and found that its effect on HbS O2 saturation and cell sickling correlated with that on both Cl--independent and Cl--dependent K+ transport, implying that, at low PO2s, KCC activity correlated with HbS polymerization. The importance of these results to understanding the pathophysiology of SCD, and for the design of chemotherapeutic agents to ameliorate or prevent SCC, is discussed.     

Mechanism of action of phalloidin on the polymerization of muscle actin

Under conditions where muscle actin only partially polymerizes, or where it does not polymerize at all, a significant enhancement of polymerization was observed if equimolar phalloidin was also present. The increased extent of polymerization in the the presence of phalloidin can be explained by the reduced critical actin concentration of partially polymerized populations at equilibrium. Under such conditions, the rate of polymerization, as judged by the length of time to reach half the viscosity plateau, was found to be essentially independent of the phalloidin concentration. Moreover, the initial rate of polymerization of actin was also found to be independent of phalloidin concentration. However, phalloidin apparently causes a reduction in the magnitude of the reverse rates in the polymerization reaction, as was demonstrated by the lack of depolymerization of phalloidin-treated actin polymers. This effect of phalloidin is also supported by the identification of actin nuclei and short polymers in populations of G-actin incubated with phalloidin in the absence of added KCl. Our conclusion, then, is that phalloidin influences the polymerization of actin by stabilizing nuclei and polymers as they are formed.     

Fiber depolymerization

Depolymerization is, by definition, a crucial process in the reversible assembly of various biopolymers. It may also be an important factor in the pathology of sickle cell disease. If sickle hemoglobin fibers fail to depolymerize fully during passage through the lungs then they will reintroduce aggregates into the systemic circulation and eliminate or shorten the protective delay (nucleation) time for the subsequent growth of fibers. We study how depolymerization depends on the rates of end- and side-depolymerization, k(end) and k(side), which are, respectively, the rates at which fiber length is lost at each end and the rate at which new breaks appear per unit fiber length. We present both an analytic mean field theory and supporting simulations showing that the characteristic fiber depolymerization time tau= square root 1/k(end)k(side) depends on both rates, but not on the fiber length L, in a large intermediate regime 1 < k(side)L(2)/k(end) < (L/d)(2), with d the fiber diameter. We present new experimental data which confirms that both mechanisms are important and shows how the rate of side depolymerization depends strongly on the concentration of CO, acting as a proxy for oxygen. Our theory remains rather general and could be applied to the depolymerization of an entire class of linear aggregates, not just sickle hemoglobin fibers.     

Potential of isoquercitrin as antisickling agent: a multi-spectroscopic,thermophoresis and molecular modeling approach

Abstract

Sickle cell disease is an inherited disease caused by point mutation in hemoglobin (β-globin gene). Under oxygen saturation, sickle hemoglobin form polymers, leading to rigid erythrocytes. The transition of the blood vessels is altered and initiated by the adhesion of erythrocytes, neutrophils and endothelial cells. Sickle Hemoglobin (HbS) polymerization is a major cause in red blood cells (RBC), promoting sickling and destruction of RBCs. Isoquercitrin, a medicinal bioactive compound found in various medicinal plants, has multiple health benefits. The present study examines the potential of isoquercitrin as an anti-sickle agent, showing a significant decrease in the rate of polymerization as well as sickling of RBCs. Isoquercitrin-induced graded alteration in absorbance and fluorescence of HbS, confirmed their interaction. A negative value of ΔG° strongly suggests that it is a spontaneous exothermic reaction induced by entropy. Negative ΔH° and positive ΔS° predicted that hydrogen and hydrophobic binding forces interfered with a hydrophobic microenvironment of β6Val leading to polymerization inhibition of HbS. HbS-Isoquercitrin complex exhibits helical structural changes leading to destabilization of the HbS polymer as confirmed by CD spectroscopy. MST and DSC results indicate greater changes in thermophoretic mobility and thermal stability of sickle hemoglobin in the presence of isoquercitrin, respectively. These findings were also supported by molecular simulation studies using DOCK6 and GROMACS. Hence, we can conclude that isoquercitrin interacts with HbS through hydrogen bonding, which leads to polymerization inhibition. Consequently, isoquercitrin could potentially be used as a medication for the treatment of sickle cell disease.

Communicated by Ramaswamy H. Sarma     

Enzyme-ligand complexes of pyridoxine 5'-phosphate synthase: implications for substrate binding and catalysis

Pathogenesis in sickle cell disease depends on polymerization of deoxyhemoglobin S into rod-like fibers, forming gels that rigidify red cells and obstruct the systemic microvasculature. Fiber structure, polymerization kinetics and equilibria are well characterized and intimately related to pathogenesis. However, data on gel rheology, the immediate cause of obstruction, are limited, and models for structure and rheology are lacking. The basis of gel rheology, micromechanics of individual fibers, has never been examined. Here, we isolate fibers by selective depolymerization of gels produced under photolytic deliganding of CO hemoglobin S. Using differential interference contrast (DIC) microscopy, we measure spontaneous, thermal fluctuations in fiber shape to obtain bending moduli (kappa) and persistence lengths (lambda(p)). Some fibers being too stiff to decompose shape accurately into Fourier modes, we measure deviations of fiber midpoints from mean positions. Serial deviations, sufficiently separated to be independent, exhibit Gaussian distributions and provide mean-squared fluctuation amplitudes from which kappa and lambda(p) can be calculated. Lambda(p) ranges from 0.24 to 13 mm for the most flexible and stiffest fibers, respectively. This large range reflects formation of fiber bundles. If the most flexible are single fibers, then lambda(p) =13 mm represents a bundle of seven single fibers. Preliminary data on the bending variations of frozen, hydrated single fibers of HbS obtained by electron microscopy indicate that the value 0.24 mm is consistent with the persistence length of single fibers. Young's modulus is 0.10 GPa, less than for structural proteins but much larger than for extensible proteins. We consider how these results, used with models for cross-linking, may apply to macroscopic rheology of hemoglobin S gels. This new technique, combining isolation of hemoglobin S fibers and measurement of micromechanical properties based on thermal fluctuations and midpoint deviations, can be used to study fibers of mutants, hemoglobin A/S, and mixtures and hybrids of hemoglobin S.     

Evidence for carbon monoxide binding to sickle cell polymers during melting.

The melting of sickle cell hemoglobin (HbS) polymers was induced by rapid dilution using a stopped-flow apparatus. The kinetics of polymer melting were monitored using light scattering. Polymer melting in the absence of any hemoglobin ligand was compared to melting when the diluting buffer was saturated with carbon monoxide (CO). In this way the role of CO in polymer melting could be assessed. The data were analyzed using models that assumed that melting occurs only at the ends of polymers. It was further assumed that CO could only bind to HbS in the solution phase. However, our data could not be fitted to this model, where CO cannot bind directly to the polymer. Thus, CO probably binds directly to the polymers during our melting experiments. This result is discussed in terms of oxygen induced polymer melting and polymerization processes in sickle cell disease