Measuring forces between protein fibers by microscopy

We propose a general scheme for measuring the attraction between mechanically frustrated semiflexible fibers by measuring their thermal fluctuations and shape. We apply this analysis to a system of sickle hemoglobin (HbS) fibers that laterally attract one another. These fibers appear to "zip" together before reaching mechanical equilibrium due to the existence of cross-links into a dilute fiber network. We are also able to estimate the rigidities of the fibers. These rigidities are found to be consistent with sickle hemoglobin "single" fibers 20 nm in diameter, despite recent experiments indicating that fiber bundling sometimes occurs. Our estimate of the magnitude of the interfiber attraction for HbS fibers is in the range 8 +/- 7 kBT/microm, or 4 +/- 3 k(B)T/microm if the fibers are assumed, a priori to be single fibers (such an assumption is fully consistent with the data). This value is sufficient to bind the fibers, overcoming entropic effects, although extremely chemically weak. Our results are compared to models for the interfiber attraction that include depletion and van der Waals forces. This technique should also facilitate a similar analysis of other filamentous protein assembles in the future, including beta-amyloid, actin, and tubulin.     

Intermolecular contacts within sickle hemoglobin fibers

By combining X-ray crystallographic co-ordinates of sickle hemoglobin (HbS) molecules with three-dimensional reconstructions of electron micrographs of HbS fibers we have synthesized a model for the structure of the clinically relevant HbS fiber. This model largely accounts for the action of 55 point mutations of HbS whose effect on fiber formation has been studied. In addition, it predicts locations at which additional point mutations are likely to affect fiber formation. The number of intermolecular axial contacts decreases with radius until, at the periphery of the fiber, there are essentially no axial contacts. We suggest that this observation accounts for the limited radial growth of the HbS fiber and that a similar mechanism may be a factor in limiting the size of other helical particles. The methodology for the synthesis of the fiber model is applicable to other systems in which X-ray crystallographic and electron microscopic data are available.     

Molecular insights into the irreversible mechanical behavior of sickle hemoglobin

Sickle cell disease is caused by the amino acid substitution of glutamic acid to valine, which leads to the polymerization of deoxygenated sickle hemoglobin (HbS) into long strands. These strands are responsible for the sickling of red blood cells (RBCs), making blood hyper-coagulable leading to an increased chance of vaso-occlusive crisis. The conformational changes in sickled RBCs traveling through narrow blood vessels in a highly viscous fluid are critical in understanding; however, there are few studies that investigate the origins of the molecular mechanical behavior of sickled RBCs. In this work, we investigate the molecular mechanical properties of HbS molecules. A mechanical model was used to estimate the directional stiffness of an HbS molecule and the results were compared to adult human hemoglobin (HbA). The comparison shows a significant difference in strength between HbS and HbA, as well as anisotropic behavior of the hemoglobin molecules. The results also indicated that the HbS molecule experienced more irreversible mechanical behavior than HbA under compression. Further, we have characterized the elastic and compressive properties of a double stranded sickle fiber using six HbS molecules, and it shows that the HbS molecules are bound to each other through strong inter-molecular forces.     

Modification of Axial Fiber Contact Residues Impact Sickle Hemoglobin Polymerization by Perturbing a Network of Coupled Interactions

The identity of intermolecular contact residues in sickle hemoglobin (HbS) fiber is largely known. However, our knowledge about combinatorial effects of two or more contact sites or the mechanistic basis of such effects is rather limited. Lys16, His20, and Glu23 of the α-chain occur in intra-double strand axial contacts in the sickle hemoglobin (HbS) fiber. Here we have constructed two novel double mutants, HbS (K16Q/E23Q) and (H20Q/E23Q), with a view to delineate cumulative impact of interactions emanating from the above contact sites. Far-UV and visible region CD spectra of the double mutants were similar to the native HbS indicating the presence of native-like secondary and tertiary structure in the mutants. The quaternary structures in both the mutants were also preserved as judged by the derivative UV spectra of liganded (oxy) and unliganded (deoxy) forms of the double mutants. However, the double mutants displayed interesting polymerization behavior. The polymerization behaviour of the double mutants was found to be non-additive of the individual single mutants. While HbS (H20Q/E23Q) showed inhibitory effect similar to that of HbS (E23Q), the intrinsic inhibitory propensity of the associated single mutants was totally quelled in HbS (K16Q/E23Q) double mutant. Molecular dynamics (MD) simulations studies of the isolated α-chains as well as a module of the fiber containing the double and associated single mutants suggested that these contact sites at the axial interface of the fiber impact HbS polymerization through a coupled interaction network. The overall results demonstrate a subtle role of dynamics and electrostatics in the polymer formation and provide insights about interaction-linkage in HbS fiber assembly.     

The entropically favored osmotic "compression" of sickle cell hemoglobin gels

Contrary to the accurate, hard-sphere depiction of monomeric hemoglobin in solution, sickle cell hemoglobin (HbS) polymerization/gelation requires attention to molecular interactions. From the temperature dependence of the osmotic compressibility of HbS gels, we were able to extract the entropy increase for concentrating HbS in this phase. Normalized per mole of water removed, the entropy increase from gel compression DeltaS(gel) is four times the previously measured DeltaS(trans), for the transition from monomeric HbS solution to HbS gel. The positive entropy change cannot emerge from the assembly of hard spheres but can indicate remodeling of HbS fibers driven by release of ordered water. The fourfold difference in DeltaS(gel) and DeltaS(trans) suggests that the act of initial fiber/gel formation from monomeric solution differs from the process of further polymerization due to tighter packing within the gel phase.     

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.     

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.     

Hydroxy-urea protects erythrocytes against oxidative damage

Hydroxy-urea (OH-U) is used to treat sickle cell anemia by increasing hemoglobin fetal-fraction. It has been suggested that the sickle cell mutations lead to the formation of unstable HbS and release of iron, which can result in lipid peroxidation (LPO), and eventual cell damage. Since oxidative processes might be involved in pathogenesis of sickle cell disease, we investigated the antioxidant property of OH-U in a red blood cell (RBC) model. Intact RBCs or RBC membranes were exposed to t-butyl hydroperoxide (t-BHP, 0.75 mM) or iron (ferrous sulfate; 100 microM) at 37 degrees C for 60 min in the presence or absence of OH-U (1.25 mM). The extent of oxidative damage was measured by LPO (as thiobarbituric acid reactive substances, TBARS), hemoglobin oxidation (as percent of methemoglobin, metHb %), and decrease in the activities of membrane-bound Na+/K+-ATPase and Ca2+-ATPases. Our results show that OH-U inhibited t-BHP-induced LPO in fresh RBC membranes significantly (P <0.01). OH-U significantly inhibited t-BHP-mediated LPO (P <0.01) and metHb formation (P <0.01) in intact RBC. Also, OH-U inhibited iron-induced LPO and metHb formation in intact RBC (P <0.01). In addition, OH-U blocked t-BHP-mediated changes in membrane ATPase activities. Furthermore, OH-U blocked iron-mediated hydroxyl radical generation in a dose-dependent fashion. In conclusion, the observed antioxidant properties of OH-U might contribute to its therapeutic action in sickle cell disease.     

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     

Depletion-mediated red blood cell aggregation in polymer solutions

Polymer-induced red blood cell (RBC) aggregation is of current basic science and clinical interest, and a depletion-mediated model for this phenomenon has been suggested; to date, however, analytical approaches to this model are lacking. An approach is thus described for calculating the interaction energy between RBC in polymer solutions. The model combines electrostatic repulsion due to RBC surface charge with osmotic attractive forces due to polymer depletion near the RBC surface. The effects of polymer concentration and polymer physicochemical properties on depletion layer thickness and on polymer penetration into the RBC glycocalyx are considered for 40 to 500 kDa dextran and for 18 to 35 kDa poly (ethylene glycol). The calculated results are in excellent agreement with literature data for cell-cell affinities and with RBC aggregation-polymer concentration relations. These findings thus lend strong support to depletion interactions as the basis for polymer-induced RBC aggregation and suggest the usefulness of this approach for exploring interactions between macromolecules and the RBC glycocalyx.     

Analysis of the stability of hemoglobin S double strands.

The deoxyhemoglobin S (deoxy-HbS) double strand is the fundamental building block of both the crystals of deoxy-HbS and the physiologically relevant fibers present within sickle cells. To use the atomic-resolution detail of the hemoglobin-hemoglobin interaction known from the crystallography of HbS as a basis for understanding the interactions in the fibers, it is necessary to define precisely the relationship between the straight double strands in the crystal and the twisted, helical double strands in the fibers. The intermolecular contact conferring the stability of the double strand in both crystal and fiber is between the beta6 valine on one HbS molecule and residues near the EF corner of an adjacent molecule. Models for the helical double strands were constructed by a geometric transformation from crystal to fiber that preserves this critical interaction, minimizes distortion, and makes the transformation as smooth as possible. From these models, the energy of association was calculated over the range of all possible helical twists of the double strands and all possible distances of the double strands from the fiber axis. The calculated association energies reflect the fact that the axial interactions decrease as the distance between the double strand and the fiber axis increases, because of the increased length of the helical path taken by the double strand. The lateral interactions between HbS molecules in a double strand change relatively little between the crystal and possible helical double strands. If the twist of the fiber or the distance between the double strand and the fiber axis is too great, the lateral interaction is broken by intermolecular contacts in the region around the beta6 valine. Consequently, the geometry of the beta6 valine interaction and the residues surrounding it severely restricts the possible helical twist, radius, and handedness of helical aggregates constructed from the double strands. The limitations defined by this analysis establish the structural basis for the right-handed twist observed in HbS fibers and demonstrates that for a subunit twist of 8 degrees, the fiber diameter cannot be more than approximately 300 A, consistent with electron microscope observations. The energy of interaction among HbS molecules in a double strand is very slowly varying with helical pitch, explaining the variable pitch observed in HbS fibers. The analysis results in a model for the HbS double strand, for use in the analysis of interactions between double strands and for refinement of models of the HbS fibers against x-ray diffraction data.     

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.     

Anisotropy in sickle hemoglobin fibers from variations in bending and twist

We have studied the variations of twist and bend in sickle hemoglobin fibers. We find that these variations are consistent with an origin in equilibrium thermal fluctuations, which allows us to estimate the bending and torsional rigidities and effective corresponding material moduli. We measure bending by electron microscopy of frozen hydrated fibers and find that the bending persistence length, a measure of the length of fiber required before it starts to be significantly bent due to thermal fluctuations, is 130microm, somewhat shorter than that previously reported using light microscopy. The torsional persistence length, obtained by re-analysis of previously published experiments, is found to be only 2.5microm. Strikingly this means that the corresponding torsional rigidity of the fibers is only 6x10(-27)Jm, much less than their bending rigidity of 5x10(-25)Jm. For (normal) isotropic materials, one would instead expect these to be similar. Thus, we present the first quantitative evidence of a very significant material anisotropy in sickle hemoglobin fibers, as might arise from the difference between axial and lateral contacts within the fiber. We suggest that the relative softness of the fiber with respect to twist deformation contributes to the metastability of HbS fibers: HbS double strands are twisted in the fiber but not in the equilibrium crystalline state. Our measurements inform a theoretical model of the thermodynamic stability of fibers that takes account of both bending and extension/compression of hemoglobin (double) strands within the fiber.     

Nitric oxide reduces sickle hemoglobin polymerization: potential role of nitric oxide-induced charge alteration in depolymerization

We previously demonstrated that inhaling nitric oxide (NO) increases the oxygen affinity of sickle red blood cells (RBCs) in patients with sickle cell disease (SCD). Our recent studies found that NO lowered the P₅₀ values of sickle hemoglobin (HbS) hemolysates but did not increase methemoglobin (metHb) levels, supporting the role of NO, but not metHb, in the oxygen affinity of HbS. Here we examine the mechanism by which NO increases HbS oxygen affinity. Because anti-sickling agents increase sickle RBC oxygen affinity, we first determined whether NO exhibits anti-sickling properties. The viscosity of HbS hemolysates, measured by falling ball assays, increased upon deoxygenation; NO treatment reduced the increment. Multiphoton microscopic analyses showed smaller HbS polymers in deoxygenated sickle RBCs and HbS hemolysates exposed to NO. These results suggest that NO inhibits HbS polymer formation and has anti-sickling properties. Furthermore, we found that HbS treated with NO exhibits an isoelectric point similar to that of HbA, suggesting that NO alters the electric charge of HbS. NO–HbS adducts had the same elution time as HbA upon high performance liquid chromatography analysis. This study demonstrates that NO may disrupt HbS polymers by abolishing the excess positive charge of HbS, resulting in increased oxygen affinity.     

Human and mouse hemoglobin association with the transgenic mouse erythrocyte membrane

Transgenic mouse models of hemoglobinopathies unravel pathophysiological mechanisms; yet the validity of the red blood cell (RBC) model of human hemoglobin (hHb) enveloped by a mouse (m) membrane has been questioned. Isoelectric focusing of hHb and mHb from transgenic mRBC shows a greater association of mHb to the mouse membrane compared to normal hHbA, supporting a species-specific Hb-mRBC membrane interaction. Enhanced hmutant Hb (HbE, HbS and HbC)-mRBC membrane affinities correlates with enhanced membrane lipid peroxidation and parallel those reported in hRBC, lending support to transgenic mRBC as models of hemoglobinopathies. Species-specific Hb-membrane interaction may be overridden by Hb charge and conformational alterations.     

Understanding the shape of sickled red cells

To understand the physical basis of the wide variety of shapes of deoxygenated red cells from patients with sickle cell anemia, we have measured the formation rate and volume distribution of the birefringent domains of hemoglobin S fibers. We find that the domain formation rate depends on the approximately 80th power of the protein concentration, compared to approximately 40th power for the concentration dependence of the reciprocal of the delay time that precedes fiber formation. These remarkably high concentration dependences, as well as the exponential distribution of domain volumes, can be explained by the previously proposed double nucleation model in which homogeneous nucleation of a single fiber triggers the formation of an entire domain via heterogeneous nucleation and growth. The enormous sensitivity of the domain formation rate to intracellular hemoglobin S concentration explains the variable cell morphology and why rapid polymerization results in cells that do not appear sickled at all.     

Computer models of a new deoxy-sickle cell hemoglobin fiber based on x-ray diffraction data.

A new x-ray fiber diffraction pattern from deoxygenated sickle cell erythrocytes has been observed. It displays 14 layer lines with a 109 A periodicity compared with the 64 A periodicity of the "classic" sickle cell hemoglobin (HbS) fiber. These data and association energy calculations serve as a basis for computer model building. Systematic searches over four-dimensional parameter space yielded twelve protofilament models that satisfy the following constraints: (a) two HbS molecules be related by twofold screw symmetry with a translational repeat of 109 A; (b) at least one of the substituted residues in HbS, val beta 6, should participate in intermolecular contacts; and (c) the energy of intermolecular interaction be less than -24 kcal/mol. Each of the protofilament models is a zigzag mono-strand that stands in contrast to the double-stranded protofilament of the "classic" fiber. Fiber models were constructed with each of the 12 protofilament models, pseudo-hexagonally packed. Searches of variable packing parameters showed four fiber models with minimal protofilament association energies and minimal differences between calculated transforms and observed data. The R-factor was less than 0.24 for each of these four models. In three of the fiber models the protofilament association energy is between -(93 and 130) kcal, and in a fourth, the energy is -64 kcal. One protofilament model constituted three distinct fiber models of the lower energy class, and a second protofilament model packed with a higher association energy into a fourth fiber model. The selection of a unique fiber model from among these four cannot be made because of the limited available data.(ABSTRACT TRUNCATED AT 250 WORDS)     

Analysis of the Intermolecular Contacts within Sickle Hemoglobin Fibers: Effect of Site-Specific Substitutions, Fiber Pitch, and Double-Strand Disorder

An atomic model of the sickle hemoglobin (HbS) fiber was synthesized by combining the molecular coordinates of the fiber (obtained from electron microscopy) with atomic coordinates of the sickle hemoglobin double strand (obtained from X-ray crystallography). The model is stereochemically acceptable. The majority of polymerization-sensitive HbS mutants are located at fiber contact sites and the majority of the mutants that do not affect polymerization are not located at contact sites. The residues at intermolecular contacts in the fiber model are reported. We have searched the coordinate space in the vicinity of the EM reconstructions to find models with alternative sets of coordinates that satisfy the mutant data, contain 5-Å contacts between double strands, and are stereochemically acceptable. This involved a systematic examination over 297 different models. The alternative fiber models were generated with a range of fiber pitch, double-strand positions, and double-strand polarity. Models which had unacceptably close contacts between atoms, failed to satisfy the mutant data, or did not have 5-Å contacts between double strands were considered unacceptable. None of the acceptable alternative fiber models improved the agreement between the polymerization behavior of HbS mutants and their contact site location. However, several models could account for the polymerization data equally well. Residue locations for single-site HbS mutations that could discriminate between alternative fiber models are proposed. The twist of HbS fibers varies in an apparent random manner with an average rotation of 7.8 ± 2.5° per molecule and a maximum rotation of 16° per molecule. The number of interdouble-strand contacts as a function of fiber twist shows a broad maximum around 9° and may account for the observed range of fiber pitch. This study shows that the upper limit on the fiber twist could result from a loss of axial contacts and repulsive van der Waals interactions between residues involved in interstrand contacts. The loss of axial contacts limits the radial growth of the fiber. In the appendix we analyze the methodology used by I. Cretegny and S. J. Edelstein [(1993) J. Mol. Biol. 230, 733-738] to build a model of the fiber. Our examination reveals shortcomings in the methodology of Cretegny and Edelstein. One result of these shortcomings is that the model synthesized by Cretegny and Edelstein is not stereochemically acceptable because it gives rise to a large number of excessively close (less than 1.4 Å) atom-atom contacts, suggesting interpenetration of the molecular envelopes.     

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.