Mixed gelation theory. Kinetics, equilibrium and gel incorporation in sickle hemoglobin mixtures.

This paper outlines a theoretical formalism for describing the gelling behavior of sickle cell hemoglobin in mixtures with other hemoglobin and non-hemoglobin proteins. Experimental applications are reported for hybridized and unhybridized mixtures of HbS (sickle hemoglobin), HbA (adult hemoglobin), HbF (fetal hemoglobin), and HbC Harlem. The theory is a general one based on a modification of the sol—gel phase equilibrium equation to take into account the varying tendencies of different hemoglobin species to promote gelation, and specific hemoglobin interactions are encoded in gelling coefficients which quantify gelling capability. Gelling coefficients for the hemoglobin species dealt with here are evaluated by measuring incorporation into the polymer phase in S-A, S-F, and S-C_H mixtures. Given this information, the theory is found to provide accurate prodictions for the equilibrium gelling behavior of the calibrating pairs themselves when they are hybridized or unhybridized, for gelation kinetics in diverse mixtures of these species taken two, three and four at a time, for the anomalous equilibrium and kinetic gelling behavior of A- C_H mixtures, and it also accounts for a variety of results previously published by others. Apparently, given the gelling coefficients for any mutant hemoglobin, one can compute gelling behavior (equilibrium, kinetics, incorporation, etc.) in any specified mixture with any other known hemoglobin(s). The gelling coefficients for any mutant hemoglobin depend upon, and therefore provide information about, gel interactions at the mutant site. From the gelling coefficients one can also obtain the change in free energy of interaction in the gel due to the altered residue. Experimental approaches are described which allow an analysis for the gelling coefficients of any mutant hemoglobin to be performed in a few hours.     

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.     

X-ray diffraction studies of 14-filament models of deoxygenated sickle cell hemoglobin fibers. Models based on electron micrograph reconstructions

The transforms of a large number of models of deoxygenated sickle hemoglobin fibers, related to that derived from image reconstruction of electron micrographs, have been calculated and compared with X-ray diffraction data of 15 A resolution. The model of the fiber, determined from the reconstructed image, is a helix consisting of 14 filaments that associate in a specific mode to form seven pairs, or protofilaments. Pairs were identified through the pattern of filament loss in partially disassembled fibers and by the separation between molecules, in adjacent filaments, of half a molecular diameter, along the fiber axis. An alternative mode of filament association can be derived also from the surface lattice of the reconstruction, which meets these criteria for the pairing of molecular filaments. Both pairing modes have been used in the search for structures whose transforms show the best agreement with the diffraction data. Models were generated by the systematic translation of six protofilaments, taken in symmetry related pairs, in steps of 3.5 A along the fiber axis relative to a fixed central protofilament. Each translation of a protofilament corresponds to a different fiber model, whose transform was compared with observed data. In all, over 11,000 transforms were calculated. Of all the models considered, three have been found whose residuals are minimal. At 30 A resolution, similar to that of electron micrographs, the model derived from image reconstruction and the three found through our search procedure are indistinguishable. At 15 A, however, the transforms of these models show better agreement with the observed data than the transform of the reconstructed image. Comparison of residuals shows that the model derived from the reconstructed image can be rejected with 99.5% probability relative to the model, with the same pairing scheme, found by our search procedures. The two other models, derived from the alternative pairing scheme, are also more credible than the reconstructed image, but at a lower confidence level. Each of our three models is equally acceptable. Their existence may reflect structural polymorphism of the fiber.     

Universal metastability of sickle hemoglobin polymerization

Sickle hemoglobin (HbS) polymerization occurs when the concentration of deoxyHbS exceeds a well-defined solubility. In experiments using sickle hemoglobin droplets suspended in oil, it has been shown that when polymerization ceases the monomer concentration is above equilibrium solubility. We find that the final concentration in uniform bulk solutions (i.e., with negligible boundaries) agrees with the droplet measurements, and both exceed the expected solubility. To measure hemoglobin in uniform solutions, we used modulated excitation of trace amounts of CO in gels of HbS. In this method, a small amount of CO is introduced to a spatially uniform deoxyHb sample, so that less than 2% of the sample is liganded. The liganded fraction is photolyzed repeatedly and the rate of recombination allows the concentration of deoxyHbS in the solution phase to be determined, even if polymers have formed. Both uniform and droplet samples exhibit the same quantitative behavior, exceeding solubility by an amount that depends on the initial concentration of the sample, as well as conditions under which the gel was formed. We hypothesize that the early termination of polymerization is due to the obstruction in polymer growth, which is consistent with the observation that pressing on slides lowers the final monomer concentration, making it closer to solubility. The thermodynamic solubility in free solution is thus achieved only in conditions with low polymer density or under external forces (such as found in sedimentation) that disrupt polymers. Since we find that only about 67% of the expected polymer mass forms, this result will impact any analysis predicated on predicting the polymer fraction in a given experiment.     

Macrofiber structure and the dynamics of sickle cell hemoglobin crystallization

Fibers of deoxyhemoglobin S undergo spontaneous crystallization by a mechanism involving a variety of intermediate structures. These intermediate structures, in common with the fiber and crystal, consist of Wishner-Love double strands of hemoglobin S molecules arranged in different configurations. The structure of one of the key intermediates linking the fiber and crystal, called a macrofiber, has been studied by a variety of analytical procedures. The results of the analysis indicate that the intermediates involved in the fiber to crystal transition have many common structural features. Fourier analysis of electron micrographs of macrofibers confirms that they are composed of Wishner-Love double strands of hemoglobin molecules. Electron micrographs of macrofiber cross-sections reveal that the arrangement of the double strands in macrofibers resembles that seen in micrographs of the a axis projection of the crystal. This orientation provides an end-on view of the double strands which appear as paired dumb-bell-like masses. The structural detail becomes progressively less distinct towards the edge of the particle due to twisting of the double strands about the particle axis. Serial sections of macrofibers confirm that these particles do indeed rotate about their axes. The twist of the particle is right handed and its average pitch is 10,000 Å. The effect of rotation on the appearance of macrofiber cross-sections 300 to 400 Å thick can be simulated by a 15 ° rotation of an a axis crystal projection. The relative polarity of the double strands in macrofibers and crystals can be determined easily by direct inspection of the micrographs. In both macrofibers and crystals they are in an anti-parallel array.On the basis of these observations we conclude that crystallization of macrofibers involves untwisting and alignment of the double strands.     

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.     

Water proton magnetic resonance studies of normal and sickle erythrocytes Temperature and volume dependence

The temperature and cell volume dependence of the NMR water proton linewidth, spin-lattice, and spin-spin relaxation times have been studied for normal and sickle erythrocytes as well as hemoglobin A and hemoglobin S solutions. Upon deoxygenation, the spin-spin relaxation time (T₂) decreases by a factor of 2 for sickle cells and hemoglobin S solutions but remains relatively constant for normal cells and hemoglobin A solutions. The spin-lattice relaxation time (T₁) shows no significant change upon dexygenation for normal or sickle packed red cells. Studies of the change in the NMR linewidth, T₁ and T₂ as the cell hydration is changed indicate that these parameters only slightly by a 10–20% cell dehydration. This result suggests that the reported 10% cell dehydration observed with sickling is not important in the altered NMR properties. Low temperature studies of the linewidth and T₁ for oxy and deoxy hemoglobin A and hemoglobin S solutions suggest that the “bound” water possesses similar properties for all four species. The low temperature linewidth ranges from about 250 Hz at ?15°C to 500 Hz at ?36°C and analysis of the NMR curves yield hydration values near 0.4 g water/g hemoglobin for all four species. The low temperature T₁ data go through a minimum at ?35°C for measurements at 44.4 MHz and ?50°C for measurements at 17.1 MHz and are similar for oxy and deoxy hemoglobin A and hemoglobin S. These similarities in the low temperature NMR data for oxy and deoxy hemoglobin A and hemoglobin S suggest a hydrophobically driven sickling mechanism. The room temperature and low temperature relaxation time data for normal and sickle cells are interpreted in terms of a three-state model for intracellular water. In the context of this model the relaxation time data imply that type III, or irratationally bound water, is altered during the sickling process.     

Replication of ultraviolet-irradiated simian virus 40 in monkey kidney cells

This paper extends the concepts of linkage and control, previously studied in single phase allosteric and polysteric systems, to multiple phase (polyphasic) systems. In particular, a study has been made of the dependence of the solubility of sickle cell hemoglobin on oxygen partial pressure. Phase diagrams are obtained from observations of birefringence changes of hemoglobin solutions in a thin film optical cell. The effects of temperature and pH are found to be correlated largely with oxygen binding curves for non-gelling solutions. This suggests only small enthalpy and proton release changes for the gelation process. Variable time delays for the onset of birefringence were observed for partial deoxygenation of a fully oxygenated sample. The reciprocal of the time delay depends on a high power of the supersaturation ratio. The nucleation kinetics are, thereby, similar to those found in fully deoxygenated solutions in temperature-jump studies. Oxygen binding curves for non-gelling solutions of sickle cell hemoglobin were used in conjunction with the phase diagram results to evaluate oxygen binding curves for the polymer gel. Account was taken of the water content of the gel and of the large non-ideality of the solution. Analysis of the phase diagram data based on polyphasic linkage relationships suggests that some reversible oxygen-binding by the gel is present. The difference in oxygen binding between solution and gel obtained in this way is similar to that found by Hofrichter (1979) for carbon monoxide.     

Plasma annexin A5 and microparticle phosphatidylserine levels are elevated in sickle cell disease and increase further during painful crisis

Expression of phosphatidylserine (PS) on the membrane surface of red blood cells and circulating microparticles (MP) plays an important role in etiology of the hypercoagulable state of sickle cell disease (SCD), as well as in the reduced red cell life span and adhesive interactions between red cells and endothelium. Annexin A5, an intracellular protein abundantly present in endothelial cells and platelets, exhibits high affinity for PS and has been shown to inhibit several of these PS-mediated pathophysiological processes. We determined plasma annexin A5 levels and MP-associated procoagulant activity, a measure of MP-PS exposure, in 17 sickle cell patients (12 HbSS and 5 HbSC) in steady state and at presentation with a painful crisis. Twenty-five HbAA blood donors served as controls.Both annexin A5 and MP-PS were highest in HbSS patients (5.7 ng/mL, IQR 3.7-7.6 and 37.9 nM, IQR 31.9-69.8) as compared to HbSC patients (1.8 ng/mL, IQR 1.7-7.6 and 20.9 nM, IQR 10.9-29.6) and healthy controls (2.5 ng/mL, IQR 1.4-4.4 and 13.1 nM, IQR 9.5-18.5) (p = 0.01 and p < 0.001, respectively). At presentation with a painful crisis, annexin A5 and MP-PS had increased in 16 of 17 patients (p = 0.001 and p < 0.001, respectively). Most interestingly, in 7 HbSS patients the proportional increase in MP-PS exposure was higher than the proportional increase in plasma annexin A5 concentration, leading to lower annexin A5/MP-PS ratio of HbSS patients during crisis than HbAA controls (0.0027 (0.0017-0.0049) vs 0.0048 (0.0027-0.0085), p = 0.05). In conclusion, patients with SCD have elevated plasma levels of annexin A5- and PS-exposing MP. During crisis both levels increase, but in most HbSS patients MP-PS exposure increases more than annexin A5. Future studies must address a potential role of annexin A5 in modulating PS-related pathophysiological processes in SCD.     

Studies of the fiber to crystal transition of sickle cell hemoglobin in acidic polyethylene glycol

The crystallization of deoxygenated sickle cell hemoglobin in acidic (pH 5.2) polyethylene glycol (10%) has been studied in order to determine if the mechanism of crystal formation under such conditions has features in common with the mechanism of crystal formation at higher pH values in the absence of polyethylene glycol. The existence of a common mechanism of crystallization under different conditions is relevant in validating the use of the known high resolution crystal structure to interpret the fiber structure. Our findings indicate that deoxygenated sickle cell hemoglobin crystallization in acidic polyethylene glycol is initiated by fiber formation. Fibers, in turn, convert to larger structures called macrofibers within several hours (Wellems et al., 1981). Fibers and macrofibers (and their respective optical transforms) formed in acidic polyethylene glycol appear to have the same structure as their counterparts formed at higher pH values in the absence of polyethylene glycol. Early in the transition one can observe macrofibers in the process of alignment and fusion. The structural characterization of the intermediates leaves little doubt that crystallization in acidic polyethylene glycol is mediated by the same mechanism as that occurring under more physiological conditions, and that fibers are a metastable intermediate whose ultimate fate is to crystallize.     

Binding of a spin-labeled phenylalanine analog to sickle hemoglobin: EPR and NMR studies

We have synthesized a spin-label analog of phenylalanine as a competitive inhibitor probe of the sickle hemoglobin aggregation process. Sickle hemoglobin gelation measurements indicate that the spin-label phenylalanine analog is a potent inhibitor of deoxy sickle hemoglobin aggregation. We have also used spin label EPR and high-resolution proton NMR to study the interaction of the phenylalanine analog with hemoglobin, and find that the kinetic off-rate is comparable to, or slower than the hemoglobin rotational rate (i.e., greater than or equal to 10(8) s-1), and that at least one, and perhaps two significant localized interaction region(s) exist within a few angstroms of the beta chain N- and C-termini. Correlation with other known structural information suggests that the observed interaction sites may be relevant to the mechanism for inhibition of sickle hemoglobin aggregation.     

Interpretation of the osmotic behavior of sickle cell hemoglobin solutions: Different interactions among monomers and polymers

It has long been known that a simple hard particle model quantitatively explains the osmotic properties of monomeric hemoglobin near its isoelectric point. However, we find that a hard particle model is not consistent with the osmotic properties of polymerized hemoglobin and that substantial soft repulsions are indicated. With allowance for different interactions among monomers and among polymers, a self-consistent quantitative fit to the experimental data is obtained. The results suggest that the decreasing “solubility” of deoxy sickle cell hemoglobin with increasing temperature from 20 to 37°C is due to weaker repulsions between polymers at higher temperatures rather than stronger polymerization. The temperature dependence of these variables indicates that the aggregation of monomers is enthalpically and entropically driven (the latter effect being stronger), while the approach of polymers toward each other is enthalpically disfavored and entropically favored (with the former dominating). In both cases, the entropic contribution suggests that water is released. © 1998 John Wiley & Sons, Inc. Biopoly 45: 299–306, 1998     

Kinetics of sickle hemoglobin polymerization. I. Studies using temperature-jump and laser photolysis techniques

Using a combination of laser photolysis and temperature-jump techniques, the kinetics of hemoglobin S polymerization have been studied over a wide range of delay times (10(-3) to 10(5)s), concentrations (0.2 to 0.4 g/cm3) and temperatures (5 to 50 degrees C). A slow temperature-jump technique was used to induce polymerization in samples with delay times between 10(2) seconds and 10(5) seconds by heating a solution of completely deoxygenated hemoglobin S. For samples with shorter delay times, polymerization was induced by photodissociating the carbon monoxide complex in small volumes (10(-9) cm3) using a microspectrophotometer equipped with a cw argon ion laser. The photolysis technique is described in some detail because of its importance in studying hemoglobin S polymerization at physiological concentrations and temperatures. In order, to establish conditions for complete photodissociation with minimal laser heating, a series of control experiments on normal human hemoglobin was performed and theoretically modeled. The concentration dependence of the tenth time is found to decrease with increasing hemoglobin S concentration. In the range 0.2 to 0.3 g/cm3, the tenth time varies as the 36th power of the hemoglobin S concentration, while in the range 0.3 to 0.4 g/cm3 it decreases to 16th power. As the tenth times become shorter, the progress curves broaden, with the onset of polymerization becoming less abrupt. For tenth times greater than about 30 seconds, measurements with the laser photolysis technique on small volumes yield highly irreproducible tenth times, but superimposable progress curves, indicating stochastic behavior. The initial part of the progress curves from both temperature-jump and laser photolysis experiments is well fit with an equation for the concentration of polymerized monomer, delta (t) = A[cosh (Bt) -1], which results from integration of the linearized rate equations for the double nucleation mechanism described in the accompanying paper (Ferrone et al., 1985). The dependence of the parameters A and B on temperature and concentration is obtained from fitting over 300 progress curves. The rate B has a large concentration dependence, varying at 25 degrees C from about 10(-4) S-1 at 0.2 g/cm3 to about 100 s-1 at 0.4 g/cm3.     

Thermodynamics of anti-sickling agents with hemoglobin S

The effects of oxygen and a second ligand, the anti-sickling agent butylurea, on the hemoglobin S gel-solution phase equilibrium have been studied. The results have been analyzed using thermodynamic properties of the system. In particular, the solubility of deoxy hemoglobin S as a function of butylurea concentration was determined and the thermodynamic analysis shows that there are at least two cooperatively linked butylurea binding sites. Liquid phase oxygen binding studies at various butylurea concentrations show that the linkage between oxygen and butylurea binding is small. The influence of oxygen and butylurea on hemoglobin S solubility was determined by birefringence measurements. The results were interpreted by use of the Gibbs-Duhem equation which combined ligand binding expressions with the non-ideal solution properties and properties of the gel phase. The predicted influence of oxygen and butylurea upon the solubilities of hemoglobin S agrees with experimentally determined values.     

Properties of a recombinant human hemoglobin double mutant: sickle hemoglobin with Leu-88(beta) at the primary aggregation site substituted by Ala.

A recombinant double mutant of hemoglobin (Hb), E6V/L88A(beta), was constructed to study the strength of the primary hydrophobic interaction in the gelation of sickle Hb, i.e., that between the mutant Val-6(beta) of one tetramer and the hydrophobic region between Phe-85(beta) and Leu-88(beta) on an adjacent tetramer. Thus, a construct encoding the donor Val-6(beta) of the expressed recombinant HbS and a second mutation encoding an Ala in place of Leu-88(beta) was assembled. The doubly mutated beta-globin gene was expressed in yeast together with the normal human alpha-chain, which is on the same plasmid, to produce a soluble Hb tetramer. Characterizations of the Hb double mutant by mass spectrometry, by HPLC, and by peptide mapping of tryptic digests of the mutant beta-chain were consistent with the desired mutations. The absorption spectra in the visible and the ultraviolet regions were practically superimposable for the recombinant Hb and the natural Hb purified from human red cells. Circular dichroism studies on the overall structure of the recombinant Hb double mutant and the recombinant single mutant, HbS, showed that both were correctly folded. Functional studies on the recombinant double mutant indicated that it was fully cooperative. However, its gelation concentration was significantly higher than that of either recombinant or natural sickle Hb, indicating that the strength of the interaction in this important donor-acceptor region in sickle Hb was considerably reduced even with such a conservative hydrophobic mutation.     

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.     

Frequency and origin of haplotypes associated with the beta-globin gene cluster in individuals with trait and sickle cell anemia in the Atlantic and Pacific coastal regions of Colombia

Sickle cell anemia is a genetic disease with high prevalence in people of African descent. There are five typical haplotypes associated with this disease and the haplotypes associated with the beta-globin gene cluster have been used to establish the origin of African-descendant people in America. In this work, we determined the frequency and the origin of haplotypes associated with hemoglobin S in a sample of individuals with sickle cell anemia (HbSS) and sickle cell hemoglobin trait (HbAS) in coastal regions of Colombia. Blood samples from 71 HbAS and 79 HbSS individuals were obtained. Haplotypes were determined based on the presence of variable restriction sites within the β-globin gene cluster. On the Pacific coast of Colombia the most frequent haplotype was Benin, while on the Atlantic coast Bantu was marginally higher than Benin. Eight atypical haplotypes were observed on both coasts, being more diverse in the Atlantic than in the Pacific region. These results suggest a differential settlement of the coasts, dependent on where slaves were brought from, either from the Gulf of Guinea or from Angola, where the haplotype distributions are similar. Atypical haplotypes probably originated from point mutations that lost or gained a restriction site and/or by recombination events.     

A model for the sickle hemoglobin fiber using both mutation sites

The standard molecular model of the fiber of the sickle hemoglobin (HbS: beta6 Glu-->Val) has been revised to allow both beta6 mutation sites to participate in intermolecular contacts, rather than only one beta6 site as previously thought, for four molecules per 14-molecule fiber cross section. This structure accurately predicts the copolymerization of hybridized mixtures of HbS with HbA or HbC (beta6 Glu-->Lys), which could not be reconciled with prior models in which only half the beta6 sites were required for assembly. This model suggests new contacts within the fiber and raises the question of whether these cross-linked double strands could possess added stability important in such processes as nucleation.     

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.