Voxelotor does not inhibit sickle hemoglobin fiber formation upon complete deoxygenation.

The drug voxelotor (commercially known as Oxbryta) has been approved by the US Food and Drug Administration for the treatment of sickle cell disease. It is known to reduce disease-causing sickling by inhibiting the transformation of the non-polymerizing, high-oxygen-affinity R quaternary structure of sickle hemoglobin into its polymerizing, low-affinity T quaternary structure. It has not been established whether the binding of the drug has anti-sickling effects beyond restricting the change of quaternary structure. By using a laser photolysis method that employs microscope optics, we have determined that fully deoxygenated sickle hemoglobin will assume the T structure. We show that the nucleation rates essential to generate the sickle fibers are not significantly affected by voxelotor. The method employed here should be useful for determining the mechanism of sickling inhibition for proposed drugs.

The flow of sickle blood in glass capillaries: Fundamentals and potential applications.

We have characterized the imbibed horizontal flow of sickle blood into 100-µm-diameter glass capillaries. We find that blood containing sickled cells typically traverses the capillaries between three and four times as slowly as oxygenated cells from the same patient for all genotypes tested, including SS, AS, SC and Sß+ thalassemia blood. Blood from SS patients treated with hydroxyurea has a viscosity intermediate between the SS and AA values. Blood containing cells that are not rigidified, such as normal red cells or oxygenated sickle cells, follows a simple Lucas-Washburn flow throughout the length of the 3-cm capillary. By fitting the flexible-cell data to the Lucas-Washburn model, a viscosity can be derived that is in good agreement with previous measurements over a range of volume fractions and is obtained using an apparatus that is far more complex. Deoxygenation sickles and thus rigidifies the cells, and their flow begins as Lucas-Washburn, albeit with higher viscosity than flexible cells. However, the flow further slows as a dense mass of cells forms behind the meniscus and increases in length as flow progresses. By assuming that the dense mass of cells exerts a frictional force proportional to its length, we derive an equation that is formally equivalent to vertical imbibition, even though the flow is horizontal, and this equation reproduces the observed behavior well. We present a simple theory using activity coefficients that accounts for this viscosity and its variation without adjustable parameters. In the course of control experiments, we have found that deoxygenation increases the flexibility of normal human red cells, an observation only recently published for mouse cells and previously unreported for human erythrocytes. Together, these studies form the foundation for an inexpensive and rapid point-of-care device to diagnose sickle cell disease or to determine blood viscosity in resource-challenged settings.

The delay time in sickle cell disease after 40 years: A paradigm assessed.

Sickle hemoglobin polymerization commences with a striking latency period, called a "delay time" followed by abrupt polymer formation. The delay time is exceedingly concentration dependent. This discovery (40 years ago) led to the "kinetic hypothesis," that is, that the pathophysiology was related to the relationship between the delay time and the capillary transit. The delay time is well described by a double-nucleation mechanism of polymer formation. In macroscopic volumes, the delay time is highly reproducible, but in small volumes such as erythrocytes, under certain conditions, the intrinsic delay time can be augmented by a stochastic delay owing to random waiting times for the first nucleus to form. This lengthens the average delay and adds further protection from vaso-occlusion. When oxygen removal is not sudden, the growth of polymers after the delay time is limited by the rate of oxygen removal, further lengthening the time before occlusion may occur. This is important if some polymers have remained in the cell after pulmonary transit as their presence otherwise would obliterate any delay. The difficulty of deforming a cell once polymerized rationalizes the "two-step" model of vaso-occlusion in which a postcapillary adhesion event is followed by a sickling logjam. The delay time that is required is therefore generalized to be the delay time for an erythrocyte to move beyond regions in the venuoles where adherent cells have reduced the available lumen. The measurements of delay times correlate well with the severity of sickling syndromes. They also correlate with the improvements owing to the administration of hydroxyurea.

Dissecting the energies that stabilize sickle hemoglobin polymers.

Sickle hemoglobin forms long, multistranded polymers that account for the pathophysiology of the disease. The molecules in these polymers make significant contacts along the polymer axis (i.e., axial contacts) as well as making diagonally directed contacts (i.e., lateral contacts). The axial contacts do not engage the mutant ß6 Val and its nonmutant receptor region on an adjacent molecule, in contrast to the lateral contacts which do involve the mutation site. We have studied the association process by elastic light scattering measurements as a function of temperature, concentration, and primary and quaternary structure, employing an instrument of our own construction. Even well below the solubility for polymer formation, we find a difference between the association behavior of deoxy sickle hemoglobin molecules (HbS), which can polymerize at higher concentration, in comparison to COHbS, COHbA, or deoxygenated Hemoglobin A (HbA), none of which have the capacity to form polymers. The nonpolymerizable species are all quite similar to one another, and show much less association than deoxy HbS. We conclude that axial contacts are significantly weaker than the lateral ones. All the associations are entropically favored, and enthalpically disfavored, typical of hydrophobic interactions. For nonpolymerizable Hemoglobin, ΔH(o) was 35 ± 4 kcal/mol, and ΔS was 102.7 ± 0.5 cal/(mol-K). For deoxyHbS, ΔH(o) was 19 ± 2 kcal/mol, and ΔS was 56.9 ± 0.5 cal/(mol-K). The results are quantitatively consistent with the thermodynamics of polymer assembly, suggesting that the dimer contacts and polymer contacts are very similar, and they explain a previously documented significant anisotropy between bending and torsional moduli. Unexpectedly, the results also imply that a substantial fraction of the hemoglobin has associated into dimeric species at physiological conditions.

The Sickle-Cell Fiber Revisited.

Sickle cell disease is the consequence of a single point mutation on the surface of the ß chains of the hemoglobin molecule leading to the formation of rigid polymers that disrupt circulation. It has long been established that the polymers are comprised of seven pairs of double strands that are twisted replicas of the double strands found in crystals. Here, we review several newer developments that elaborate on that simple model and provide deeper insights into the process.

An α-chain modification rivals the effect of fetal hemoglobin in retarding the rate of sickle cell fiber formation.

Adults with sickle cell disease bear a mutation in the ß-globin gene, leading to the expression of sickle hemoglobin (HbS; α2ßS2). Adults also possess the gene for γ-globin, which is a component of fetal hemoglobin (HbF, α2γ2); however, γ-chain expression normally ceases after birth. As HbF does not form the fibers that cause the disease, pharmacological and gene-modifying interventions have attempted to either reactivate expression of the γ chain or introduce a gene encoding a modified ß chain having γ-like character. Here, we show that a single-site modification on the α chain, αPro114Arg, retards fiber formation as effectively as HbF. Because this addition to the repertoire of anti-sickling approaches acts independently of other modifications, it could be coupled with other therapies to significantly enhance their effectiveness.

The physical foundation of vasoocclusion in sickle cell disease.

The pathology of sickle cell disease arises from the occlusion of small blood vessels because of polymerization of the sickle hemoglobin within the red cells. We present measurements using a microfluidic method we have developed to determine the pressure required to eject individual red cells from a capillary-sized channel after the cell has sickled. We find that the maximum pressure is only ∼100 Pa, much smaller than typically found in the microcirculation. This explains why experiments using animal models have not observed occlusion beginning in capillaries. The magnitude of the pressure and its dependence on intracellular concentration are both well described as consequences of sickle hemoglobin polymerization acting as a Brownian ratchet. Given the recently determined stiffness of sickle hemoglobin gels, the observed obstruction seen in sickle cell disease as mediated by adherent cells can now be rationalized, and surprisingly suggests a window of maximum vulnerability during circulation of sickle cells.

The growth of sickle hemoglobin polymers.

The measurement of polymer growth is an essential element in characterization of assembly. We have developed a precise method of measuring the growth of sickle hemoglobin polymers by observing the time required for polymers to traverse a photolytically produced channel between a region in which polymers are created and a detection region. The presence of the polymer is functionally detected by observing its ability to create new polymers through the well-established process of heterogeneous nucleation. Using this method, we have determined the rate constants for monomer addition to and release from polymer ends, as well as their temperature dependences. At 25°C we find k(+) = 84 ± 2 mM⁻¹ s⁻¹ and k(-) = 790 ± 80 molecules/s from each end. These numbers are in accord with differential interference contrast measurements, and their ratio gives a solubility measured on individual fibers. The single-fiber solubility agrees with that measured in sedimentation experiments. The concentration dependence of the monomer addition rate is consistent with monomer addition, but not oligomer addition, to growing polymers. The concentration dependence suggests the presence of an activation enthalpy barrier, and the rate of monomer addition is not diffusion-limited. Analysis of the temperature dependence of the monomer addition rate reveals an apparent activation energy of 9.1 ± 0.6 kcal/mol.

Nucleation of sickle hemoglobin mixed with hemoglobin A: experimental and theoretical studies of hybrid-forming mixtures.

Sickle hemoglobin (HbS) is a point mutation of the two ß subunits in normal Hb (HbA) that leads to nucleated polymerization and accompanying pathology. We measured the rates of homogeneous and heterogeneous nucleation of HbS in the presence of up to 50% HbA under conditions in which hybrid HbAS molecules will also form. The replacement of 50% of HbS by HbA slows polymerization by factors of ∼100 in the physiological range, which is substantially less than previously thought. To provide a theoretical description of these data, we extended the double nucleation model for HbS polymerization to conditions in which hybridized mixtures are present. Measurements of homogeneous nucleation and the theory agree only when at least one of the molecules in the nucleus is not a hybrid. We attribute this to the necessary presence in the nucleus of a molecule that utilizes both ß-subunit mutation sites in intermolecular contacts, whereas the remaining molecules engage only one of the mutation sites. Heterogeneous nucleation appears to require an even greater number of nonhybrid molecules, presumably because of the need for the nucleus to attach to the polymer as well as to form internal bonds. These results also provide insights into the pathophysiology of sickle cell disease, including the occasional severe events that strike persons in whom both HbS and HbA are expressed, a condition known as sickle trait. The studies reported here are necessary for understanding physiologically relevant polymerization in the presence of ligands as well as therapeutically relevant copolymerizing inhibitors.

The microrheology of sickle hemoglobin gels.

Sickle cell disease is a rheological disease, yet no quantitative rheological data exist on microscopic samples at physiological concentrations. We have developed a novel method for measuring the microrheology of sickle hemoglobin gels, based on magnetically driven compression of 5- to 8-microm-thick emulsions containing hemoglobin droplets approximately 80 microm in diameter. Using our method, by observing the expansion of the droplet area as the emulsion is compressed, we were able to resolve changes in thickness of a few nanometers with temporal resolution of milliseconds. Gels were formed at various initial concentrations and temperatures and with different internal domain structure. All behaved as Hookean springs with Young's modulus from 300 to 1500 kPa for gels with polymerized hemoglobin concentration from 6 g/dl to 12 g/dl. For uniform, multidomain gels, Young's modulus mainly depended on the terminal concentration of the gel rather than the conditions of formation. A simple model reproduced the quadratic dependence of the Young's modulus on the concentration of polymerized hemoglobin. Partially desaturated samples also displayed quadratic concentration dependence but with a smaller proportionality coefficient, as did samples that were desaturated in steps; such samples were significantly less rigid than gels formed all at once. The magnitude of the Young's modulus provides quantitative support for the dominant models of sickle pathophysiology.

Fiber depolymerization: fracture, fragments, vanishing times, and stochastics in sickle hemoglobin.

The well-characterized rates, mechanisms, and stochastics of nucleation-dependent polymerization of deoxyhemoglobin S (HbS) are important in governing whether or not vaso-occlusive sickle cell crises will occur. The less well studied kinetics of depolymerization may also be important, for example in achieving full dissolution of polymers in the lungs, in resolution of crises and/or in minimizing gelation-induced cellular damage. We examine depolymerization by microscopic observations on depolymerizing HbS fibers, by Monte Carlo simulations and by analytical characterization of the mechanisms. We show that fibers fracture. Experimental scatter of rates is consistent with stochastic features of the analytical model and Monte Carlo results. We derive a model for the distribution of vanishing times and also show the distribution of fracture-dependent fiber fragment lengths and its time dependence. We describe differences between depolymerization of single fibers and bundles and propose models for bundle dissolution. Our basic model can be extended to dissolution of gels containing many fibers and is also applicable to other reversible linear polymers that dissolve by random fracture and end-depolymerization. Under the model, conditions in which residual HbS polymers exist and facilitate repolymerization and thus pathology can be defined; whereas for normal polymers requiring cyclic polymerization and depolymerization for function, conditions for rapid cycling due to residual aggregates can be identified.

Free energy of sickle hemoglobin polymerization: a scaled-particle treatment for use with dextran as a crowding agent.

Fundamental to the analysis of protein polymerization is the free energy of association, typically determined from solubility. It has been previously shown that concentrated 70 kDa dextran lowers the solubility of sickle hemoglobin, due to molecular crowding, and provides a useful ranking tool for the effects of inhibitors and molecular modifications. Because hemoglobin occupies a substantial volume as well, crowding effects of both hemoglobin and dextran contribute to the nonideality of the solution. We show how scaled-particle theory can be used to account for both types of crowding, thus allowing the determination of solubility in the absence of dextran, given data measured in its presence. The approach adopted approximates dextran as a sphere with a volume that decreases as the concentration of dextran increases. We use an asymptotic relation to describe the volume, which decreases nearly linearly by a factor of two over the range studied, from 60 to 230 mg/ml. This compression is similar to previously observed compression of sephadex beads and ficoll solutions. In the limit of low hemoglobin concentrations, the theory reduces to the previously-used approach of Ogston. Our method therefore provides a means of measuring the free energy of association of molecules that occupy significant volume fractions, even when assisted by the crowding of dextran and we present a tabulation of all known free energies of polymerization of sickle hemoglobin measured in the presence of dextran.

Metastable polymerization of sickle hemoglobin in droplets.

Sickle cell disease arises from a genetic mutation of one amino acid in each of the two hemoglobin beta chains, leading to the polymerization of hemoglobin in the red cell upon deoxygenation, and is characterized by vascular crises and tissue damage due to the obstruction of small vessels by sickled cells. It has been an untested assumption that, in red cells that sickle, the growing polymer mass would consume monomers until the thermodynamically well-described monomer solubility was reached. By photolysing droplets of sickle hemoglobin suspended in oil we find that polymerization does not exhaust the available store of monomers, but stops prematurely, leaving the solutions in a supersaturated, metastable state typically 20% above solubility at 37 degrees C, though the particular values depend on the details of the experiment. We propose that polymer growth stops because the growing ends reach the droplet edge, whereas new polymer formation is thwarted by long nucleation times, since the concentration of hemoglobin is lowered by depletion of monomers into the polymers that have formed. This finding suggests a new aspect to the pathophysiology of sickle cell disease; namely, that cells deoxygenated in the microcirculation are not merely undeformable, but will actively wedge themselves tightly against the walls of the microvasculature by a ratchet-like mechanism driven by the supersaturated solution.

Targeting HbS Polymerization.

The mutation of ß6 from glu to val in hemoglobin is responsible for the polymer formation that leads to vaso-occlusion, and a range of severe consequences in sickle cell disease. The treatment of the disease can be addressed in many ways, but the prevention of polymer formation is one of the most fundamental approaches one can take. Such prevention includes affecting the polymer structure, or dilution of the fraction of polymerizable hemoglobin. The latter approach includes (1) induction of HbF, which does not itself, nor in hybrid form, join sickle polymers, or (2) restricting the allosteric change in hemoglobin that occurs in oxygen delivery, and which is required for polymer formation. These approaches will be critically reviewed, as well as the most recent developments that show the benefits of simply swelling the volume of the red cell.

Solid nuclei and liquid droplets: A parallel treatment for 3 phase systems.

For solid phase self assembly into crystals or large diameter polymers, the presence of a liquid-liquid demixing transition has been known to have an accelerating effect on the nucleation process. We present a novel approach to the description of accelerated nucleation in which the formation of solid phase aggregates and liquid-like aggregates compete as parallel pathways to formation of dense phases. The central idea is that the small aggregates that would ultimately form the liquid phase are sufficiently labile to sample the configurations that would form the solid, so that the growing cluster begins as a liquid, and switches into growth as a solid when the aggregates have equal free energies. This can accelerate the reaction even when the liquid-demixed state is thermodynamically unfavorable. The rate-limiting barrier is therefore the energy at which there is a transition between liquid and solid, and the effective nucleus size is then concentration independent, even though for both nucleated demixing and nucleated crystallization, the nucleus size does depend on concentration. These ideas can be expressed in a chemical potential formalism that has been successfully used in nucleation of sickle hemoglobin, but not to our knowledge previously employed in describing LLD processes. The method is illustrated by considering existing data on Lysozyme.

Water, Ions, and Hemoglobin: Effects on Allostery and Polymerization.

Proteins that function in aqueous solution can be perturbed by the solvent. Here we present experimental studies on two such interactions in the hemoglobin molecule. (1) Hemoglobin's oxygen binding is altered by introduction of crowding species or osmoticants, such as sucrose, through the linked binding of ions such as Cl or CO2, but not otherwise. This rules out a significant role of buried surface in the allosteric energetics. (2) Sickle hemoglobin (HbS) polymerizes more readily in high concentrations of phosphate buffer. Such polymerization is analyzed quantitatively here for the first time in terms of the double nucleation mechanism. The changes in solubility are found to account for the increase in monomer addition rates and nucleation rates without requiring additional parameter adjustments. In the analysis, we also show how the analytical formulation of HbS nucleation may be adapted to include water that occupies the interstices between the assembled molecules. While such a "correction" has been applied to the equilibrium process, it has not previously been applied to the nucleation process.

The Hb A variant (beta73 Asp-->Leu) disrupts Hb S polymerization by a novel mechanism.

Polymerization of a 1:1 mixture of hemoglobin S (Hb S) and the artificial mutant HbAbeta73Leu produces a dramatic morphological change in the polymer domains in 1.0 M phosphate buffer that are a characteristic feature of polymer formation. Instead of feathery domains with quasi 2-fold symmetry that characterize polymerization of Hb S and all previously known mixtures such as Hb A/S and Hb F/S mixtures, these domains are compact structures of quasi-spherical symmetry. Solubility of Hb S/Abeta73Leu mixtures was similar to that of Hb S/F mixtures. Kinetics of polymerization indicated that homogeneous nucleation rates of Hb S/Abeta73Leu mixtures were the same as those of Hb S/F mixtures, while exponential polymer growth (B) of Hb S/Abeta73Leu mixtures were about three times slower than those of Hb S/F mixtures. Differential interference contrast (DIC) image analysis also showed that fibers in the mixture appear to elongate between three and five times more slowly than in equivalent Hb S/F mixtures by direct measurements of exponential growth of mass of polymer in a domain. We propose that these results of Hb S/Abeta73Leu mixtures arise from a non-productive binding of the hybrid species of this mixture to the end of the growing polymer. This "cap" prohibits growth of polymers, but by nature is temporary, so that the net effect is a lowered growth rate of polymers. Such a cap is consistent with known features of the structure of the Hb S polymer. Domains would be more spherulitic because slower growth provides more opportunity for fiber bending to spread domains from their initial 2-fold symmetry. Moreover, since monomer depletion proceeds more slowly in this mixture, more homogeneous nucleation events occur, and the resulting gel has a far more granular character than normally seen in mixtures of non-polymerizing hemoglobins with Hb S. This mixture is likely to be less stiff than polymerized mixtures of other hybrids such as Hb S with HbF, potentially providing a novel approach to therapy.