A model for the sickle hemoglobin fiber using both mutation sites

The Sickle-Cell Fiber Revisited

Sickle cell disease is the consequence of a single point mutation on the surface of the β 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.

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.

Targeting HbS Polymerization

The mutation of β6 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.

Probing the Twisted Structure of Sickle Hemoglobin Fibers via Particle Simulations

Polymerization of sickle hemoglobin (HbS) is the primary pathogenic event of sickle cell disease. For insight into the nature of the HbS polymer fiber formation, we develop a particle model-resembling a coarse-grained molecular model-constructed to match the intermolecular contacts between HbS molecules. We demonstrate that the particle model predicts the formation of HbS polymer fibers by attachment of monomers to rough fiber ends and the growth rate increases linearly with HbS concentration. We show that the characteristic 14-molecule fiber cross section is preserved during growth. We also correlate the asymmetry of the contact sites on the HbS molecular surface with the structure of the polymer fiber composed of seven helically twisted double strands. Finally, we show that the same asymmetry mediates the mechanical and structural properties of the HbS polymer fiber.

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 β6 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.

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.

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 β 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 β-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 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.

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.

Heterogeneous nucleation in sickle hemoglobin: experimental validation of a structural mechanism

Sickle hemoglobin polymerizes by two types of nucleation: homogeneous nucleation of aggregates in solution, and heterogeneous nucleation on preexisting polymers. It has been proposed that the same contact that is made in the interior of the polymer between the mutant site beta6 and its receptor pocket on an adjacent molecule is the primary contact site for the heterogeneous nucleus. We have constructed cross-linked hybrid molecules in which one beta-subunit is from HbA with Glu at beta6, and the other is from HbS with a Val at beta6. We measured solubility (using sedimentation) and polymerization kinetics (using laser photolysis) on cross-linked hybrids, and cross-linked HbS as controls. We find approximately 4000 times less heterogeneous nucleation in the cross-linked AS molecules than in cross-linked HbS, in strong confirmation of the proposal. In addition, changes in stability of the nucleus support a further proposal that more than one beta6 contact is involved in the homogeneous nucleus.

Sickle hemoglobin polymer stability probed by triple and quadruple mutant hybrids

As part of an effort to understand the interactions in HbS polymerization, we have produced and studied a recombinant triple mutant, D6A(alpha)/D75Y(alpha)/E121R(beta), and a quadruple mutant comprising the preceding mutation plus the natural genetic mutation of sickle hemoglobin, E6V(beta). These recombinant hemoglobins expressed in yeast were extensively characterized, and their structure and oxygen binding cooperativity were found to be normal. Their tetramer-dimer dissociation constants were within a factor of 2 of HbA and HbS. Polymerization of these mutants mixed with HbS was investigated by a micromethod based on volume exclusion by dextran. The elevated solubility of mixtures of HbS with HbA and HbF in dextran could be accurately predicted without any variable parameters. Relative to HbS, the copolymerization probability of the quadruple mutant/HbS hybrid was found to be 6.2, and the copolymerization probability for the triple mutant/HbS hybrid was 0.52. The pure quadruple mutant had a solubility slightly above that of its hybrid with HbS. One way to explain these results is to require significant cis-trans differences in the polymer and that HbA assemble above 42.5 g/dl. A second way to explain these data is by the modification of motional freedom, thereby changing vibrational entropy in the polymer.