Kinetics of sickle hemoglobin polymerization. III. Nucleation rates determined from stochastic fluctuations in polymerization progress curves

The polymerization kinetics of sickle cell hemoglobin are found to exhibit stochastic variations when observed in very small volumes (approximately 10(-10) cm3). The distribution of progress curves has been measured at several temperatures for a 4.50 mM-hemoglobin S sample using a laser-photolysis, light-scattering technique. The progress curves at a given temperature are superimposable when translated along the time axis, showing that the variability of the kinetic progress curves results primarily from fluctuations in the time at which polymerization is initiated. The shapes of the initial part of the progress curves are well-fitted using the functional form I(t) = Io + As exp (Bt), derived from a dual nucleation model. When the distribution of the measured tenth times is broad, the rate of homogeneous nucleation can be obtained by fitting the exponential tail of the distribution. As the distribution sharpen, the rate of homogeneous nucleation can be estimated by modelling the width of the distribution function using a simple Monte-Carlo simulation of the polymerization kinetics. Using the rates of homogeneous nucleation obtained from the distributions, the rates of heterogeneous nucleation and polymer growth can be obtained from the experimental parameters As and B. The resulting nucleation rates are roughly 1000 times greater than those obtained from an analysis of bulk kinetic data. The results provide strong support for the dual-nucleation mechanism and show that the distribution of progress curves provides a powerful independent method for measuring the rate of homogeneous nucleation and thereby obtaining values for the other principal rates of the mechanism.     

Kinetics of sickle hemoglobin polymerization. II. A double nucleation mechanism

A double nucleation mechanism for the polymerization of sickle hemoglobin is described. The mechanism accounts for all of the major kinetic observations: the appearance of a delay, the high concentration dependence of the delay time, and the stochastic behavior of slowly polymerizing samples in small volumes. The mechanism postulates that there are two pathways for polymer formation: polymerization is initiated by homogeneous nucleation in the solution phase, followed by nucleation of additional polymers on the surface of existing ones. This second pathway is called heterogeneous nucleation. Since the surface of polymers is continuously increasing with time, heterogeneous nucleation provides a mechanism for the extreme autocatalysis that is manifested as an apparent delay in the kinetic progress curves. In this mechanism, each spherulitic domain of polymers is considered to be initiated by a single homogeneous nucleation event. The mechanism explains the irreproducibility of the delay time for single domain formation as arising from stochastic fluctuations in the time at which the homogeneous nucleus for the first polymer is formed. Integration of the linearized rate equations that describe this model results in a simple kinetic form: A[cosh(Bt)-1] (Bishop & Ferrone, 1984). In the accompanying paper (Ferrone et al., 1985) it was shown that the initial 10 to 15% of progress curves, with delay times varying from a few milliseconds to over 10(5) seconds, is well fit by this equation. In this paper, we present an approximate statistical thermodynamic treatment of the equilibrium nucleation processes that shows how the nucleus sizes and nucleation equilibrium constants depend on monomer concentration. The equilibrium model results in expressions for B and B2A as a function of monomer concentration in terms of five adjustable parameters: the bimolecular addition rate of a monomer to the growing aggregate, the fraction of polymerized monomers that serve as heterogeneous nucleation sites, the free energy of intermolecular bonding within the polymer, and two parameters that describe the free energy change as a function of size for the bonding of the heterogeneous nucleus to a polymer surface. This model provides an excellent fit to the data for B and B2A as a function of concentration using physically reasonable parameters. The model also correctly predicts the time regime in which stochastic behavior is observed for polymerization in small volumes.     

Solubility of fluoromethemoglobin S: effect of phosphate and temperature on polymerization

The polymerization properties of the fully liganded fluoromet derivative of hemoglobin S (FmetHb S) were investigated by electron microscopy and absorption spectroscopy. Polymerization progress curves, as measured by increasing sample turbidity at 700 nm, exhibit a delay time (t(d)) consistent with the double nucleation mechanism. The pattern of fiber growth, as monitored by electron microscopy, is also indicative of a heterogeneous nucleation process, and dimensions of the fibers were found to be comparable to that of deoxyHb S. The polymerization rate constant (1/t(d)) depends exponentially on Hb S concentration, and the size of the homogeneous and heterogeneous nuclei also depend on FmetHb S concentration. As for deoxyHb S, higher concentrations of protein and phosphate favor fiber formation, while lower temperatures inhibit polymerization. Solubility experiments reveal, however, that eight times more FmetHb S is required for polymerization. The current studies further show that reaction order is independent of phosphate concentration if Hb S activity and not concentration is considered. The allosteric effector, inositol hexaphosphate (IHP), promotes fiber formation, and temperature-dependent reaggregation of FmetHb S suggests that IHP stabilizes pregelation aggregates. These studies show that FmetHb S resembles deoxyHb S in many of its polymerization properties; however, IHP-bound FmetHb S potentially provides a unique avenue for future studies of the early stages of Hb S polymerization and the effect of tertiary and quaternary protein structure on the polymerization process.     

Kinetics of the polymerization of hemoglobin S: studies below normal erythrocyte hemoglobin concentration.

The kinetics of polymerization of deoxyhemoglobin S have been studied by measuring transverse water proton relaxation times (T₂) in hemoglobin solutions. As seen by other techniques, the kinetic profile consists of a delay time followed by a decrease in T₂ during polymerization. The length of the delay time can be decreased and the rate of change of T₂ can be increased by increasing the concentration of hemoglobin S or non-gelling hemoglobin or ovalbumin. At a total protein concentration of about 210 mg/ml the kinetic profiles in all three cases are indistinguishable suggesting that a non-specific protein-protein interaction may be involved in the kinetics of polymerization. In addition, it is suggested that no polymer formation occurs during the delay period.     

Fluctuations in the polymerization of sickle hemoglobin. A simple analytic model

Using the stochastic theory of chemical reactions and the theory of first passage times, a simple analytic expression is derived for the distribution of delay times that has been observed in studies of the polymerization kinetics of sickle hemoglobin under conditions where the polymerization progress curves exhibit stochastic variation. The rate of homogeneous nucleation can be readily extracted from such experiments using this expression. This work constitutes a significant addition to the rather limited number of examples where contact can be successfully made between the stochastic theory of chemical kinetics and experiment.     

The effects of erythrocyte membranes on the nucleation of sickle hemoglobin

Pathology in sickle cell disease begins with nucleation-dependent polymerization of deoxyhemoglobin S into stiff, rodlike fibers that deform and rigidify red cells. We have measured the effect of erythrocyte membranes on the rate of homogeneous nucleation in sickle hemoglobin, using preparations of open ghosts (OGs) with intact cytoskeletons from sickle (SS) and normal adult (AA) red cells. Nucleation rates were measured by inducing polymerization by laser photolysis of carboxy sickle hemoglobin and observing stochastic variation of replicate experiments of the time for the scattering signals to reach 10% of their respective maxima. By optical imaging of membrane fragments added to a hemoglobin solution we contrast the rate of nucleation immediately adjacent to membrane fragments with nucleation in a region of the same solution but devoid of membranes. From analysis of 29,272 kinetic curves obtained, we conclude that the effect of AA OGs is negligible (10% enhancement of nucleation rates +/-20%), whereas SS OGs caused 80% enhancement (+/-20%). In red cells, where more membrane surface is available to Hb, this implies enhancement of nucleation by a factor of 6. These experiments represent a 10-fold improvement in precision over previous approaches and are the first direct, quantitative measure of the impact of erythrocyte membranes on the homogeneous nucleation process that is responsible for polymer initiation in sickle cell disease.     

Nanosecond time-resolved absorption studies of human oxyhemoglobin photolysis intermediates.

The time-resolved spectra of photoproducts from ligand photodissociation of oxyhemoglobin are measured in the Soret spectral region for times from 10 ns to 320 microseconds after laser photolysis. Four processes are detected at a heme concentration of 80 microM: a 38-ns geminate recombination, a 137-ns tertiary relaxation, and two bimolecular processes for rebinding of molecular oxygen. The pseudo-first-order rate constants for rebinding to the alpha and beta subunits of hemoglobin are 3.2 x 10(4) s-1 (31 microseconds lifetime) and 9.4 x 10(4) s-1 (11 microseconds lifetime), respectively. The significance of kinetic measurements made at different heme concentrations is discussed in terms of the equilibrium compositions of hemoglobin tetramer and dimer mixtures. The rebinding rate constants for alpha and beta chains are observed to be about two times slower in the dimer than in the tetramer, a finding that appears to support the observation of quaternary enhancement in equilibrium ligand binding by hemoglobin tetramers.     

Monomer diffusion into polymer domains in sickle hemoglobin.

The gelation of sickle hemoglobin includes the formation of spherulitic arrays of polymers, known as polymer domains, which are an intrinsic result of the polymer formation mechanism. We have observed the diffusion of monomers into domains as they form, which substantially increases the total concentration of hemoglobin within the domain. The maximum total concentration attained is comparable with the pellet concentration of 0.5-0.55 g/cm3 obtained in sedimentation experiments. The half time for this process is approximately 50 s for domains of 25 microns radius, and is approximately independent of temperature. The shape of the diffusion progress curves as well as the deduced diffusion constants, and their weak temperature dependence are consistent with a simple model of hemoglobin monomer diffusion into the domain.     

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 line-width, 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 deoxygenation 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 are affected 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 degrees C to 500 Hz at -36 degrees 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 degrees C for measurements at 44.4 MHz and -50 degrees 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 irrotationally bound water, is altered during the sickling process.     

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

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

Homogeneous nucleation in sickle hemoglobin: stochastic measurements with a parallel method.

The homogeneous nucleation rate for sickle hemoglobin polymerization has been measured for concentrations from 3.9 to 4.9 mM and temperatures from 13 degrees C to 35 degrees C by observing the stochastic fluctuations of the time to complete 10% of the reaction after photolysis of the carboxy derivative. To allow efficient data collection, a mesh was used to divide the photolysis beam into an array of smaller beams, which allowed parallel observation of about 100 different regions. Nucleation rates measured here are consistent with more restricted previously published data and, when combined with directly measured monomer addition rates, are consistent with previous analysis of progress curves. By describing these rates with equilibrium nucleation theory, the concentration of nuclei and hence their stability can be ascertained. Consequently, the chemical potential by which a monomer is attached to the polymer is determined. This attachment energy ranges from -6.6 to -8.0 kcal/mol between 15 degrees C and 35 degrees C. The enthalpic part of that chemical potential is found to be equal to the enthalpy determined by solubility measurements, as expected from thermodynamic considerations. The entropic portion of the contact chemical potential contributes from -21.4 to -8.7 kcal/mol. The vibrational chemical potential of monomers in the polymer ranges from -25.7 to -27.4 kcal/mol over the same temperatures.     

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.     

Mutational analysis of phenylalanine beta 85 in the valine beta 6 acceptor pocket during hemoglobin S polymerization.

Hemoglobin (Hb) S containing Leu, Ala, Thr, or Trp substitutions at beta 85 were made and expressed in yeast in an effort to evaluate the role of Phe-beta 85 in the acceptor pocket during polymerization of deoxy Hb S. The four Hb S variants have the same electrophoretic mobility as Hb S, and these beta 85 substitutions do not significantly affect heme-globin interactions and tetramer helix content. Hb S containing Trp-beta 85 had decreased oxygen affinity, whereas those with Leu-, Ala-, and Thr-beta 85 had increased oxygen affinity. All four supersaturated beta 85 variants polymerized with a delay time as does deoxy Hb S. This is in contrast to deoxy Hb S containing Phe-beta 88, Ala-beta 88, Glu-beta 88, or Glu-beta 85, which polymerized with no clear delay time (Adachi K, Konitzer P, Paulraj CG, Surrey S, 1994, J Biol Chem 269:17477-17480; Adachi K, Reddy LR, Surrey S, 1994, J Biol Chem 269:31563-31566). Leu substitution at beta 85 accelerated deoxy Hb S polymerization, whereas Ala, Thr, or Trp substitution inhibited polymerization. The length of the delay time and total polymer formed for these beta 85 Hb S variants depended on hemoglobin concentration in the same fashion as for deoxy Hb S: the higher the concentration, the shorter the delay time and the more polymer formed. Critical concentrations required for polymerization of deoxy Hb SF veta 85L, Hb SF beta 85A, Hb SF beta 85T, and Hb SF beta 85W are 0.65-, 2.2-, 2.5- and 3-fold higher, respectively, than Hb S.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Effect of peroxodisulphate ions on functional behaviour of hemoglobin.

The influence of ammonium peroxodisulphate on the functional state of human hemoglobin was studied. The investigation techniques included: laser photolysis, spectrophotometry and pH measurements. Two different actions of the peroxodisulphate ions upon hemoglobin seem to occur; a) a proton consuming process and an increase of the 4th CO-binding rate constant, l'4, but not yet oxidation of the heme iron (when S2O8(2-) and heme concentrations were of the same order), and b) a marked oxidation effect (when S2O8(2-) was added in excess).     

Facilitation of Hb S polymerization by the substitution of Glu for Gln at beta 121

In an effort to clarify the role of Glu-beta 121 of Hb S molecules in polymerization, we studied the solubility and kinetics of polymerization of various mixtures of deoxyhemoglobins S (Glu-beta 6----Val) and D Los Angeles (Glu-beta 121----Gln). It is known that patients with Hb S-D Los Angeles have a relatively severe clinical course. Mixtures of Hb S and Hb D Los Angeles polymerized after a distinct delay time, the length of which depended on the initial hemoglobin concentration and the fraction of Hb S in the mixture. There was a linear relationship between the logarithmic plot of delay time and initial hemoglobin concentration. The line for a 1:1 mixture of Hb S and Hb D Los Angeles shifted to the right of that for deoxy-Hb S by 0.08. This shift is much smaller than the shift of 0.32 for 1:1 AS mixtures. From these data, the probability factor for nucleation of S-D Los Angeles hybrid hemoglobin was calculated to be 1.16, which is higher than that of Hb S (1.0) and AS hybrid hemoglobin (0.5). The degree of co-polymerization of Hb D Los Angeles in S-D Los Angeles mixtures was similar to that of Hb A in AS mixtures. The critical concentration for the polymerization of Hb D Los Angeles was between that of Hb A and Hb Machida, which has the same amino acid substitution (Glu----Gln) at the beta 6 position. These results suggest that the protein interaction of Hb S molecules during nucleation involves at least two steps. First, the Val-beta 6 of a Hb S molecule interacts hydrophobically with the Phe-beta 85 and the Leu-beta 88 of an adjacent Hb S molecule. In the second step, Glu-beta 121 weakens the interaction with His-beta 116 and Pro-alpha 114. The substitution of Glu-beta 121----Gln may strengthen this second reaction and facilitate nucleation as well as polymerization.     

Mechanism of inhibition of sickling by dimethyl adipimidate. Effects of intertetramer cross-linking

Dimethyl adipimidate (DMA), an effective antisickling agent in vitro, reacts with free amino groups producing chemically modified and cross-linked molecules. In this report, we have investigated the effect of cross-linked hemoglobin tetramers on sickle hemoglobin polymerization. Since the extent of cross-linking is pH-dependent, we first compared the solubilities of deoxygenated hemolysates prepared from sickle cells previously treated with dimethyl adipimidate at either pH 7.4 or 8.4. The solubility of the hemolysate increased from 18.6 +/- 0.8 g/dl in the untreated sample to 20.9 +/- 1.5 g/dl (pH 7.4) and to 25.4 +/- 3.0 g/dl (pH 8.4) after dimethyl adipimidate treatment. Removal of cross-linked hemoglobin tetramers from hemolysate obtained from dimethyl adipimidate-treated cells abolished part of this effect; at pH 7.4, the solubility decreased from 20.9 +/- 1.5 to 19.4 +/- 0.2 and at pH 8.4 from 25.4 +/- 3.0 to 21.0 +/- 1.5. However, the ratio of [14C]DMA-labelled hemoglobin in the sol phase to that in the gel phase in the unfractionated hemolysate was 1.17 at pH 7.4 and 1.25 at pH 8.4, suggesting that part of the cross-linked hemoglobin tetramers was incorporated into the gel. In order to further investigate the effect of cross-linked hemoglobin tetramers on sickle hemoglobin polymerization, we separated cross-linked hemoglobin tetramers on a gel-filtration column, prepared mixtures of untreated sickle hemoglobin and cross-linked hemoglobin tetramers and studied the polymerization of these mixtures. The Csat of the untreated hemolysate increased progressively from 18.6 +/- 0.8 to 22.5 +/- 0.8 g/dl with 33% cross-linked hemoglobin tetramers. The hemoglobin concentration in the gel decreased from 43 +/- 1.0 to 33.8 +/- 1.0 g/dl with 33% cross-linked hemoglobin tetramers, while the pellet volume fraction, phi p, increased with and almost approached 1 at 50% cross-linked hemoglobin tetramers. In addition, the sol phase contained a higher molecular weight distribution of cross-linked hemoglobin tetramers than the gel phase. These observations suggest that a loose polymer was formed in the gel phase with a hemoglobin concentration much lower than that of the control. Thus, polymerization of sickle hemoglobin is inhibited by: (1) exclusion of higher molecular weight cross-linked hemoglobin tetramers from the gel, and (2) loose incorporation of cross-linked hemoglobin tetramers into the gel, perhaps preventing lateral packing and formation of tightly ordered fibers.     

Comparison of the state of deoxyhemoglobin S molecules in solution and in fibers by hydrogen exchange kinetics

Hydrogen exchange kinetics of deoxyhemoglobin S gel and deoxyhemoglobin A solution were compared at 4.8 mM tetramer concentration, 25 degrees C, and in sodium phosphate buffer at pH 7.0 with gamma/2 = 0.2 by means of microdialysis using tritium as a trace label. Cyanomethemoglobin A in solution and as crosslinked crystals were compared under the same conditions. The exchange values from 15 to 10(4) min were fitted to a power law, and the distribution function of exchange rates was calculated. There was no significant difference in the distribution for deoxyhemoglobin S gel and deoxyhemoglobin A. Exchange from crosslinked cyanomethemoglobin crystals was less in the early time region than for the solution state, but after 600 min the exchange curves were the same. This resulted in a larger area for the distribution function, although the predominate rates were nearly the same. The effect of polymerization on conformational fluctuations was very small, smaller than the effect of crosslinking hemoglobin crystals.