Biomedical subjects

Peter G Vekilov

Publications and source records attributed to Peter G Vekilov.

At least 19 recordsLinked to original sources

PubMed2006

Metastable mesoscopic clusters in solutions of sickle-cell hemoglobin.

Sickle cell hemoglobin (HbS) is a mutant, whose polymerization while in deoxy state in the venous circulation underlies the debilitating sickle cell anemia. It has been suggested that the nucleation of the HbS polymers occurs within clusters of dense liquid, existing in HbS solutions. We use dynamic light scattering with solutions of deoxy-HbS, and, for comparison, of oxy-HbS and oxy-normal adult hemoglobin, HbA. We show that solutions of all three Hb variants contain clusters of dense liquid, several hundred nanometers in size, which are metastable with respect to the Hb solutions. The clusters form within a few seconds after solution preparation and their sizes and numbers remain relatively steady for up to 3 h. The lower bound of the cluster lifetime is 15 ms. The clusters exist in broad temperature and Hb concentration ranges, and occupy 10(-5)-10(-2) of the solution volume. The results on the cluster properties can serve as test data for a potential future microscopic theory of cluster stability and kinetics. More importantly, if the clusters are a part of the nucleation mechanism of HbS polymers, the rate of HbS polymerization can be controlled by varying the cluster properties.

Biophysics↗

PubMed2006

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.

Automation↗

PubMed2006

Corresponding-states laws for protein solutions.

The solvent around protein molecules in solutions is structured and this structuring introduces a repulsion in the intermolecular interaction potential at intermediate separations. We use Monte Carlo simulations with isotropic, pair-additive systems interacting with such potentials. We test if the liquid-liquid and liquid-solid phase lines in model protein solutions can be predicted from universal curves and a pair of experimentally determined parameters, as done for atomic and colloid materials using several laws of corresponding states. As predictors, we test three properties at the critical point for liquid-liquid separation: temperature, as in the original van der Waals law, the second virial coefficient, and a modified second virial coefficient, all paired with the critical volume fraction. We find that the van der Waals law is best obeyed and appears more general than its original formulation: A single universal curve describes all tested nonconformal isotropic pair-additive systems. Published experimental data for the liquid-liquid equilibrium for several proteins at various conditions follow a single van der Waals curve. For the solid-liquid equilibrium, we find that no single system property serves as its predictor. We go beyond corresponding-states correlations and put forth semiempirical laws, which allow prediction of the critical temperature and volume fraction solely based on the range of attraction of the intermolecular interaction potential.

Biophysics↗

PubMed2006

Multiple extrema in the intermolecular potential and the phase diagram of protein solutions.

Recent experiments have revealed several surprising features of the phase equilibria in protein solutions: liquid-liquid phase separation which is, in some cases, metastable with respect to the liquid-solid equilibrium, and in others-unobservable; widely varying crystallization enthalpies, including completely athermal crystallization; the co-existence of several crystalline polymorphs; and others. Other studies have shown that the solvent molecules at the hydrophobic and polar patches on the protein molecular surfaces are structured, introducing repulsive forces at surface separations equal to several water molecule sizes. In search of a causal link between the latter and former findings, we apply Monte Carlo simulation techniques in the investigation of phase diagrams associated with globular biological molecules in solution. We account for the solvent structuring via short-range isotropic two-body intermolecular potentials exhibiting multiple extrema. We show that the introduction of a repulsive maximum or a secondary attractive minimum at separations longer than the primary attractive minimum has dramatic effects on the phase diagram: liquid-liquid separation curves are driven to lower or higher temperatures, the sensitivity of the solubility curve (liquidus) to temperature, i.e., the enthalpy of crystallization, is significantly reduced or enhanced, metastable liquid-liquid separation may become stable and vice versa, and both low- and high-density crystalline phases are observed. The similarity of these features of the simulated phase behavior to those observed experimentally suggests that at least some of the mysteries of the protein phase equilibria may be due to the structuring of the solvent around the protein molecular surfaces. Another conclusion is that at least some of the dense liquids seen in protein solutions may be stable and not metastable with respect to a solid phase.

Computer Simulation↗

PubMed2006

A fast response mechanism for insulin storage in crystals may involve kink generation by association of 2D clusters.

Crystals that are likely rhombohedral of Zn-insulin hexamers form in the islets of Langerhans in the pancreases of many mammals. The suggested functions of crystal formation is to protect the insulin from proteases and increase the degree of conversion of soluble proinsulin. To accomplish these ends, crystal growth should be fast and adaptable to rate fluctuations in the conversion reaction. Zn-insulin crystals grow layer by layer. Each layer spreads by the attachment of molecules to kinks located at the layers' edges, also called steps. The kinks are thought to be generated either by thermal fluctuations, as postulated by Gibbs, or by 1D nucleation of new crystalline rows. The kink density determines the rate at which steps advance, and these two kink-generation mechanisms lead to weak near-linear responses of the growth rate to concentration variations. We demonstrate for the crystallization of Zn-insulin a mechanism of kink generation whereby 2D clusters of several insulin molecules preformed on the terraces between steps associate to the steps. This mechanism results in several-fold-higher kink density, a faster rate of crystallization, and a high sensitivity of the kinetics to small increases of the solute concentration. If the found mechanism operates during insulin crystallization in vivo, it could be a part of the biological regulation of insulin production and function. For other crystallizing materials in biological and nonbiological systems, this mechanism provides an understanding of the often seen nonlinear acceleration of the kinetics.

Animals↗

PubMed2006

Nucleation of protein crystals under the influence of solution shear flow.

Several recent theories and simulations have predicted that shear flow could enhance, or, conversely, suppress the nucleation of crystals from solution. Such modulations would offer a pathway for nucleation control and provide a novel explanation for numerous mysteries in nucleation research. For experimental tests of the effects of shear flow on protein crystal nucleation, we found that if a protein solution droplet of approximately 5 microL (2-3 mm diameter at base) is held on a hydrophobic substrate in an enclosed environment and in a quasi-uniform constant electric field of 2 to 6 kV cm(-1), a rotational flow with a maximum rate at the droplet top of approximately 10 microm s(-1) is induced. The shear rate varies from 10(-3) to 10(-1) s(-1). The likely mechanism of the rotational flow involves adsorption of the protein and amphiphylic buffer molecules on the air-water interface and their redistribution in the electric field, leading to nonuniform surface tension of the droplet and surface tension-driven flow. Observations of the number of nucleated crystals in 24- and 72-h experiments with the proteins ferritin, apoferritin, and lysozyme revealed that the crystals are typically nucleated at a certain radius of the droplet, that is, at a preferred shear rate. Variations of the rotational flow velocity resulted in suppression or enhancement of the total number of nucleated crystals of ferritin and apoferritin, while all solution flow rates were found to enhance lysozyme crystal nucleation. These observations show that shear flow may strongly affect nucleation, and that for some systems, an optimal flow velocity, leading to fastest nucleation, exists. Comparison with the predictions of theories and simulations suggest that the formation of ordered nuclei in a "normal" protein solution cannot be affected by such low shear rates. We conclude that the flow acts by helping or suppressing the formation of ordered nuclei within mesoscopic metastable dense liquid clusters. Such clusters were recently shown to exist in protein solutions and to constitute the first step in the nucleation mechanism of many protein and nonproteinsystems.

Adsorption↗

PubMed2005

Entropy and surface engineering in protein crystallization.

Protein crystallization remains a key limiting step in the characterization of the atomic structures of proteins and their complexes by X-ray diffraction methods. Current data indicate that standard screening procedures applied to soluble well folded prokaryotic proteins yield X-ray diffraction crystals with an approximately 20% success rate and for eukaryotic proteins this figure may be significantly lower. Protein crystallization is predominantly dependent on entropic effects and the driving force appears to be the release of ordered water from the sites of crystal contacts. This is countered by the entropic cost of ordering of protein molecules and by the loss of conformational freedom of side chains involved in the crystal contacts. Mutational surface engineering designed to create patches with low conformational entropy and thereby conducive to formation of crystal contacts promises to be an effective tool allowing direct enhancement of the success rate of macromolecular crystallization.

Crystallization↗

PubMed2005

Spinodal for the solution-to-crystal phase transformation.

The formation of crystalline nuclei from solution has been shown for many systems to occur in two steps: the formation of quasidroplets of a disordered intermediate, followed by the nucleation of ordered crystalline embryos within these droplets. The rate of each step depends on a respective free-energy barrier and on the growth rate of its near-critical clusters. We address experimentally the relative significance of the free-energy barriers and the kinetic factors for the nucleation of crystals from solution using a model protein system. We show that crystal nucleation is 8-10 orders of magnitude slower than the nucleation of dense liquid droplets, i.e., the second step is rate determining. We show that at supersaturations of three or four k(B)T units, crystal nuclei of five, four, or three molecules transform into single-molecule nuclei, i.e., the significant nucleation barrier vanishes below the thermal energy of the molecules. We show that the main factor, which determines the rate of crystal nucleation, is the slow growth of the near-critical ordered clusters within the quasidroplets of the disordered intermediate. Analogous to the spinodal in supersaturated fluids, we define a solution-to-crystal spinodal from the transition to single-molecule crystalline nuclei. We show that heterogeneous nucleation centers accelerate nucleation not only because of the wettinglike effects that lower the nucleation barrier, as envisioned by classical theory, but by helping the kinetics of growth of the ordered crystalline embryos.

Journal Article↗

PubMed2005

Kinetics of two-step nucleation of crystals.

When the nucleation of a stable crystalline phase directly in a supersaturated old phase is greatly retarded, the crystal nuclei might nucleate within faster-forming particles of an intermediate phase. Here we present a theoretical investigation of the kinetics of this two-step nucleation of crystals and derive general expressions for the time dependence of the number of crystals nucleated within the particles of the intermediate phase. The results reveal that crystal nucleation can be strongly delayed by the slow growth of the particles and/or by the slow nucleation of the crystals in them. Furthermore, the linear part of the time dependence of the number of nucleated crystals is determined by the formation rate of the intermediate particles. This is in contrast with the one-step nucleation of crystals when this linear part is determined by the rate of crystal nucleation directly in the old phase. Criteria are proposed for distinction between the one- and two-step nucleation mechanisms, based on the supersaturation dependence of the delay time for nucleation. The application of the theoretical approach to the analysis of experimental data on the nucleation of crystals and other ordered aggregates of protein and other soluble materials is discussed.

Journal Article↗

PubMed2005

Nucleation of ordered solid phases of proteins via a disordered high-density state: phenomenological approach.

Nucleation of ordered solid phases of proteins triggers numerous phenomena in laboratory, industry, and in healthy and sick organisms. Recent simulations and experiments with protein crystals suggest that the formation of an ordered crystalline nucleus is preceded by a disordered high-density cluster, akin to a droplet of high-density liquid that has been observed with some proteins; this mechanism allowed a qualitative explanation of recorded complex nucleation kinetics curves. Here, we present a simple phenomenological theory that takes into account intermediate high-density metastable states in the nucleation process. Nucleation rate data at varying temperature and protein concentration are reproduced with high fidelity using literature values of the thermodynamic and kinetic parameters of the system. Our calculations show that the growth rate of the near-critical and supercritical ordered clusters within the dense intermediate is a major factor for the overall nucleation rate. This highlights the role of viscosity within the dense intermediate for the formation of the ordered nucleus. The model provides an understanding of the action of additives that delay or accelerate nucleation and presents a framework within which the nucleation of other ordered protein solid phases, e.g., the sickle cell hemoglobin polymers, can be analyzed.

Computer Simulation↗

PubMed2005

A metastable prerequisite for the growth of lumazine synthase crystals.

Dense liquid phases, metastable with respect to a solid phase, form in solutions of proteins and small-molecule materials. They have been shown to serve as a prerequisite for the nucleation of crystals and other ordered solid phases. Here, using crystals of the protein lumazine synthase from Bacillus subtilis, which grow by the generation and spreading of layers, we demonstrate that within a range of supersaturations the only mechanism of generation of growth layers involves the association of submicrometer-size droplets of the dense liquid to the crystal surface. The dense liquid is metastable not only with respect to the crystals, but also with respect to the low-concentration solution: dynamic light scattering reveals that the droplets' lifetime is limited to several seconds, after which they decay into the low-concentration solution. The short lifetime does not allow growth to detectable dimensions so that liquid-liquid phase separation is not observed within a range of conditions broader than the one used for crystallization. If during their lifetime the droplets encounter a crystal surface, they lower their free energy not by decay, but by transformation into crystalline matter, ensuring perfect registry with the substrate. These observations illustrate two novel features of phase transformations in solutions: the existence of doubly metastable, short-lifetime dense phases and their crucial role for the growth of an ordered solid phase.

Crystallization↗

PubMed2005

Kinetics and mechanisms of protein crystallization at the molecular level.

This chapter focuses on the processes by which a protein molecule in a supersaturated solution joins a protein crystal. The pair of proteins ferritin/apoferritin is used as an example. The most commonly used technique in such investigations has been atomic force microscopy. I discuss the modifications and tests of the atomic force microscope necessary to obtain real-time, in situ molecular resolution imaging. Then, I review tests that establish a quantitative correspondence between the continuous models of crystal growth and the discrete nature of the processes at the molecular level. I address the issue of whether the incorporation of a molecule from a solution into a growth site on the crystal surface is limited by the slow rate of decay of an Eyring-type transition state. The conclusion is that, on the contrary, a scenario, envisioned by Smoluchowski and Debye, is followed in which the kinetics is only limited by the rate diffusion over the free-energy barrier of interaction between two molecules, or an incoming molecule and a surface. Review of the data for many other protein and nonprotein systems suggests that this conclusion is valid not only for the crystallization of ferritin/apoferritin, but also for many other protein and small-molecule crystallization systems. Finally, I review results establishing that the pathway that a molecule from a solution takes on its way to an incorporation site on the crystal surface is indirect: it includes adsorption on the surface and two-dimensional diffusion toward the incorporation site. These results will likely contribute to the understanding at the molecular level not only of the processes of crystallization of proteins and small molecules, but also of the deposition of layers of proteins and other soft materials on substrates, and of other processes of self-assembly in solution.

Animals↗

PubMed2004

Crystallization of transmembrane proteins in cubo: mechanisms of crystal growth and defect formation.

Crystallization of membrane proteins is a major stumbling block en route to elucidating their structure and understanding their function. The novel concept of membrane protein crystallization from lipidic cubic phases, "in cubo", has yielded well-ordered crystals and high-resolution structures of several membrane proteins, yet progress has been slow due to the lack of understanding of the molecular mechanisms of protein transport, crystal nucleation, growth, and defect formation in cubo. Here, we examine at molecular and mesoscopic resolution with atomic force microscopy the morphology of in cubo grown bacteriorhodopsin crystals in inert buffers and during etching by detergent. The results reveal that crystal nucleation occurs following local rearrangement of the highly curved lipidic cubic phase into a lamellar structure, which is akin to that of the native membrane. Crystals grow within the bulk cubic phase surrounded by such lamellar structures, whereby transport towards a growing crystalline layer is constrained to within an individual lamella. This mechanism leads to lack of dislocations, generation of new crystalline layers at numerous locations, and to voids and block boundaries. The characteristic macroscopic lengthscale of these defects suggests that the crystals grow by attachment of single molecules to the nuclei. These insights into the mechanisms of nucleation, growth and transport in cubo provide guidance en route to a rational design of membrane protein crystallization, and promise to further advance the field.

Bacteriorhodopsins↗

PubMed2004

Smooth transition from metastability to instability in phase separating protein solutions.

For insight into the structure and dynamics of phases emerging upon crossing the metastability/instability boundary we monitor with optical microscopy, in real time and in real space, the generation of a dense liquid phase in high-concentration solutions of the protein lysozyme after temperature quenches into thermodynamically defined metastable and unstable regions. We show with this system, which is a poor fit to mean-field assumptions, that the evolution of the structure factor during nucleation is similar to that during spinodal decomposition and reveals no singularity predicted upon crossing the metastability boundary. We introduce two kinetic definitions of the metastability/instability boundary that yield values within approximately 1.5 K, i.e., the boundary appears as an area rather than a line, which is near and above the thermodynamic prediction. Delay times for the appearance of the new phase in the unstable regime are significant, i.e., new-phase growth is hindered by kinetic barriers. While our results agree with predictions of the non-mean-field theories of phase transformations, the experimentally observed behavior is richer than the one envisioned by theory.

Journal Article↗

PubMed2004

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.

Biopolymers↗

PubMed2004

Interplay of impurities and solution flow as determinants of step pattern dynamics.

The first theory of step pattern evolution, the kinematic wave theory, employed the assumption of impurity effects on step kinetics. On the other hand, recent results have been considered within a framework linking step patterns to the mutual orientation of the solution flow and step motion directions in arbitrarily pure solutions. We explore the consequences of combining impurity and solution flow effects on the dynamics of the surface morphology of the (101) face of potassium dihydrogen phosphate (KDP) crystals. We employ phase-shifting interferometry for real time in situ monitoring of these dynamics. We find that, at solution supersaturations sigma</=0.035, step bunches form on all three vicinals of the (101) face regardless of the mutual orientation of the step motion and solution flow directions. Testing the mechanism of impurity-step pattern interactions, we show that bunching is caused by impurity molecules that adsorb on the surface and slow down and destabilize step trains without inducing growth cessation, i.e., the mechanism is inherently different from the one established for the (100) KDP face. We show that at sigma>0.040 impurities do not affect step bunching, and it is controlled by the direction of the solution flow, i.e., two distinct regimes of step bunching exist. The transition between the two regimes is governed by the exposure times of the terraces between steps tau : shorter tau's at higher growth rates lead to lower surface concentration of impurities and suppress the impurity effects on step kinetics and bunching.

Journal Article↗

PubMed2004

Liquid-liquid phase separation in hemoglobins: distinct aggregation mechanisms of the beta6 mutants.

Reversible liquid-liquid (L-L) phase separation in the form of high concentration hemoglobin (Hb) solution droplets is favored in an equilibrium with a low-concentration Hb solution when induced by inositol-hexaphosphate in the presence of polyethylene glycol 4000 at pH 6.35 HEPES (50 mM). The L-L phase separation of Hb serves as a model to elucidate intermolecular interactions that may give rise to accelerated nucleation kinetics of liganded HbC (beta6 Lys) compared to HbS (beta6 Val) and HbA (beta6 Glu). Under conditions of low pH (pH 6.35) in the presence of inositol-hexaphosphate, COHb assumes an altered R-state. The phase lines for the three Hb variants in concentration and temperature coordinates indicate that liganded HbC exhibits a stronger net intermolecular attraction with a longer range than liganded HbS and HbA. Over time, L-L phase separation gives rise to amorphous aggregation and subsequent formation of crystals of different kinetics and habits, unique to the individual Hb. The composite of R- and T-like solution aggregation behavior indicates that this is a conformationally driven event. These results indicate that specific contact sites, thermodynamics, and kinetics all play a role in L-L phase separation and differ for the beta6 mutant hemoglobins compared to HbA. In addition, the dense liquid droplet interface or aggregate interface noticeably participates in crystal nucleation.

Amino Acid Substitution↗

PubMed2004

Crystallization mechanisms of hemoglobin C in the R state.

Crystallization of the mutated hemoglobin, HbC, which occurs inside red blood cells of patients expressing betaC-globin and exhibiting the homozygous CC and the heterozygous SC (in which two mutant beta-globins, S and C, are expressed) diseases, is a convenient model for processes underlying numerous condensation diseases. As a first step, we investigated the molecular-level mechanisms of crystallization of this protein from high-concentration phosphate buffer in its stable carbomonoxy form using high-resolution atomic force microscopy. We found that in conditions of equilibrium with the solution, the crystals' surface reconstructs into four-molecule-wide strands along the crystallographic a (or b) axis. However, the crystals do not grow by the alignment of such preformed strands. We found that the crystals grow by the attachment of single molecules to suitable sites on the surface. These sites are located along the edges of new layers generated by two-dimensional nucleation or by screw dislocations. During growth, the steps propagate with random velocities, with the mean being an increasing function of the crystallization driving force. These results show that the crystallization mechanisms of HbC are similar to those found for other proteins. Therefore, strategies developed to control protein crystallization in vitro may be applicable to pathology-related crystallization systems.

Crystallization↗