Mechanisms of Homogeneous Nucleation of Polymers of Sickle Cell Anemia Hemoglobin in Deoxy State

Direct observation of heterogeneous formation of amyloid spherulites in real-time by super-resolution microscopy

Protein misfolding in the form of fibrils or spherulites is involved in a spectrum of pathological abnormalities. Our current understanding of protein aggregation mechanisms has primarily relied on the use of spectrometric methods to determine the average growth rates and diffraction-limited microscopes with low temporal resolution to observe the large-scale morphologies of intermediates. We developed a REal-time kinetics via binding and Photobleaching LOcalization Microscopy (REPLOM) super-resolution method to directly observe and quantify the existence and abundance of diverse aggregate morphologies of human insulin, below the diffraction limit and extract their heterogeneous growth kinetics. Our results revealed that even the growth of microscopically identical aggregates, e.g., amyloid spherulites, may follow distinct pathways. Specifically, spherulites do not exclusively grow isotropically but, surprisingly, may also grow anisotropically, following similar pathways as reported for minerals and polymers. Combining our technique with machine learning approaches, we associated growth rates to specific morphological transitions and provided energy barriers and the energy landscape at the level of single aggregate morphology. Our unifying framework for the detection and analysis of spherulite growth can be extended to other self-assembled systems characterized by a high degree of heterogeneity, disentangling the broad spectrum of diverse morphologies at the single-molecule level.

Real-time super-resolution microscopy analysis reveals the growth kinetics, morphology, and abundance of human insulin amyloid spherulites with different growth pathways.

Temperature-dependent Self assembly of biofilaments during red blood cell sickling

Molecular self-assembly plays vital role in various biological functions. However, when aberrant molecules self-assemble to form large aggregates, it can give rise to various diseases. For example, the sickle cell disease andAlzheimer's disease are caused by self-assembled hemoglobin fibers and amyloid plaques, respectively. Here we studythe assembly kinetics of such fibers using kinetic Monte- Carlo simulation. We focus on the initial lag time of thesehighly stochastic processes, during which self-assembly is very slow. The lag time distributions turn out to be similarfor two very different regimes of polymerization, namely, a) when polymerization is slow and depolymerization is fast,and b) the opposite case, when polymerization is fast and depolymerization is slow. Using temperature dependent on-and off-rates for hemoglobin fiber growth, reported in recent in-vitro experiments, we show that the mean lag time canexhibit non-monotonic behavior with respect to change in temperature.

Oscillations in the nucleation preexponential

Oscillations in the preexponential of the nucleation rate are due to the discrete nature of small nuclei. An accurate elementary expression to describe such oscillations is derived in the limit of a high nucleation barrier. The result is applied to the standard Becker-Döring equation in two and three dimensions, and to the lowest-energy nucleation path in a cold lattice gas with Glauber and Metropolis dynamics (equivalent to an Ising model on a square lattice) where oscillation effects can be more pronounced.

On the Mechanism of Self-Assembly by a Hydrogel-Forming Peptide

Self-assembling peptide-based hydrogels are a class of tunable soft materials that have been shown to be highly useful for a number of biomedical applications. The dynamic formation of the supramolecular fibrils that compose these materials has heretofore remained poorly characterized. A better understanding of this process would provide important insights into the behavior of these systems and could aid in the rational design of new peptide hydrogels. Here, we report the determination of the microscopic steps that underpin the self-assembly of a hydrogel-forming peptide, SgI_37-49. Using theoretical models of linear polymerization to analyze the kinetic self-assembly data, we show that SgI_37-49 fibril formation is driven by fibril-catalyzed secondary nucleation and that all the microscopic processes involved in SgI_37-49 self-assembly display an enzyme-like saturation behavior. Moreover, this analysis allows us to quantify the rates of the underlying processes at different peptide concentrations and to calculate the time evolution of these reaction rates over the time course of self-assembly. We demonstrate here a new mechanistic approach for the study of self-assembling hydrogel-forming peptides, which is complementary to commonly used materials science characterization techniques.

Quantitative prediction of erythrocyte sickling for the development of advanced sickle cell therapies

Sickle cell disease is induced by a mutation that converts normal adult hemoglobin to sickle hemoglobin (HbS) and engenders intracellular polymerization of deoxy-HbS and erythrocyte sickling. Development of anti-sickling therapies requires quantitative understanding of HbS polymerization kinetics under organ-specific conditions, which are difficult to assess with existing experimental techniques. Thus, we developed a kinetic model based on the classical nucleation theory to examine the effectiveness of potential anti-sickling drug candidates. We validated this model by comparing its predictability against prior in vivo and in vitro experimental results. We used the model to quantify the efficacy of sickling inhibitors and obtain results consistent with recent screening assays. Global sensitivity analysis on the kinetic parameters in the model revealed that the solubility, nucleation rate prefactor, and oxygen affinity are quantities that dictate HbS polymerization. This finding provides quantitative guidelines for the discovery of intracellular processes to be targeted by sickling inhibitors.

Faster Sickling Kinetics and Sickle Cell Shape Evolution during Repeated Deoxygenation and Oxygenation Cycles

Kinetics of cell sickling and morphological change have been recognized as important parameters that are correlated closely with altered blood rheology and vasoocclusion in microcirculation. A microfluidic transient hypoxia assay was developed to create repeated hypoxia-normoxia cycles for real time observation of repetitive sickling and unsickling of freely suspended red blood cells (RBCs) from sickle cell disease patients. Cell sickling behavior and kinetics were found to be influenced by its previous sickling-unsickling processes accumulatively, where those sickled RBCs that had a history of sickling in a previous hypoxia cycle would sickle again in subsequent hypoxia/sickling cycles and the collective sickling kinetics became progressively faster (with reduced delay time and higher sickled fraction versus deoxygenation time). Individual sickled RBCs would sickle into drastically different shapes randomly in subsequent hypoxia/sickling cycles, however, the collective shape distribution retained similar characteristics. These observations indicate a gradual worsening trend in sickling kinetics over repeated hypoxia cycles, as well as a relatively stable collective shape characteristics within a limited number of hypoxia-normoxia cycles.

Simultaneous polymerization and adhesion under hypoxia in sickle cell disease

Patients with sickle cell disease (SCD) suffer from painful vasoocclusive crises. Polymerization of sickle hemoglobin (HbS) in RBCs is generally considered a major contributor to such crisis events. Here, we present the simultaneous and synergistic coupling of adhesion and HbS polymerization. We show that the age of RBCs in circulation plays an important role in mediating this synergistic effect on blood rheology and clinical symptoms. In particular, the youngest RBCs exhibit unique adhesion dynamics, whereby polymerized HbS fiber bundles grow from cell surfaces to serve as sites of cytoadherence. Our molecular-level simulations show how the attachment and dissociation of molecular bonds influence adhesion dynamics. These results provide a framework that could elucidate the mechanistic basis of SCD vasoocclusive pain crises.

Polymerization and adhesion, dynamic processes that are hallmarks of sickle cell disease (SCD), have thus far been studied in vitro only separately. Here, we present quantitative results of the simultaneous and synergistic effects of adhesion and polymerization of deoxygenated sickle hemoglobin (HbS) in the human red blood cell (RBC) on the mechanisms underlying vasoocclusive pain crisis. For this purpose, we employ a specially developed hypoxic microfluidic platform, which is capable of inducing sickling and unsickling of RBCs in vitro, to test blood samples from eight patients with SCD. We supplemented these experimental results with detailed molecular-level computational simulations of cytoadherence and biorheology using dissipative particle dynamics. By recourse to image analysis techniques, we characterize sickle RBC maturation stages in the following order of the degree of adhesion susceptibility under hypoxia: sickle reticulocytes in circulation (SRs) → sickle mature erythrocytes (SMEs) → irreversibly sickled cells (ISCs). We show that (i) hypoxia significantly enhances sickle RBC adherence; (ii) HbS polymerization enhances sickle cell adherence in SRs and SMEs, but not in ISCs; (iii) SRs exhibit unique adhesion dynamics where HbS fiber projections growing outward from the cell surface create multiple sites of adhesion; and (iv) polymerization stimulates adhesion and vice versa, thereby establishing the bidirectional coupling between the two processes. These findings offer insights into possible mechanistic pathways leading to vasoocclusion crisis. They also elucidate the processes underlying the onset of occlusion that may involve circulating reticulocytes, which are more abundant in hemolytic anemias due to robust compensatory erythropoiesis.

Modeling of the Inhibitory Effect of Nanoparticles on Amyloid β Fibrillation

Experiments have shown that charged nanoparticles (NP) inhibit, partially or completely, the aggregation of Aβ protein monomers into fibrils. The equilibrium fibril content is found to be inversely proportional to the concentration of NP. In this work, we report a kinetic model for the fibrillation of Aβ protein in the presence of NP. In the model, apart from nucleation, elongation and fragmentation processes, the effect of NP is considered to cause a conformational change to the protein monomer, making the latter incompatible for aggregation. The simulated results explain the growth kinetics of pure Aβ (1-40) protein, and the kinetics in the presence of NP. The NP-monomer interaction considered in the model captures the significant effect of NP on the fibrillation process at a very molar ratio (NP to Aβ monomer) as low as 10^-4. The model predictions are compared with two different NP systems, namely, gold and silica NP. The model can be applied to explain the inhibitory effect of other additives such as small molecules, NP, lipids, and surfactants that show a similar inhibition trend for fibril formation of Aβ and other proteins.

Physical principles of filamentous protein self-assembly kinetics

The polymerization of proteins and peptides into filamentous supramolecular structures is an elementary form of self-organization of key importance to the functioning biological systems, as in the case of actin biofilaments that compose the cellular cytoskeleton. Aberrant filamentous protein self-assembly, however, is associated with undesired effects and severe clinical disorders, such as Alzheimer's and Parkinson's diseases, which, at the molecular level, are associated with the formation of certain forms of filamentous protein aggregates known as amyloids. Moreover, due to their unique physicochemical properties, protein filaments are finding extensive applications as biomaterials for nanotechnology. With all these different factors at play, the field of filamentous protein self-assembly has experienced tremendous activity in recent years. A key question in this area has been to elucidate the microscopic mechanisms through which filamentous aggregates emerge from dispersed proteins with the goal of uncovering the underlying physical principles. With the latest developments in the mathematical modeling of protein aggregation kinetics as well as the improvement of the available experimental techniques it is now possible to tackle many of these complex systems and carry out detailed analyses of the underlying microscopic steps involved in protein filament formation. In this paper, we review some classical and modern kinetic theories of protein filament formation, highlighting their use as a general strategy for quantifying the molecular-level mechanisms and transition states involved in these processes.

Modeling the Effect of Monomer Conformational Change on the Early Stage of Protein Self-Assembly into Fibrils

Filamentous self-assembly of proteins is an important process implicated in a plethora of human diseases and of interest for nanotechnology. Using rate equations, we analyze the early stage of the process in solutions that initially contain fibrillation-passive protein monomers and in which the nascent fibrils are practically insoluble. The analysis is based on a model accounting for the conformational and/or other changes the passive monomers experience to transform themselves into fibrillation-active monomers and thus become fibril nuclei. The model allows exact, comprehensive, and simple mathematical description of the early stage of fibrillation, which reveals the usually neglected role of the nucleation nonstationarity in this stage of fibrillation. We obtain exact and user-friendly expressions for experimentally accessible quantities such as the size distribution of fibrils, their number and mass concentrations, the rate and nonstationary period of fibril nucleation, and the delay time of fibril formation. Analyzing available experimental data, we find that the theory successfully describes the fibrillation time course of pathological and nonpathological ataxin-3, a protein involved in the neurodegenerative disorder spinocerebellar ataxia type-3. The analysis provides mechanistic insight into the reason for the higher fibril nucleation and elongation rates of the pathological ataxin-3.

Protein Polymerization into Fibrils from the Viewpoint of Nucleation Theory

The assembly of various proteins into fibrillar aggregates is an important phenomenon with wide implications ranging from human disease to nanoscience. Using general kinetic results of nucleation theory, we analyze the polymerization of protein into linear or helical fibrils in the framework of the Oosawa-Kasai (OK) model. We show that while within the original OK model of linear polymerization the process does not involve nucleation, within a modified OK model it is nucleation-mediated. Expressions are derived for the size of the fibril nucleus, the work for fibril formation, the nucleation barrier, the equilibrium and stationary fibril size distributions, and the stationary fibril nucleation rate. Under otherwise equal conditions, this rate decreases considerably when the short (subnucleus) fibrils lose monomers much more frequently than the long (supernucleus) fibrils, a feature that should be born in mind when designing a strategy for stymying or stimulating fibril nucleation. The obtained dependence of the nucleation rate on the concentration of monomeric protein is convenient for experimental verification and for use in rate equations accounting for nucleation-mediated fibril formation. The analysis and the results obtained for linear fibrils are fully applicable to helical fibrils whose formation is describable by a simplified OK model.

Photophysical characterization of sickle cell disease hemoglobin by multi-photon microscopy

The photophysical properties of human sickle cell disease (SCD) Hemoglobin (Hb) is characterized by multi-photon microscopy (MPM). The intrinsic two-photon excited fluorescence (TPEF) signal associated with extracted hemoglobin was investigated and the solidified SCD variant (HbS) was found to demonstrate broad emission peaking around 510 nm when excited at 800 nm. MPM is used to dynamically induce and image HbS gelling by photolysis of deoxygenated HbS. For comparison, photolysis conditions were applied to a healthy variant of human hemoglobin (HbA) and found to remain in solution not forming fibers. The use of this signal to study the mechanism of HbS polymerization associated with the sickling of SCD erythrocytes is discussed.

Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters

Nanoparticle dynamics impact a wide range of biological transport processes and applications in nanomedicine and natural resource engineering. Differential dynamic microscopy (DDM) was recently developed to quantify the dynamics of submicron particles in solutions from fluctuations of intensity in optical micrographs. Differential dynamic microscopy is well established for monodisperse particle populations, but has not been applied to solutions containing weakly scattering polydisperse biological nanoparticles. Here we use bright-field DDM (BDDM) to measure the dynamics of protein-rich liquid clusters, whose size ranges from tens to hundreds of nanometers and whose total volume fraction is less than 10(-5). With solutions of two proteins, hemoglobin A and lysozyme, we evaluate the cluster diffusion coefficients from the dependence of the diffusive relaxation time on the scattering wave vector. We establish that for weakly scattering populations, an optimal thickness of the sample chamber exists at which the BDDM signal is maximized at the smallest sample volume. The average cluster diffusion coefficient measured using BDDM is consistently lower than that obtained from dynamic light scattering at a scattering angle of 90°. This apparent discrepancy is due to Mie scattering from the polydisperse cluster population, in which larger clusters preferentially scatter more light in the forward direction.

Label-free and depth resolved optical sectioning of iron-complex deposits in sickle cell disease splenic tissue by multiphoton microscopy

Multiphoton microscopy (MPM) imaging of intrinsic two-photon excited fluorescence (TPEF) is performed on humanized sickle cell disease (SCD) mouse model splenic tissue. Distinct morphological and spectral features associated with SCD are identified and discussed in terms of diagnostic relevance. Specifically, spectrally unique splenic iron-complex deposits are identified by MPM; this finding is supported by TPEF spectroscopy and object size to standard histopathological methods. Further, iron deposits are found at higher concentrations in diseased tissue than in healthy tissue by all imaging methods employed here including MPM, and therefore, may provide a useful biomarker related to the disease state. These newly characterized biomarkers allow for further investigations of SCD in live animals as a means to gain insight into the mechanisms impacting immune dysregulation and organ malfunction, which are currently not well understood.

A simple, rapid, low-cost diagnostic test for sickle cell disease

This communication describes a very simple, rapid and inexpensive point-of-care diagnostic test for sickle cell disease (SCD) that can conclusively differentiate between blood samples from normal healthy individuals, sickle cell trait carriers and SCD patients using the characteristic blood stain patterns produced by each sample on paper.

Patchy supramolecules as versatile tools to probe hydrophobicity in nanoglobular systems

We describe precise supramolecules that enable the evaluation of the effective hydrophobicity of amphiphilic or "patchy" nanoglobular systems. These supramolecules exhibit the lower critical solution temperature phenomenon, which provides a quantitative measure of their effective hydrophobicity. Specifically, two isomeric 8-aryl-2'-deoxyguanosine derivatives with a transposed pair of methylene groups self-assemble into hexadecameric nanoglobular supramolecular G-quadruplexes (SGQs) that show large differences in their transition temperatures as determined by turbidity and differential scanning calorimetry studies. Molecular modeling studies suggested that differential clustering of the hydrophobic patches on the surface is responsible for the striking differences between the two isomeric supramolecules.

Predicting the morphology of sickle red blood cells using coarse-grained models of intracellular aligned hemoglobin polymers

Sickle red blood cells (SS-RBCs) exhibit heterogeneous cell morphologies (sickle, holly leaf, granular, etc.) in the deoxygenated state due to the polymerization of the sickle hemoglobin. Experimental evidence points to a close relationship between SS-RBC morphology and intracellular aligned hemoglobin polymers. Here, we develop a coarse-grained (CG) stochastic model to represent the growth of the intracellular aligned hemoglobin polymer domain. The CG model is calibrated based on the mechanical properties (Young's modulus, bending rigidity) of the sickle hemoglobin fibers reported in experiments. The process of the cell membrane transition is simulated for physiologic aligned hemoglobin polymer configurations and mean corpuscular hemoglobin concentration. Typical SS-RBC morphologies observed in experiments can be obtained from the current model as a result of the intracellular aligned hemoglobin polymer development without introducing any further ad hoc assumptions. It is found that the final shape of SS-RBCs is primarily determined by the angular width of the aligned hemoglobin polymer domain, but it also depends, to a lesser degree, on the polymer growth rate and the cell membrane rigidity. Cell morphologies are quantified by structural shape factors, which agree well with experimental results from medical images.

Size distribution of amyloid nanofibrils

We consider the size distribution of amyloid nanofibrils (protofilaments) in nucleating protein solutions when the nucleation process occurs by the mechanism of direct polymerization of β-strands (extended peptides or protein segments) into β-sheets. Employing the atomistic nucleation theory, we derive a general expression for the stationary size distribution of amyloid nanofibrils constituted of successively layered β-sheets. The application of this expression to amyloid β(1-40) (Aβ(40)) fibrils allows us to determine the nanofibril size distribution as a function of the protein concentration and temperature. The distribution is most remarkable with its exhibiting a series of peaks positioned at "magic" nanofibril sizes (or lengths), which are due to deep local minima in the work for fibril formation. This finding of magic sizes or lengths is consistent with experimental results for the size distribution of aggregates in solutions of Aβ(40) proteins. Also, our approach makes it possible to gain insight into the effect of point mutations on the nanofibril size distribution, an effect that may play a role in experimentally observed substantial differences in the fibrillation lag-time of wild-type and point-mutated amyloid-β proteins.

Cellular Reprogramming toward the Erythroid Lineage

Haemoglobinopathies such as thalassaemia and sickle cell disease present a major health burden. Currently, the main forms of treatment for these diseases are packed red blood cell transfusions and the administration of drugs which act to nonspecifically reactivate the production of foetal haemoglobin. These treatments are ongoing throughout the life of the patient and are associated with a number of risks, such as limitations in available blood for transfusion, infections, iron overload, immune rejection, and side effects associated with the drug treatments. The field of cellular reprogramming has advanced significantly in the last few years and has recently culminated in the successful production of erythrocytes in culture. This paper will discuss cellular reprogramming and its potential relevance to the treatment of haemoglobinopathies.

Atomistic theory of amyloid fibril nucleation

We consider the nucleation of amyloid fibrils at the molecular level when the process takes place by a direct polymerization of peptides or protein segments into β-sheets. Employing the atomistic nucleation theory (ANT), we derive a general expression for the work to form a nanosized amyloid fibril (protofilament) composed of successively layered β-sheets. The application of this expression to a recently studied peptide system allows us to determine the size of the fibril nucleus, the fibril nucleation work, and the fibril nucleation rate as functions of the supersaturation of the protein solution. Our analysis illustrates the unique feature of ANT that the size of the fibril nucleus is a constant integer in a given supersaturation range. We obtain the ANT nucleation rate and compare it with the rates determined previously in the scope of the classical nucleation theory (CNT) and the corrected classical nucleation theory (CCNT). We find that while the CNT nucleation rate is orders of magnitude greater than the ANT one, the CCNT and ANT nucleation rates are in very good quantitative agreement. The results obtained are applicable to homogeneous nucleation, which occurs when the protein solution is sufficiently pure and/or strongly supersaturated.

Free heme and the polymerization of sickle cell hemoglobin

In search of novel control parameters for the polymerization of sickle cell hemoglobin (HbS), the primary pathogenic event of sickle cell anemia, we explore the role of free heme, which may be excessively released in sickle erythrocytes. We show that the concentration of free heme in HbS solutions typically used in the laboratory is 0.02-0.04 mole heme/mole HbS. We show that dialysis of small molecules out of HbS solutions arrests HbS polymerization. The addition of 100-260 μM of free heme to dialyzed HbS solutions leads to rates of nucleation and polymer fiber growth faster by two orders of magnitude than before dialysis. Toward an understanding of the mechanism of nucleation enhancement by heme, we show that free heme at a concentration of 66 μM increases by two orders of magnitude the volume of the metastable clusters of dense HbS liquid, the locations where HbS polymer nuclei form. These results suggest that spikes of the free heme concentration in the erythrocytes of sickle cell anemia patients may be a significant factor in the complexity of the clinical manifestations of sickle cell anemia. The prevention of free heme accumulation in the erythrocyte cytosol may be a novel avenue to sickle cell therapy.

Insight into the correlation between lag time and aggregation rate in the kinetics of protein aggregation

Under favorable conditions, many proteins can assemble into macroscopically large aggregates such as the amyloid fibrils that are associated with Alzheimer's, Parkinson's, and other neurological and systemic diseases. The overall process of protein aggregation is characterized by initial lag time during which no detectable aggregation occurs in the solution and by maximal aggregation rate at which the dissolved protein converts into aggregates. In this study, the correlation between the lag time and the maximal rate of protein aggregation is analyzed. It is found that the product of these two quantities depends on a single numerical parameter, the kinetic index of the curve quantifying the time evolution of the fraction of protein aggregated. As this index depends relatively little on the conditions and/or system studied, our finding provides insight into why for many experiments the values of the product of the lag time and the maximal aggregation rate are often equal or quite close to each other. It is shown how the kinetic index is related to a basic kinetic parameter of a recently proposed theory of protein aggregation.

Kinetics of intermediate-mediated self-assembly in nanosized materials: a generic model

We propose in this paper a generic model of a nonstandard aggregation mechanism for self-assembly processes of a class of materials involving the mediation of intermediates consisting of a polydisperse population of nanosized particles. The model accounts for a long induction period in the process. The proposed mechanism also gives insight on future experiments aiming at a more comprehensive picture of the role of self-organization in self-assembly processes.

Free heme in micromolar amounts enhances the attraction between sickle cell hemoglobin molecules

We probe the role of free heme in the interactions between sickle cell hemoglobin (HbS) molecules in simulated physiological solutions: polymerization of deoxy-HbS is the primary pathogenic event of sickle cell anemia, and HbS releases heme after autoxidation more readily than normal adult hemoglobin. We characterize these interactions in terms of osmotic virial coefficients, which we determine by static light scattering. We analyze the results in the heme-hemoglobin system using the Kirkwood-Goldberg model. We show that in the absence of heme, the HbS molecules weakly attract and the attraction is not due to the lowered-as a result of the sickle cell mutation-molecular charge. We show that the part of the interface between the two alphabeta dimers, exposed in the deoxy-state, plays a crucial role in this attraction. We show that heme at micromolar concentrations induces strong attraction between the hemoglobin molecules. We show that the high efficacy of the heme results from the statistics of electrostatic and hydrophobic interactions between the heme and hemoglobin molecules.

Tunable gel formation by both sonication and thermal processing in a cholesterol-based self-assembly system

A family of asymmetric cholesterol-based fluorescent organogelators containing naphthalimide, connected by two acylamines and different alkyl-chain spacers, have been designed and prepared. These compounds can gelate a variety of organic solvents with both ultrasound stimuli and general sol-gel processes. The self-assembly and gelling properties of the compounds depend on the length of the alkyl chains and can be controlled by ultrasound stimuli and renewed by a thermodynamic process. The morphologies and surface wetabilities of the xerogels prepared from these gelators are strongly affected by environmental stimuli. The mechanism of the process was investigated by confocal laser scanning microscopy, transmission or scanning electron microscopy, wide-angle X-ray scattering analysis, and rheological experiments. The studies reveal that the cooperation and relative competition of multiple intermolecular interactions, influenced by the sonication or thermal stimulus, are the main contributors for the aggregation or nucleation processes; this results in the macrodifferences in morphology and surface properties. These results provide a deeper understanding of the intermediate transition state of the gel during use of an ultrasound stimulus.

Theoretical issues relating to thermally reversible gelation by supermolecular fiber formation

Existing models of the thermodynamics and dynamics of self-assembly are summarized to provide a context for discussing the difficulties that arise in modeling supermolecular fiber assembly and the formation of thermally reversible gels through fiber growth and branching. Challenging problems in this field, such as the physical origin of fibers of uniform diameter and fiber twisting, the kinetics of fiber growth, the hierarchical bundling of fibers into "superfibers", fiber branching, gelation through fiber impingement and the associated phenomenon of fractal fiber network and spherulite formation, and the origin and control of structural polymorphism in the fiber and superfiber geometry, are discussed from a personal perspective. Suggestions are made for integrating current research efforts into a more coherent multiscale description of fiber formation and gelation on molecular, mesoscopic, and macroscopic scales.

Universal distributions generated in a nucleation pulse

Asymptotic analysis of the nucleation-growth equations describing a nucleation pulse of arbitrary duration is performed. It is discovered that after extended growth an asymptotic distribution is established, which is not of any standard form (Gauss, log-normal, etc.). Regardless of the mass exchange mechanism between the nucleus and the metastable phase, in the extremes of long and short pulses the shapes of the distribution become universal, with additional insensitivity of either the maximum or, respectively, the width to the duration of the pulse.

Relationship between beta4 hydrogen bond and beta6 hydrophobic interactions during aggregate, fiber or crystal formation in oversaturated solutions of hemoglobin A and S

Oversaturated deoxy-alpha(2)beta(2)(T4V) aggregated instantly without a delay time, which is in contrast to the delay time before the generation of fibers of deoxy-HbS and deoxy-alpha(2)beta(2)(E6V,D73H). Solubility of deoxy-alpha(2)beta(2)(T4V) was approximately 10-fold lower than that of deoxy-HbS and was similar to oxy- and deoxy-alpha(2)beta(2)(E6V,T4V). These results indicate that beta4Val in HbA in the oxy and deoxy forms with or without beta6Val facilitates hydrophobic interaction of the A-helix with the EF helix of adjacent molecules without forming a beta4/beta73 hydrogen bond. Deoxy-HbA generated crystals following aggregation as does HbC-Harlem(alpha(2)beta(2)(E6V,D73N)), while alpha(2)beta(2)(T4V) and alpha(2)beta(2)(D73H) as well as HbS, alpha(2)beta(2)(E6V,D73H) and alpha(2)beta(2)(E6V,T4V) in the oxy and deoxy forms did not form crystals, indicating in addition to the strength of beta6 amino acid hydrophobicity that the synergism between the beta4Thr hydrogen bond and beta6 hydrophobic interaction free energies on the A-helix play a critical role in formation of fibers versus crystalline nuclei during phase transition.

Phase separation and crystallization of hemoglobin C in transgenic mouse and human erythrocytes

Individuals expressing hemoglobin C (beta6 Glu-->Lys) present red blood cells (RBC) with intraerythrocytic crystals that form when hemoglobin (Hb) is oxygenated. Our earlier in vitro liquid-liquid (L-L) phase separation studies demonstrated that liganded HbC exhibits a stronger net intermolecular attraction with a longer range than liganded HbS or HbA, and that L-L phase separation preceded and enhanced crystallization. We now present evidence for the role of phase separation in HbC crystallization in the RBC, and the role of the RBC membrane as a nucleation center. RBC obtained from both human homozygous HbC patients and transgenic mice expressing only human HbC were studied by bright-field and differential interference contrast video-enhanced microscopy. RBC were exposed to hypertonic NaCl solution (1.5-3%) to induce crystallization within an appropriate experimental time frame. L-L phase separation occurred inside the RBC, which in turn enhanced the formation of intraerythrocytic crystals. RBC L-L phase separation and crystallization comply with the thermodynamic and kinetics laws established through in vitro studies of phase transformations. This is the first report, to the best of our knowledge, to capture a temporal view of intraerythrocytic HbC phase separation, crystal formation, and dissolution.

The impact of supramolecular chemistry in medicine: removing the border between infectious and non-infectious diseases

The concept, molecular self-assembly, has a profoundly novel effect on thoughts and efforts related to medicine and pharmacology. This new style of thinking calls for a range of new researches based on new predictions about disease mechanisms (especially autoimmune diseases, endocrinopathies, and neoplasms) and relevant treatment strategies (superstructural pharmaceuticals). Thanks to this new point of view the most fundamental issue in physiology is the quest of how biological systems exert control on the self-assembly of their components and the most fundamental issue in pathology is the quest of how self-assembly of an undesired superstructure triggers a network of events that result in a particular disease state. Therefore, every disease (infectious or non-infectious) must have a superstructural disease agent (SDA). Sophisticated superstructures like bacteria and viruses are stable and long living and thus infectious but simpler SDAs are unstable and short living thus less infectious. Then we can see how diseases like sarcoidosis, currently classified as non-infectious, are indeed infectious. From this point of view, the fact that one viral infection is protective against a second viral infection can be seen as a superstructural drug that protects against a superstructural disease agent. So it becomes understandable how one opportunistic infection in a late-stage HIV-infected individual may cause de-establishment of HIV-infection in a long-term survivor.

The double nucleation model for sickle cell haemoglobin polymerization: full integration and comparison with experimental data

Sickle cell haemoglobin (HbS) polymerization reduces erythrocyte deformability, causing deleterous vaso-occlusions. The double-nucleation model states that polymers grow from HbS aggregates, the nuclei, (i) in solution (homogeneous nucleation), (ii) onto existing polymers (heterogeneous nucleation). When linearized at initial HbS concentration, this model predicts early polymerization and its characteristic delay-time (Ferrone et al. J Mol Biol 183(4):591-610, 611-631, 1985). Addressing its relevance for describing complete polymerization, we constructed the full, non-linearized model (Simulink), The MathWorks). Here, we compare the simulated outputs to experimental progress curves (n = 6-8 different [HbS], 3-6 mM range, from Ferrone's group). Within 10% from start, average root mean square (rms) deviation between simulated and experimental curves is 0.04 +/- 0.01 (25 degrees C, n = 8; mean +/- standard error). Conversely, for complete progress curves, averaged rms is 0.48 +/- 0.04. This figure is improved to 0.13 +/- 0.01 by adjusting heterogeneous pathway parameters (p < 0.01): the nucleus stability (sigma(2) micro( cc ): + 40%), and the fraction of polymer surface available for nucleation (phi), from 5e(-7), (3 mM) to 13 (6 mM). Similar results are obtained at 37 degrees C. We conclude that the physico-chemical description of heterogeneous nucleation warrants refinements in order to capture the whole HbS polymerization process.

Role of the beta4Thr-beta73Asp hydrogen bond in HbS polymer and domain formation from multinucleate-containing clusters

Fiber formation and domain formation from deoxy-HbS as well as from beta4 and beta73 HbS variants were investigated after temperature jump using DIC microscopy to gain a basic understanding of the determinants involved. Oversaturated deoxy-HbS generated numerous 14-stranded fibers and formed ovoid-shaped, multispherulitic domains. Domain number increased linearly as a function of time. Oversaturated deoxy-alpha2beta2(E6V,T4S) also generated time-dependent, ovoid-shaped spherulitic domains like HbS and alpha 2beta2(E6V,D73H) in the deoxy form. In contrast, alpha 2beta2(E6V,T4Y) and HbC-Harlem (alpha2beta2(E6V,D73N)) in the deoxy form generated time-dependent, ball-shaped domains containing many straight, crystalline-like fibers without evidence of branching. Some of these domains formed large needlelike crystals after overnight incubation. The inhibitory effect on polymer formation by beta4Tyr in HbS was stronger than that by beta4Ser but weaker than that by beta73Asn or beta73Leu. In contrast, both deoxy- and oxy-alpha2beta2(E6V,T4V) promoted formation of tiny, disordered amorphous aggregates without a delay time like oxy-HbS, which is in contrast to formation after a delay time of needlelike fibers for alpha 2beta2(E6V,D73L). Solubilities for both deoxy- and oxy-alpha 2beta2(E6V,T4V) were similar to that of deoxy-alpha 2beta2(E6V,D73H) but approximately 10-fold lower than that of deoxy-HbS. These results suggest that the strength of the hydrogen bond between beta4Thr and beta73Asp and the balance between the hydrogen bond and beta6Val hydrophobic interactions in deoxy-HbS polymers control formation of different types of fibers in a single domain or lead to formation of disordered, non-nucleated amorphous aggregates. These results also lead to a model in which multinucleation rather than a single-nucleation event occurs in a single cluster to generate numerous fibers growing from a single domain.

Determination of the transition-state entropy for aggregation suggests how the growth of sickle cell hemoglobin polymers can be slowed

Sickle cell anemia is associated with the mutant hemoglobin HbS, which forms polymers in red blood cells of patients. The growth rate of the polymers is several micrometers per second, ensuring that a polymer fiber reaches the walls of an erythrocyte (which has a 7-microm diameter) within a few seconds after its nucleation. To understand the factors that determine this unusually fast rate, we analyze data on the growth rate of the polymer fibers. We show that the fiber growth follows a first-order Kramers-type kinetics model. The entropy of the transition state for incorporation into a fiber is 95 J mol(-1) K(-1), very close to the known entropy of polymerization. This agrees with a recent theoretical estimate for the hydrophobic interaction and suggests that the gain of entropy in the transition state is due to the release of the last layer of water molecules structured around contact sites on the surface of the HbS molecules. As a result of this entropy gain, the free-energy barrier for incorporation of HbS molecules into a fiber is negligible and fiber growth is unprecedentedly fast. This finding suggests that fiber growth can be slowed by components of the red cell cytosol, native or intentionally introduced, which restructure the hydration layer around the HbS molecules and thus lower the transition state entropy for incorporation of an incoming molecule into the growing fiber.

Sickle-cell haemoglobin polymerization: is it the primary pathogenic event of sickle-cell anaemia?

Sickle cell anaemia is associated with a mutant haemoglobin, HbS, which forms polymers in the red blood cells of patients. The primary role of the HbS polymerization for the pathophysiology has been questioned: observations in patients and model organisms contradict deterministic scenarios of sickling crises triggered by polymerization. However, results with knock-out sickle-cell mice, which were cured by delaying HbS polymerization, reconfirm polymerization's primary role. To reconcile the contradictory observations, this article reviews recent findings on two steps in polymerization: homogeneous nucleation of fibres, and their growth. The fibre growth is faster by far than for any other protein ordered structure. This is due to a negligible free-energy barrier for incorporation into a fibre, determined by an entropy gain, stemming from the release of water molecules structured around HbS. The kinetics of fibre nucleation have shown that the formation of the polymer nucleus is preceded by a metastable droplet of a dense liquid. The properties of the dense liquid are sensitive functions of solution composition, including components in micro- and nanomolar amounts. This mechanism allows low-concentration solution components to strongly affect the nucleation kinetics, accounting for the high variability of the disease. These insights can potentially be utilized for control of HbS polymerization and treatment of the disease.

Two-step mechanism of homogeneous nucleation of sickle cell hemoglobin polymers

Sickle cell anemia is a debilitating genetic disease that affects hundreds of thousands of babies born each year worldwide. Its primary pathogenic event is the polymerization of a mutant, sickle cell, hemoglobin (HbS); and this is one of a line of diseases (Alzheimer's, Huntington's, prion, etc.) in which nucleation initiates pathophysiology. We show that the homogeneous nucleation of HbS polymers follows a two-step mechanism with metastable dense liquid clusters serving as precursor to the ordered nuclei of the HbS polymer. The evidence comes from data on the rates of fiber nucleation and growth and nucleation delay times, the interaction of fibers with polarized light, and mesoscopic metastable HbS clusters in solution. The presence of a precursor in the HbS nucleation mechanism potentially allows low-concentration solution components to strongly affect the nucleation kinetics. The variations of these concentrations in patients might account for the high variability of the disease in genetically identical patients. In addition, these components can potentially be utilized for control of HbS polymerization and treatment of the disease.