Monte Carlo simulation of the heterotypic aggregation kinetics of platelets and neutrophils.

The heterotypic aggregation of cell mixtures or colloidal particles such as proteins occurs in a variety of settings such as thrombosis, immunology, cell separations, and diagnostics. Using the set of population balance equations (PBEs) to predict dynamic aggregate size and composition distributions is not feasible. The stochastic algorithm of Gillespie for chemical reactions (. J. Comput. Phys. 22:403-434) was reformulated to simulate the kinetic behavior of aggregating systems. The resulting Monte Carlo (MC) algorithm permits exact calculation of the decay rates of monomers and the temporally evolving distribution of sizes and compositions of the aggregates. Moreover, it permits calculation of all moments of these distributions. Using this method, we explored the heterotypic aggregation of fully activated platelets and neutrophils in a linear shear flow of shear rate G = 335 s(-1). At plasma concentrations, the half-lives of homotypically aggregating platelet and neutrophil singlets were 8.5 and 2.4 s, respectively. However, for heterotypic aggregation, the half-lives for platelets and neutrophils decreased to 2.0 and 0.11 s, respectively, demonstrating that flowing neutrophils accelerate capture of platelets and growth of aggregates. The required number of calculations per time step of the MC algorithm was typically a small fraction of Omega(1/2), where Omega is the initial number of particles in the system, making this the fastest MC method available. The speed of the algorithm makes feasible the deconvolution of kernels for general biological heterotypic aggregation processes.     

Monte Carlo simulations of peptide solvation

To increase our understanding of peptide–water interactions, we are simulating the behavior of water molecules in the intermolecular channels of [Phe⁴Val⁶]antamanide dododecahydrate crystals. There is good overall agreement between the positions predicted using two alternative potential functions and those that have been observed by x-ray diffraction. Detailed differences between the predictions for the two potential functions are discussed.     

Inhibition of protein aggregation and amyloid formation by small molecules

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Monte Carlo simulations of ionic channel selectivity

Monte Carlo simulations have been developed to study the selectivityof ionic channels in biological membranes. The channel is consideredto be in either of two possible states: (i) densely packed withions, the ions moving in single file in one direction, or alternatively,(ii) sparsely packed, where holes could appear at any particulartime thereby allowing bidirectional movement of ions. The twomodels enable us to envisage a quantitative flux of permeableions in the presence of smaller sized ions, taking into considerationtheir concentrations in the bulk solutions, the ion-channelinteractions and probability with which they fill up the channel.The programs are written in FORTRAN-77 (MS-FORTRAN) for an IBM-compatiblepersonal computer. From the simulation results we observe anenzymatic function of the channel and also note that the smallersized ions tend to block the movement of permeable ions. Thesimulations represent a technique for visualization of the factorsthat decide ionic permeability and help in manipulating theireffects with ease and speed which would otherwise involve intricateexperimental setups. Received on September 7, 1990; accepted on January 14, 1991     

Confinement effects on the thermodynamics of protein folding: Monte Carlo simulations

The effects of chaperonin-like cage-induced confinement on protein stability have been studied for molecules of varying sizes and topologies. Minimalist models based on Gō-like interactions are employed for the proteins, and density-of-states-based Monte Carlo simulations are performed to accurately characterize the thermodynamic transitions. This method permits efficient sampling of conformational space and yields precise estimates of free energy and entropic changes associated with protein folding. We find that confinement-driven stabilization is not only dependent on protein size and cage radius, but also on the specific topology. The choice of the confining potential is also shown to have an effect on the observed stabilization and the scaling behavior of the stabilization with respect to the cage size.     

Surfactant effects on amyloid aggregation kinetics

There is strong experimental evidence of the influence of surfactants (e.g., fatty acids) on the kinetics of amyloid fibril formation. However, the structures of mixed assemblies and interactions between surfactants and fibril-forming peptides are still not clear. Here, coarse-grained simulations are employed to study the aggregation kinetics of amyloidogenic peptides in the presence of amphiphilic lipids. The simulations show that the lower the fibril formation propensity of the peptides, the higher the influence of the surfactants on the peptide self-assembly kinetics. In particular, the lag phase of weakly aggregating peptides increases because of the formation of mixed oligomers, which are promoted by hydrophobic interactions and favorable entropy of mixing. A transient peak in the number of surfactants attached to the growing fibril is observed before reaching the mature fibril in some of the simulations. This peak originates from transient fibrillar defects consisting of exposed hydrophobic patches on the fibril surface, which provide a possible explanation for the temporary maximum of fluorescence observed sometimes in kinetic traces of the binding of small-molecule dyes to amyloid fibrils.     

Grazers and grass: Monte Carlo simulations

To illustrate the interplay between grazers and grass, we present a novel Monte Carlo model including grass-island growth, consumption of grass by grazers, and birth, migration and death of grazers. The rates of the former and three latter processes are assumed to depend on the environment so that the conventional mean-field approximation does not hold (in particular, the model takes into account that grass grows on the grass-island boundaries, and grazers are mobile and prefer to stay on the areas covered by grass). Due to the feedback between various processes, as expected, the model predicts stable regimes and irregular oscillations of the area of the grass islands and grazer population. The patterns observed are however different compared to those predicted by conventional Monte Carlo prey-predator models. Specifically, there is no tendency for grazers and grass to segregate. The mean-field version of the model is briefly discussed as well.     

Solvent-amino acid interaction energies in three-dimensional-lattice Monte Carlo simulations of a model 27-mer protein: Folding thermodynamics and kinetics

Amino acid residue-solvent interactions are required for lattice Monte Carlo simulations of model proteins in water. In this study, we propose an interaction-energy scale that is based on the interaction scale by Miyazawa and Jernigan. It permits systematic variation of the amino acid-solvent interactions by introducing a contrast parameter for the hydrophobicity, C(s), and a mean attraction parameter for the amino acids, omega. Changes in the interaction energies strongly affect many protein properties. We present an optimized energy parameter set for best representing realistic behavior typical for many proteins (fast folding and high cooperativity for single chains). Our optimal parameters feature a much weaker hydrophobicity contrast and mean attraction than does the original interaction scale. The proposed interaction scale is designed for calculating the behavior of proteins in bulk and at interfaces as a function of solvent characteristics, as well as protein size and sequence.     

Interpreting the aggregation kinetics of amyloid peptides

Amyloid fibrils are insoluble mainly beta-sheet aggregates of proteins or peptides. The multi-step process of amyloid aggregation is one of the major research topics in structural biology and biophysics because of its relevance in protein misfolding diseases like Alzheimer's, Parkinson's, Creutzfeld-Jacob's, and type II diabetes. Yet, the detailed mechanism of oligomer formation and the influence of protein stability on the aggregation kinetics are still matters of debate. Here a coarse-grained model of an amphipathic polypeptide, characterized by a free energy profile with distinct amyloid-competent (i.e. beta-prone) and amyloid-protected states, is used to investigate the kinetics of aggregation and the pathways of fibril formation. The simulation results suggest that by simply increasing the relative stability of the beta-prone state of the polypeptide, disordered aggregation changes into fibrillogenesis with the presence of oligomeric on-pathway intermediates, and finally without intermediates in the case of a very stable beta-prone state. The minimal-size aggregate able to form a fibril is generated by collisions of oligomers or monomers for polypeptides with unstable or stable beta-prone state, respectively. The simulation results provide a basis for understanding the wide range of amyloid-aggregation mechanisms observed in peptides and proteins. Moreover, they allow us to interpret at a molecular level the much faster kinetics of assembly of a recently discovered functional amyloid with respect to the very slow pathological aggregation.     

3D-Lattice Monte Carlo simulations of model proteins. Size effects on folding thermodynamics and kinetics

Recently, we devised an energy scale to vary systematically amino-acid residue-solvent interactions for Monte Carlo simulations of lattice-model proteins in water. For 27-mer proteins, the folding behavior varies appreciably with the choice of interaction parameters. We now perform similar simulations with 64-mers to study the size dependence of the optimal energy parameter set for representing realistic behavior typical of many real proteins (i.e. fast folding and high cooperativity for single chains). We find that 64-mers are considerably more stable and more cooperative compared to 27-mers. The optimal interfacial-interaction-energy parameter set, however, is relatively size independent.     

The effect of macromolecular crowding on protein aggregation and amyloid fibril formation

Macromolecular crowding is expected to have several significant effects on protein aggregation; the major effects will be those due to excluded volume and increased viscosity. In this report we summarize data demonstrating that macromolecular crowding may lead to a dramatic acceleration in the rate of protein aggregation and formation of amyloid fibrils, using the protein alpha-synuclein. The aggregation of alpha-synuclein has been implicated as a critical factor in development of Parkinson's disease. Various types of polymers, from neutral polyethylene glycols and polysaccharides (Ficolls, dextrans) to inert proteins, are shown to accelerate alpha-synuclein fibrillation. The stimulation of fibrillation increases with increasing length of polymer, as well as increasing polymer concentration. At lower polymer concentrations (typically up to approximately 100 mg/ml) the major effect is ascribed to excluded volume, whereas at higher polymer concentrations evidence of opposing viscosity effects become apparent. Pesticides and metals, which are linked to increased risk of Parkinson's disease by epidemiological studies, are shown to accelerate alpha-synuclein fibrillation under conditions of molecular crowding.     

Monte Carlo simulations on marker grouping and ordering

Four global algorithms, maximum likelihood (ML), sum of adjacent LOD score (SALOD), sum of adjacent recombinant fractions (SARF) and product of adjacent recombinant fraction (PARF), and one approximation algorithm, seriation (SER), were used to compare the marker ordering efficiencies for correctly given linkage groups based on doubled haploid (DH) populations. The Monte Carlo simulation results indicated the marker ordering powers for the five methods were almost identical. High correlation coefficients were greater than 0.99 between grouping power and ordering power, indicating that all these methods for marker ordering were reliable. Therefore, the main problem for linkage analysis was how to improve the grouping power. Since the SER approach provided the advantage of speed without losing ordering power, this approach was used for detailed simulations. For more generality, multiple linkage groups were employed, and population size, linkage cutoff criterion, marker spacing pattern (even or uneven), and marker spacing distance (close or loose) were considered for obtaining acceptable grouping powers. Simulation results indicated that the grouping power was related to population size, marker spacing distance, and cutoff criterion. Generally, a large population size provided higher grouping power than small population size, and closely linked markers provided higher grouping power than loosely linked markers. The cutoff criterion range for achieving acceptable grouping power and ordering power differed for varying cases; however, combining all situations in this study, a cutoff criterion ranging from 50 cM to 60 cM was recommended for achieving acceptable grouping power and ordering power for different cases.     

The role of water in amyloid aggregation kinetics

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Effective water model for Monte Carlo simulations of proteins

We present an effective theory for water. Our goal is to formulate on accurate model for the effects of solvation on protein dynamics, without incurring the huge computational cost and the slow temporal evolution typical of molecular dynamics simulations of liquids. We replace the individual water molecules in an all-atom potential with a local dielectric density field, with self interactions given by the Landau-Ginzburg free energy and external interactions by Lennard-Jones forces at the surface of the protein atoms. We explore conformational space with finite temperature Monte Carlo dynamics, using parallel Langevin and Fourier acceleration algorithms well suited to data-parallel computer architectures such as the Connection Machine. To establish the validity of our approximations, we compare our electrostatic contribution to the solvalion energy with the results of Lim, Bashford, and Karplus using a conventional static continuum dielectric cavity model, and the non electrostatic contributions with estimates of hydrophohic surface free energy. Our model can also accommodate ionic charges and temperature fluctuations, We propose future investigations extending our effective theory of solvation to include explicit orientational entropy and hydroxen-bonding terms. © 1995 John Wiley & Sons, Inc.     

Monte Carlo simulations of plasma membrane corral-induced EGFR clustering

Experimental evidence suggests that the cell membrane is a highly organized structure that is compartmentalized by the underlying membrane cytoskeleton (MSK). The interaction between the cell membrane and the cytoskeleton led to the “picket-fence” model, which was proposed to explain certain aspects of membrane compartmentalization. This model assumes that the MSK hinders and confines the motion of receptors and lipids to compartments in the membrane. However, the impact of the MSK on receptor clustering, aggregation, and downstream signaling remains unclear. For example, some evidence suggests that the MSK enhances dimerization, while other evidence suggests decreased dimerization and signaling. Herein, we use computational Monte Carlo simulations to examine the effects of MSK density and receptor concentration on receptor dimerization and clustering. Preliminary results suggest that the MSK may have the potential to induce receptor clustering, which is a function of both picket-fence density and receptor concentration.     

Non-native protein aggregation kinetics

Experimental kinetics of non-native protein aggregation are of practical importance in that they help dictate viable processing, formulation, and storage conditions for biotechnology products, and appear to play a role in determining the onset of a number of diseases. Fundamentally, aggregation kinetics provide insights into the identity of key intermediates in the process, and quantitative tests of available models of aggregation. Although aggregation kinetics often display seemingly disparate behaviors across different proteins and sample conditions, this review illustrates how many of these can be understood within a general framework that treats aggregation as a multi-stage process, and how most available kinetic models of aggregation can be grouped hierarchically in terms of which stage(s) they include. This provides an aid for workers seeking a mechanistic interpretation of in vitro aggregation kinetics, for discriminating among competing models, and in designing experiments to assess in vitro protein stability. Limitations and the utility of purely kinetic approaches to studying aggregation, clarifications of common misperceptions regarding experimental aggregation kinetics, and some outstanding challenges in the field are briefly discussed.     

Monte Carlo simulations shed light on Bathsheba's suspect breast

In 1654, Rembrandt van Rijn painted his famous painting Bathsheba at her Bath. Over the years, the depiction of Bathsheba's left breast and especially the presence of local discoloration, has generated debate on whether Rembrandt's Bathsheba suffered from breast cancer. Historical, medical and artistic arguments appeared to be not sufficient to prove if Bathsheba's model truly suffered from breast cancer. However, the bluish discoloration of the breast is an intriguing aspect from a biomedical optics point of view that might help us ending the old debate. By using Monte Carlo simulations in combination with the retinex theory of color vision, we showed that is highly unlikely that breast cancer results in a local bluish discoloration of the skin as is present on Bathsheba's breast. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lipid-cholesterol interactions. Monte Carlo simulations and theory.

Results of Monte Carlo calculations of order parameter profiles of lipid chains interacting with cholesterol are presented. Cholesterol concentrations in the simulations are sufficiently large that it is possible to analyze profiles for chains which are near neighbors of two or more cholesterol molecules, chains which are neighbors to a single cholesterol, and chains which are not near any cholesterol molecules. The profiles, show that cholesterol acts to significantly decrease the ability of neighboring chains to undergo trans-gauche isomeric rotations, although these chains are not all forced into all-trans conformations. The effect is significantly greater for chains which are neighbors to more than one cholesterol. The Monte Carlo results are next used as a guide to develop a theoretical model for lipid-cholesterol mixtures. The properties of this model and the phase diagram which it predicts are described. The phase diagram is then compared with experimentally determined phase diagrams. The model calculations and the computer simulations upon which they are based yield a molecular mechanism for several of the observed phases exhibited by lipid-cholesterol mixtures. The theoretical model predicts that at low temperatures the system should exhibit solid phase immiscibility.