Component and state separation in DMPC/DSPC lipid bilayers: a Monte Carlo simulation study

In this paper a two-state, two-component, Ising-type model is used to simulate the lateral distribution of the components and gel/fluid state acyl chains in dimyristoylphosphatidylcholine/distearoylphosphatidylcholine (DMPC/DSPC) lipid bilayers. The same model has been successful in calculating the excess heat capacity curves, the fluorescence recovery after photobleaching (FRAP) threshold temperatures, the most frequent center-to-center distances between DSPC clusters, and the fractal dimensions of gel clusters (Sugar, I. P., T. E. Thompson, and R. L. Biltonen, 1999. Biophys. J. 76:2099-2110). Depending on the temperature and mole fraction the population of the cluster size is either homogeneous or inhomogeneous. In the inhomogeneous population the size of the largest cluster scales with the size of the system, while the rest of the clusters remain small with increasing system size. In a homogeneous population, however, every cluster remains small with increasing system size. For both compositional and fluid/gel state clusters, threshold temperatures-the so-called percolation threshold temperatures-are determined where change in the type of the population takes place. At a given mole fraction, the number of percolation threshold temperatures can be 0, 1, 2, or 3. By plotting these percolation threshold temperatures on the temperature/mole fraction plane, the diagrams of component and state separation of DMPC/DSPC bilayers are constructed. In agreement with the small-angle neutron scattering measurements, the component separation diagram shows nonrandom lateral distribution of the components not only in the gel-fluid mixed phase region, but also in the pure gel and pure fluid regions. A combined diagram of component and state separation is constructed to characterize the lateral distribution of lipid components and gel/fluid state acyl chains in DMPC/DSPC mixtures. While theoretical phase diagrams of two component mixtures can be constructed only in the case of first-order transitions, state and component separation diagrams can be constructed whether or not the system is involved in first-order transition. The effects of interchain interactions on the component and state separation diagrams are demonstrated on three different models. The influences of state and component separation on the in-plane and off-plane membrane reactions are discussed.     

Monte Carlo simulation of lipid mixtures: finding phase separation.

The nonideal mixing of phosphatidylserine (PS) and phosphatidylcholine (PC) binary lipid mixtures was studied by computer simulation based on a model wherein the excess energy of mixing is divided between an electrostatic term and one adjustable term delta Em that includes all other nonideal interactions. The lateral distribution of the lipids and the energy of the mixtures were obtained by using Kawasaki relaxation in a canonical ensemble. The Gibbs free energies were calculated by Kirkwood's coupling parameter method. The simulation results are strongly dependent on simulation size for sizes smaller than about 1000 lipids. Nonideal interaction between lipids can result in large scale separation of lipid phases of different composition at reasonable delta Em values as well as clustering of like lipids. In plots of total Gibbs free energy of mixing versus PS mole fraction in PS/PC, the boundaries of the two phase region could be accurately determined. The electrostatic interaction influences cluster size and shape, and also the composition of phases in the two-phase region.     

Receptor aggregation by intermembrane interactions: a Monte Carlo study

The lateral organization of receptors on cell surfaces is critically important to their function; many receptors transmit transmembrane signals when redistributed into clusters, while the response of others is potentiated by their aggregation. Cell-cell contact can play a crucial role in receptor aggregation, even when the bonds between receptors on one cell and ligands on the other are monovalent. Monte Carlo simulations on a two-membrane model were carried out to determine whether weak enthalpic interactions among receptors in one membrane, and among ligands in another, can work synergistically to give large-scale clustering when the two membranes are brought into contact. The simulations give support to such a clustering mechanism. In addition, because clustering is a cooperative process akin to a phase separation, individual receptors and ligands may undergo repeated binding and unbinding while in a clustered "phase," and a single ligand could interact with multiple different receptor partners. The results suggest a resolution of the dichotomy between serial triggering and aggregation models of T cell activation.     

Direct Sampling of Local Density Fluctuations in Monte Carlo Simulations

A novel method for accelerating Monte Carlo simulations of fluids based on a direct sampling of local density fluctuations by a multiparticle move is proposed. The method is expected to be particularly efficient for inhomogeneous pure fluids consisting of spherical or moderately nonspherical molecules which is confirmed by a sample simulation of a Lennard-Jones fluid in a slit pore. An analogous method for a mixture, a direct sampling of local concentration fluctuations by swapping particles of different species, is successfully tested on a liquid mixture of argon and nitrogen.     

Anomalous subdiffusion in fluorescence photobleaching recovery: a Monte Carlo study

Anomalous subdiffusion is hindered diffusion in which the mean-square displacement of a diffusing particle is proportional to some power of time less than one. Anomalous subdiffusion has been observed for a variety of lipids and proteins in the plasma membranes of a variety of cells. Fluorescence photobleaching recovery experiments with anomalous subdiffusion are simulated to see how to analyze the data. It is useful to fit the recovery curve with both the usual recovery equation and the anomalous one, and to judge the goodness of fit on log-log plots. The simulations show that the simplest approximate treatment of anomalous subdiffusion usually gives good results. Three models of anomalous subdiffusion are considered: obstruction, fractional Brownian motion, and the continuous-time random walk. The models differ significantly in their behavior at short times and in their noise level. For obstructed diffusion the approach to the percolation threshold is marked by a large increase in noise, a broadening of the distribution of diffusion coefficients and anomalous subdiffusion exponents, and the expected abrupt decrease in the mobile fraction. The extreme fluctuations in the recovery curves at and near the percolation threshold result from extreme fluctuations in the geometry of the percolation cluster.     

Anomalous diffusion due to binding: a Monte Carlo study.

In classical diffusion, the mean-square displacement increases linearly with time. But in the presence of obstacles or binding sites, anomalous diffusion may occur, in which the mean-square displacement is proportional to a nonintegral power of time for some or all times. Anomalous diffusion is discussed for various models of binding, including an obstruction/binding model in which immobile membrane proteins are represented by obstacles that bind diffusing particles in nearest-neighbor sites. The classification of binding models is considered, including the distinction between valley and mountain models and the distinction between singular and nonsingular distributions of binding energies. Anomalous diffusion is sensitive to the initial conditions of the measurement. In valley models, diffusion is anomalous if the diffusing particles start at random positions but normal if the particles start at thermal equilibrium positions. Thermal equilibration leads to normal diffusion, or to diffusion as normal as the obstacles allow.     

Insertion and hairpin formation of membrane proteins: a Monte Carlo study.

Some particular effects of a lipid membrane on the partitioning and the concomitant folding processes of model proteins have been investigated using Monte Carlo methods. It is observed that orientational order and lateral density fluctuations of the lipid matrix stabilize the orientation of helical proteins and induce a tendency of spontaneous formation of helical hairpins for helices longer than the width of the membrane. The lateral compression of the lipids on a hairpin leads to the extrusion of a loop at the trans side of the membrane. The stability of the hairpin can be increased by the design of appropriate groups of hydrophilic and hydrophobic residues at the extruded loop. It is shown that in the absence of lipids the orientation of proteins is not stable and the formation of hairpins is absent. Some analogies between the formation of helical hairpins in membranes and the formation of hairpins in polymer liquid crystals are discussed. The simulations indicate that the insertion process follows a well-defined pattern of kinetic steps.     

Monte Carlo studies of lipid / water interfaces

The results of a series of numerical simulations of the aqueous interface near several types of lipid bilayer headgroups are presented. The Monte Carlo method was used to study 172 water molecules located between two lipid bilayers separated by 24.5 Å. The types of headgroups used in the studies include phosphorylcholine, -ethanolamine and -serine. The quantities calculated were molecular density, dipolar orientation and number of hydrogen bonds as functions of the distance from the interfacial regions. The data point out important differences in the organization of the interfacial water for each of the three different lipids.     

Sources of anomalous diffusion on cell membranes: a Monte Carlo study

A stochastic random walk model of protein molecule diffusion on a cell membrane was used to investigate the fundamental causes of anomalous diffusion in two-dimensional biological media. Three different interactions were considered: collisions with fixed obstacles, picket fence posts, and capture by, or exclusion from, lipid rafts. If motion is impeded by randomly placed, fixed obstacles, we find that diffusion can be highly anomalous, in agreement with previous studies. In contrast, collision with picket fence posts has a negligible effect on the anomalous exponent at realistic picket fence parameters. The effects of lipid rafts are more complex. If proteins partition into lipid rafts there is a small to moderate effect on the anomalous exponent, whereas if proteins are excluded from rafts there is a large effect on the anomalous exponent. In combination, these mechanisms can explain the level of anomaly in experimentally observed membrane diffusion, suggesting that anomalous diffusion is caused by multiple mechanisms whose effects are approximately additive. Finally, we show that the long-range diffusion rate, D(macro), estimated from fluorescence recovery after photobleaching studies, can be much smaller than D(micro), the small-scale diffusion rate, and is highly sensitive to obstacle densities and other impeding structures.     

Monte Carlo study of sI hydrogen hydrates

In this study, we perform grand canonical Monte Carlo simulations to evaluate the hydrogen storage capacity of structure I (sI) hydrogen hydrates at pressures up to 500 MPa. Initially, we calculate the upper limit of H₂ content of sI hydrates by studying the hypothetical sI hydrate, where H₂ is the single guest component. It is found that the storage capacity of the hypothetical pure H₂ sI hydrate could reach 3.5 wt% at 500 MPa and 274 K. Depending on pressure, the large cavities of the pure H₂ hydrate can accommodate up to three H₂ molecules while the small ones are singly occupied at most, even at pressures as high as 500 MPa, without any double occupancy being observed. Subsequently, the binary H₂–ethylene oxide (EO) hydrate is examined. In this case, the large cavities are occupied by a single EO molecule while the small cavities can accommodate at most a single H₂ molecule. Such configuration results in a maximum H₂ content of only 0.37 wt%. The hydrogen storage capacity does not improve significantly even in case when EO is replaced by a component with smaller molecular weight.     

Monte Carlo simulation of the water in a channel with charges.

A Monte Carlo simulation of water in a channel with charges suggests the existence of water in immobile, high density, essentially glasslike form near the charges. The channel model has a conical section with an opening through which water molecules can pass, at the narrow end of the cone, and a cylindrical section at the other end. When the charges are placed near the narrow section of the model, the "glass" effectively blocks the channel; with the charges removed, the channel opens. The effect can be determined from the rate of passage of the water molecules through the pore, from the average orientation of the water molecule, and from distortion of the distribution of molecules. In the simulations carried out to date, no external ions have been considered. In addition to the energy, the Helmholtz free energy has been calculated.     

Ion-binding properties of calbindin D9k: a Monte Carlo simulation study

Monte Carlo simulations are used to calculate the binding constant of two Ca2+ ions to the protein bovine calbindin D9k. The change in binding constant with respect to mutation of charged amino acids, presence of various electrolytes, protein concentration, solution pH, and competitive binding of monovalent ions is investigated. Each of these factors may have a large influence on the binding constant. The simulations are performed in a dielectric continuum model, the so-called primitive model of electrolyte theory, with a fixed protein structure and a uniform dielectric permittivity. The calculated binding constants are in excellent agreement with experimental data and describe changes in the binding constant over six orders of magnitude.     

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.     

Nature of the stacking of nucleic acid bases in water: a Monte Carlo simulation

The results of a Monte Carlo simulation of the hydration of uracil and thymine molecules, their stacked dimers and hydrogen-bonded base pairs are presented. Simulations have been performed in a cluster approximation. The semiempirical atom-atom potential functions have been used (cluster consisting of 200 water molecules). It has been shown that the stacking interactions of uracil and thymine molecules in water arise mainly due to the increase in the water-water interaction during the transition from monomers to dimer. It has been found out that stacked base associates are more preferable than base pairs in water. This preference is mainly due to the energetically more favourable structure of water around the stack.     

Time- and space-resolved Monte Carlo study of water radiolysis for photon,electron and ion irradiation

Time-dependent yields of the most important products of water radiolysis , ^•OH, H^•, H₃O⁺, H₂, OH⁻ and H₂O₂ have been calculated for ⁶⁰Co-photons, electrons, protons, helium- and carbon-ions incident onto water. G values have been evaluated for the interval from 1 ps to 1 μs after initial energy deposition as a function of time, as well as after 1 ns and at the end of the chemical stage as a function of linear energy transfer (LET), covering an interval from approximately 0.2 up to 750 keV/μm by means of different particle types. In this work, the modules of the biophysical Monte Carlo track structure code PARTRAC dealing with the simulation of prechemical and chemical stages have been improved to extend interaction data sets for heavier ions. Among other newly selected parameter values, the thermalisation distance between the point of generation and hydration of subexcitation electrons has been adopted from recent data in the literature. As far as data from the literature are available, good agreement has been found with the calculated time- and LET-dependent yields in this work, supporting the selection of the revised parameter values.     

Monte Carlo simulation of diffusion and reaction in water radiolysis – a study of reactant `jump through' and jump distances

In Monte Carlo simulations of water radiolysis, the diffusion of reactants can be approximated by “jumping” all species randomly, to represent the passage of a short period of time, and then checking their separations. If, at the end of a jump, two reactant species are within a distance equal to the reaction radius for the pair, they are allowed to react in the model. In principle, the possibility exists that two reactants could “jump through” one another and end up with a separation larger than the reaction radius with no reaction being scored. Ignoring this possibility would thus reduce the rate of reaction below that intended by such a model. By making the jump times and jump distances shorter, any error introduced by `jump through' is made smaller. This paper reports numerical results of a systematic study of `jump through' in Monte Carlo simulations of water radiolysis. With a nominal jump time of 3 ps, it is found that more than 40% of the reactions of the hydrated electron with itself and of the H atom with itself occur when reactions during `jump through' are allowed. For all other reactions, for which the effect is smaller, the contributions of `jump through' lie in the range l%–16% of the total. Corrections to computed rate constants for two reactions are evaluated for jump times between 0.1 and 30 ps. It is concluded that jump-through corrections are desirable in such models for jump times that exceed about 1 ps or even less. In a separate study, we find that giving all species of a given type the same size jump in a random direction yields results that are indistinguishable from those when the jump sizes are selected from a Gaussian distribution. In this comparison, the constant jump size is taken to be the root-mean-square jump size from the Gaussian distribution. Received: 8 September 1997 / Accepted in revised form: 27 October 1997     

Taboo-based Monte Carlo Search as a Method to Improve Sampling Efficiency

Abstract

Taboo-based Monte Carlo search which restricts the sampling of the region near an old configuration, is developed. In this procedure, Monte Carlo simulation and random search method are combined to improve the sampling efficiency. The feasibility of this method is tested on global optimization of a continuous model function, melting of the 256 Lennard-Jones particles at T? = 0.680 and ρ? = 0.850 and polypeptides (alanine dipeptide and Metenkephalin). From the comparison of results for the model function between our method and other methods, we find the increase of convergence rate and the high possibility of escaping from the local energy minima. The results of the Lennard-Jones solids and polypeptides show that the convergence property to reach the equilibrium state is better than that of others. It is also found that no significant bias in ensemble distribution is detected, though taboo-based Monte Carlo search does not sample the correct ensemble distribution owing to the restriction of the sampling of the region near an old configuration.     

Monte Carlo simulation of physicochemical processes of liquid water radiolysis

The paper describes developments of the physicochemical part of a computer code system that estimates DNA strand break induction on plasmid pBR322 DNA. In order to test the reliability of the model, we evaluated the dielectric function and the time-dependent yield of chemical species in the presence of OH radical scavenger or dissolved oxygen. Results agree with measurements on the radiolysis of liquid water. When a hybrid model of a liquid inelastic cross-section and a vapour elastic cross-section is used, energy deposition by vibrational excitations is estimated to be approximately 11% of total energy deposition. Received: 4 March 1996 / Accepted in revised form: 14 November 1996