Monte Carlo studies of the hydrocarbon region of lipid bilayers

We present the results of a Monte Carlo study of systems of hydrocarbon chains attached to a plane interface and interacting through hard core repulsive forces only. The chain-order parameters which we find in our studies are compared to experimental results (NMR and ESR). The role of “kink” states and the relevance of our studies to theoretical models are also discussed.     

Interactions of cationic-hydrophobic peptides with lipid bilayers: a Monte Carlo simulation method

We present a computational model of the interaction between hydrophobic cations, such as the antimicrobial peptide, Magainin2, and membranes that include anionic lipids. The peptide's amino acids were represented as two interaction sites: one corresponds to the backbone alpha-carbon and the other to the side chain. The membrane was represented as a hydrophobic profile, and its anionic nature was represented by a surface of smeared charges. Thus, the Coulombic interactions between the peptide and the membrane were calculated using the Gouy-Chapman theory that describes the electrostatic potential in the aqueous phase near the membrane. Peptide conformations and locations near the membrane, and changes in the membrane width, were sampled at random, using the Metropolis criterion, taking into account the underlying energetics. Simulations of the interactions of heptalysine and the hydrophobic-cationic peptide, Magainin2, with acidic membranes were used to calibrate the model. The calibrated model reproduced structural data and the membrane-association free energies that were measured also for other basic and hydrophobic-cationic peptides. Interestingly, amphipathic peptides, such as Magainin2, were found to adopt two main membrane-associated states. In the first, the peptide resided mostly outside the polar headgroups region. In the second, which was energetically more favorable, the peptide assumed an amphipathic-helix conformation, where its hydrophobic face was immersed in the hydrocarbon region of the membrane and the charged residues were in contact with the surface of smeared charges. This dual behavior provides a molecular interpretation of the available experimental data.     

Monte Carlo studies of lipid chains and gramicidin A in a model membrane

The Monte Carlo method has been used to simulate the equilibrium properties of a planar array of 94 saturated lipid chains and one monomer of Gramicidin A. Chains are free to move laterally in the layer plane and to change conformation via gauche rotations and long axis rotations in a continuum. All non-hydrogen atoms on chains and on the Gramicidin A monomer interact via 6-12 potentials, and periodic boundary conditions are imposed. Calculated results consist of order parameter profiles for C-14 and C-16 chains. Profiles are calculated for chains which are neighbors to the Gramicidin A molecule and for chains which are not neighbors to the peptide. The main conclusion is that the average conformations of the chains neighboring the Gramicidin A monomer are very similar to those of the bulk chains.     

Combined Monte Carlo and molecular dynamics simulation of hydrated lipid-cholesterol lipid bilayers at low cholesterol concentration

We have applied a hybrid equilibration and sampling procedure for the atomic level simulation of a hydrated lipid bilayer to systems consisting of dipalmitoyl phosphatidylcholine (DPPC) and cholesterol, and palmitoyl-oleyl phosphatidylcholine (POPC) at low (approximately 6%) cholesterol concentration. The procedure is applied to bilayers of 94 molecules of DPPC, 6 molecules of cholesterol, and 3205 water molecules, and to bilayers of 120 molecules of POPC, 8 molecules of cholesterol, and 4268 water molecules, at a temperature of 325 K. After equilibration, three separate 400-ps continuous molecular dynamics runs, separated by 10,000 configurational bias Monte Carlo steps, were carried out for each system. Properties of the systems were calculated and averaged over the three separate runs. Results of the simulations are presented and compared with experimental data and with other recent simulations of DPPC and cholesterol, and of pure DPPC, and pure POPC. Certain properties of the bilayers are indistinguishable from cholesterol-free bilayers, including lateral diffusion and electron density. Other properties, most notably the order parameter profile, show the effect of cholesterol even at low concentrations.     

Monte Carlo studies of a model for lipid-gramicidin A bilayers.

This paper presents results of Monte Carlo simulations of a full bilayer of 200 lipid chains and one gramicidin A dimer. Simulations are described for systems with lipid chains of 14, 16, and 18 carbons, respectively. Using accepted potential functions to calculate interactions between all non-hydrogen atoms a Monte Carlo configuration sampling is generated from which order parameter profiles are calculated and specific configurations are displayed. Results are compared with experimental data for lipid-gramicidin bilayers.     

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.     

Monte Carlo simulation of two-component bilayers: DMPC/DSPC mixtures

In this paper, we describe a relatively simple lattice model of a two-component, two-state phospholipid bilayer. Application of Monte Carlo methods to this model permits simulation of the observed excess heat capacity versus temperature curves of dimyristoylphosphatidylcholine (DMPC)/distearoylphosphatidylcholine (DSPC) mixtures as well as the lateral distributions of the components and properties related to these distributions. The analysis of the bilayer energy distribution functions reveals that the gel-fluid transition is a continuous transition for DMPC, DSPC, and all DMPC/DSPC mixtures. A comparison of the thermodynamic properties of DMPC/DSPC mixtures with the configurational properties shows that the temperatures characteristics of the configurational properties correlate well with the maxima in the excess heat capacity curves rather than with the onset and completion temperatures of the gel-fluid transition. In the gel-fluid coexistence region, we also found excellent agreement between the threshold temperatures at different system compositions detected in fluorescence recovery after photobleaching experiments and the temperatures at which the percolation probability of the gel clusters is 0.36. At every composition, the calculated mole fraction of gel state molecules at the fluorescence recovery after photobleaching threshold is 0.34 and, at the percolation threshold of gel clusters, it is 0.24. The percolation threshold mole fraction of gel or fluid lipid depends on the packing geometry of the molecules and the interchain interactions. However, it is independent of temperature, system composition, and state of the percolating cluster.     

The folding thermodynamics and kinetics of crambin using an all-atom Monte Carlo simulation

We present a novel Monte Carlo simulation of protein folding, in which all heavy atoms are represented as interacting hard spheres. This model includes all degrees of freedom relevant to folding, all side-chain and backbone torsions, and uses a Go potential. In this study, we focus on the 46 residue alpha/beta protein crambin and two of its structural components, the helix and helix hairpin. For a wide range of temperatures, we recorded multiple folding events of these three structures from random coils to native conformations that differ by less than 1 A C(alpha) dRMS from their crystal structure coordinates. The thermodynamics and kinetic mechanism of the helix-coil transition obtained from our simulation shows excellent agreement with currently available experimental and molecular dynamics data. Based on insights obtained from folding its smaller structural components, a possible folding mechanism for crambin is proposed. We observed that the folding occurs via a cooperative, first order-like process, and that many folding pathways to the native state exist. One particular sequence of events constitutes a "fast-folding" pathway where kinetic traps are avoided. At very low temperatures, a kinetic trap arising from the incorrect packing of side-chains was observed. These results demonstrate that folding to the native state can be observed in a reasonable amount of time on desktop computers even when an all-atom representation is used, provided the energetics sufficiently stabilize the native state.     

Interactions of hydrophobic peptides with lipid bilayers: Monte Carlo simulations with M2delta

We introduce here a novel Monte Carlo simulation method for studying the interactions of hydrophobic peptides with lipid membranes. Each of the peptide's amino acids is represented as two interaction sites: one corresponding to the backbone alpha-carbon and the other to the side chain, with the membrane represented as a hydrophobic profile. Peptide conformations and locations in the membrane and changes in the membrane width are sampled using the Metropolis criterion, taking into account the underlying energetics. Using this method we investigate the interactions between the hydrophobic peptide M2delta and a model membrane. The simulations show that starting from an extended conformation in the aqueous phase, the peptide first adsorbs onto the membrane surface, while acquiring an ordered helical structure. This is followed by formation of a helical-hairpin and insertion into the membrane. The observed path is in agreement with contemporary understanding of peptide insertion into biological membranes. Two stable orientations of membrane-associated M2delta were obtained: transmembrane (TM) and surface, and the value of the water-to-membrane transfer free energy of each of them is in agreement with calculations and measurements on similar cases. M2delta is most stable in the TM orientation, where it assumes a helical conformation with a tilt of 14 degrees between the helix principal axis and the membrane normal. The peptide conformation agrees well with the experimental data; average root-mean-square deviations of 2.1 A compared to nuclear magnetic resonance structures obtained in detergent micelles and supported lipid bilayers. The average orientation of the peptide in the membrane in the most stable configurations reported here, and in particular the value of the tilt angle, are in excellent agreement with the ones calculated using the continuum-solvent model and the ones observed in the nuclear magnetic resonance studies. This suggests that the method may be used to predict the three-dimensional structure of TM peptides.     

Insertion of peptide chains into lipid membranes: An off-lattice Monte Carlo dynamics model

A combination of dynamic Monte Carlo simulation techniques with a hydropathy scale method for the prediction of the location of transmembrane fragments in membrane proteins is described. The new hydropathy scale proposed here is based on experimental data for the interactions of tripeptides with phospholipid membranes (Jacobs, R.E., White, S.H. Biochemistry 26:6127–6134, 1987) and the self-solvation effect in protein systems (Roseman, M.A., J. Mol. Biol. 200:513–522, 1988). The simulations give good predictions both for the state of association and the orientation of the peptide relative to the membrane surface of a number of peptides including Magainin2, M2δ, and melittin. Furthermore, for Pf1 bacterio-phage coat protein, in accord with experiment, the simulations predict that the C-terminus forms a transmembrane helix and the N-terminus forms a helix which is adsorbed on the surface of the bilayer. Finally, the present series of simulations provide a number of insights into the mechanism of insertion of peptides into cell membranes. © 1993 Wiley-Liss, Inc.     

Structural studies of polymer-cushioned lipid bilayers.

The structure of softly supported polymer-cushioned lipid bilayers, prepared in two different ways at the quartz-solution interface, were determined using neutron reflectometry. The polymer cushion consisted of a thin layer of branched, cationic polyethyleneimine (PEI), and the bilayers were formed by adsorption of small unilamellar dimyristoylphosphatidylcholine (DMPC) vesicles. When vesicles were first allowed to adsorb to a bare quartz substrate, an almost perfect bilayer formed. When the polymer was then added to the aqueous solution, it appeared to diffuse beneath this bilayer, effectively lifting it from the substrate. In contrast, if the polymer layer is adsorbed first to the bare quartz substrate followed by addition of vesicles to the solution, there is very little interaction of the vesicles with the polymer layer, and the result is a complex structure most likely consisting of patchy multilayers or adsorbed vesicles.     

Monte Carlo simulation of biospecific interactions

Numerical simulations of the stochastic time evolution of biospecific interactions are described and show that when molecular populations are large, time course predictions match those obtained using a deterministic expression. When population size is decreased the effects of stochastic noise become apparent. The significance of stochastic noise in sensitive binding-based assay systems suggests an immediate need for models of this type.     

Monte Carlo approach to the analysis of the rotational diffusion of wormlike chains

A Monte Carlo analysis is presented which establishes a relationship between the rotational diffusion coefficients and the flexibility (persistence length, P) of short, wormlike chains. The results of this analysis are presented in terms of experimentally observable quantities; namely, the rotational relaxation times for the field-free decay of optical anisotropy. The pertinent theoretical quantity is R, defined as the ratio of the longest rotational relaxation time of a wormlike chain to the transverse rotational relaxation time of a rigid cylinder having the same axial length (L) and segmental volume. R, so defined, is essentially independent of the axial ratio of the cylinder for any value of L/P within the range of validity of the present analysis (axial ratio > 20; 0.1 < L/P < 5). It is pointed out that P can be determined with reasonable accuracy even in the absence of a precise knowledge of the local hydrodynamic radius of the chain.     

Monte Carlo simulation of myoglobin primary to helical structure

A Monte Carlo simulation is presented of the formation of the individual helices of myoglobin from their primary to their helical structures. A simplified model in which each amino acid residue is replaced by a single interaction center is used. The small helices formed are in good agreement with experiment, while the larger helices are moderately well reproduced.     

Monte Carlo simulation studies on the prediction of protein folding types from amino acid composition.

In the methodology development for statistical prediction of protein structures, the founders of different methods usually selected different sets of proteins to test their predicted results. Therefore, it is hard to make a fair comparison according to the results they reported. Even if the predictions by different methods are performed for the same set of proteins, there is still such a problem: a method better that the other for one set of proteins would not necessarily remain so when applied to another set of proteins. To tackle this problem, a Monte Carlo simulation method is proposed to establish an objective criterion to measure the accuracy of prediction for the protein folding type. Such an objective accuracy is actually corresponding to the asymptotical limit genereated during the Monte Carlo simulation process. Based on that, it has been found that the average objective accuracy for predicting the all-alpha, all-beta, alpha + beta, and alpha/beta proteins by the least Euclid's distance method (Nakashima, H., K. Nishikawa, and T. Ooi. 1986. J. Biochem. 99:152-162) is 73.0% and that by the least Minkowski's distance method (Chou, P.Y. 1989. Prediction in Protein Structure and the Principles of Protein Conformation. Plenum Press. New York. 549-586) is 70.9%, indicating that the former is better than the latter. However, according to the original reports, the latter claimed a rate of correct prediction with 79.7% but the former with only 70.2%, leading to a completely opposite conclusion. This indicates the necessity of establishing an objective criterion, and a comparison is meaningful only when it is based on the objective criterion. The simulation method and the idea developed here also can be applied to examine any other statistical prediction methods.     

Interactions of alpha-helices with lipid bilayers: a review of simulation studies

Membrane proteins, of which the majority seem to contain one or more alpha-helix, constitute approx. 30% of most genomes. A complete understanding of the nature of helix/bilayer interactions is necessary for an understanding of the structural principles underlying membrane proteins. This review describes computer simulation studies of helix/bilayer interactions. Key experimental studies of the interactions of alpha-helices and lipid bilayers are briefly reviewed. Surface associated helices are found in some membrane-bound enzymes (e.g. prostaglandin synthase), and as stages in the mechanisms of antimicrobial peptides and of pore-forming bacterial toxins. Transmembrane alpha-helices are found in most integral membrane proteins, and also in channels formed by amphipathic peptides or by bacterial toxins. Mean field simulations, in which the lipid bilayer is approximated as a hydrophobic continuum, have been used in studies of membrane-active peptides (e.g. alamethicin, melittin, magainin and dermaseptin) and of simple membrane proteins (e.g. phage Pf1 coat protein). All atom molecular dynamics simulations of fully solvated bilayers with transmembrane helices have been applied to: the constituent helices of bacteriorhodopsin; peptide-16 (a simple model TM helix); and a number of pore-lining helices from ion channels. Surface associated helices (e.g. melittin and dermaseptin) have been simulated, as have alpha-helical bundles such as bacteriorhodopsin and alamethicin. From comparison of the results from the two classes of simulation, it emerges that a major theoretical challenge is to exploit the results of all atom simulations in order to improve the mean field approach.