Membranes computer simulation

MD simulations of model membrane systems have provided a unique view of lipid interactions at a molecular level of resolution [21], Due to the inherent fluidity and heterogeneity in lipid membranes, computer simulation is an attractive tool. MD simulations allow us to obtain structural, dynamic, and energetic information about model lipid membranes. Comparing calculated structural properties from our simulations to experimental values, such as areas and volumes per lipid, and electron density profiles, allows validation of our models. With molecular resolution, we are able to probe lipid-lipid interactions at a level difficult to achieve experimentally. 

M. Muller, K. Katsov, and M. Schick (2003) Coarse-grained models and collective phenomena in membranes Computer simulation of membrane fusion. J. Polym. Sci. B 41, pp. 1441-1450... 

Models and Collective Phenomea in Membranes Computer Simulation of Membrane... 

Interactions between macromolecules (protems, lipids, DNA,.. . ) or biological structures (e.g. membranes) are considerably more complex than the interactions described m the two preceding paragraphs. The sum of all biological mteractions at the molecular level is the basis of the complex mechanisms of life. In addition to computer simulations, direct force measurements [98], especially the surface forces apparatus, represent an invaluable tool to help understand the molecular interactions in biological systems. 

Simple considerations show that the membrane potential cannot be treated with computer simulations, and continuum electrostatic methods may constimte the only practical approach to address such questions. The capacitance of a typical lipid membrane is on the order of 1 j.F/cm-, which corresponds to a thickness of approximately 25 A and a dielectric constant of 2 for the hydrophobic core of a bilayer. In the presence of a membrane potential the bulk solution remains electrically neutral and a small charge imbalance is distributed in the neighborhood of the interfaces. The membrane potential arises from... 

In Sec. 3 our presentation is focused on the most important results obtained by different authors in the framework of the rephca Ornstein-Zernike (ROZ) integral equations and by simulations of simple fluids in microporous matrices. For illustrative purposes, we discuss some original results obtained recently in our laboratory. Those allow us to show the application of the ROZ equations to the structure and thermodynamics of fluids adsorbed in disordered porous media. In particular, we present a solution of the ROZ equations for a hard sphere mixture that is highly asymmetric by size, adsorbed in a matrix of hard spheres. This example is relevant in describing the structure of colloidal dispersions in a disordered microporous medium. On the other hand, we present some of the results for the adsorption of a hard sphere fluid in a disordered medium of spherical permeable membranes. The theory developed for the description of this model agrees well with computer simulation data. Finally, in this section we demonstrate the applications of the ROZ theory and present simulation data for adsorption of a hard sphere fluid in a matrix of short chain molecules. This example serves to show the relevance of the theory of Wertheim to chemical association for a set of problems focused on adsorption of fluids and mixtures in disordered microporous matrices prepared by polymerization of species. 

Let us proceed with the second interesting example concerning application of the ROZ equations. We would Hke first to mention that simple fluids confined to slits with permeable membranes have been studied by both computer simulations and theory, see, e.g.. Refs. 49-52. The simplest way is to visualize a permeable membrane as a barrier of finite height and width. To our best knowledge, no studies of a system containing multiple barriers of a more sophisticated geometry than the sHt-Hke have been undertaken so... 

Our main focus in this chapter has been on the applications of the replica Ornstein-Zernike equations designed by Given and Stell [17-19] for quenched-annealed systems. This theory has been shown to yield interesting results for adsorption of a hard sphere fluid mimicking colloidal suspension, for a system of multiple permeable membranes and for a hard sphere fluid in a matrix of chain molecules. Much room remains to explore even simple quenched-annealed models either in the framework of theoretical approaches or by computer simulation. 

In general, the rate of permeation of the permeating species is difficult to calculate. It is a complex matter which intimately involves a knowledge of the structure and dynamics of the membrane and the structure and dynamics of the complex fluid mixture in contact with it on one side and the solvent on the other side. Realistic membranes with realistic fluids are beyond the possibihties of theoretical treatment at this time. The only way of dealing with anything at all reahstic is by computer simulation. Even then one is restricted to rather simplified models for the membrane. 

The only feasible procedure at the moment is molecular dynamics computer simulation, which can be used since most systems are currently essentially controlled by classical dynamics even though the intermolecular potentials are often quantum mechanical in origin. There are indeed many intermolecular potentials available which are remarkably reliable for most liquids, and even for liquid mixtures, of scientific and technical importance. However potentials for the design of membranes and of the interaction of fluid molecules with membranes on the atomic scale are less well developed. 

The favourable properties which mark out vesicles as protocell models were confirmed by computer simulation (Pohorill and Wilson, 1995). These researchers studied the molecular dynamics of simple membrane/water boundary layers the bilayer surface fluctuated in time and space. The model membrane consisted of glycerine-1-monooleate defects were present which allowed ion transport to occur, whereby negative ions passed through the bilayer more easily than positive ions. The membrane-water boundary layer should be particularly suited to reactions which are accelerated by heterogeneous catalysis. Thus, the authors believe that these vesicles fulfil almost all the conditions required for the first protocells on earth ... 

Pohorille, A. New, M.H. Schweighofer, K. Wilson, M.A., Computer simulations of small molecules in membranes, in Membrane permeability 100 years since Ernst Overton, Deamer, D., Ed., Current Topics in Membranes. Academic San Diego, 1999, pp. 49-76... 

Goetz, R. and Lipowsky, R. (1998). Computer simulations of bilayer membranes self-assembly and interfacial tension, J. Chem. Phys., 108, 7397-7409. 

Pohorille, A., New, M. H., Schweighofer, K. and Wilson, M. A. (1999). Insights from computer simulations into the interactions of small molecules with lipid bilayers. In Membrane Permeability, Vol. 48 100 Years Since Ernest Overton, eds. Deamer, D. W., Kleinzeller, A. and Fambrough, D. M., Academic Press, San Diego pp. 50-76. 

Wong-Ekkabut, J., Baoukina, S., Triampo, W., Tang, I.M., Tieleman, D.P., Monticelli, L. Computer simulation study of fullerene translocation through lipid membranes. Nat. Nanotechnol. 2008, 3, 363-8. 

Faraldo-Gomez, J.D., Forrest, L.R., Baaden, M., Bond, P.J., Domene, C., Patargias, G., Cuthbertson, J., Sansom, M.S.P. Conformational sampling and dynamics of membrane proteins from 10-nanosecond computer simulations. Proteins Struct. Funct. Bioinformatics 2004, 57, 783-91. 

When the concentration in the donor compartment remains constant during the experiment, the concentration in the receptor compartment increases regularly at first, then attains a plateau. For an ideal system with the thickness of a biological membrane a maximum increase in concentration of 130 times can be predicted by computer simulation. This system gives an experimental physicochemical example of a transformation of scalar chemical energy into a vectorial catalysis effect. ... 

When the same kind of electrode is introduced in a solution with a high pH (i.e., pH= 10) and a lower substrate concentration (first order kinetics), an oscillation in time of the measured pH inside the membrane spontaneously occurs. This enzyme, which has been extensively studied, does not give oscillation for any conditions of pH and substrate concentration. The period of oscillation is around one-half minute, and the oscillation is abolished by introducing an enzyme inhibitor. The phenomenon can be explained by the autocatalytic effect and by a feedback action of OH- diffusion in from the outside solution. The diffusion of this ion is quicker than the diffusion of the substrate. There is a qualitative agreement between the computer simulation and the experimental results. 

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