Computer simulation lipid bilayer

There has been considerable interest in the simulation of lipid bilayers due to their biological importance. Early calculations on amphiphilic assemblies were limited by the computing power available, and so relatively simple models were employed. One of the most important of these is the mean field approach of Marcelja [Marcelja 1973, 1974], in which the interaction of a single hydrocarbon chain with its neighbours is represented by two additional contributions to the energy function. The energy of a chain in the mean field is given by ... 

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... 

Figure 13 Center-of-mass mean-square displacements computed from MD simulations at 323 K. (a) DPPC motion in the plane of a lipid bilayer averaged over 10 ps (b) DPPC motion in the plane of a lipid bilayer averaged over 100 ps (c) comparison of the DPPC m-plane mean-square displacement to linear and power law functions of time (d) comparison of the center-of-mass mean-square displacement from an MD simulation of liquid tetradecane to a linear function of time.

A review is given of the application of Molecular Dynamics (MD) computer simulation to complex molecular systems. Three topics are treated in particular the computation of free energy from simulations, applied to the prediction of the binding constant of an inhibitor to the enzyme dihydrofolate reductase the use of MD simulations in structural refinements based on two-dimensional high-resolution nuclear magnetic resonance data, applied to the lac repressor headpiece the simulation of a hydrated lipid bilayer in atomic detail. The latter shows a rather diffuse structure of the hydrophilic head group layer with considerable local compensation of charge density. 

The previous result is an important one. It indicates that there can be yet another fruitful route to describe lipid bilayers. The idea is to consider the conformational properties of a probe molecule, and then replace all the other molecules by an external potential field (see Figure 11). This external potential may be called the mean-field or self-consistent potential, as it represents the mean behaviour of all molecules self-consistently. There are mean-field theories in many branches of science, for example (quantum) physics, physical chemistry, etc. Very often mean-field theories simplify the system to such an extent that structural as well as thermodynamic properties can be found analytically. This means that there is no need to use a computer. However, the lipid membrane problem is so complicated that the help of the computer is still needed. The method has been refined over the years to a detailed and complex framework, whose results correspond closely with those of MD simulations. The computer time needed for these calculations is however an order of 105 times less (this estimate is certainly too small when SCF calculations are compared with massive MD simulations in which up to 1000 lipids are considered). Indeed, the calculations can be done on a desktop PC with typical... 

Xiang, T. X. and Anderson, B. D. (2002). A computer simulation of functional group contributions to free energy in water and a DPPC lipid bilayer, Biophys. J., 82, 2052-2066. 

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. 

MacCallum, J.L., Bennett, W.F.D., Tieleman, D.P. Distribution of amino acids in a lipid bilayer from computer simulations. Biophys. J. 2008, 94, 3393 04. 

Since frequencies for EPR spectroscopy are -100 times higher than those for NMR spectroscopy, correlation times (Chapter 3) must be less than 10-9 s if sharp spectra are to be obtained. Sharp bands may sometimes be obtained for solutions, but samples are often frozen to eliminate molecular motion spectra are taken at very low temperatures. For spin labels in lipid bilayers, both the bandwidth and shape are sensitively dependent upon molecular motion, which may be either random or restricted. Computer simulations are often used to match observed band shapes under varying conditions with those predicted by theories of motional broadening of lines. Among the many spin-labeled compounds that have been incorporated into lipid bilayers are the following ... 

H. Heller, M. Schaefer, and K. Schulten, Workshop on High Performance Computing and Grand Challenges in Structural Biology, Florida State University, Tallahassee, FL, Jan. 24-27, 1992. Construction, Molecular Dynamics Simulation and Analysis of a Lipid Bilayer. 

Bemporad D, Essex JW, Luttmann C. Permeation of small molecules through a lipid bilayer A computer simulation study. J Phys Chem B 2004 108 4875-84. 

Bemporad D, Luttmann C, Essex JW. Computer simulation of small molecule permeation across a lipid bilayer Dependence on bilayer properties and solute volume, size, and cross-sectional area. Biophys J 2004 87 1-13. 

The top panel of Fig. 3.2 presents a selection of results for the lateral organization of some simple one- and two-component lipid bilayers that have been investigated by computer-simulation calculations and atomic force microscopy. A pronounced degree of lateral heterogeneity in terms of lipid domains is found. The lipid domains are either solid hpid patches in fluid bilayers or fluid lipid patches in solid bilayers. In lipid mixtures, the domains may reflect incomplete phase separation. The sizes, the morphology, and the topology of the lipid domain patterns depend on the lipid composition and the thermodynamic conditions. The domains can be enhanced or suppressed by adding further lipid components or solutes [36]. 

The QCM has added valuable information about the mechanism of vesicle fusion on a surface. For instance, Kasemo and coworkers have unraveled the formation of planar lipid bilayers on Si02 and glassy surfaces by means of the QCM with dissipation (QCM-D) technique in conjunction with SPR, atomic force microscopy (AFM), and computer simulations [5-12]. They found that the process of bilayer formation occurs in three successive steps (1) in the first stage, vesicles attach to the surface via inter molecular interactions (2) at a critical surface coverage, the vesicles start to rupture, fuse on the surface, and thus form bilayer islands coexisting with vesicles and uncovered substrate (3) eventually, a coherent bilayer is formed covering the entire surface. 

The force calculation method described here promises to be of value in a variety of molecular mechanics simulations. It should be particularly useful in calculations on systems of high charge density, such as nucleic acids and lipid bilayers, where the accurate treatment of solvent by means of the explicit treatment of water molecules and ions is most computationally challenging. Preliminary calculations on small molecules show that the method can readily be incorporated into standard energy minimization and molecular dynamics computations. 

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