A Wang-Landau study of a lattice model for lipid bilayer self-assembly. 2012

Lili Gai, and Katie Maerzke, and Peter T Cummings, and Clare McCabe
Department of Chemical and Biomolecular Engineering, Vanderbilt University, Nashville, Tennessee 37235, USA.

The Wang-Landau (WL) Monte Carlo method has been applied to simulate the self-assembly of a lipid bilayer on a 3D lattice. The WL method differs from conventional Monte Carlo methods in that a complete density of states is obtained directly for the system, from which properties, such as the free energy, can be derived. Furthermore, from a single WL simulation, continuous curves of the average energy and heat capacity can be determined, which provide a complete picture of the phase behavior. The lipid model studied consists of 3 or 5 coarse-grained segments on lattices of varying sizes, with the empty lattice sites representing water. A bilayer structure is found to form at low temperatures, with phase transitions to clusters as temperature increases. For 3-segment chains, varying lattice sizes were studied, with the observation that the ratio of chain number to lattice area (i.e., area per lipid) affects the phase transition temperature. At small ratios, only one phase transition occurs between the bilayer and cluster phases, while at high lipid ratios the phase transition occurs in a two-step process with a stable intermediate phase. This second phase transition was not observed in conventional Metropolis Monte Carlo simulations on the same model, demonstrating the advantage of being able to perform a complete scan of the whole temperature range with the WL method. For longer 5-segment chains similar phase transitions are also observed with changes in temperature. In the WL method, due to the extensive nature of the energy, the number of energy bins required to represent the density of states increases as the system size increases and so limits its practical application to larger systems. To improve this, an extension of the WL algorithm, the statistical-temperature Monte Carlo method that allows simulations with larger energy bin sizes, has recently been proposed and is implemented in this work for the 3-segment lattice model. The results obtained are in good agreement with the original WL method and appear to be independent of the energy bin size used.

UI MeSH Term Description Entries
D008051 Lipid Bilayers Layers of lipid molecules which are two molecules thick. Bilayer systems are frequently studied as models of biological membranes. Bilayers, Lipid,Bilayer, Lipid,Lipid Bilayer
D008958 Models, Molecular Models used experimentally or theoretically to study molecular shape, electronic properties, or interactions; includes analogous molecules, computer-generated graphics, and mechanical structures. Molecular Models,Model, Molecular,Molecular Model
D008968 Molecular Conformation The characteristic three-dimensional shape of a molecule. Molecular Configuration,3D Molecular Structure,Configuration, Molecular,Molecular Structure, Three Dimensional,Three Dimensional Molecular Structure,3D Molecular Structures,Configurations, Molecular,Conformation, Molecular,Conformations, Molecular,Molecular Configurations,Molecular Conformations,Molecular Structure, 3D,Molecular Structures, 3D,Structure, 3D Molecular,Structures, 3D Molecular
D009010 Monte Carlo Method In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993) Method, Monte Carlo
D006358 Hot Temperature Presence of warmth or heat or a temperature notably higher than an accustomed norm. Heat,Hot Temperatures,Temperature, Hot,Temperatures, Hot
D000465 Algorithms A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task. Algorithm

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