Optimum Monte Carlo Simulations: Some Exact Results

We obtain exact results for the acceptance ratio and mean squared displacement in Monte Carlo simulations of the simple harmonic oscillator in $D$ dimensions. When the trial displacement is made uniformly in the radius, we demonstrate that the results are independent of the dimensionality of the space. We also study the dynamics of the process via a spectral analysis and we obtain an accurate description for the relaxation time.Comment: 17 pages, 8 figures. submitted to J. Phys.

Simulations of a single membrane between two walls using a Monte Carlo method

Quantitative theory of interbilayer interactions is essential to interpret x-ray scattering data and to elucidate these interactions for biologically relevant systems. For this purpose Monte Carlo simulations have been performed to obtain pressure P and positional fluctuations sigma. A new method, called Fourier Monte-Carlo (FMC), that is based on a Fourier representation of the displacement field, is developed and its superiority over the standard method is demonstrated. The FMC method is applied to simulating a single membrane between two hard walls, which models a stack of lipid bilayer membranes with non-harmonic interactions. Finite size scaling is demonstrated and used to obtain accurate values for P and sigma in the limit of a large continuous membrane. The results are compared with perturbation theory approximations, and numerical differences are found in the non-harmonic case. Therefore, the FMC method, rather than the approximations, should be used for establishing the connection between model potentials and observable quantities, as well as for pure modeling purposes.Comment: 10 pages, 10 figure

A Simple Model of Liquid-liquid Phase Transitions

In recent years, a second fluid-fluid phase transition has been reported in several materials at pressures far above the usual liquid-gas phase transition. In this paper, we introduce a new model of this behavior based on the Lennard-Jones interaction with a modification to mimic the different kinds of short-range orientational order in complex materials. We have done Monte Carlo studies of this model that clearly demonstrate the existence of a second first-order fluid-fluid phase transition between high- and low-density liquid phases

Monte Carlo study of the effect of beta 2-microglobulin on the binding cleft of the HLA-A2 complex.

Peptide recognition by class I products of the major histocompatibility complex requires association of the class I heavy chain with beta 2-microglobulin. We present results of Monte Carlo simulations of the beta-pleated sheet floor of the human class I MHC molecule, HLA-A2, with and without beta 2-microglobulin. We find a significant effect of beta 2-microglobulin on the side chains of residues near a region that would accommodate the C-terminus of a bound peptide. By modeling simultaneously each loop and its neighboring strand at either end of the class I cleft, we find that beta 2-microglobulin restricts the conformational space of residues that are central to binding peptides. The effect is most pronounced for R97 and H114 and somewhat less important for Y99 and Y116, the latter forming strong hydrogen bonds with neighboring residues in the heavy chain itself