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A Metropolis Monte Carlo method has been developed for studying the effects of dielectric constant and counterion charge density and distribution on the energetics of formation and equilibria of the regular arrays or domain structures formed by bacterial lipopolysaccharides. The method utilizes a regular triangular prism primitive as a reductive structural representation of each lipopolysaccharide anchor (lipid A molecule). Charges for the two phosphate groups are localized at one apex and midway along the opposite side of the regular triangular top face of each prism. The counterions are not localized but are represented as a fine cloud of charge modeled by distributing the total charge over a fine two-dimensional cubic lattice. The six alkyl chains of the lipid A molecule are aligned along the long axes of the prism and are contained by its faces. All prisms are confined to the same plane but are allowed to translate within the plane and to rotate about axes perpendicular to the plane. The potential energy function contains an electrostatic term and a van der Waals term. A discontinuous dielectric is used to separate the aqueous and hydrophobic areas of the system. Trial moves involve both a rotational and a translational operation. The configurations predicted by this method are consistent with the crystal morphologies which have been observed for lipopolysaccharides. This analysis readily allows the evaluation of thermodynamic properties, such as heat capacity, entropy, and energy. The root mean square average separation of units was also calculated as a function of iteration number.

A metropolis Monte Carlo method for analyzing the energetics and dynamics of lipopolysaccharide supramolecular structure and organization