Laguerre-Intersection Method for Implicit Solvation

Abstract: Laguerre tessellations of macromolecules capture properties such as molecular interface surfaces, volumes and cavities. Explicit solvent molecular dynamics simulations of a macromolecule are slow as the number of solvent atoms considered typically increases by order of magnitude. Implicit methods model the solvent via continuous corrections to the force field based on estimates of the solvent exposed surface areas of individual atoms, gaining speed at the expense of accuracy. However, Laguerre cells of exterior atoms tend to be overly large or unbounded. Our method, the Laguerre-Intersection method, caps cells in a physically accurate manner by considering the intersection of the space-filling diagram with the Laguerre tessellation. This method optimizes an adjustable parameter, the weight, to ensure the areas and volumes of capped cells exposed to solvent are as close as possible, on average, to those computed from equilibrated explicit solvent simulations. The contact planes are radical planes, meaning that as the solvent weight is varied, cells remain constant. We test the consistency of our model using a high-quality trajectory of HIV-protease, a dimer with flexible loops and open-close transitions. We also compare our results with interval-arithmetic Gauss-Bonnet based method. Optimal solvent parameters quickly converge, which we use to illustrate the increased accuracy of the Laguerre-Intersection method over two recently proposed methods as compared to the explicit model.