Laguerre-Intersection Method for Implicit Solvation

Abstract

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 introduce surface-dependent corrections to the force field, gaining speed at the expense of accuracy. Properties such as molecular interface surfaces, volumes and cavities are captured by Laguerre tessellations of macromolecules. However, Laguerre cells of exterior atoms tend to be overly large or unbounded. Our method, the inclusion-exclusion based Laguerre-Intersection method, caps cells in a physically accurate manner by considering the intersection of the space-filling diagram with the Laguerre tessellation. We optimize 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, interior 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 fidelity of the Laguerre-Intersection method over two recently proposed methods as compared to the explicit model.