A fast variational method for the construction of resolution adaptive [formula omitted]-smooth molecular surfaces

Abstract

We present a variational approach to smooth molecular (proteins, nucleic acids) surface constructions, starting from atomic coordinates, as available from the protein and nucleic acid data banks. Molecular dynamics (MD) simulations traditionally used in understanding protein and nucleic acid folding processes, are based on molecular force fields, and require smooth models of these molecular surfaces. To accelerate MD simulations, a popular methodology is to employ coarse grained molecular models, which represent clusters of atoms with similar physical properties by psuedo-atoms, resulting in coarser resolution molecular surfaces. We consider generation of these mixed-resolution or adaptive molecular surfaces. Our approach starts from deriving a general form second order geometric partial differential equation in the level-set formulation, by minimizing a first order energy functional which additionally includes a regularization term to minimize the occurrence of chemically infeasible molecular surface pockets or tunnel-like artifacts. To achieve even higher computational efficiency, a fast cubic B-spline C 2 interpolation algorithm is also utilized. A narrow band, tri-cubic B-spline level-set method is then used to provide C 2 smooth and resolution adaptive molecular surfaces.