  In this article, we apply the binary level set method to the Variational
Implicit Solvent Model (VISM), which is a theoretical and computational tool to
study biomolecular systems with complex topology. Central in VISM is an
effective free energy of all possible interfaces separating solutes (e.g.,
proteins) from solvent (e.g., water). Previously, such a functional is
minimized numerically by the level set method to determine the stable
equilibrium conformations and solvation free energies. We vastly improve the
speed by applying the binary level set method, in which the interface is
approximated by a binary level set function that only takes value $\pm 1$ on
the solute/solvent region, leading to a discrete formulation of VISM energy.
The surface area is approximated by convolution of an indicator function with a
compactly supported kernel. The VISM energy can be minimized by iteratively
"flipping" the binary level set function in a steepest descent fashion.
Numerical experiments are performed to demonstrate the accuracy and performance
of our method.
