  Coarse-grained modeling and efficient computer simulations are critical to
the study of complex molecular processes with many degrees of freedom and
multiple spatiotemporal scales. Variational implicit-solvent model (VISM) for
biomolecular solvation is such a modeling framework, and its initial success
has been demonstrated consistently. In VISM, an effective free-energy
functional of solute-solvent interfaces is minimized, and the surface energy is
a key component of the free energy. In this work, we extend VISM to include the
solute mechanical interactions, and develop fast algorithms and GPU
implementation for the extended variational explicit-solute implicit-solvent
(VESIS) molecular simulations to determine the underlying molecular equilibrium
conformations. We employ a fast binary level-set method for minimizing the
solvation free energy of solute-solvent interfaces and construct an
adaptive-mobility gradient descent method for solute atomic optimization. We
also implement our methods in GPU. Numerical tests and applications to several
molecular systems verify the accuracy, stability, and efficiency of our methods
and algorithms. It is found that our new methods and GPU implementation improve
the efficiency of the molecular simulation significantly over the CPU
implementation. Our fast computational techniques may enable us to simulate
very large systems such as protein-protein interactions and membrane dynamics
for which explicit-solvent all-atom molecular dynamics simulations can be very
expensive.
