  In the past decade, variational implicit solvation models (VISM) have
achieved great success in solvation energy predictions. However, all existing
VISMs in literature lack the uniqueness of an energy minimizing solute-solvent
interface and thus prevent us from studying many important properties of the
interface profile. To overcome this difficulty, we introduce a new constrained
VISM and conduct a rigorous analysis of the model. Existence, uniqueness and
regularity of the energy minimizing interface has been studied. A necessary
condition for the formation of a sharp solute-solvent interface has been
derived. Moreover, we develop a novel approach to the variational analysis of
the constrained model, which provides a complete answer to a question in our
previous work [55]. Model validation and numerical implementation have been
demonstrated by using several common biomolecular modeling tasks. Numerical
simulations show that the solvation energies calculated from our new model
match the experimental data very well.

Analysis of PDEs