A new approach to constrained total variation solvation models and the study of solute-solvent interface profiles

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.