This project concerns computer studies of the solvation of molecules---the attraction and association of the solvent (such as water or salted water) molecules with solute (such as alcohol, protein, etc.) molecules. The PI develops a new continuum-solvent approach in which an equilibrium solute-solvent interface is defined to minimize a solvation free-energy functional. There are three essential components of this new approach: (1) a diffuse-interface description of solute-solvent interfaces that incorporates different kinds of molecular interactions; (2) the molecular mechanics of solute atoms; and (3) a multiscale method for the solute-solvent molecular interaction and the motion of solute atoms. All these are closely connected to other studies in applied and computational mathematics such as geometrical motions of surfaces and multiscale computations. The PI implements several new computational techniques, including the construction of initial solutions, an efficient local method, and stable calculations of free energy. He also carries out the related numerical analysis on convergence, stability, and errors. The proposed theory and methods are validated by the comparison with molecular dynamics simulations and known experiments.
Molecular interactions determine structures and functions of biological systems. For example, drug cure diseases because the correct molecular interactions occur. While much effort has been made to the study of drug designs, it is now widely accepted that new theories must be developed. In this regard, the proposed research is of great interest, since it brings rigorous mathematics into a challenging study of life sciences. It is hoped that results of this project can be used to better understand why some drugs cure diseases better than others, to make new biomaterial that can better protect our homeland, and to develop sophisticated nanotechnologies that allow us to manipulate molecules for our daily lives. In addition to potential applications to many areas of national interest, this project creates an education and training program that prepares mathematics students to do research in biologcal science. This is clearly a needed and challenging task.
