Computational Modeling and Numerical Analysis of Solvation of Molecules

本项目涉及分子溶剂化的计算机研究——溶剂（如水或盐水）分子与溶质（如酒精、蛋白质等）分子的相互吸引和结合。PI开发了一种新的连续溶剂方法，其中定义了平衡溶质-溶剂界面，以最小化溶剂化自由能泛函。这种新方法有三个基本组成部分：(1)溶质-溶剂界面的扩散界面描述，其中包含不同种类的分子相互作用；(2)溶质原子的分子力学；(3)溶质-溶剂分子相互作用和溶质原子运动的多尺度方法。所有这些都与应用数学和计算数学的其他研究密切相关，例如曲面的几何运动和多尺度计算。PI实现了一些新的计算技术，包括初始解的构造、有效的局部方法和稳定的自由能计算。他还对收敛性、稳定性和误差进行了相关的数值分析。通过与分子动力学模拟和已知实验的比较，验证了所提理论和方法的正确性。分子间的相互作用决定了生物系统的结构和功能。例如，药物治愈疾病是因为正确的分子相互作用发生了。虽然在研究药物设计方面已经付出了很大的努力，但现在人们普遍认为必须发展新的理论。在这方面，提议的研究是非常有趣的，因为它将严格的数学带入了具有挑战性的生命科学研究中。希望这个项目的结果可以用来更好地理解为什么有些药物比其他药物更能治愈疾病，制造新的生物材料，更好地保护我们的家园，并开发复杂的纳米技术，使我们能够在日常生活中操纵分子。除了在许多国家利益领域的潜在应用之外，该项目还创建了一个教育和培训计划，为数学专业的学生做生物科学研究做准备。这显然是一项必要且具有挑战性的任务。

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.