Computational Modeling and Numerical Analysis of Solvation of Molecules

本计画系关于分子溶剂化的电脑研究--溶剂分子（如水或盐水）与溶质分子（如酒精、蛋白质等）的吸引与缔合。分子。 PI发展了一种新的连续介质-溶剂方法，定义了一个平衡溶质-溶剂界面，以最小化溶剂化自由能泛函，该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，包括不同类型的分子相互作用，（2）溶质原子的分子力学，（3）溶质原子的分子动力学。（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中的其他研究密切相关，如曲面的几何运动和多尺度计算。 PI实现了几种新的计算技术，包括初始解的构造、有效的局部方法和自由能的稳定计算。 他还进行了相关的数值分析的收敛性，稳定性和错误。 通过与分子动力学模拟和已知实验的比较，验证了所提出的理论和方法的正确性。 例如，药物治疗疾病，因为正确的分子相互作用发生。 尽管人们在药物设计的研究上付出了很多努力，但现在人们普遍认为必须发展新的理论。在这方面，拟议的研究具有很大的意义，因为它将严格的数学引入了具有挑战性的生命科学研究。 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好地治疗疾病，制造新的生物材料，可以更好地保护我们的家园，并开发先进的纳米技术，使我们能够操纵分子为我们的日常生活。 除了在许多国家感兴趣的领域的潜在应用外，该项目还创建了一个教育和培训计划，为数学学生做好生物科学研究的准备。 这显然是一项必要和具有挑战性的任务。

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.