Hybrid Computational Models and Robust Numerical Methods for Electrostatic Interactions in Biomolecules

该项目开发了生物分子系统中静电相互作用的混合计算模型和稳健的数值方法。在不同的层次上建立了计算模型。它们包括具有原子细节的变分平均场模型，特别是离子尺寸效应，以及处理单个离子的蒙特卡罗模拟模型。这些模型与一种先进的生物分子溶剂化变分方法相结合。设计并分析了一种求解椭圆界面问题和计算介质边界力的稳健数值方法。为了加速相关的大规模计算，开发了特殊的接口代数多重网格法和GPU(图形处理单元)实现。数值分析的重点是所提出的格式的精度，特别是边界力近似的精度。蛋白质和DNA等生物分子是原子的集合，其中很大一部分是带电的。带电的生物分子使溶剂(水或盐水)极化，并产生离子，这些离子是溶液中可移动的带电粒子。静电或电荷相互作用产生的强大作用力决定了潜在生物系统的结构、动力学和功能。例如，静电相互作用影响药物分子与目标分子的结合方式，这反过来又决定了药物在治疗疾病的过程中的有效性。通过现代数学理论和计算工具的发展，该项目旨在从分子水平上了解生物系统的基本原理，并推动计算数学的研究。该项目的成功可能有助于降低实验经常需要的高昂成本，并加快药物发现的进程。此外，这种高度跨学科的研究为不同水平的学生带来了在计算数学和分子生物科学的界面上接受培训的机会。这样的培训对于在竞争激烈的国际环境中保持我们的科研实力至关重要。

This project develops hybrid computational models and robust numerical methods for electrostatic interactions in biomolecular systems. The computational models are constructed at different levels. They include variational mean-field models with atomistic details, particularly ionic size effects, and Monte Carlo simulation models for treating individual ions. These models are coupled with an advanced, variational approach to the solvation of biomolecules. A robust numerical method for solving the related elliptic interface problem and calculating the dielectric boundary force is designed and analyzed. Special interface algebraic multigrid methods and the GPU (Graphics Processing Unit) implementation are developed to accelerate the related large-scale computations. Numerical analysis focuses on the accuracy of the proposed schemes, particularly that of the boundary force approximation.Biomolecules such as proteins and DNA are assemblies of atoms of which a significant portion are charged. Charged biomolecules polarize the solvent (water or salted water) and produce ions that are mobile charged particles in the solution. The electrostatic or charge-charge interaction gives rise to strong forces that determine the structure, dynamics, and function of underlying biological systems. For instance, the electrostatic interaction affects how a drug molecule binds to a target molecule, which in turn determines how effective the drug is in the process of curing a disease. Through the development of modern mathematical theories and computational tools, this project aims at understanding the fundamental principles of biological systems at the molecular level and advancing the research of computational mathematics. The success of this project can potentially help reduce the high cost often needed for experiments and speed up the process of drug discovery. In addition, this highly interdisciplinary research brings opportunities for students at different levels to receive training at the interface of computational mathematics and molecular biological science. Such training is critical to keeping our strength in scientific research in an competitive international environment.