Treecode-Accelerated Implicit Solvent Models for Biomolecular Simulations

目前的生物分子模拟无法达到研究构象变化（如蛋白质折叠）所需的长时间尺度。其中一个主要的障碍是计算蛋白质周围溶剂水分子之间的静电力的高成本。为了解决这个问题，本项目采用了一种隐式溶剂模型，其中静电势满足Poisson-Boltzmann（PB）方程。由于分子表面的几何复杂性、介电函数的不连续性和计算域的无界性，PB方程的数值解提出了挑战。研究人员将克服这些困难，开发一个边界积分PB求解器使用一个新的笛卡尔树码算法屏蔽库仑相互作用。树码加速的PB求解器将在基准示例（如柯克伍德的球面解）上进行测试，并将结果与使用其他PB求解器获得的结果进行比较。除了静电势，该代码将被扩展到计算其他重要的数量，如溶剂化自由能和溶剂化动力学所需的力量。 当前生物分子模拟面临的一个障碍是计算系统中分子之间的自诱导静电力的费用。单靠计算机硬件的进步还不能达到研究长时间分子动力学所必需的改进。因此，该项目的重点是改进这些计算机模拟中使用的数学算法。除了能够实现更准确和有效的生物分子模拟外，所开发的算法还可能用于静电力发挥作用的其他应用，例如在燃料电池中建模电荷传输。该项目将通过支持将由PI指导的博士后的研究来帮助培训科学劳动力。

Current biomolecular simulations are unable to reach the long time scales needed to study conformation changes such as protein folding. One of the main obstacles is the high cost of computing the electrostatic forces among the solvent water molecules surrounding the protein. To address this issue, this project adopts an implicit solvent model in which the electrostatic potential satisfies the Poisson-Boltzmann (PB) equation. Numerical solution of the PB equation poses a challenge due to the geometric complexity of the molecular surface, the discontinuity in the dielectric function, and the unbounded computational domain. The investigators will overcome these difficulties by developing a boundary integral PB solver using a new Cartesian treecode algorithm for screened Coulomb interactions. The treecode-accelerated PB solver will be tested on benchmark examples such as Kirkwood's solution for a spherical surface, and the results will be compared with those obtained using other PB solvers. In addition to the electrostatic potential, the code will be extended to compute other important quantities such as the solvation free energy and solvation forces needed for dynamics. One obstacle facing current biomolecular simulations is the expense of computing the self-induced electrostatic forces among the molecules in the system. Advances in computer hardware alone won't achieve the improvements necesssary for studying long time molecular dynamics. This project therefore focuses on improving the mathematical algorithms used in these computer simulations. In addition to enabling more accurate and efficient biomolecular simulations, the algorithms developed will be potentially useful in other applications where electrostatic forces play a role, for example in modeling charge transport in fuel cells. The project will contribute to training the scientific workforce by supporting the research of a postdoc who will be mentored by the PI.