CAREER: Scalable Mathematical and Computational Models for Biomolecular Modeling

拟议的活动旨在创建建模大生物分子的数学和计算方法。蛋白质、DNA和核酸的动力学和采样的计算机模拟有望成为理解结构和功能之间的关系以及计算机辅助药物设计的工具。感兴趣的过程包括蛋白质动力学和折叠以及对其他细胞成分的研究。尽管在这一领域取得了重大进展，但在目前技术可以常规进行的模拟与具有生物学意义的过程和系统的复杂性之间仍然存在差距。所提出的数学和计算方法将克服原子动力学和采样所固有的大小和时间尺度限制，同时保持生物系统的原子分辨率。新方法将通过一个名为ProtoMol的开源和可扩展软件框架传播用于研究和教育目的，并在一系列系统中进行测试，从小蛋白到驻留在脂质双层中的钾通道。这些新算法将转化为比当前方法快一个或多个数量级的加速。这项技术将使扩大的蛋白质组学领域和处理来自人类基因组计划的数据时迫切需要的模拟成为可能。为了研究动力学过程，利用分子动力学(MD)生成了生物大分子的轨迹。为了克服时间尺度的限制，引入了多时间步(MTS)积分器。然而，即使是这些方法也受到稳定性的限制，因此在MD中使用的时间步长并没有显著增加。PI建议为MD设计不受稳定性限制的多尺度算法。为了实现这一目标，研究将分两个阶段进行：_rst将通过克服这些方法中存在的不稳定性来扩展PI在更稳定的MTS数值积分器方面的工作。这将使MD的速度比目前的方法快两到八倍。第二阶段包括使用辛半隐式方法来计算MD，该方法使用一种分裂来清楚地分离多个时间尺度，并以更接近的方式合并较快和不那么有趣的时间尺度。根据所需的精确度，加速两个数量级或更多是可能的。这项建议还将解决统计抽样的相关问题。生物分子体系大的构象空间给传统的采样方法，如MD和蒙特卡罗方法，或两者的结合带来了许多困难，所有这些方法的超级性能都随着系统规模的增加而下降。我们将使用一种有偏的混合蒙特卡罗方法，该方法几乎与系统大小成线性关系。这将比MD、MC或传统的混合MC方法加速一到两个数量级。这项研究项目和教学之间的协同作用将在几个层面上发生。在数据结构和应用算法、数值方法和生物分子建模的计算方法方面，将加强由PI教授的本科生和研究生课程的材料。工程和理科学生的学习模块将在ProtoMol中开发，以促进对生物大分子行为的理解。

The proposed activities aim to create mathematical and computational methods for modeling large biological molecules. Computational simulation of dynamics and sampling of proteins, DNA, and nucleic acids promise to be a tool for understanding the relationship between structure and function, and for computer assisted drug design. Processes of interest include protein dynamics and folding and the study of other cellular components. Despite significant progress in the field, there is still a gap between the simulations that can be routinely performed with current technology and the complexity of processes and systems of biological interest. The proposed mathematical and computational methods will overcome the size and time scale limitations inherent in atomistic dynamics and sampling, while preserving the atomistic resolution of the biological systems. The new methods will be disseminated for research and educational purposes through an open source and scalable software framework called ProtoMol, and tested in a range of systems, from small proteins to potassium channels that reside in lipid bilayers. These new algorithms will translate into speedups of one or more orders of magnitude over current methodologies. This technology will enable simulations that are sorely needed in the expanding field of proteomics and the processing of data from the human genome project. To study dynamical processes, trajectories of large biomolecules are generated using molecular dynamics (MD). In an attempt to overcome the time scale limitations, multiple time stepping (MTS) integrators have been introduced. Nevertheless, even these methods have been limited by stability, and thus the time steps used in MD have not been dramatically increased. The PI proposes to devise multiscale algorithms for MD that are not limited by stability. To accomplish this goal, research will proceed in two phases: the _rst will extend the PI's work on stabler MTS numerical integrators by overcoming instabilities present in these methods. This will allow an estimated two- to eight-fold speedup over current methods for MD. The second phase involves the use of a symplectic semi-implicit method for MD using a splitting that separates cleanly many time scales, and incorporates the faster and less interesting ones in a more approximate manner. Speedups of two orders of magnitude or more are possible, depending on the degree of accuracy desired. This proposal will also tackle the related problem of statistical sampling. The large conformational space of biomolecular systems causes many difficulties to traditional sampling methodologies such as MD and Monte Carlo methods, or hybrids of both, all of which super performance degradation as the system size increases. We will use a biased hybrid Monte Carlo method that scales nearly linearly with system size. This will produce speedups of one or two orders of magnitude over MD, MC, or conventional hybrid MC methods. Synergy between this research project and teaching will occur at several levels. There will be an enhancement of materials of undergraduate and graduate courses taught by the PI, on data structures and applied algorithms, numerical methods, and computational methods for biomolecular modeling. Learning modules for engineering and science students will be developed in ProtoMol to facilitate an understanding of the behavior of large biological molecules.