DynSyst_Special_Topics: Dynamics and Control of Bio-molecular Systems using Geometric Model Reduction and Stochastic Variational Integrators.

提出的研究将为涉及多尺度的随机机械系统的动态模拟和最终控制开发新的几何模型简化方法以及计算方法。这些新的动力学和模拟工具将应用于特定的分子和生物分子系统。几何模型简化中一个令人兴奋的发展是将旋转半径作为粗变量的发展，同时发现了一些特定的精细变量，这些变量可以作为诱发构象变化的触发器。进一步发展和更深入地了解这些触发因素对于最终控制生物分子构象变化和反应将是重要的。伴随着这些几何模型约简技术的是随机异步变分积分方法的理论和计算发展，以及它们在多时间尺度随机机械系统的模拟和控制中的应用。具有多时间尺度和大量自由度的随机多尺度哈密顿系统（可能有约束）的保结构积分器在计算化学、分子动力学和生物物理学中有很大的需求。通过在经典分子动力学开源代码LAMMPS中集成新的类算法，所提出的工作将对这些领域产生直接和实质性的影响。生物分子通常对噪声有很强的抵抗力；同时，这些分子可能对低能量结构驱动有反应。通过计算这些有组织的机制，提出的研究将促进生物分子控制和设计的新范式和新实验方法的发展。通过鉴定恶性细胞和/或已知病原体膜特异性分子的共振频率，提出的研究有可能促进发现和开发一类新的非侵入性和无毒治疗方法。基于碳或金纳米管/纳米棒的注射和电磁激发的新癌症疗法已经处于临床试验阶段。

The proposed research will develop novel geometric model reduction methods along with computational methods for the dynamical simulation and eventual control of stochastic mechanical systems involving multiple-scales. These new dynamical and simulation tools will be applied to specific molecular and biomolecular systems. An exciting development in geometric model reduction has been the development of the radii of gyration as coarse variables along with the discovery of specific fine variables that act as triggers that induce conformation changes. A further development of and deeper understanding of such triggers will be important in the eventual control of biomolecular conformation changes and reactions. Going along with these geometric model reduction techniques is the theoretical and computational development of stochastic asynchronous variational integration methods and their applications to the simulation and control of stochastic mechanical systems spanning many temporal-scales.Structure-preserving integrators for stochastic multiscale Hamiltonian systems (possibly with constraints) characterized by multiple time scales and a large number of degrees of freedom are in great demand in computational chemistry, molecular dynamics and biophysics. The proposed work will have a direct and substantial impact on those fields by integrating a new class algorithms in the classical molecular dynamics open source code LAMMPS. Bio-molecules are in general robust to noise; at the same time, these molecules may be responsive to low energy structured actuation. By allowing for the computation of these organized mechanisms, the proposed research will facilitate the development of a new paradigm and novel experimental methods for the control and design of bio-molecules. The proposed research through the identification of resonant frequencies of molecules specific to the membrane of malignant cells and/or known pathogens has the potential to facilitate the discovery and development of a new class of non-invasive and nontoxic therapies. New cancer therapies based on the injection and electro-magnetic excitation of carbon or gold nanotubes/nanorods are already at the clinical trial stage.