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

拟议的研究将开发新的几何模型简化方法沿着与计算方法的动态模拟和最终控制的随机力学系统，涉及多尺度。这些新的动力学和模拟工具将被应用于特定的分子和生物分子系统。几何模型简化的一个令人兴奋的发展是旋转半径作为粗变量的发展，沿着发现了特定的细变量，这些细变量作为引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器将是重要的生物分子构象变化和反应的最终控制。与这些几何模型降阶技术一起沿着的是随机异步变分积分方法的理论和计算发展，以及它们在跨越多个时间尺度的随机力学系统的模拟和控制中的应用。随机多尺度Hamilton系统的保结构积分器在计算化学、分子动力学和生物物理学中，以多个时间尺度和大量自由度为特征的（可能具有约束）方法有着巨大的需求。通过在经典分子动力学开放源代码LAMMPS中集成一类新的算法，本文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是鲁棒的;同时，这些分子可以响应于低能量结构化致动。通过允许这些有组织的机制的计算，拟议的研究将促进一个新的范例和新的实验方法的控制和设计的生物分子的发展。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，拟议的研究有可能促进发现和开发一类新的非侵入性和无毒疗法。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.