Stochastic dynamics for multiscale biology

描述（由申请人提供）：复杂的生物系统越来越多地受到数学建模的研究，特别是随机模拟。先进的数学方法将用于生成下一代计算方法和算法，用于(1)制定这些模型，(2)模拟或抽样其随机动力学，(3)将其简化为用于多尺度模拟的更简单的近似模型，以及(4)优化其未知或部分已知的参数以适应观察到的行为和/或测量。所提出的方法基于应用统计和随机数学的进展，包括算子代数、量子场论、随机过程、统计物理、机器学习和相关数学基础领域的进展。这项工作的核心技术将是使用化学主方程的算子代数公式。

DESCRIPTION (provided by applicant): Complex biological systems are increasingly subject to investigation by mathematical modeling in general and stochastic simulation in particular. Advanced mathematical methods will be used to generate next-generation computational methods and algorithms for (1) formulating these models, (2) simulating or sampling their stochastic dynamics, (3) reducing them to simpler approximating models for use in multiscale simulation, and (4) optimizing their unknown or partly known parameters to fit observed behaviors and/or measurements. The proposed methods are based on advances in applied statistical and stochastic mathematics, including advances arising from operator algebra, quantum field theory, stochastic processes, statistical physics, machine learning, and related mathematically grounded fields. A central technique in this work will be the use of the operator algebra formulation of the chemical master equation. The biological systems to be studied include and are representative of high-value biomedical target systems whose complexity and spatiotemporal scale requires improved mathematical and computational methods, to obtain the scientific understanding underlying future medical intervention. Cancer research is broadly engaged in signal transduction systems and complexes with feedback, for which the yeast Ste5 MARK pathway is a model system. DNA damage sensing (through ATM) and repair control (though p53 and Mdm2) are at least equally important to cancer research owing to the central role that failure of these systems play in many cancers. The dendritic spine synapse system is central to neuroplasticity and therefore human learning and memory. It is critical to understand this neurobiological system well enough to protect it against neurodegenerative diseases and environmental insults. The project seeks fundamental mathematical breakthroughs in stochastic and multiscale modeling that will enable the scientific understanding of these complex systems necessary to create effective medical interventions of the future.