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一般的数学建模，特别是随机模拟的调查。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）模拟或采样其随机动态，（3）将其简化为更简单的近似模型，用于多尺度模拟，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。所提出的方法是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，机器学习和相关的数学接地领域所产生的进步。在这项工作中的一个中心技术将是使用的化学主方程的算子代数制定。 待研究的生物系统包括并代表高价值的生物医学目标系统，其复杂性和时空尺度需要改进的数学和计算方法，以获得未来医疗干预的科学理解。癌症研究广泛涉及信号转导系统和具有反馈的复合物，其中酵母Ste 5 MARK通路是模型系统。DNA损伤检测（通过ATM）和修复控制（通过p53和Mdm 2）至少对癌症研究同样重要，因为这些系统的失败在许多癌症中发挥着核心作用。树突棘突触系统是神经可塑性的核心，因此人类的学习和记忆。了解这个神经生物学系统是至关重要的，足以保护它免受神经退行性疾病和环境的伤害。该项目寻求在随机和多尺度建模方面的基本数学突破，这将使科学理解这些复杂系统，从而创造未来有效的医疗干预措施。

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.