非高斯随机动力系统分析及其应用

This project mainly studies the dynamic behavior of Non-gaussian stochastic dynamical systems and its application in biophysics. Stochastic fluctuations play an important role in inducing phenotypic diversity in gene expression process, moreover, the production of proteins occur in a burst, so it is more suitable to use Non-Gaussian Lévy noise to express the fluctuations of gene regulation systems. The details of the project are as follows: (1) The project will characterize the maximal likely trajectories for the stochastic gene regulation system by nonlocal Fokker-Planck equation; (2) The project will examine the most probable transition pathways under non-Gaussian Lévy noise by minimizing the Onsager-Machlup action functional, to characterize the most probable transition pathways between different metastable states for the stochastic gene regulation system; (3) The project will consider the molecular and cellular biological phenomena of stochastic narrow escape and microtubule transport by asymptotic analysis and stochastic numerical simulation. The aim of this project is to develop new methods for studying non-gaussian stochastic dynamical systems and to apply them to molecular cytology. We make quantitative prediction through the dynamic system model with predictable function, and then analyze the information of the stochastic dynamical systems through available experimental data. In this way, the developed models will provide new insights into non-Gaussian stochastic dynamics.

本项目主要研究非高斯随机动力系统的动力学行为的刻画及其在生物物理领域的应用。基于基因表达过程中随机噪声是诱发表型多样性的重要因素，且非高斯Lévy过程能够更准确的模拟基因表达过程蛋白质生成过程的突发脉冲性质。项目具体内容：(1)通过非局部Fokker-Planck方程，刻画非高斯Lévy噪声影响下基因调控系统的最可能的演化轨道；（2）通过最小化Onsager-Machlup作用泛函刻画随机基因调控系统在不同亚稳态之间的最可能的转移路径；（3）通过渐近分析和随机数值模拟考虑细胞内离子从细胞膜上的离子通道逃离出的分子细胞生物学现象以及微管运输现象。本项目旨在发展新的研究非高斯随机动力系统的方法，并运用到分子细胞学实例中。项目借助具有可预测功能的动力系统模型做出定量预测，进而通过已有实验数据分析随机系统的信息，为细胞生物学的非高斯随机动力学研究提供新方法和新工具。

随机动力系统是对随机因素影响下复杂系统的合适的数学建模，能够描述一些确定性系统所不能描述的现象。本项目通过随机动力系统的确定性量化，刻画了细胞内离子从细胞膜上的离子通道逃离出的分子细胞生物学现象以及微管运输现象，将随机动力系统和非局部偏微分方程联系起来，从而提出了一种研究细胞生物随机动力系统的新思路。基于Fokker-Planck方程和Onsager-Machlup作用泛函，通过最小化Onsager-Machlup作用泛函，构建了最有可能转移路径，刻画了细胞内受体和配体结合的最可能位点和最大结合概率。通过渐近分析和随机数值模拟，项目研究为由数据驱动的随机动力系统的建模提供理论和技术的支持，为细胞生物学的随机动力学研究提供新方法和新工具。