Multi-scale stochastic systems motivated by biological models

由生物模型驱动的多尺度随机系统

• 批准号: RGPIN-2015-06573
• 负责人: Popovic, Lea
• 金额: $ 1.24万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=708535
• 关键词: Multi; scale; stochastic; systems; motivated

The challenge of systems biology is identifying how interactions of the proteome and genome produce the function and behaviour of a cell. Cells are inherently "noisy" systems, and how complex biochemical pathways are affected by intrinsic and extrinsic stochasticity is not well understood. A cellular network can be modelled mathematically using the principles of chemical kinetics. At the cellular level, chemical dynamics are often dominated by the action of regulatory molecules present at levels of only a few copies per cell. Intrinsic noise due to random fluctuations of these components can have significant consequences, and stochastic modelling is necessary in order to fully describe the set of possible outcomes. In many cases reaction rates can also vary over several orders of magnitude, which implies that fluctuations of effective changes in abundances occur on multiple time-scales. Many important intracellular processes, from biochemical signalling to gene regulation, are also greatly affected by the location and motility of the molecular types involved. Stochastic models of these systems use density dependent continuous time Markov chains to represent the evolution of different types of species connected by the prescribed set of interactions between them. For prediction and simulation purposes it is useful to reduce the modelling and computational complexity of the problem, while still capturing the essential stochastic behaviour of the system. The multiscale nature of the models may be exploited in order to reduce some of the complexity. A rigorous approach poses a number of interesting and challenging mathematical questions. The primary goal of my research program is to develop model reduction techniques for such stochastic models and identify the possible effects due to noise. This involves deriving novel results combining nonlinear dynamics with stochastic averaging, diffusion approximations and large deviations for density dependent Markov chains on multiple time scales. Specific short and long term goals will allow us to better understand: (i) the combined effect of stochastic reactions and molecular movement in spatial propagation of outcomes; as well as (ii) the effect of rare events in multi-scale reaction dynamics, and their role in enhancing and spatially spreading bistable dynamics and specific initial outcomes. In the long run, they will help us identify a set of spatial phenomena arising in heterogeneous reaction systems with multiple time-scales, and conditions under which they arise. The mathematical tools developed along the way will allow us to give a probabilistic analysis of the long term behaviour of heterogeneous reaction diffusion systems. This is an ongoing research program, for which I have already developed an appropriate mathematical framework for multi-scale density dependent continuous time Markov chains and derived a number of relevant results.

系统生物学的挑战是确定蛋白质组和基因组的相互作用如何产生细胞的功能和行为。细胞天生就是“嘈杂的”系统，复杂的生化途径如何受到内在和外在的随机性的影响还不是很清楚。细胞网络可以用化学动力学原理进行数学建模。在细胞水平上，化学动力学通常由调控分子的作用主导，每个细胞只有几个拷贝。这些成分的随机波动引起的本征噪声可能会产生重大后果，为了充分描述一组可能的结果，必须建立随机模型。在许多情况下，反应速率也可能在几个数量级上变化，这意味着丰度的有效变化在多个时间尺度上发生波动。许多重要的细胞内过程，从生化信号到基因调控，也受到所涉及的分子类型的位置和运动性的很大影响。 这些系统的随机模型使用密度相关的连续时间马尔可夫链来表示不同类型物种之间通过规定的相互作用集而联系在一起的进化。为了预测和仿真的目的，在仍然捕获系统的基本随机行为的同时，降低问题的建模和计算复杂性是有用的。可以利用模型的多尺度特性来降低一些复杂性。严谨的方法提出了许多有趣和具有挑战性的数学问题。我的研究计划的主要目标是为这种随机模型开发模型简化技术，并确定噪声可能造成的影响。这涉及到将非线性动力学与多时间尺度上的密度依赖马氏链的随机平均、扩散近似和大偏差相结合的新结果。具体的短期和长期目标将使我们能够更好地理解：(I)随机反应和分子运动在结果空间传播中的综合效应；以及(Ii)罕见事件在多尺度反应动力学中的作用，以及它们在增强和空间传播双稳态动力学和特定初始结果方面的作用。从长远来看，它们将帮助我们识别在具有多个时间尺度的多相反应系统中出现的一系列空间现象，以及它们产生的条件。沿途开发的数学工具将使我们能够对多相反应扩散系统的长期行为进行概率分析。这是一个正在进行的研究项目，为此，我已经为多尺度密度依赖的连续时间马氏链建立了一个合适的数学框架，并得出了一些相关的结果。