Large Deviations and Driven Processes for Stochastic Models of Gene Expression and Its Regulation

这个项目将发展数学来预测和描述影响细胞群体中基因表达的罕见的随机事件。细胞群体在压力下的生存和进化往往依赖于一小部分异常细胞。例如，药物暴露会导致肿瘤中大多数癌细胞死亡，但一小部分细胞存活并导致耐药性的产生。最近的研究表明，这种细胞差异是由基因表达过程中的罕见事件驱动的，因此有必要在基因表达的随机描述中开发罕见事件的定量模型。该项目由数学科学和分子与细胞生物学部门联合支持，将开发和应用非平衡统计力学和大偏差理论的方法来创建基因表达中罕见事件及其在不同细胞过程中的调控框架。该理论将解决当前的研究问题：(1)细胞调控机制如何控制基因表达中罕见事件的概率？(2)如何在罕见事件发生的条件下表征基因表达？(3)能否确定控制机制以实现理想的罕见事件？这些答案的应用范围从合成生物学到了解HIV-1感染的潜伏期。将指导研究生和本科生进行生物系统的跨学科研究，并将研究活动与研究生和本科生的教学有效结合。综合的研究、教学和推广活动将为未来的科学家将随机数学应用于分子生物学做好准备。导致表型转变的罕见事件是当前生物学研究中反复出现的主题。在某些情况下，表型转换是由基因表达的内在随机性驱动的。相应地，需要开发一种理论框架来分析基因表达的随机模型中的罕见事件。非平衡统计力学的最新发展，使用大偏差理论，已经导致了一个框架，用于分析以罕见事件为条件的马尔可夫过程，并用于用条件自由驱动过程来表示这种过程。本项目的目标是应用并进一步发展这一理论框架，以定量描述基因表达及其调控的随机模型中的大偏差。具体目标将集中于开发分析和计算方法来表征基因表达的一般模型中的大偏差，包括a)基于启动子的调控，b)转录后调控和c)反馈调控。这项研究将导致对细胞调控机制如何影响罕见事件概率的定量洞察，这可以用来设计实现期望的罕见事件的最佳控制机制。一个特别的焦点将是对HIV-1病毒感染的潜伏期进行建模。分析需要来自物理和应用数学的工具和方法，这些工具和方法将与教学工作相结合，以有效地培养专注于生命科学跨学科研究的学生和未来的科学家。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project will develop mathematics to predict and characterize rare, random events affecting gene expression in a population of cells. The survival and evolution of cell populations under stress often depends on a small fraction of outlier cells. For example, drug exposure leads to cell death for most cancer cells in a tumor, but a small fraction survive and lead to development of drug resistance. Recent research shows that such cellular differences are driven by rare events during gene expression, and there is a need to develop quantitative models of rare events in stochastic descriptions of gene expression. This project, supported jointly by the Divisions of Mathematical Sciences and Molecular and Cellular Biology, will develop and apply approaches from non-equilibrium statistical mechanics and large deviation theory to create a framework for rare events in gene expression and its regulation in diverse cell processes. The theory will address current research questions: (1) How do cell regulatory mechanisms control probability of rare events in gene expression? (2) How can one characterize gene expression conditional on rare event occurrences? (3) Can control mechanisms be determined to realize desirable rare events? The answers will have applications ranging from synthetic biology to understanding latency in HIV-1 infections. Graduate and undergraduate students will be mentored in interdisciplinary research on biological systems, and research activities will be effectively integrated with teaching at graduate and undergraduate levels. The integrated research, teaching and outreach activities will prepare future scientists to apply stochastic mathematics to molecular biology.Rare events which lead to phenotypic transitions are a recurring theme in current biological research. In several cases phenotypic switching is driven by the intrinsic stochasticity of gene expression. Correspondingly, there is a need to develop a theoretical framework for analyzing rare events in stochastic models of gene expression. Recent developments in non-equilibrium statistical mechanics, using large deviation theory, have led to a framework for analyzing Markovian processes conditioned on rare events and for representing such processes by conditioning-free driven processes. The goal of this project is to apply and further develop this theoretical framework to quantitatively characterize large deviations in stochastic models of gene expression and its regulation. The specific aims will focus on developing analytical and computational approaches for characterizing large deviations in general models of gene expression with a) promoter-based regulation, b) post-transcriptional regulation and c) feedback regulation. This research will lead to quantitative insights into how cellular regulatory mechanisms impact rare event probabilities which can be used to design optimal control mechanisms for realization of desired rare events. A particular focus will be modeling latency in HIV-1 viral infections. The analysis requires tools and approaches from physics and applied mathematics which will be integrated with teaching efforts to effectively train students and future scientists focusing on interdisciplinary research in the life sciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.