Stochastic Modeling and Inference of Gene Networks

活细胞内的环境是令人难以置信的嘈杂，生化物种随机地相互碰撞和反应。这种固有的概率性质，加上细胞物种的低种群数量，导致单个细胞内蛋白质拷贝数量随着时间的推移而出现相当大的随机波动。越来越多的证据表明，这种随机动力学在细胞内发挥着重要的功能作用。此外，许多疾病状态被归因于特定蛋白质中噪音水平的升高。生化过程的随机分析在很大程度上依赖于蒙特卡罗模拟技术，而蒙特卡罗模拟技术的计算成本很高。此外，这些技术不能提供封闭形式的解决方案，从而能够系统地了解随机变异性在这些系统中是如何调节的。这个项目将通过开发基于矩闭合方案的易于计算的方法来克服这些挑战，以研究基因调控网络的随机动力学。将研究将系统的统计特性与生物相关参数相关联的各种解析近似。蛋白质噪音水平的签名非但不是障碍，反而可以为潜在的基因网络拓扑提供信息。这个项目将建立数学技术，利用蛋白质水平上的随机性的定量测量来推断基因和蛋白质之间的调节相互作用。生物数据正在以快速的速度收集，迫切需要创新的数据分析方法。实验技术的进步使得可以测量单个细胞中蛋白质水平的波动，这携带了有用的信息来探索基因和蛋白质之间的相互作用。在这个项目中，将开发利用这些波动的统计特性来表征细胞过程的工具，并将提供给广泛的科学界使用。蛋白质水平的随机变异与细菌的抗生素耐药性、肿瘤的非突变选择以及将致病的人类病毒(如HIV)推向抗药性休眠状态有关。这项研究将改善这些疾病系统背后的基因网络的特征，因此这项研究将对医学产生更广泛的影响。该项目的许多成果将被纳入不同部门开设的各种课程，为学生提供跨学科的培训和研究经验，使他们能够接触到数学和生物科学。

The environment within living cells is incredibly noisy with biochemical species randomly bumping and reacting with each other. This inherent probabilistic nature along with low population counts of cellular species creates considerable stochastic fluctuations in protein copy numbers over time inside individual cells. Increasing evidence suggests that this stochastic dynamics plays important functional roles within cells. Moreover, many diseased states have been attributed to elevated noise levels in specific proteins. Stochastic analysis of biochemical processes relies heavily on Monte Carlo simulation techniques that come at a significant computational cost. In addition, these techniques do not provide closed-form solutions that enable a systematic understanding of how stochastic variability is regulated in these systems. This project will overcome these challenges by developing computationally tractable methodologies based on moment closure schemes for studying stochastic dynamics of gene regulatory networks. Various analytical approximations that relate statistical properties of the system to biologically relevant parameters will be investigated. Far from being a hindrance, signatures of protein noise levels can be informative of the underlying gene network topology. This project will build mathematical techniques that harness quantitative measurements of stochasticity in protein levels for inferring regulatory interactions between genes and proteins.Biological data is being collected at a rapid rate and innovative methods for analyzing data are critically needed. Advances in experimental techniques allow measurements of fluctuations in protein levels in individual cells, which carry useful information to probe interactions between genes and proteins. In this project, tools exploiting statistical properties of these fluctuations to characterize cellular processes will be developed and will be made available for the broad scientific community to use. Stochastic variability in protein levels has been implicated in bacterial antibiotic resistance, mutation-independent selection of tumors and driving pathogenic human viruses, e.g., HIV, into a drug-resistant dormant state. This research will improve the characterizations of gene networks underlying these disease systems and thus this research will have a broader impact on medicine. Many of the results of this project will be incorporated into various courses offered across different departments providing interdisciplinary training and research experience to students at the interface of mathematical and biological sciences.