Mathametical modeling of cell fate transitions regulated by ultra-feedbacks

细胞命运转变（细胞类型之间的转换）是发育和生长的关键基础过程。 疾病进展。控制细胞命运转变的基因调控网络通常涉及阳性 反馈回路最近的数据表明，高度相互关联的正反馈回路（定义为超 反馈电路）具有额外的功能，但目前对这些功能的理解并不清楚。 网络是不完整的，部分原因是缺乏理论和数学方法来分析这类网络。 复杂的电路上皮-间充质转化（EMT），一个过程中，刚性上皮细胞 转化为能动的间充质形式，是细胞命运转变的一个例子， 反馈电路EMT发生在正常和病理条件下，如转移。最近 这些发现提出了两个复杂的细胞特性，使得EMT难以直观地理解： 多个中间EMT态的形成和EMT的部分可逆性。的职能 调节这两种细胞特性的超反馈电路还有待定义。的目标 提出的研究是通过开发新的方法来更深入地了解EMT的这些特性， 描述超反馈电路的模型和理论。我们将联合收割机结合真实的代数几何， 稳定性分析和数值方法，以确定超反馈引起的稳定的稳态 系统，我们将应用该方法来分析细胞类型的EMT谱。我们将部分量化 可逆EMT与新的理论框架的基础上信息论和动力系统。 理论驱动的模拟和实验将进行研究如何超反馈电路 控制可逆性我们将描述超反馈回路在细胞运动和增殖中的作用 在EMT中使用多尺度建模和活细胞成像。该提案提出了新的方法， 分析一个大的，新兴的家庭动力系统包含广泛的网络结构， 理解信息传递和保留的新理论框架，以及一个新的 多尺度建模框架，用于具有复杂状态转换和多个数据源的系统 随机性拟议的研究解决了关于两个因素之间相互作用的基本问题。 EMT的重要和新出现的特性（其多态性和有限的可逆性）， 数学创新，它将提供关键的见解基因调控细胞命运的转变， 在发展和疾病进展过程中。该项目的成功将导致新的量化 EMT信息和用于更好地理解EMT性质和用于分析其它细胞的新概念 涉及超反馈回路的命运转变

Cell fate transition (conversion between cell types) is a fundamental process critical for development and disease progression. Gene regulatory networks controlling cell fate transitions often involve positive feedback loops. Recent data suggest that highly interconnected positive feedback loops (defined as ultra- feedback circuit in this proposal) have additional functions, but the current understanding of these networks is incomplete, partly due to the lack of theories and mathematical methods to analyze such complex circuits. Epithelial-mesenchymal transition (EMT), a process in which rigid epithelial cells convert to motile mesenchymal forms, is an example of cell fate transitions that are regulated by ultra- feedback circuits. EMT occurs in both normal and pathological conditions such as metastasis. Recent discoveries suggest two complex cellular properties that make EMT difficult to understand intuitively: the formation of multiple intermediate EMT states and the partial reversibility of EMT. The functions of the ultra-feedback circuits in regulating the two cellular properties are yet to be defined. The goal of the proposed study is to gain deeper understanding of these properties of EMT by developing new methods, models and theories to characterize the ultra-feedback circuits. We will combine real algebraic geometry, stability analysis and numerical methods to identify stable steady states that arise from ultra-feedback systems, and we will apply the method to analyze the EMT spectrum of cell types. We will quantify partially reversible EMT with a new theoretical framework based on information theory and dynamical systems. Theory driven simulations and experiments will be performed to examine how ultra-feedback circuits control reversibility. We will characterize the roles of ultra-feedback circuits in cell motility and proliferation during EMT using multiscale modeling and live-cell imaging. The proposal brings about new methods to analyze a large, emerging family of dynamical systems containing a wide range of network structures, a new theoretical framework for understanding information transmission and retainment, and a new multiscale modeling framework for systems with complex state transitions and multiple sources of stochasticity. The proposed study addresses fundamental questions about the interplay between two important and emerging properties of EMT (its multistate nature and its restricted reversibility) with mathematical innovations, and it will provide critical insights into gene regulations of cell fate transitions during development and disease progression. The success of the project will lead to new quantitative information of EMT and new concepts for better understanding EMT properties and for analyzing other cell fate transitions involving ultra-feedback circuits.