Mathametical modeling of cell fate transitions regulated by ultra-feedbacks

细胞命运转换(细胞类型之间的转换)是发育和 疾病的发展。控制细胞命运转变的基因调控网络通常包括积极的 反馈循环。最近的数据表明，高度互联的正反馈环路(定义为超 本提案中的反馈电路)具有附加功能，但目前对这些功能的理解 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些 复杂的电路。上皮-间充质转化(EMT)，即刚性上皮细胞 转化为可移动的间充质形式，是超微结构调控细胞命运转变的一个例子 反馈电路。EMT既发生在正常情况下，也发生在病理情况下，如转移。近期 这些发现表明了两种复杂的细胞特性，这使得人们很难直观地理解EMT： 多重中间EMT态的形成和EMT的部分可逆性。的功能 超反馈电路在调节这两种细胞特性中的作用尚不明确。的目标是 建议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。我们将结合实代数几何， 超反馈稳定定态识别的稳定性分析和数值方法 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是基于信息论和动力学系统的新理论框架。 将进行理论驱动的仿真和实验，以检验超反馈电路如何 控制可逆性。我们将描述超反馈电路在细胞运动和增殖中的作用 在EMT期间，使用多尺度建模和活细胞成像。这项提议带来了新的方法来 分析包含广泛网络结构的一大类新兴动力系统， 理解信息传递和保留的新理论框架和新的 具有复杂状态转移和多源的系统的多尺度建模框架 随机性。拟议的研究解决了关于两者之间相互作用的基本问题 EMT的重要和新兴特性(其多态性质和受限可逆性) 数学创新，它将为细胞命运转换的基因调控提供关键的见解 在发育和疾病发展过程中。该项目的成功将带来新的量化 EMT的信息以及更好地理解EMT属性和分析其他细胞的新概念 涉及超反馈电路的命运转变。

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.