Theory and Measurement of Cell Population Dynamics with Cell-Cell Interaction (TMCC)

了解复杂的多细胞生物体长期以来一直专注于基因网络（因为基因相互作用） 但同样重要的是细胞群体的动态（因为细胞相互作用）。一个组织就是一个细胞社会 由多种细胞类型组成，尽管细胞的相对数量是稳定的，但其比例是确定的。 这些细胞以不同的速度生长（分裂）。组织如何确保细胞类型身份的稳定性， 组织组成还允许灵活性，例如在再生过程中，当细胞类型和它们的比例改变时？ 从单细胞分辨率分析，我们现在知道，任何细胞群体，即使是单一类型，实际上是一个 不同（亚）类型亚群体的异质混合。因此，细胞群体动力学 比原来想象的复杂。传统的模型必须进行修改，以整合所有以下属性， 一种形式：1.非遗传异质性，细胞在不同（Meta）稳定状态x_i中的共存 （功能状态，亚型）形成大小为n_i的亚种群i，它们共同定义了一个稳定的种群 状态n;这些子群体之间的状态转换，i到j，可能是可逆的，速率为M_ij; 3.净值增长 率g_i在这些亚群中不同，允许竞争;和4.细胞间通过特异性 可能影响M_ij或g_i的信号（亚群内和亚群之间）。现有的动力学理论 从生态学到化学反应再到细胞群体， 元素因此，一个新的理论框架，非线性人口平衡分析，这是基于 提出了非线性随机动力系统的广义理论。这次合作的学术目标 一个项目是推进理论，但它涉及使用单细胞（sc）RNASeq组合的实验 以及一种新发明的细胞条形码方法，以克服scRNASeq的缺点， 破坏性快照测量。第一部分（理论）将首先建立一个正式的框架来描述 细胞-细胞相互作用下的生长和转化率与亚群丰度n_i的关系 预测存在（多个）稳定的人口配置n（目标1）。要分析的建模框架 将开发条形码数据（目标2）。第II部分（实验）将用scRNASeq测量这些量 以确定在1000个细胞中定义细胞状态Xi的转录组并鉴定亚群。 这将与细胞独特的，遗传的和表达的DNA条形码的新方法相结合， 跟踪细胞谱系动态，揭示有关生长和状态转换速率的动态（目标3）。应用 这种分析是对癌细胞和成纤维细胞的混合培养物（对癌症有影响）的分析， 将被中和抗体操纵（目标4），理论预测，其主要新奇是 互动，将受到考验。这个项目不是特定实例的特别“数学建模”， 在系统生物学中很常见，但发展了一类系统的一般理论， 为后生动物生物学，并在这样做将有利于未来的努力，在模拟各种具体的情况。

Understanding the complex multicellular organisms has long focused on gene networks (because genes interact) but of equal importance is the dynamics of cell populations (because cells interact). A tissue is a cell society comprised of a variety of cell types whose the relative numbers are held at a stable, defined ratio despite the fact that these cells grow (divide) at distinct rates. How does the tissue ensure stability of cell type identities and tissue composition yet allows for flexibility, e.g. during regeneration when cell types and their ratios change? From single-cell resolution analysis we now know that any cell population, even of a single type, is actually a heterogeneous mix of subpopulations of different (sub)types. Therefore, cell population dynamics is more complex than originally thought. Traditional models must be revised to integrate all the following properties in one formalism: 1.Non-genetic heterogeneity, the co-existence of cells in distinct (meta)stable states x_i (functional states, subtypes) forming subpopulations i of size n_i which collectively define a stable population state n; 2. State transitions between these subpopulations, i to j, possibly reversible, at rates M_ij; 3. Net growth rates g_i that differ in these subpopulations, allowing for competition; and 4. Cell-cell interactions via specific signals (within and between subpopulations) that may affect M_ij or g_i. None of existing theories of the dynamics of an ensemble of entities, ranging from ecologies to chemical reactions to cell populations, consider all these elements. Hence, a new theoretical framework, nonlinear population balance analysis which is based on the broader theory of non-linear stochastic dynamical system is proposed. The scholarly goal of this collaborative project is to advance THEORY but it involves EXPERIMENTS that use a combination of single-cell (sc) RNASeq and a newly invented cell-barcode method to overcome the shortcoming of scRNASeq which allows only destructive snapshot measurements. PART I (THEORY) will first establish a formal framework to describe the relationship of growth and transition rates under cell-cell interactions and the abundance n_i of subpopulations to predict existence of (multiple) stable population configurations n (Aim 1). A modeling framework to analyze the barcode data will be developed (Aim 2). PART II (EXPERIMENT) will measure these quantities with scRNASeq to determine the transcriptomes that define the cell state xi in 1000s of cells and identify the subpopulations. This will be combined with a new method of cell-unique, inherited and expressed DNA-barcodes that will permit the tracking cell lineage dynamics that reveals dynamics about growth and state transition rates (Aim 3). Applying this analysis to mixed cultures of cancer cells and fibroblasts (with implications for cancer) whose interactions will be manipulated by neutralizing antibodies (Aim 4), the theory predictions, whose chief novelty is the role of interactions, will be tested. This project is not ad hoc “mathematical modeling” of a given instance, which is common in systems biology, but develops a general theory of a class of systems which plays an eminent role for metazoan biology and in doing so will facilitate future efforts in modelling of a variety of specific instances.