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

长期以来，人们对复杂的多细胞生物体的理解主要集中在基因网络上(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)。组织是一个细胞社会 由各种类型的细胞组成，它们的相对数量保持在稳定的、定义的比率上，尽管 这些细胞以不同的速度生长(分裂)的事实。组织如何确保细胞类型的稳定性和 组织成分是否允许灵活性，例如在细胞类型及其比例发生变化时的再生过程中？ 通过单细胞分辨率分析，我们现在知道，任何细胞群体，即使是单一类型的，实际上都是 不同(亚)类型的亚种群的异质性混合。因此，细胞种群动态更多 比最初想象的要复杂。必须对传统模型进行修改，以在中集成以下所有属性 一种形式：1.非遗传异质性，即处于不同(亚)稳定状态的细胞共存 (功能状态、亚型)形成大小为n_i的子种群i，它们共同定义了一个稳定的种群 状态n；2.这些子种群i到j之间的状态转换，可能是可逆的，速率为M_ij；3.净增长 在这些亚群中不同的速率g_i，允许竞争；以及4.通过特定的细胞-细胞相互作用 可能影响M_ij或G_i的信号(子种群内和子种群之间)。现有的动力学理论 从生态到化学反应再到细胞群体的实体集合，考虑所有这些 元素。因此，一个新的理论框架--非线性人口平衡分析，是建立在 提出了更广泛的非线性随机动力系统理论。这项合作的学术目标是 该项目旨在推进理论，但它涉及使用单细胞(Sc)RNAseq组合的实验 一种新发明的细胞条形码方法，以克服scRNASeq仅允许 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过渡率与亚群丰度n_i的关系 预测是否存在(多个)稳定的总体构型n(目标1)。要分析的建模框架 将开发条形码数据(目标2)。第二部分(实验)将使用scRNASeq测量这些量 确定在1000个细胞中定义细胞状态xi的转录本，并确定亚群。 这将与一种新的细胞唯一、遗传和表达的DNA条形码方法相结合，这将允许 跟踪细胞谱系动力学，揭示关于生长和状态转移率的动力学(目标3)。施药 这项对癌细胞和成纤维细胞混合培养的分析(与癌症有关)，其相互作用 将被中和抗体操纵(目标4)，理论预测，其主要新奇之处是 相互作用，将被测试。该项目不是对给定实例进行特别的“数学建模”，而是 在系统生物学中很常见，但发展了一类系统的一般理论，这类系统扮演着重要的角色 对于后生动物生物学，这样做将有助于今后对各种具体实例进行建模。

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.