Dynamics of Non-equalibrium Cell State Transitions in Cell Populations

(克隆)细胞群体的非遗传异质性，暗示着多个亚群体在 表面上均一的癌细胞群体是肿瘤细胞的标志。这些亚群代表 多稳态系统的离散不同(吸引子)态，并建立系统的动态平衡 人口分布。当人口受到干扰时，例如，由于消除了一个亚群或一种药物 经过一次典型的“松弛”后，原有的人口分布得到了有力的恢复。 过程，表明细胞群体是一个复杂的、非平衡的动态平衡状态。事实上， 亚群表现出不同的生物学特性。我们和其他人最近发现，亚群 表现出不同的生长速度和恶性潜能，它们可以在两者之间切换(过渡) 其他，自发的或对干扰的反应(包括治疗)，并影响彼此的成长 和转换率。此外，在抗癌药物存在的情况下，这种表型可塑性和相对生长 例如，亚种群的比率可能会发生变化，以有利于赋予 治疗。所有这些都增加了一层直到最近才完全意识到的复杂性--这使得常见的 通过测量“杀伤曲线”(假定为同质人群的百分比)来研究抗癌药物的实践 因药物剂量而致死)明显过于简单化。因此，这个跨学科协作项目的目标是， 涉及数学家和实验学家，是第一个开发通用数学模型的人 框架，该框架考虑了由于动态异构性而导致的上述复杂性 背离均匀细胞群体的传统观念(目标1)；第二， 在一系列细胞培养实验中验证这一理论(目标2)。模型系统由同基因细胞组成 具有两个不同亚群的种群表现出不同的生长和过渡率。它是顺从的 分析模型虽然在数学上很简单，但已经做出了有趣的违反直觉的预测。 我们已经建立了三种癌细胞系(两种乳腺癌和一种)的基线特征 白血病)，表现出所有上述复杂的非遗传动态异质性，因此将提供 一个合适的平台，用于(I)通过可靠的 可测量的人口松弛时间进程，以及(Ii)提供直接测量的参数值 通过纵向监控数字视频中的单细胞行为来实现增殖和状态转移率- 显微镜。实践的结果是一个广泛实用的分析框架，这要归功于该理论所依赖的 仅基于容易测量的子总体松弛来提取关于人口类型的信息 药物的“杀灭”或刺激抗药性的异质性和相关潜力。这将耗费- 有效扩展当前的原始杀伤曲线测量，以考虑细胞群体的异质性 和可塑性是药物治疗失败的主要罪魁祸首。

Non-genetic heterogeneity of (clonal) cell populations, implying the coexistence of multiple subpopulations in an apparently uniform cancer cell population, is a hallmark of tumor cells. These subpopulations represent discretely distinct (attractor) states of a multi-stable system and establish a dynamical equilibrium of the population distribution. When the population is perturbed, e.g. by elimination of one subpopulation or a drug treatment, the original population distribution is robustly reestablished after a characteristic “relaxation” process, indicating that the cell population is a complex, non-equilibrium homeostatic state. Indeed, the subpopulations exhibit distinct biological properties. We and others recently found that the subpopulations display differential growth rates and malignancy potential, that they can switch (transition) between each other, spontaneously or in response to perturbations (including therapy), and influence each other’s growth and switching rate. Moreover in the presence of anticancer drug this phenotype plasticity and relative growth rates of subpopulations can shift, for instance, to favor the subpopulation that confers resilience to the treatment. All this adds a layer of complexity not yet fully appreciated until recently –which makes the common practice of studying cancer drugs by measuring the “kill curve” (% of a presumably homogenous population killed as function of drug dose) overtly simplistic. Thus, the goal of this collaborative interdisciplinary project, involving mathematicians and experimentalists, are first, to develop a generic mathematical modeling framework that takes into account the above complications due to the dynamic heterogeneity that entail a departure from the traditional notion of uniform homogeneous cell populations (Aim 1); and second, to validate the theory in a series cell culture experiments (Aim 2). The model system consists of isogenic cell populations with two distinct subpopulations displaying differential growth and transition rates. It is amenable to analytic models, which albeit mathematically simple, already makes interesting counterintuitive predictions. We have established the baseline-characteristics of three cancer cell lines (two breast cancer and one leukemia) that exhibit all the above complexities of non-genetic dynamic heterogeneity and thus will provide a suited platform to (i) validate qualitatively distinct and quantitative model predictions through the reliably measurable population relaxation time courses, and (ii) provide the directly measured parameter values for proliferation and state transition rates through longitudinal monitoring of single-cell behaviors in digital video- microscopy. The practical outcome is an analysis framework of broad utility that thanks to the theory relies only on the readily measurable subpopulation relaxation to extract information about the type of population heterogeneity and associated potential of drugs to either “kill off” or to stimulate resistance. This will cost- effectively expand current primitive kill-curve measurements to take into account cell population heterogeneity and plasticity which are the major culprits of failure in drug treatment.