Dynamics of Non-equalibrium Cell State Transitions in Cell Populations

（克隆）细胞群体的非遗传异质性，意味着多个亚群的共存， 一个明显均匀的癌细胞群，是肿瘤细胞的标志。这些亚群代表了 离散不同的（吸引）状态的多稳定系统，并建立一个动态平衡的 人口分布当种群受到干扰时，例如通过消除一个亚群或药物 处理，原始的人口分布是鲁棒重建后，一个特征的“放松” 这表明细胞群体是一个复杂的、非平衡的稳态。持续增 亚群表现出不同的生物学特性。我们和其他人最近发现， 显示不同的生长速度和恶性潜力，它们可以在每一个之间切换（过渡） 其他的，自发的或对干扰（包括治疗）的反应，并影响彼此的成长 和切换速率。此外，在抗癌药物的存在下，这种表型可塑性和相对生长 例如，亚群的比率可以改变，以有利于赋予适应力的亚群。 治疗所有这一切都增加了一层复杂性，直到最近才得到充分的认识--这使得 通过测量“杀伤曲线”（假定同质群体的百分比）来研究癌症药物的实践 杀死作为药物剂量的函数）明显地简单化。因此，这个跨学科合作项目的目标， 涉及数学家和实验学家，首先，开发一个通用的数学模型， 考虑到上述复杂性的框架，由于动态异质性， 与传统的均匀同质细胞群概念（目标1）的偏离;第二， 在一系列细胞培养实验中验证该理论（目标2）。模型系统由等基因细胞组成 具有两个不同亚群的种群显示出不同的生长和过渡率。它是顺从的 到分析模型，虽然数学上很简单，但已经做出了有趣的反直觉预测。 我们已经建立了三种癌细胞系（两种乳腺癌和一种乳腺癌）的基线特征。 白血病），其表现出所有上述非遗传动态异质性的复杂性，因此将提供 一个合适的平台，以（i）通过可靠的 可测量的群体弛豫时间过程，以及（ii）提供直接测量的参数值， 通过纵向监测数字视频中的单细胞行为， 显微镜实践结果是一个具有广泛实用性的分析框架，这要归功于理论依赖 仅对易于测量的子总体进行松弛，以提取关于总体类型的信息 异质性和相关的潜在药物“杀死”或刺激耐药性。这将花费- 有效地扩展了当前原始曲线测量以考虑细胞群体异质性 和可塑性，这是药物治疗失败的主要原因。

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.