Dynamics of Non-equalibrium Cell State Transitions in Cell Populations

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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.