Vito QUARANTA

Department of Cancer Biology; Center for Quantitative Systems Biology, Vanderbilt University School of Medicine, Nashville, TN, USA.

Modeling cell population dynamics from stochastic single-cell fates in response to perturbation.

With a high-throughput clonal Fractional Proliferation (cFP) assay, we simultaneously track in real-time the proliferation dynamics of hundreds to thousands of single-cell derived clones in a cell population exposed to perturbations (Frick et al, 2015, DOI: 10.1002/jcp.24888). In the mutant EGFR-addicted PC9 lung cancer cell line treated with the EGFR inhibitor erlotinib, cell fates within each clone vary from cell-to-cell, even between siblings (death, quiescence, continued division). Nonetheless, this fate heterogeneity within a clone gives rise to a stable drug-induced proliferation (DIP) rate, which can be considered as an effective metric of clonal fitness in the presence of drug. Fitness varies from clone to clone, and is approximately normally distributed. Measurement error or mixed clone ancestry could not account for this variation, since DIP rates of isogenic PC9 sublines isolated from single cells and propagated in long-term culture (PC9-DS1/95) exhibited the same normal distribution and maintained it for over 25 generations. Similar distributions were obtained from many additional oncogene-addicted cell lines, rigorously re-derived from single cells. Thus, a mutated driver oncogene does not ensure clonal homogeneity of response, even when genetic background diversity is minimized.

To explore whether this clonal fitness heterogeneity is of consequence to cell population dynamics, we constructed a Polyclonal Growth (PG) mathematical model able to incorporate theoretical or experimental DIP rates as parameters. Since DIP rate distributions are normal, they are entirely defined by two parameters, mean and variance. Inputting the average DIP rate of parental PC9 predicts that the cell population will completely succumb to treatment. In contrast, with the rate distribution parameters as input, a completely different result was obtained: the size of the erlotinib treated population dropped to half ~5 days, but then rebounded to initial values after ~11 days. The PG model predicted similar dynamics of erlotinib response for several mutant EGFR-addicted cell lines: in every cell line tested, rebound occurred within days to weeks, after initial drops to varying depths. Time to rebound is affected primarily by the extent to which clonal fitness distributions extend into positive territory. These rebound effects were verified experimentally, although ODE simulations of the PG model could not capture the observed variability in time to rebound. However, using stochastic simulations of the PG model, we are able to differentiate the effects of clonal fitness heterogeneity from those of stochastic cell fate decisions (intrinsic noise), and show that the latter may cause significant variability in the trajectories of population dynamics (e.g., time to rebound), as observed experimentally. These findings indicate that realistic evaluation of cancer dynamics in response to drug require modeling of clonal fitness heterogeneity and stochastic cell fates.