A Minimal Model of Inoculum-Dependent Growth in Cancer Cell Cultures

In recent years the tools of statistical physics have been successfully employed in dealing with the stochastic phenomena that have surfaced in the context of microbial population studies. In a given environment a cell has access to a large set of physiological macrostates (or phenotypes) in a similar way to how a degrees-of-freedom-rich physical system in contact with a heat reservoir can be found in one of its macroscopic configurations. The statistical laws that govern how such state spaces are explored are believed to share similar principles. In particular, how fluctuations in the environment, possibly dependent on population size, might be related to the phenotypic variability (represented by maximum growth rate variability) observed in population ensembles appears to be a relevant problem suited to a statistical physics approach. In a study co-authored by the relators of this thesis, the extent of such dependence was tested by looking at how population parameters of two widely used cancer cell lines ( Jurkat and K562), grown in fixed carbon-limited media, were modulated by the size of the initial density. The maximum growth rate and its fluctuations across populations turned out to exhibit a complex dependence on initial cell densities that could not be captured by predictions of traditional deterministic models of population growth, and the current understanding of how single-cell heterogeneities tend to be averaged out when large numbers of individuals are involved. Because both Jurkat and K562 cells are known to produce growth-stimulating factors that sustain in vitro proliferation, the authors propose that weakly cooperative interactions mediated by such factors at low densities are responsible for the observed feedback between the maximum growth rate and the inoculum size. For high starting densities instead, the population consumes quickly its potential for expansion as it runs out of nutrient supply faster, ultimately reaching the carrying capacity. On the blueprint of these findings and in light of the aforementioned statistical considerations we develop a minimal stochastic model that accounts for growth factor-mediated cooperation and finite nutrient availability and that is in principle able to make predictions about the connection between maximum growth rate variability and environmental fluctuations, encoded in the varying amounts of growth stimulating chemicals present in the medium. We simulate the model with the Gillespie algorithm and compare the results qualitatively with the experiments. We conclude that some of the observed empirical trends can be partially explained, and further improvement ( e.g. including in the model a description of the lag-time) could contribute to better predictive performance.