title: Stochastic multi-scale models of competition within heterogeneous cellular populations: Simulation methods and mean-field analysis.
abstract: We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance to therapy since the rescued population is less sensitive to therapy.
authors.affiliation: Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain; Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain.
authors.forename: Roberto de la
authors.initials: R
authors.lastname: Cruz
authors.affiliation: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK.
authors.forename: Pilar
authors.initials: P
authors.lastname: Guerrero
authors.affiliation: Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA; Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, MA 02215, USA.
authors.forename: Fabian
authors.initials: F
authors.lastname: Spill
authors.affiliation: Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain; Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain; ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain; Barcelona Graduate School of Mathematics (BGSMath), Barcelona, Spain.
authors.forename: Tomás
authors.initials: T
authors.lastname: Alarcón
mesh_terms: D015687:Cell Hypoxia; D016922:Cellular Senescence; D003198:Computer Simulation; D016193:G1 Phase; D006801:Humans; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D011336:Probability; D016196:S Phase; D013269:Stochastic Processes
keywords: Cell cycle; Multi-scale modelling; Radiotherapy; Scaling laws; Stochastic population dynamics