Stochasticity and Drug Effects in Dynamical Model for Cancer Stem Cells

SIMPLE SUMMARY: Phenotypical heterogeneity constitutes a feature of tumors that strongly impacts their growth and stability as well as possible therapies. Among the biological models that take this aspect into account we considered the Cancer Stem Model, which assumes the tumor population to be composed of stem cells and differentiated cells. Aim of our study was to include biologically originated stochastic factors in the model and investigate its impact on the tumor evolution numerically. In addition, we developed a model compatible with our main system in order to describe possible therapies, and considered their outcomes in some examples. Our results are consistent with state-of-the-art research in the field and confirm the descriptive power of the Cancer Stem Model. ABSTRACT: The Cancer Stem Model allows for a dynamical description of cancer colonies which accounts for the existence of different families of cells, namely stem cells, highly proliferating and quasi-immortal, and differentiated cells, both undergoing cellular processes under numerous activated pathways. In the present work, we investigate a dynamical model numerically, as a system of coupled differential equations, and include a plasticity mechanism, of differentiated cells turning into a stem state if the stem concentration drops low. We are particularly interested in the stability of the model once we introduce stochastically evolving parameters, associated with environmental and cellular intrinsic variabilities, as well as the response of the model after introducing a drug therapy. As long as we stay within the characteristic time scale of the system, defined on the base of the needed time for the trajectories to converge on stable states, we observe that the system remains stable for the main parameters evolving stochastically according to white noise. As for the drug treatments, we discuss a model both for the kinetics and the dynamics of the substance in the organism, and then consider the impact of different types of therapies in a few particular examples, outlining some interesting mechanisms, such as the tumor growth paradox, that possibly impact the outcome of therapy significantly.