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We investigate the formation of cancer stem cells and their role in maintaining avascular solid tumors. For this purpose, we provide a mathematical framework to study the major biological interpretations on the stemness of cancerous cells (stochastic scheme) and the self-renewal ability of particular progenitor cells (hierarchical scheme). These interpretations are related to the genetic characteristics of cancer, which could be described by a set of mechanisms shared by all types of cancer, i.e., hallmarks of cancer. Hallmarks of cancer relate cellular genetics, differentiation and heterogeneity, and tumor micro-environment (TME). To reach our goal, based on hallmarks of cancer, we propose a hybrid discrete-continuous model that combines continual interactions of cellular genetics and tumor micro-environment. Using this model, we conduct computational experiments on EMT6/Ro tumor to study the possibility of stochastic and hierarchical schemes. Our experiments suggest that even in well-suited genomic and micro-environmental conditions, a tumor survives only when the majority of tumor cells are in the stemness state (stochastic approach), or progenitor to CSC transition exists (hierarchical approach). In the lack of progenitor to CSC transition, in the hierarchical scheme, the tumor fades away due to the CSCs malnutrition. These results are supported by a sensitivity analysis of the model parameters. Although our computational experiments are carried out for the EMT6/Ro tumor, due to the generic nature of this approach, we believe, this work could provide insights regarding similar behaviors in other tumors.
Pirastehzad et al. (Wed,) studied this question.