A physical mechanism of heterogeneity and micro-metastasis in stem cells, cancer cells, and cancer stem cells.

Abstract

Heterogeneity is ubiquitous in stem cells (SC), cancer cells (CS), and cancer SC (CSC). This heterogeneity manifests in the form of diverse sub-populations of SC, CS, and CSC with self-renewal and unique regeneration capacity. Moreover, the progeny of CSC possess multiple plasticity and cancerous characteristics. Many studies have demonstrated that cancer heterogeneity is among the greatest obstacles to successful anti-cancer therapy. This leads to incomplete therapy and transitory efficacy. Furthermore, numerous micro-metastases lead to the spread of tumor cells widely across the body; this is the beginning of metastasis. Epigenetic processes (DNA methylation and histone remodification) represent sources of heterogeneity. In this study, we develop a mathematical model to quantify the heterogeneity of SC, CS, and CSC, taking into consideration both genetic and epigenetic effects. We reveal the roles and physical mechanisms of heterogeneity in SC, CSC, and cancer cells. Under the adiabatic regime (relatively fast regulatory binding and effective coupling among genes), seven native states (SC, CSC, cancer, premalignant, normal, lesion, and hyperplasia) emerge. Under the non-adiabatic regime (relatively slow regulatory binding and effective weak coupling among genes), SC, CS, CSC, and differentiated states emerge and become diffusive, partially explaining the origin of heterogeneity. In other words, slow regulatory binding that mimics epigenetic effects can give rise to heterogeneity. Moreover, we calculated the entropy production rate and Fano factor, which can be used to quantify the thermodynamic cost and the degrees of the variations or the fluctuations as the parameter ω (representing the speed of regulatory binding/unbinding relative to the synthesis/degradation) changes. Elucidating the origins of heterogeneity and the dynamical relationships between intra-tumoral cells has a clear clinical significance and will improve the understanding of the cellular basis of treatment response, therapeutic resistance, and cancer metastasis.