Phenotypic heterogeneity in modeling cancer evolution

Abstract

The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous population of stem cells (SCs) and their associated progenitors. The fate of a malignant mutation is determined not only by overall stem cell and non-stem cell growth rates but also differentiation and dedifferentiation rates. We investigate the effect of such a complex population structure on the evolution of malignant mutations. We derive exactly calculated results for the fixation probability of a mutant arising in each of the subpopulations. The exactly calculated results are in almost perfect agreement with the numerical simulations. Moreover, a condition for evolutionary advantage of a mutant cell versus the wild type population is given in the present study. We also show that microenvironment-induced plasticity in invading mutants leads to more aggressive mutants with higher fixation probability. Our model predicts that decreasing polarity between stem and non-stem cells’ turnover would raise the survivability of non-plastic mutants; while it would suppress the development of malignancy for plastic mutants. The derived results are novel and general with potential applications in nature; we discuss our model in the context of colorectal/intestinal cancer (at the epithelium). However, the model clearly needs to be validated through appropriate experimental data. This novel mathematical framework can be applied more generally to a variety of problems concerning selection in heterogeneous populations, in other contexts such as population genetics, and ecology.

The invasion of de-differentiating cancer cells into hierarchical tissues

“…He showed that in the presence of non-linear feedback, de-differentiation can lower the rates of tumor initiation and progression. Interestingly, this prediction is opposite to the prediction by Shirayeh et al [32], in which they showed that de-differentiation can increase the rate of tumor initiation in the absence of non-linear feedback. The discrepancy between these two predictions actually reveals the complexities brought by the non-linear feedback which deserves special attention in future study.…”

“…Previous work has e.g. considered how de-differentiation influences the waiting time to carcinogenesis [31], the fixation probability of a mutant [32, 33], the phenotypic equilibrium [34–36], transient overshoots [37, 38], and radiation sensitivity [29]. However, the adaptive significance of de-differentiation is still poorly understood: Under which circumstances would de-differentiation arise in the first place and rise in abundance?…”

Noise propagation in metabolic pathways: the role of growth-mediated feedback

“…is the displacement on z i because of reaction j. Because of the linearizations (12), the stationary values of the second order moments equations provided by (24) are the solutions of a linear system, whose formal expression is achieved according to straighforward, though cumbersome computations, and is not here reported. The order of the system, by properly exploiting the simmetries, is:…”

“…Fluctuations in growth rate are known to be responsible for phenotypic heterogeneity, although the mechanisms behind them are still matter of investigation [19], [20]. A large effort has been spent to investigate such phenotypic heterogeneity since it is supposed to be involved in cellular growth control and cancer initiation (see [12] and references therein). Within this framework, metabolism has recently gained interest since the intrinsic noise in gene expression and enzymes accumulation has been shown to propagate to growth rate fluctuations through metabolic fluxes, according to singlecell experiments [9], [13], [22].…”

The invasion of de-differentiating cancer cells into hierarchical tissues

“…More recently, special attention has been paid to the effect of de-differentiation on the cellular hierarchy by mathematical modeling of their impact. Previous works have considered how de-differentiation influences the waiting time to carcinogenesis [30], the fixation probability of a mutant [31,32], the phenotypic equilibrium [33][34][35], transient overshoots [36,37], and radiation sensitivity [29]. However, the adaptive significance of de-differentiation is still poorly understood: Under which circumstances would de-differentiation arise in the first place and rise in abundance?…”