On the dynamics of neutral mutations in a mathematical model for a homogeneous stem cell population

Abstract

The theory of the clonal origin of cancer states that a tumour arises from one cell that acquires mutation(s) leading to the malignant phenotype. It is the current belief that many of these mutations give a fitness advantage to the mutant population allowing it to expand, eventually leading to disease. However, mutations that lead to such a clonal expansion need not give a fitness advantage and may in fact be neutral—or almost neutral—with respect to fitness. Such mutant clones can be eliminated or expand stochastically, leading to a malignant phenotype (disease). Mutations in haematopoietic stem cells give rise to diseases such as chronic myeloid leukaemia (CML) and paroxysmal nocturnal haemoglobinuria (PNH). Although neutral drift often leads to clonal extinction, disease is still possible, and in this case, it has important implications both for the incidence of disease and for therapy, as it may be more difficult to eliminate neutral mutations with therapy. We illustrate the consequences of such dynamics, using CML and PNH as examples. These considerations have implications for many other tumours as well.

Mathematical model of adult stem cell regeneration with cross-talk between genetic and epigenetic regulation

“…Previous modeling studies based on the cell population dynamics have indicated that feedback regulation to the proliferation is important to maintain the homeostasis of tissue growth (23)(24)(25). The exploration and analysis of models that include transit-amplifying progenitor cells and terminally differentiated cells have suggested that multiple feedback mechanisms at different lineage stages can influence the speed of tissue regeneration for better performance (17,(26)(27)(28).…”

Robustness of differentiation cascades with symmetric stem cell division

“…Related models have been proposed by Traulsen et al [7,26,28,29], where they use a Moran process to study the competition between two populations as a function of the duplication probability to find that the probability of invasion is an increasing function of the duplication probability of the invader population. We observe similar results, only for small values of the duplication rate p. For larger values of p, the probability of invasion decreases, as the invader population becomes extinct due the extinction mechanisms that we have characterized in this paper.…”

“…They showed that these tissues strongly suppress the cells that are carrying multiple mutations. Traulsen et al [29] have studied the effect of different kinds of mutations and showed that although neutral mutations often lead to clonal extinction, disease is still possible, and in this case, it may become difficult to eliminate neutral mutations with therapy.…”

Complete Numerical Solution of the Diffusion Equation of Random Genetic Drift

“…The process of random genetic drift plays a fundamental role in molecular evolution and the behavior of genes in finite populations (Crow and Kimura 1970;Kimura 1983). Beyond this, some of the ideas and techniques used in random genetic drift have a wider use, for example, with applications to cancer (Zhu et al 2011;Traulsen et al 2013) and range expansion (Slatkin and Excoffier 2012).To set the stage for the present work, consider a single locus with genetic variation due to the segregation of more than one allele in the population. The population size is assumed finite, so random genetic drift generally occurs, and the number of copies of a particular allele at the locus changes randomly over time.…”

“…The process of random genetic drift plays a fundamental role in molecular evolution and the behavior of genes in finite populations (Crow and Kimura 1970;Kimura 1983). Beyond this, some of the ideas and techniques used in random genetic drift have a wider use, for example, with applications to cancer (Zhu et al 2011;Traulsen et al 2013) and range expansion (Slatkin and Excoffier 2012).…”