Abstract
Cancer initiation, progression, and the emergence of drug resistance are driven by specific genetic and/or epigenetic alterations such as point mutations, structural alterations, DNA methylation and histone modification changes. These alterations may confer advantageous, deleterious or neutral effects to mutated cells. Previous studies showed that cells harboring two particular alterations may arise in a fixed-size population even in the absence of an intermediate state in which cells harboring only the first alteration take over the population; this phenomenon is called stochastic tunneling. Here, we investigated a stochastic Moran model in which two alterations emerge in a cell population of fixed size. We developed a novel approach to comprehensively describe the evolutionary dynamics of stochastic tunneling of two mutations. We considered the scenarios of large mutation rates and various fitness values and validated the accuracy of the mathematical predictions with exact stochastic computer simulations. Our theory is applicable to situations in which two alterations are accumulated in a fixed-size population of binary dividing cells.
Highlights
Genetic and epigenetic alterations in signaling pathways, DNA repair mechanisms, the cell cycle, and apoptosis lead to abnormal reproduction, death, migration, genome stability, and other behaviors of cells, which may lead to the onset and progression of cancer [1]
Biological knowledge about population dynamics and molecular mechanisms of tumorigenesis, invasion, and therapeutic resistance have been incorporated into the mathematical models; for instance, tissue structures in particular cancer types [11,12,13,14,15,16] and the evolution of drug resistance in cancer cells [17,18,19] were considered
Existing methods do not take into account all possible fitness effects of the individual cell types – such as increased fitness of cells with one mutation as compared to those with zero or two mutations. We addressed these scenarios to provide a general description of stochastic tunneling in a tumor cell population of constant size
Summary
Genetic and epigenetic alterations in signaling pathways, DNA repair mechanisms, the cell cycle, and apoptosis lead to abnormal reproduction, death, migration, genome stability, and other behaviors of cells, which may lead to the onset and progression of cancer [1]. Epigenetic alterations can induce abnormalities in gene expression within cancer cells [5]. Drug resistance in cancer cells is acquired by genetic and/or epigenetic changes: in the treatment of chronic myeloid leukemia, for instance, combination therapy of imatinib (Gleevec, STI571) and dasatinib (BMS-35482) often fails due to the emergence of only one or two genetic alterations within the tyrosine kinase domain of BCR-ABL [6]. While experimental studies have identified specific (epi)genetic changes and their consequences for cancer progression and drug resistance, mathematical investigations have provided insights into how tumor cells accumulate such alterations during tumorigenesis. Biological knowledge about population dynamics and molecular mechanisms of tumorigenesis, invasion, and therapeutic resistance have been incorporated into the mathematical models; for instance, tissue structures in particular cancer types [11,12,13,14,15,16] and the evolution of drug resistance in cancer cells [17,18,19] were considered
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