Abstract
Cancer cells frequently undergo chromosome missegregation events during mitosis, whereby the copies of a given chromosome are not distributed evenly among the two daughter cells, thus creating cells with heterogeneous karyotypes. A stochastic model tracing cellular karyotypes derived from clonal populations over hundreds of generations was recently developed and experimentally validated, and it was capable of predicting favorable karyotypes frequently observed in cancer. Here, we construct and study a Markov chain that precisely describes karyotypic evolution during clonally expanding cancer cell populations. The Markov chain allows us to directly predict the distribution of karyotypes and the expected size of the tumor after many cell divisions without resorting to computationally expensive simulations. We determine the limiting karyotype distribution of an evolving tumor population, and quantify its dependency on several key parameters including the initial karyotype of the founder cell, the rate of whole chromosome missegregation, and chromosome-specific cell viability. Using this model, we confirm the existence of an optimal rate of chromosome missegregation probabilities that maximizes karyotypic heterogeneity, while minimizing the occurrence of nullisomy. Interestingly, karyotypic heterogeneity is significantly more dependent on chromosome missegregation probabilities rather than the number of cell divisions, so that maximal heterogeneity can be reached rapidly (within a few hundred generations of cell division) at chromosome missegregation rates commonly observed in cancer cell lines. Conversely, at low missegregation rates, heterogeneity is constrained even after thousands of cell division events. This leads us to conclude that chromosome copy number heterogeneity is primarily constrained by chromosome missegregation rates and the risk for nullisomy and less so by the age of the tumor. This model enables direct integration of karyotype information into existing models of tumor evolution based on somatic mutations.
Highlights
Cancer genomic heterogeneity, which is often driven by genomic instability, enables Darwinian selection, leading to tumor metastasis and increased resistance to therapeutic pressures [1,2,3]
Chromosomal instability (CIN) is a hallmark of cancer and it results from persistent chromosome segregation errors during cell division
CIN has been shown to play a key role in drug resistance and tumor metastasis
Summary
Cancer genomic heterogeneity, which is often driven by genomic instability, enables Darwinian selection, leading to tumor metastasis and increased resistance to therapeutic pressures [1,2,3]. A frequent, yet understudied source of genetic heterogeneity is numerical chromosomal instability, which allows cancer cells to rapidly vary the number of copies of each chromosome (karyotype) through whole chromosome missegregation events during mitosis [4,5,6,7] This karyotypic heterogeneity can lead to tumor cells with varying fitness levels depending on the potency and distribution of oncogenes (proliferative) and tumor suppressor genes (antiproliferative) on individual chromosomes [8]. Laughney et al addressed this limitation by building a stochastic model that tracks single cell karyotypes derived from clonal populations over hundreds of generations, while simultaneously allowing the cumulative proliferative or anti-proliferative effects of genes encoded on individual chromosomes to alter cellular viability [4] This model incorporates chromosome-specific scores derived from a recent genomic analysis by Davoli et al [8], which weighs individual chromosomes based on the potency and chromosomal distribution of oncogenes (proliferative, contributing positively) and tumor suppressor genes (anti-proliferative, contributing negatively).
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