Heterogeneity, turn-over rate and karyotype space shape susceptibility to missegregation-induced extinction

Abstract

The phenotypic efficacy of somatic copy number alterations (SCNAs) stems from their incidence per base pair of the genome, which is orders of magnitudes greater than that of point mutations. One mitotic event stands out in its potential to significantly change a cells SCNA burden-a chromosome missegregation. We present a general deterministic framework for modeling chromosome missegregations and use it to evaluate the possibility of missegregation-induced population extinction (MIE). The model predicts critical curves that separate viable from non-viable populations as a function of their turnover- and missegregation rates. Missegregation- and turnover rates estimated from a PAN-cancer scRNA-seq dataset of 15,464 cells are then compared to predictions. The majority of tumors across all cancer types had missegregation- and turnover rates that were within viable regions of the parameter space. When a dependency of missegregation rate on karyotype was introduced, karyotypes associated with low missegregation rates acted as a stabilizing refuge, rendering MIE impossible unless turnover rates are exceedingly high. Intra-tumor heterogeneity, including heterogeneity in missegregation rates, increases as tumors progress, rendering MIE unlikely. Author SummaryWhen a cell missegregates a chromosome while dividing, the chance is high that its two daughter cells will behave drastically different from each other and from their parental cell. Chromosome missegregations are therefore one of the most powerful forces of phenotypic diversity. We developed a mathematical model of chromosome missegregations that allows for this cell-to-cell diversity to be accounted for. The model serves to help understand how selection acts upon cells with versatile chromosome contents, as a tool for genotype-to-phenotype mapping in various microenvironments. As a first application example we used the model to address whether there exists an upper limit on missegregation rate, beyond which cancer populations collapse. Chromosome missegregations are common. They occur in 1.2-2.3% per mitosis in normal cells [1] and in cancer cells their rate is between one and two orders of magnitudes higher [2]. The model revealed that the upper limit of missegregation rate is a function of the tumors turnover rate (i.e. how fast the tumor renews itself). In heterogenous populations however, cells with low missegregation rates protect the population from collapse. Intra-tumor heterogeneity, including heterogeneity in missegregation rates, increases as tumors progress, rendering missegregation-induced extinction unlikely.