Intra-tumor heterogeneity, turnover rate and karyotype space shape susceptibility to missegregation-induced extinction.

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 cell's SCNA burden-a chromosome missegregation. A stochastic model of chromosome mis-segregations has been previously developed to describe the evolution of SCNAs of a single chromosome type. Building upon this work, we derive a general deterministic framework for modeling missegregations of multiple chromosome types. The framework offers flexibility to model intra-tumor heterogeneity in the SCNAs of all chromosomes, as well as in missegregation- and turnover rates. The model can be used to test how selection acts upon coexisting karyotypes over hundreds of generations. We use the model to calculate missegregation-induced population extinction (MIE) curves, that separate viable from non-viable populations as a function of their turnover- and missegregation rates. Turnover- and missegregation rates estimated from scRNA-seq data are then compared to theoretical predictions. We find convergence of theoretical and empirical results in both the location of MIE curves and the necessary conditions for MIE. When a dependency of missegregation rate on karyotype is introduced, karyotypes associated with low missegregation rates act 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.