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

Author summaryChromosome missegregations are common. They occur in 1.2-2.3% per mitosis in normal cells and in cancer cells their rate is between one and two orders of magnitudes higher. When 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. The model revealed that the upper limit of missegregation rate is a function of the tumor's 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. 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.

Automated summary

Chromosome missegregations are common and can lead to drastic differences between daughter cells and parental cells. A mathematical model has been developed to account for cell-to-cell diversity caused by missegregations. The model can be used to understand selection and genotype-to-phenotype mapping, and has application in studying the upper limit of missegregation rate in cancer populations.