A Markov chain for numerical chromosomal instability in clonally expanding populations

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.

Pervasive chromosomal instability and karyotype order in tumour evolution

“…However, the observed pattern of SCNA acquisition in 41% of our cohort in which the neutral or scrambled models outperform the weighted model might reflect neutral karyotype evolution or the need for cancer-type specific chromosome arm weightings 14,15 . Notably, we see more evidence for subclonal selection in WGD tumours which may be consistent with WGD being a transformative event during subclonal evolution ( Figure 2D, S13F,G) 12,13 .…”

“…Consistent with ongoing selection on cellular karyotypes, the OG-TSG score significantly correlated with the burden of arm-level alterations in the MRCA (Figure 2A To understand subclonal SCNA dynamics within each tumour, we adapted our previous model that predicts population karyotypes over time 12,13 . We used arm-level copy number profiles from each tumour's MRCAs as the starting point and compared how different iterations of the model predict the observed subclonal tumour karyotypes ( Figure 2C, S13A,B, Methods 3.1-2).…”

MEDICC2: whole-genome doubling aware copy-number phylogenies for cancer evolution

“…Despite these limitations, systematically determining the number and order of whole chromosome missegregations, arm-level SCNAs and focal events that have occurred in the evolutionary history of a tumour has not previously been performed on a large scale and has previously been the preserve of theoretical mathematical modelling [54,55] . MEDICC2 enables the reconstruction and timing of the individual SCNA events present in the evolutionary history of a tumour that may overlap and build upon one another.…”

Invasion of homogeneous and polyploid populations in nutrient-limiting environments

“…the process of generating new clonal lines. A next step will be to extend our model to include mutation events, specifically chromosome mis-segregations that contribute extensively to diversify ploidy of a population [31,32]. The additional DNA content of high-ploidy cells, though energetically costly, brings a masking effect against the deleterious consequences of chromosome losses [22].…”

“…All these energetic contingencies determine whether phenotypic differences between goers and growers manifest as such, and explain why non-proliferative arrested cells can have the same motility as cycling cells [30]. A future extension will be to integrate our model of the potential cost of high ploidy with existing Markov models of the robustness benefits it can provide against deleterious mutations [22,31,32]. With a better understanding of the nature of the double-edged sword of high ploidy, we aim to contribute towards personalized combination-therapies with cytotoxic drugs and inhibitors of signal transduction pathways such as MTOR-Is.…”