Mathematical model for karyotype evolution describing mouse pretumor and tumor cells

During cell division, mis-segregation of duplicated chromosomes generates cells with perturbed karyotypes which after multiple cell divisions lead to tumor tissues. Experimentally it was found that in living mouse with enhanced chromosome mis-segregation, chromosome gains dominate over chromosome losses both in pretumor and tumor tissues. Additionally, it was also shown that tumor cells predominantly have extra copies of chromosome 15, as compared to other chromosomes. However, what causes observed gains over losses and why chromosome 15 predominantly appears with extra copies is still unknown. By developing a mathematical model, that includes chromosome mis-segregation, apoptosis and proliferation, we study karyotype evolution over multiple generations. By comparing our model results with experimental data for pretumor cells, we found that observed dominating chromosome gains over losses can be explained by pronounced apoptosis or slower proliferation of cells with chromosome losses. For explaining excess of chromosome 15 in tumor cells, our model predicts that these cells proliferate two fold faster than cells with two copies of chromosome 15. Based on this we conclude that enhanced proliferation is the main driver of tumor karyotype evolution.