Evolving copy number gains promote tumor expansion and bolster mutational diversification.

The timing and fitness effect of somatic copy number alterations (SCNA) in cancer evolution remains poorly understood. Here we present a framework to determine the timing of a clonal SCNA that encompasses multiple gains. This involves calculating the proportion of time from its last gain to the onset of population expansion (lead time) as well as the proportion of time prior to its first gain (initiation time). Our method capitalizes on the observation that a genomic segment, while in a specific copy number (CN) state, accumulates point mutations proportionally to its CN. Analyzing 184 whole genome sequenced samples from 75 patients across five tumor types, we commonly observe late gains following early initiating events, occurring just before the clonal expansion relevant to the sampling. These include gains acquired after genome doubling in more than 60% of cases. Notably, mathematical modeling suggests that late clonal gains may contain final-expansion drivers. Lastly, SCNAs bolster mutational diversification between subpopulations, exacerbating the circle of proliferation and increasing heterogeneity.

Elements and evolutionary determinants of genomic divergence between paired primary and metastatic tumors.

Can metastatic-primary (M-P) genomic divergence measured from next generation sequencing reveal the natural history of metastatic dissemination? This remains an open question of utmost importance in facilitating a deeper understanding of metastatic progression, and thereby, improving its prevention. Here, we utilize mathematical and computational modeling to tackle this question as well as to provide a framework that illuminates the fundamental elements and evolutionary determinants of M-P divergence. Our framework facilitates the integration of sequencing detectability of somatic variants, and hence, paves the way towards bridging the measurable between-tumor heterogeneity with analytical modeling and interpretability. We show that the number of somatic variants of the metastatic seeding cell that are experimentally undetectable in the primary tumor, can be characterized as the path of the phylogenetic tree from the last appearing variant of the seeding cell back to the most recent detectable variant. We find that the expected length of this path is principally determined by the decay in detectability of the variants along the seeding cell's lineage; and thus, exhibits a significant dependence on the underlying tumor growth dynamics. A striking implication of this fact, is that dissemination from an advanced detectable subclone of the primary tumor can lead to an abrupt drop in the expected measurable M-P divergence, thereby breaking the previously assumed monotonic relation between seeding time and M-P divergence. This is emphatically verified by our single cell-based spatial tumor growth simulation, where we find that M-P divergence exhibits a non-monotonic relationship with seeding time when the primary tumor grows under branched and linear evolution. On the other hand, a monotonic relationship holds when we condition on the dynamics of progressive diversification, or by restricting the seeding cells to always originate from undetectable subclones. Our results highlight the fact that a precise understanding of tumor growth dynamics is the sine qua non for exploiting M-P divergence to reconstruct the chronology of metastatic dissemination. The quantitative models presented here enable further careful evaluation of M-P divergence in association with crucial evolutionary and sequencing parameters.