Abstract 6549: Investigating the effects of density and frequency-dependent selection on subpopulations of cancer cells defined by copy number
Authors: Veith Thomas A. , Schultz Andrew , Andor Noemi , Alahmari Saeed 
Published: April 2023

Intratumoral heterogeneity is a major obstacle for many cancer therapies. Treatment modalities which target a particular phenotype select for cells with different phenotypes. For example, chemotherapy which targets fast-dividing cells may select for a tumor composed of slower-dividing cells which cannot be effectively targeted by the drug. We hypothesize that subpopulations (SPs) of cells defined by somatic copy number alterations (sCNAs) differ in how quickly they divide and how well they can compete at high population densities. Additionally, we expect that sCNA-defined SPs affect the fitness of one another through cooperative (e.g., exchange of growth factors) and competitive (resource depletion) interactions. To test these hypotheses and compare the relative effects of (i) density and (ii) frequency-dependent selection on tumor evolution, we have developed two mathematical models integrated with experimental and computational techniques. In both models, we evaluate the growth dynamics of cancer cell SPs defined by sCNAs detected in single cell RNA/DNA-sequencing data from 4 gastric cancer cell lines (HGC-27, KATOIII, NUGC-4, SNU-16). To investigate the effects of density dependent selection (i), we start by growing the cell lines in our lab in order to infer growth rate (r) and carrying capacity (K). Next, linear models are built correlating pathway expression levels with r/K values. We tested 50 KEGG pathways previously identified as differentially expressed between r and K-selected cells as transcriptomic biomarkers of growth parameters. The best fitting models are then used to infer SP-specific r/K values. For growth, we found r as a function of the KEGG pathway ‘RNA Polymerase’ (R2 = 0.9636, p-val=0.0019). For carrying capacity, we used ‘Pathways in Cancer’ (R2 = 0.7898, p-val=0.0629). In each cell line, an r/K tradeoff existed between at least one pair of SPs, suggesting sCNAs indeed have effect on r/K parameters. For frequency-dependent selection (ii), we use an inverse game theory algorithm which takes SP frequencies over time as input and outputs a parameterization for the replicator equation to recapitulate detected frequencies and predict future growth. The algorithm uses a penalized least squares method that takes the error to be the difference between replicator equation output and SP frequency input. SP growth over time can then be modeled with the replicator equation to characterize conditions for co-existence or dominance. These approaches reveal the dynamics of heterogeneous tumor growth, and make it possible to compare the relative influence of different selective pressures. We can examine how the growth of a tumor would change with the elimination of a given SP. This greater understanding can contribute to a better design of evolution-based therapies that avoid, or at least delay, the evolution of resistance to treatment.

Citation Format: Thomas A. Veith, Andrew Schultz, Noemi Andor, Saeed Alahmari. Investigating the effects of density and frequency-dependent selection on subpopulations of cancer cells defined by copy number. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 6549.