Abstract A014: Models of neighbors and space: frequency and density dependent dynamics of tumor evolution
Authors: Veith Thomas , Schultz Andrew , Alahmari Saeed , Andor Noemi 
Published: May 2022

Abstract
Mutations matter in cancer. Loss of function in a gene such as tp53 is advantageous for tumor progression. However, we also know that cells can share similar mutational burdens but exhibit starkly different phenotypes. The heterogeneous nature of cancer cell populations that comprise a tumor compounds this problem, and is a known source of treatment failure. We hypothesize that density conditions in the tumor microenvironment select for particular cellular phenotypes. Additionally, we posit that a cell’s neighbor can affect its phenotypes through interactions such as the exchange of growth factors or competition for resources – a phenomenon known as frequency-dependent selection. To test these hypotheses and compare the relative effects of density and frequency dependent selection on tumor evolution, we have developed two mathematical models integrated with experimental and computational techniques. In both models, we investigate the growth dynamics of subclonal populations defined by somatic copy number alterations detected by single cell RNA/DNA-sequencing data in 5 gastric cancer cell lines. For density dependence, we have identified transcriptomic biomarkers of growth rate (r) and carrying capacity (K). These r/K biomarkers are used to parameterize logistic, power-law, and Gompertzian models to evaluate which best captures the observed growth. In the case of frequency dependent selection, we have deployed an inverse game theory algorithm which takes the subclonal frequencies and finds parameterizations for the replicator equation which can recapitulate the detected frequencies. The algorithm uses a penalized least squares method that takes the error in parameterization to be the difference between replicator equation output and detected subclonal frequencies. For density dependence, we tested 25 KEGG pathways as transcriptomic biomarkers of cell line growth parameters. Of these, ‘Pathways in cancer’ fit best for growth rate (R2 = 0.9965) and ‘p53 signaling pathway’ fit best for carrying capacity (R2 = 0.9701). In 4 out of 5 cells lines, all 3 growth models that were tested fit the data well (R2 ≥ 0.93), with logistic being the best fit or tied for best fit. In each cell line, an r/K tradeoff existed between at least 2 subclones, suggesting density conditions will indeed select for certain subclones. In the case of frequency dependence, we found the best fit parameterizations for the replicator equation indicate competition is less intense between different subclones than when a subclone competes with itself. This suggests a cell’s neighbor will have an effect on its growth. Taken together, these approaches reveal the dynamics of heterogeneous tumor growth, and make it possible to compare the relative influence of different types of evolutionarily selective pressures. For example, we can examine how the growth of a tumor would change with the elimination of one subclone. 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 Veith, Andrew Schultz, Saeed Alahmari, Noemi Andor. Models of neighbors and space: frequency and density dependent dynamics of tumor evolution [abstract]. In: Proceedings of the AACR Special Conference on the Evolutionary Dynamics in Carcinogenesis and Response to Therapy; 2022 Mar 14-17. Philadelphia (PA): AACR; Cancer Res 2022;82(10 Suppl):Abstract nr A014.