Gregory J. Kimmel, Mark Dane, Laura M. Heiser, Philipp M. Altrock and Noemi Andor

Read the paperBoth assumptions were incorporated in a partial differential equations (PDE) model of growth dynamics in polyploid populations of various subpopulation compositions. At the core of the model lies the assumption that chemotactic/haptotactic response to an energy gradient is a function of the cell’s energetic needs. This trade-off implies that, in energy-poor environments, heterogeneous populations will segregate spatially, with more energy-demanding cells leading the front of tumor growth and invasion. In contrast, for an energy-rich environment we expect the cells to grow in a similar way as they will have no need to search for places of higher energy density. We calibrated the model to recapitulate spatial growth patterns measured for the HCC1954 ductal breast carcinoma cell line in 48 different ECM environments. The inferred parameter space revealed three clusters, with different ECMs segregating mainly into different clusters. The two largest clusters differed mostly in their chemotactic/haptotactic- and energy diffusion coefficients; while the small cluster stood out by a high sensitivity to low energy and fast chemotactic/haptotactic response. The cells’ energy consumption rate was negatively correlated with RNA-seq derived expression of the corresponding ECM. A potential explanation for this negative correlation is that our model does not account for the possibility that cells can replace the ECM they degrade. The slower the rate of this replacement is, the higher the consumption rate appears to be.

**Figure 1**. Imbalance between nutrient efficacy and chemotactic superiority accelerates invasion of polyploid populations: subpopulation will segregate and only one type dominates at the invasion front.

In contrast to cell lines, WGD events in primary tumors are mostly clonal, not subclonal. Clones carrying a doubled genome often sweep over the population, such that by the time the tumor is detected, the diploid ancestor no longer exists. A related scenario is advanced, therapy-exposed tumors shown to revert to genomic stability, potentially bringing a WGD population back to a genomic state that more closely resembles its diploid ancestral state (4). The model presented here can investigate how dynamics between the two subpopulations unfold in both of these scenarios—early, shortly after the WGD or late, after therapy exposure. This would characterize what circumstances prevent the WGD carrying clone from becoming dominant or from retaining its dominance and could help explain WGD incidence in primary and recurrent tumors.

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- Kimmel GJ, Dane M, Heiser LM, Altrock PM, Andor N. Integrating mathematical modeling with high throughput imaging explains how polyploid populations behave in nutrient-sparse environments. Cancer Res [Internet]. American Association for Cancer Research; 2020 [cited 2020 Oct 5]; Available from: https://cancerres.aacrjournals.org/content/early/2020/09/16/0008-5472.CAN-20-1231
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