Spatial vs. non-spatial eco-evolutionary dynamics in a tumor growth model

Abstract

Metastatic prostate cancer is initially treated with androgen deprivation therapy (ADT). However, resistance typically develops in about 1 year - a clinical condition termed metastatic castrate-resistant prostate cancer (mCRPC). We develop and investigate a spatial game (agent based continuous space) of mCRPC that considers three distinct cancer cell types: (1) those dependent on exogenous testosterone (T), (2) those with increased CYP17A expression that produce testosterone and provide it to the environment as a public good (T), and (3) those independent of testosterone (T). The interactions within and between cancer cell types can be represented by a 3 × 3 matrix. Based on the known biology of this cancer there are 22 potential matrices that give roughly three major outcomes depending upon the absence (good prognosis), near absence or high frequency (poor prognosis) of T cells at the evolutionarily stable strategy (ESS). When just two cell types coexist the spatial game faithfully reproduces the ESS of the corresponding matrix game. With three cell types divergences occur, in some cases just two strategies coexist in the spatial game even as a non-spatial matrix game supports all three. Discrepancies between the spatial game and non-spatial ESS happen because different cell types become more or less clumped in the spatial game - leading to non-random assortative interactions between cell types. Three key spatial scales influence the distribution and abundance of cell types in the spatial game: i. Increasing the radius at which cells interact with each other can lead to higher clumping of each type, ii. Increasing the radius at which cells experience limits to population growth can cause densely packed tumor clusters in space, iii. Increasing the dispersal radius of daughter cells promotes increased mixing of cell types. To our knowledge the effects of these spatial scales on eco-evolutionary dynamics have not been explored in cancer models. The fact that cancer interactions are spatially explicit and that our spatial game of mCRPC provides in general different outcomes than the non-spatial game might suggest that non-spatial models are insufficient for capturing key elements of tumorigenesis.

Towards multi-drug adaptive therapy

“…Competition parameters are described by certain inequalities for given treatment dynamics. We summarize these inequalities in Supplemental Materials for convenience: Table 1 (under treatment) and Table 2 (no treatment) 28,45,60 . Since there is cell-cell competition and niche partitioning with respect to association with surrounding vasculature, we assume that all coefficients are positive and bounded between 0 and 1.…”

“…1B, red). Adaptive therapies have now been tested experimentally 26,26,27 and are 44 currently being applied across multiple clinical trials (NCT02415621; NCT03511196; NCT03543969; NCT03630120) at the 45 Moffitt Cancer Center 28 . These adaptive therapies capitalize on competition for space and resources between drug-sensitive 46 and slow growing drug-resistant populations 13,29,30 .…”

“…Next, we 98 parameterize a previously published Lotka-Volterra model of treatment dynamics (see refs. 28,38,45 ), by fitting the model to 99 prostate-serum-antigen blood biomarker (PSA) data from all patients (figure 3, dashed red lines).…”

“…For details on the 260 specific implementation and parameterization of the model used in figures 4, 6, and 7, we refer the reader to Supplemental 261 Information and to refs. 28,45 .…”

Modelling bistable tumour population dynamics to design effective treatment strategies

“…There is a rich literature of mathematical models for tumour clonal evolution that undergoes treatments (e.g., [17][18][19][20][21][22][23]). In contrast, models of cellular plastic responses to treatments are relatively limited and recent (e.g., [24][25][26], see also reviews [27][28][29]).…”