Spatial interactions modulate tumor growth and immune infiltration.

Lenia, a cellular automata framework used in artificial life, provides a natural setting to design, implement, and analyze mathematical models of cancer progression and treatment. Lenia's suitability as a cancer model is derived from the strong parallels between artificial life and cancer evolution: morphogenesis, homeostasis, motility, reproduction, growth, stimuli response, evolvability, and adaptation. Historically, agent-based models of cancer progression have been constructed with rules that govern birth, death and migration based on local availability for space, with attempts to map local rules to emergent global growth dynamics. In contrast, Lenia provides a flexible framework for considering a spectrum of local (cell-scale) to global (tumor-scale) dynamics by defining an interaction kernel governing density-dependent growth dynamics. First, we show Lenia can recapitulate a range of cancer model classifications including local or global, deterministic or stochastic, non-spatial or spatial, single or multi-population, and off or on-lattice. Lenia is subsequently used to develop data-informed models of 1) single-population growth dynamics, 2) multi-population cell-cell competition models, and 3) cell migration or chemotaxis. Mathematical modeling provides several important mechanistic insights into tumor-immune interactions. First, we find that short-range interaction kernels provide a mechanism for tumor cell survival under conditions for strong Allee effects. Next, we find that asymmetric interaction tumor-immune kernels lead to poor immune response and alter the the spatial variegation of tumor density. Finally, modeling recapitulates immune-ECM interactions where patterns of collagen formation evolve as a mechanism of immune escape, leading to an inverse relationship between disease stage and immune coverage.