Speaker
Description
The understanding of tissue dynamics is critical across various biological contexts, including morphogenesis, regeneration, and tumor proliferation. While traditional models often focus on volume exclusion, this work investigates the emergence of spatial patterns driven by competition for a shared resource, such as oxygen \cite{Gatenby1996}. We present a family of coarse-grained evolution models that incorporate phenotypic traits and cellular heterogeneity via an effective proliferation rate derived from cell-cycle variations. To facilitate theoretical analysis, we introduce a quasi-stationary approximation for the resource dynamics, which we show numerically to be highly accurate across a wide range of macroscopic parameters.
In the case of a single population, the dynamics resemble those of the FKPP equation \cite{Kolmogorov1937, Hadeler1975}. For competitive systems involving two cellular lineages \cite{Volpert1994}, we find that the fitter population, characterized by a higher proliferation rate for a given resource level, progressively takes over the spatial domain as an invading pattern, while the less fit population retreats.
Our results indicate that collective invasion speed is primarily governed by the proliferation rate of the fittest population, suggesting a "winner-takes-all" dynamic in the long-term tissue organizationand providing a tool to study dominant phenotypic traits in heterogeneous tissues without necessitating underlying genetic variability.
Bibliography
@article{Gatenby1996,
author = {R. A. Gatenby and E. T. Gawlinski},
title = {A reaction-diffusion model of cancer invasion},
journal = {Cancer Research},
volume = {56},
pages = {5743--5753},
year = {1996},
note = {[1] Provides the biological/RD foundation.}
}
@article{Hadeler1975,
author = {K. P. Hadeler and F. Rothe},
title = {Travelling fronts in nonlinear diffusion equations},
journal = {Journal of Mathematical Biology},
volume = {2},
number = {3},
pages = {251--263},
year = {1975},
doi = {10.1007/BF00277156}
}
@article{Kolmogorov1937,
author = {A. N. Kolmogorov and I. G. Petrovskii and N. S. Piskunov},
title = {A study of the diffusion equation with increase in the amount of substance, and its application to a biological problem},
journal = {Bulletin of Moscow University, Mathematics and Mechanics},
year = {1937}
}
@book{Volpert1994,
author = {A. I. Volpert and V. A. Volpert},
title = {Traveling Wave Solutions of Parabolic Systems},
publisher = {American Mathematical Society},
address = {Providence, RI},
year = {1994}
}
