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Travelling waves in a minimal go-or-grow model of cell invasion (2404.11251v1)
Published 17 Apr 2024 in math.AP and q-bio.CB
Abstract: We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis in the fast switching regime shows that the total cell density in the two-population go-or-grow model can be described in terms of a single reaction-diffusion equation with density-dependent diffusion and proliferation. Using the connection to single-population models, we study travelling wave solutions, showing that the wave speed in the go-or-grow model is always bounded by the wave speed corresponding to the well-known Fisher-KPP equation.
- R. A. Fisher. The wave of advance of advantageous genes. Annals of Eugenics, 7(4):355–369, 1937.
- A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem. Moskovskogo University Bulletin of Mathematics, 1(6):1–25, 1937.
- P. Gerlee and S. Nelander. The impact of phenotypic switching on glioblastoma growth and invasion. PLoS Computational Biology, 8(6):e1002556, 2012.
- P. Gerlee and S. Nelander. Travelling wave analysis of a mathematical model of glioblastoma growth. Mathematical Biosciences, 276:75–81, 2016.
- Traveling waves of a go-or-grow model of glioma growth. SIAM Journal on Applied Mathematics, 78(3):1778–1801, 2018.
- Traveling wave speed and profile of a “go or grow” glioblastoma multiforme model. Communications in Nonlinear Science and Numerical Simulation, 118:107008, 2023.
- Phenotypic switching mechanisms determine the structure of cell migration into extracellular matrix under the ’go-or-grow’ hypothesis. arXiv preprint arXiv:2401.07279, 2024.
- A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment. Biophysical Journal, 92(1):356–365, 2007.
- In vivo switching of human melanoma cells between proliferative and invasive states. Cancer Research, 68(3):650–656, 2008.
- D. Tosh and J. M. W. Slack. How cells change their phenotype. Nature Reviews Molecular Cell Biology, 3(3):187–194, 2002.
- Cellular phenotype switching and microvesicles. Advanced Drug Delivery Reviews, 62(12):1141–1148, 2010.
- J. Canosa. On a nonlinear diffusion equation describing population growth. IBM Journal of Research and Development, 17(4):307–313, 1973.
- J. D. Murray. Mathematical Biology I: An Introduction. Springer New York, 2001.
- Travelling wave analysis of cellular invasion into surrounding tissues. Physica D: Nonlinear Phenomena, 428:133026, 2021.
- Collective and single cell behavior in epithelial contact inhibition. Proceedings of the National Academy of Sciences, 109(3):739–744, 2012.
- Mechanical constraints and cell cycle regulation in models of collective cell migration. arXiv preprint arXiv:2401.08805, 2024.
- Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion. Proceedings of the Royal Society A, 477(2256):20210593, 2021.
- Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons. Studies in Applied Mathematics, 151(4):1471–1497, 2023.