Extended logistic growth model for heterogeneous populations

Journal of Theoretical Biology
Wang JinMatthew J Simpson

Abstract

Cell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature, cell proliferation is typically modelled using a classical logistic equation which neglects variations in the proliferation rate. In this work, we consider a discrete mathematical model of cell migration and cell proliferation, modulated by volume exclusion (crowding) effects, with variable rates of proliferation across the total population. We refer to this variability as heterogeneity. Constructing the continuum limit of the discrete model leads to a generalisation of the classical logistic growth model. Comparing numerical solutions of the model to averaged data from discrete simulations shows that the new model captures the key features of the discrete process. Applying the extended logistic model to simulate a proliferation assay using rates from recent experimental literature shows that neglecting the role of heterogeneity can, at times, lead to misleading results.

Citations

Oct 20, 2019·Scientific Reports·Anudeep SurendranMatthew J Simpson
Jun 16, 2019·Bulletin of Mathematical Biology·Ana Victoria Ponce BobadillaTomás Alarcón
Aug 12, 2018·Bulletin of Mathematical Biology·Anudeep SurendranMatthew J Simpson
Nov 24, 2020·Proceedings. Mathematical, Physical, and Engineering Sciences·Anudeep SurendranMatthew J Simpson
Mar 14, 2021·Journal of Mathematical Biology·Sean T VittadelloMatthew J Simpson
Mar 18, 2021·Journal of the Royal Society, Interface·John T NardiniKevin B Flores
Mar 21, 2021·Bulletin of Mathematical Biology·Wang JinMatthew J Simpson
Jan 2, 2022·Journal of Theoretical Biology·Matthew J SimpsonRuth E Baker

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