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Extended logistic growth model for heterogeneous populations.

Authors
  • Jin, Wang1
  • McCue, Scott W1
  • Simpson, Matthew J2
  • 1 School of Mathematical Sciences, Queensland University of Technology (QUT) Brisbane, Queensland, Australia. , (Australia)
  • 2 School of Mathematical Sciences, Queensland University of Technology (QUT) Brisbane, Queensland, Australia. Electronic address: [email protected] , (Australia)
Type
Published Article
Journal
Journal of Theoretical Biology
Publisher
Elsevier
Publication Date
Feb 23, 2018
Identifiers
DOI: 10.1016/j.jtbi.2018.02.027
PMID: 29481822
Source
Medline
Keywords
License
Unknown

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.

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