RT Journal Article
SR Electronic
T1 Extended logistic growth model for heterogeneous populations
JF bioRxiv
FD Cold Spring Harbor Laboratory
SP 231100
DO 10.1101/231100
A1 Wang Jin
A1 Scott W McCue
A1 Matthew J Simpson
YR 2017
UL http://biorxiv.org/content/early/2017/12/08/231100.abstract
AB 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, the standard approach to model cell proliferation in the mathematical biology literature is to use 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 heterogeneity in the rates of proliferation of individual cells within the population. 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 lead to misleading results.