Abstract
Standard differential equation-based models of collective cell behaviour, such as the logistic growth model, invoke a mean-field assumption which is equivalent to assuming that individuals within the population interact with each other in proportion to the average population density. Implementing such assumptions implies that the dynamics of the system are unaffected by spatial structure, such as the formation of patches or clusters within the population. Recent theoretical developments have introduced a class of models, known as moment dynamics models, which aim to account for the dynamics of individuals, pairs of individuals, triplets of individuals, and so on. Such models enable us to describe the dynamics of populations with clustering, however, little progress has been made with regard to applying moment dynamics models to experimental data. Here, we report new experimental results describing the formation of a monolayer of cells using two different cell types: 3T3 fibroblast cells and MDA MB 231 breast cancer cells. Our analysis indicates that the 3T3 fibroblast cells are relatively motile and we observe that the 3T3 fibroblast monolayer forms without clustering. Alternatively, the MDA MB 231 cells are less motile and we observe that the MDA MB 231 monolayer formation is associated with significant clustering. We calibrate a moment dynamics model and a standard mean-field model to both data sets. Our results indicate that the mean-field and moment dynamics models provide similar descriptions of the 3T3 fibroblast monolayer formation whereas these two models give very different predictions for the MDA MD 231 monolayer formation. These outcomes indicate that standard mean-field models of collective cell behaviour are not always appropriate and that care ought to be exercised when implementing such a model.
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Acknowledgements
We appreciate the advice and assistance of Associate Professor David Leavesley, Dr. Kerry Manton and Dr Leo de Boer. This research is supported by the Australian Research Council Discovery Project DP120100551, and the 2011 International Exchange Scheme funded by the Royal Society.
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Simpson, M.J., Binder, B.J., Haridas, P. et al. Experimental and Modelling Investigation of Monolayer Development with Clustering. Bull Math Biol 75, 871–889 (2013). https://doi.org/10.1007/s11538-013-9839-0
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DOI: https://doi.org/10.1007/s11538-013-9839-0