Cell density and cell size dynamics during in vitro tissue growth experiments: Implications for mathematical models of collective cell behaviour

We present a detailed experimental data set describing a tissue growth experiment where a population of cells is initially distributed uniformly, at low density, on a two-dimensional substrate, and grows to eventually form a confluent monolayer. Using image processing tools, we provide precise information about temporal changes in the number of cells, the location of cells and the total area occupied by cells. This information shows that the increase in area occupied by the cell population is affected by both the increase in cell number as well as an increase in the average size of the cells. We show that standard approaches to interpret such experiments, where the cell size is typically treated as a constant, can lead to errors. Furthermore we show that a standard, discrete, random walk model of biological cell motility and cell proliferation should not be used to represent our experimental data set since this standard model treats all cells as having a constant size that does not change with time. Instead, we introduce a generalization of the standard model which allows agents in the random walk model to move, proliferate and grow in size, and we show that the data produced by this more general model is consistent with our experimental data set.