Quantifying the roles of cell motility and cell proliferation in a circular barrier assay

Abstract

Moving fronts of cells are essential features of embryonic development, wound repair and cancer metastasis. This paper describes a set of experiments to investigate the roles of random motility and proliferation in driving the spread of an initially confined cell population. The experiments include an analysis of cell spreading when proliferation was inhibited. Our data have been analysed using two mathematical models: a lattice-based discrete model and a related continuum partial differential equation model. We obtain independent estimates of the random motility parameter, D, and the intrinsic proliferation rate, l, and we confirm that these estimates lead to accurate modelling predictions of the position of the leading edge of the moving front as well as the evolution of the cell density profiles. Previous work suggests that systems with a high l/D ratio will be characterized by steep fronts, whereas systems with a low l/D ratio will lead to shallow diffuse fronts and this is confirmed in the present study. Our results provide evidence that continuum models, based on the Fisher-Kolmogorov equation, are a reliable platform upon which we can interpret and predict such experimental observations.

Distinguishing between mechanisms of cell aggregation using pair-correlation functions

“…7(a)] and area [ Fig. 7(b)] of the cells in the images was estimated using Matlab's imaging processing toolbox [8,22,24]. With this data we calculated the average area per cell µ and the average length scale √ µ.…”

Experimental and Modelling Investigation of Monolayer Development with Clustering

“…Similarly, our moment dynamics model assumes that the motion of individual cells is unaffected by cell-to-cell adhesion and it would also useful to include experimental markers of cell-to-cell adhesion (Shiozaki et al 1991;Takeichi 1991) so that we can assess whether this assumption is reasonable or whether is necessary to incorporate adhesion effects into the moment dynamics model (Johnston et al 2012). Our work could also be extended by considering spatiallyvariable initial conditions, such as in a scratch assay (Maini et al 2004a(Maini et al , 2004b or a barrier assay (Simpson et al 2013) where a spatially-variable moment dynamics model ) could be applied. Finally, our mathematical modelling platform could be extended by taking a lattice-free approach (Codling et al 2008).…”

Spatial moment dynamics for collective cell movement incorporating a neighbour-dependent directional bias

“…In some cases of collective cell movement, it is necessary to consider a non-homogeneous setting, where the average density of cells is higher or lower in certain regions. For example, a nonhomogeneous initial condition would be required for the modelling of cell invasion assays in which moving fronts of cells are formed [36,60]. However, while moment models incorporating terms for density-dependent birth, death and movement have been derived for a spatially non-homogeneous case, solving the dynamics up to at least second order is more complicated and as a result has received significantly less attention than simpler homogeneous systems [37].…”

“…'Local mean-field' models, such as reaction-diffusion equations, allow the average density of individuals to be expressed as a function of the location in space, however, they still tend to ignore the effects of small-scale spatial structure on the population [37]. For example, the Fisher-Kolmogorov equation [38,39] has been used to describe both cell migration, incorporated in a diffusion term and proliferation in the form of a logistic growth function [21,36].…”

“…Simulations of IBMs produce synthetic data that can be compared with experimental images [36] and may shed some light on the underlying mechanisms responsible for emerging spatial structure [17], however, they are quite intractable mathematically. Deriving a formal mathematical representation gives more insight into the population-level dynamics of such systems and provides scope for a more rigorous analysis [37].…”