How domain growth is implemented determines the long term behaviour of a cell population through its effect on spatial correlations

Robert J. H. Ross; R. E. Baker; C. A. Yates

The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/041509 doi: bioRxiv preprint The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/041509 doi: bioRxiv preprint In Fig. 6 the effect of domain growth via GM2 on agent density can be seen. In this case we see that GM2 causes the steady-state density predicted by the MFA to be correct. This is because GM2 is more effective at breaking up agent clusters than GM1, potentially 'freeing-up' one lattice site for four agents in each row/column every growth event. This counteracts the effect of the spatial correlations created by agent proliferation. GM2 also causes agents to change neighbouring agents in the IBM, and so further reduces the spatial correlations associated with agent proliferation. Despite this we see that the correlations ODE model still more accurately predicts the rate at which the agent density evolves, while also accurately approximating the steady-state density in the IBM. In Fig. 7 the effect of GM2 on spatial correlations can be seen in both the correlations ODE model and calculated directly from the IBM. In contrast to GM1 we see that as the growth rate is increased the spatial correlations decrease. We also see that at the steady-state density F = 1, this provides the reason as to why the agent steady-state predicted by the MFA is correct.