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

In Fig. 4 the effects of domain growth via GM1 on the evolution of the macroscopic agent density can be seen. We see that the inclusion of GM1 causes the steady-state density predicted by the standard MFA, Eq. (28), to be incorrect. The steady-state density calculated from an ensemble average from the IBM is lower than the MFA predicts, which the correlation ODE model (Eq. (27)) is able to capture. The rate at which the agent density increases is also reduced in the IBM due to spatial correlations, and the correlations ODE model better approximates this than the MFA. One may expect domain growth to decrease spatial correlations by 'breaking-up' existing agent clusters which, in turn, would allow greater agent movement and cause the MFA to be more accurate. However, the nature of GM1 means that it does not break up agents effectively, only potentially 'freeing-up' one lattice site for two agents in each row/column every growth event (see Fig. 1 ). GM1 also does not cause agents to make 16 author/funder. All rights reserved. No reuse allowed without permission.