. They won't stop moving entirely, but let's assume they slow down whenever they are in happy company. How would that clustering effect change the

Now we leave everything as before, except that the clustering effect is additionally implemented. For this purpose, we count the number of direct neighbors of each agent. If this number is larger than zero for certain agents, we reduce the hopping rates of these specific agents by a factor of 10 during the next MC cycle. Again we plot the invasion profiles:

The result is remarkable:

As a consequence of the clustering effect, the profiles are changed from about Gaussian to almost exponential shape (showing up as linear lines in the semi-log plot).

This offers a completely new, simple, and testable mechanism for explaining the mostly exponential invasion profiles observed in the experiments. It does not require any explicit assumptions about the diffusion of chemical signalling molecules. The only parameters are the maximum diffusion constant of the agents, their detection range for sensing closeby fellows, and the reduced diffusion constant in the clustering mode.

Future tests:

- The initial density of the cells in the monolayer should drastically affect the invasion process. A small density will reduce the probability of cluster formation and thus drive the system back to the normal, Gaussian diffusion of the agents.

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