Another interesting feature of the clustering effect (compare posts [4] and [5]) is the emergence of two relatively distinct phases in the invasion profiles:

Close to the cell monolayer at z=0, the cell density is high, so that clusters have a high probability. This leads to a small average diffusion constant and, thus, a weakly invasive phase close to the surface.

At some point, the absolute cell density and the corresponding cluster probability fall below the critical value and most cells switch to a high diffusion constant. A strongly invasive phase is formed further in the bulk.

The following MC simulation demonstrates this effect:

Remarkably, many of the measured invasion profiles show qualitatively such a bi-phasic behaviour:

Note that for technical reasons the coordinate of the monolayer is not at z=0. No attempt has been made to fit the data.

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Some side remark: As mentioned already in [6], the value P_cum[z=1] can be interpreted as the invaded fraction of cells. When we zoom into the simulation result above, we can see that this fraction increases from about 0.63 to 0.86 within the time interval between t=20 and t=100 units.

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