Thursday, May 7, 2009

Cell invasion (3) : Effect of cell proliferation

Our biologists tell me that there might be some cell division be going on during the invasion process. I included a corresponding proliferation term to the master equation.
P_z^{(t+1)}=\;\ldots\; +\alpha P_z^{(t)}.

In the figures below, dashed lines correspond the case with zero growth rate, solid lines to a growth rate of alpha=0.01.

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Symmetric case

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Drift to the right (chemo-attractant)

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Drift to the left (chemo-repellant)

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Generally, the effects on the z-profiles are more of a quantitative nature. Drastic differences result for the surface cell density versus time.