## Monday, May 25, 2009

### Cell invasion (5) : Cooperation via Chemotaxis

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It is known that cells can communicate with each other via signalling molecules that are diffusing in the extracellular matrix (e.g. cytokines). Would such chemotaxis be compatible with the apparent backward drift component observed in the motion of invading cells ?

To include chemotaxis into the cell invasion model, we assume that the effective drift velocity is proportional to the local gradient of the "cytokine" concentration. This leads to the following set of coupled equations:

Drift-diffusion of cells:
\frac{\partial}{\partial t}c(z,t) = - \frac{\partial}{\partial z}\left[v(z,t)\;c(z,t)\right] + D_c \frac{\partial^2}{\partial z^2}c(z,t),
v(z,t) = s\; \frac{\partial}{\partial z} g(z,t)
\frac{\partial}{\partial t}g(z,t) = p\!\cdot\!c(z,t) + D_g \frac{\partial^2}{\partial z^2}g(z,t) - d\!\cdot\!g(z,t)