Question
Consider two cells on a flat surface. One cell secretes a chemokine to which the other responds. Show that the steady-state concentration profile of chemokine
Consider two cells on a flat surface. One cell secretes a chemokine to which the other responds. Show that the steady-state concentration profile of chemokine emanating from the first cell is
C(r) = R2F/D*1/r
where R is the radius of the cell, F is the secretion rate (molecules/area time), and D is the diffusion coefficient of the chemokine. The distance from the cell surface is r. Use the cell flux equation to calculate the time it would take for the responding cell to migrate to the signaling cell if there is no random motion ( = 0) given the following values:
(C) = 20 cm2/sec-M, D = 10-6 cm2/sec, R = 5 m, Production rate = 5,000 molecules/cell/sec
Hint: Show that the constitutive equation for J reduces to v = dC/dr, where v is the velocity of the cell.
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