You have designed a chemotaxis model to measure cell flux in response to a chemokine concentration gradient. Your design consists of a Petri dish filled with agar gel that has two rectangular holes cut in it (see diagram). In one hole, you add tumor necrosis factor (TNF-D) at a concentration of 10 µg/ml. In the other hole, you add 106 leukocytes/ml. Assume that the concentrations do not change significantly even
when the system reaches steady state.
a) Assume that the partition coefficient at the boundary of agar and saline is 1.0 for TNF-D. Write an expression for the concentration profile of TNF-D in agar along the x-axis at steady state.]
b) The leukocytes migrate up the chemokine (TNF-D concentration gradient from one well to the other with a random motility coefficient (essentially, an effective diffusion coefficient for cell migration) of 1.4×10-7 cm2 /s. Assuming steady state, estimate the cell flux relative to fixed coordinates.
c) Estimate a mass transfer coefficient for cell migration through the agar gel.
d) Explain briefly how your analysis would change if you do not assume that you have already reached steady state. Would your estimated value for mass transfer coefficient from part (c) remain constant? Explain why or why not.