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I have a spherical mass of cells say $150\mu m$ in diameter.The ball of cells are surrounded by a "bag" $100nm$ thick.

These cells constantly express a receptor called avidin.The concentration of receptor is $10^{-7} M$.

Avidin binds the ligand called biotin. The kd is $10^{-15M}$, and the koff (dissociation half life) in the order of days ( say 1day). The diffusion constant of biotin is $350 \mu m^2 /s$ in the mass of cells as well as through the bag.

Say I completely saturate all the cells' avidin with biotin. Then I place the bag of cells in pure water.

How long would it take for 95% of all the biotin to come off the cells' and into the water?

There are two phenomenon I think here, diffusion of biotin and dissociation of biotin from the receptor.

I understand the principles of kd and ficks law. However I can't be sure if I should assume the rate limiting step is diffusion or dissociation!

I provide all the constants necessary to work out this problem, I think. If you need any more info I can try to fill you in.

Thanks!

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  • $\begingroup$ Let's say if have understood: "kd" and "koff" are rates of dissociation? I don't understand very well what they mean and the units they are measured in. If you provide this information I may come up with an estimation. In addition to that, I don't understand the relation between cells and the "bag". A little scheme may help. $\endgroup$
    – Victor Buendía
    Commented Jul 22, 2017 at 14:32

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