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Is the first time that I am asking something here, so I apologize if it is not the place, or I am not clear enough.

I am working on this problem where I have a protein place between 2 surfaces (top and bottom). The protein is bound originally to the surface in the top (a membrane) and can diffuse in this surface with a diffusion coefficient Dt. However, when the protein gets in contact with the second surface in the bottom, the protein can bind to this surface and diffuses with a diffusion coefficient Db. Do you think that it is possible to estimate an effective diffusion coefficient for the protein? Or the lower motility will be the limiting factor? Db

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Ruddi Rodriguez
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1 Answers1

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If the protein attaches to the bottom surface at a rate $k$ and detaches at a rate $\nu$ then the probability of finding the protein attached to the bottom surface at any given moment is:

$$ P = \frac{\nu^{-1}}{k^{-1}+\nu^{-1}} $$

The mean diffusion coefficient is then just a weighted average:

$$ \langle D\rangle = PD_b + (1-P)D_t $$

You can see this to be true by computing the mean-square displacement over a time interval $k^{-1}+\nu^{-1}$, which I'll leave as an easy exercise.

lemon
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