Question

A protein has a diffusion coefficient in water of D = 10-6 cm2/s. How long does it take for the protein to diffuse 10 μm (typical radius of a cell)? Consider 3D diffusion.

Answer 1

Answer:

0.5s

Explanation:

Relevant Equation:

Einstein's Approximation

$t=\frac{d^2}{2D}$

Where

• t is time used for diffusion
• d is the mean value of distance diffused
• D is diffusion coefficient

Typically, Einstein's approximation equation is accurate enough to be used in 3D biological diffusion while still being simple to use, thus this will be our go-to equation.

When plugging in the given parameters (Don't forget to convert units)

$t=\frac{d^2}{2D}\frac{(10*10^{-6})^2}{2*(10^-6)^{-4}}$

$t= 0.5\ s$

Which is considered slow for usual chemical reaction in cells, which is why transport proteins are usually used to move protein across the cell