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.

Respuesta :

Answer:

0.5s

Explanation:

Relevant Equation:

Einstein's Approximation

[tex]t=\frac{d^2}{2D}[/tex]

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)

[tex]t=\frac{d^2}{2D}\frac{(10*10^{-6})^2}{2*(10^-6)^{-4}}[/tex]

[tex]t= 0.5\ s[/tex]

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