# Homework Help: Translational friction coefficient of spheres: Biophysics

1. Dec 13, 2008

### physicsstudent14

1. The problem statement, all variables and given/known data

Prove that the translation friction coefficient for a sphere (protein) with a molecular weight of 25 kiloDaltons is approximately 60% the translation friction coefficient for a 100 kiloDalton protein sphere.

2. Relevant equations

Stoke's Law: f = 6πηr
where f = translation friction coefficient,η = viscosity coefficient, r = radius of the molecule

S = (M(1-Vρ))/(Nf)
S = Svedberg, M = molecular weight, V = specific volume, ρ = density, N = Avogadro's number, f = translation friction coefficient

V = (4/3)πr3

3. The attempt at a solution

I know that N = 6.02 x 1023, so that should not change between the 2 proteins. S will definitely change, but that is determined experimentally by ultracentrifugation, and that was not provided.

I can rearrange the Svedberg equation into f = M(1-Vρ))/(NS) = 6πηr. Theoretically, the 25 kilodalton protein should have a lower S value and a lower radius, but how do I get quantities for those values? When I plug M into the equation and compare them, I get a difference of 25%, not 60%.

Am I missing another equation? I'm having trouble starting this problem because there are so many quantities (ρ,η,S,V,r) that I do not know.

I would really appreciate it if someone could point me in the right direction. Thanks!