Sedimentation etc Topic 3 Part 1 Biophysics

General Principles f v F (like mg) Sphere: f 0 = 6  R Other particle: get r = f/ f 0 and f = r f 0 Example – prolate with a = 3 and b = 2

Sedimentation 1-  is the buoyancy factor ~ 1-  o /  (if  o >  then it floats). s = sedimentation coefficient, [s] = Svedberg, 1 x sec = 1 Svedberg. Density of medium,  = m o /  V, V = volume. is specific volume, volume/mass of substance in solution (V/m)

Determining s Analytical Centrifuge This instrument scans absorption along the centrifuge cell as a function of time – giving concentration.

Determining s v b = dr b /dt =  2 sr b, where the subscript b signifies the boundary (so r b is the boundary between solvent and solution). So plot ln(r b ) vs t and get slope which is equal to  2 s.

Determining s Diffusion blurs boundary D = RT/N A f,

More on s Depends on temperature and viscosity so define for standard conditions s depends on M and f (shape) so if know M can get f (shape information/stokes radius)

Density Gradient used for separation

Real data on hemoglobin free and bound to haptoglobin

Electrophoresis Now have F = ZeE, fv = ZeE. Mobility, U = v/E = Ze/f Sphere: U = Ze/(6  R)

Movement on a Gel This is a gaussian centered around x = x o +  Ft With rms of, velocity =  F,  = 1/(6  r) with r = radius and  = viscosity D =  k B T = diffusion constant

Running DNA on a Gel Closed small plasmids give discrete bands Long DNA tunnels and separation goes as 1/mass Can get screening from lots of cations 2-D electrophoresis good for large pieces of DNA Genome project used Saenger method

Running Plectonemic helices L = T + W For DNA at several Kbp, helices run by writhe and hence (for constant twist), L Topoisomers for DNA of defined length give gaussian band due to different energies Wang Paper supercoil.jpg