Sedimentation etc

Topic 3 Part 1

Biophysics

General Principlesf v

F (like mg)

Sphere: f0 = 6R

Other particle: get r = f/ f0 and f = r f0

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 10-13 sec = 1 Svedberg.Density of medium, = mo/V, V = volume. is specific volume, volume/mass of substance in solution (V/m)

v

s

r

v

fN

ρv1M2

A

v

v

Determining sAnalytical Centrifuge

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

Determining s

vb = drb/dt = 2srb, where the subscript b signifies the boundary (so rb is the boundary between solvent and solution).

So plot ln(rb) vs t and get slope which is equal to 2s.

Determining sDiffusion blurs boundary

D = RT/NAf,

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/fSphere: U = Ze/(6R)

Movement on a Gel

2

0

tD2

Ftxx

etD

1

2

Nt,xC

π

This is a gaussian centered around x = xo + Ft

With rms of , velocity = F,

= 1/(6r) with r = radius and = viscosity

D = kBT = diffusion constant

txCxFxx

txCD

t

txC2

2,

,,

tD

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

http://www.cbs.dtu.dk/staff/dave/roanoke/supercoil.jpg