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