Sedimentation etc
Topic 3 Part 1
Biophysics
General Principles
f v
F (like
mg)
Sphere:
f
0
= 6
ph
R
Other particle: get r = f/
f
0
and f = r f
0
Example
–
prolate with a = 3 and b = 2
Sedimentation
1

r
is the buoyancy factor ~ 1

r
o
/
r
(if
r
o
>
r
then it floats).
s = sedimentation coefficient, [s] = Svedberg, 1 x 10

13
sec = 1 Svedberg.
Density of medium,
r
= m
o
/
V, V = volume.
is specific volume,
volume/mass of substance in solution (V/m)
v
s
r
v
f
N
ρ
v
1
M
2
A
v
v
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
= Ze
E
, fv = ZeE.
Mobility, U = v/E = Ze/f
Sphere: U = Ze/(6
ph
R)
Movement on a Gel
2
0
tD
2
Ft
x
x
e
tD
1
2
N
t
,
x
C
π
This is a gaussian centered around x = x
o
+
Ft
With rms of , velocity =
F,
= 1/(6
ph
r) with r = radius and
h
= viscosity
D =
k
B
T = diffusion constant
t
x
C
x
F
x
x
t
x
C
D
t
t
x
C
2
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
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