Sedimentation, electrophoresis

Sedimentation, electrophoresis
Biophysics lecture
Talián Csaba Gábor
21. 03.2012.

sedimentation = settling
Sedeo 2, sedi, sessum – sit
Aim:
1 - separation
2 - measure the size or mass of the
particles

F upthrust = ρ mVg
ρρ km
m, ρ
v
F g= mg
Sedimentation in a gravity field
F frict= fv
F = F +
g
upthrust
F
frict
ρVg
− ρm
Vg =
spherical
particle
to calculate
v
to measure
V = 4
sed
fv
F − F =
g
upthrust
F
frict
v = constant
3 r3π Ffrict = 6πη0rv
=
(η 0: viscosity of the medium)
2r
ρ m: density of the medium; m: mass, ρ: density, v: velocity of the moving spherical particle
2
( − ρ )
ρ m g
9η
0

Sedimentation in a centrifugal field:
1. Sedimentation velocity method
Aim: measurement of molecular mass (r ≈ nm)
methods based on gravity are not effective
How to calculate the forces?
F frict =
fv
F centrifug =
2
mrω
2
ρ ρ rω
ρ
m
mVa
=
Fupthrust =
m
Spinning system: a = rω2

What is centrifugal force?
No acceleration Acceleration
F cf = -mrω 2

F frict =
fv
Fcentrifug =
2
mrω
Fupthrust m =
2 m 2
2⎛
ρm
⎞
fv = mrω
− ρm
rω
= mrω
⎜1−
⎟
ρ
⎝ ρ ⎠
but
a = rω 2
2
ρ rω
ρ
m
Upon sedimentation the velocity of the particle
increases while going further from axis! (v ≠ constant)

Theodore Svedberg
Swedish chemist
(1884-1971)
Nobel-prize in 1926
S
=
v
2
rω
to measure
⎛ ρk
⎞
m⎜1−
⎟
=
⎝ ρ ⎠
f
to calculate
S = sedimentation constant
Unit: 1 Sv = 10 -13 s
Sedimentation
velocity for unit
acceleration
shape factor!
Relationship between shape factor (f) and diffusion constant (D):
k ⋅T
D
R ⋅T
N D
To determine the mass sedimentation
methods must be combined with
diffusion measurements.
f
=
=
A ⋅
kkkk:::: Boltzmann constant
R: R: R: R: universal gas constant
NNNN : Avogadro-number.
=
∙ ∙
∙ ∙ ( −
)

Normal centrifuge
Centrifuge
Supercentrifuge: 20-50.000 rpm (revolution per minute)
Ultracentrifuge: over 50.000 rpm
Analytical centrifuge: determination of size and mass of molecules
Preparative centrifuge: separation of molecules based on their mass and size
angle rotor
swing-out rotor

Velocity boundary sedimentation method
A: boundary
B: plateau
: concentration profile without diffusion

2. Sedimentation equilibrium method
low speed centrifugation
diffusion
Jean Baptiste Perrin
French physicist
(1870-1942)
Nobel-prize in 1926
sedimentation

Energy
energia
E 2
E 1
to calculate
c 2
c 1
c
c
c
1
2
=
e
E −E
1 −
kT
m ⎛ ρ ⎞
ω ⎜ − ⎟
2 ⎝ ρ ⎠
2
( ) 2 2
r r
2 m E1 − E2
= 1
2 −
2⎛
ρm
⎞
mω
⎜1−
⎟
⎝ ρ ⎠
( ) 2 2
r −
2 ln =
2 r1
c1
2kT
to measure
No influence of the molecular shape!
1

Advantages of the analytical ultracentrifugation
No standards are required
AUC is sensitive, precise, accurate and robust (yes – all at a time!)
No interactions with a stationary phase or matrix
Wide range of molar masses can be investigated in the same
experiment – works well for peptides to viruses.
No protein modifications required
No change in mobile phase – your protein is examined in exactly the
same solvent in which you want to study it
Theory of sedimentation is well understood

F centrifug =
3. Density gradient method
2
mrω
Fupthrust m =
2
ρ rω
ρ
m
If ρ = ρ m then F c = mrω 2 = F up and v = 0!
High molecular mass, small size:
CsCl, CsBr, glycerol, sucrose (saccharose), ficoll
Blood lipoproteins

Differential centrifugation/
cellular fractionation
Albert Claude
Belgian biologist
(1899-1983)
Nobel-prize in 1974
mitochondria microsomes lysosomes

Electrophoresis
Ionic double layer
Arne Tiselius
Swedish biochemist
(1902-1971)
Nobel-prize in 1948

Coulomb-force: Friction force:
F c = QE = ZeE
E= electric field strength
e = elementary charge
Z= charge number
Till when is the particle accelerating?
F F = : until ZeE = fv
c
u el = v
E
up
electrophoretic mobility
= Ze
f
Ze
6πηr
F f = fv
v = velocity
f = shape factor
For spherical molecules:
ZeE = 6πηrv
(Stokes-law)
= Radius of molecule is
to be calculated

Agarose gel electrophoresis

SYBR green

SDS polyacrylamide gel electrophoresis (SDS-PAGE)
sodium-dodecyl-sulphate
TEMED (tetramethylethylenediamine)
ammonium-persulphate

Coomassie Brillant Blue
+ protein

Native PAGE

Isoelectric focusing (IEF)

2D electrophoresis

pH pH pH 33
3 3
pH pH 10
10
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