Transcript Presentation453.10

Lecture 10 – Ultracentrifugation/Sedimentation
Ch 24
pages 636-643
Ultracentrifugation and Sedimentation
Sedimentation is a technique used to separate, purify and
analyze all kind of cellular components
It can be understood using a simple mechanical analogy.
Consider a mass m falling through a fluid. Opposing the
gravitational force:
F  mg
g
is a buoyant force:
and a frictional force:
Fb  m0 g  mV2 g
F  fv
m is the mass of the particle, m0 the mass of the displaced
fluid, V2 the specific volume of the particle,  the density of
the fluid, f is the frictional coefficient of the falling body, v
the steady-state velocity reached during motion
Ultracentrifugation and Sedimentation
At steady state the terminal velocity is obtained from the force
balance
Fg  Fb  F f  0
From which it follows
v


m 1  V2  g
f
This terms that follows is called buoyancy

m 1  V2 

Ultracentrifugation and Sedimentation
The sedimentation experiment is juxtaposed with the free fall
problem in the picture:
Ultracentrifugation and Sedimentation
Fc  w 2 rm
is the centrifugal force, where w is the angular velocity, r is the
distance from the solute particle to the axis, and w2r is the
centrifugal acceleration
Fb  w 2 rm0  w 2 rmV2 
is the buoyant force
F  fv
is the frictional force
Ultracentrifugation and Sedimentation
By direct analogy, the steady state velocity of a solute particle
being spun in a centrifuge tube can be obtained by balancing all
forces once again:
Fc  Fb  F  0


dr m 1  V2  2
v

w r  sw 2 r
dt
f
Here we have introduced the sedimentation coefficient:

m 1  V2 
s
f

Its dimensions are sec, but a more
convenient unit of measure for s is the
Svedberg: S=10-13 s
Standard Sedimentation Coefficient
If we remember the definition of frictional coefficient from
Stoke’s law, then:



m 1  V2  m 1  V2 
s

f
6hR

 and h are dependent on solvent and temperature, while R
brings about again the molecular properties of the molecule
undergoing sedimentation
Standard Sedimentation Coefficient
Values for s are usually reported in Svedberg and referred to a
pure water solvent at 293K=20oC. It is useful to use these
conditions to standardize the measured sedimentation
coefficients s. The standard sedimentation coefficient is:
s 20, w 

m 1  V2  20, w

6h20, w R
A sedimentation coefficient measured under other conditions, i.e.
in a buffered aqueous solution b and/or at another temperature
T can be related to standard conditions by the equation:
s 20, w  sT ,b
1  V   h
1  V  h
2
20, w
2
20, w
Standard Sedimentation Coefficient
s 20, w  sT ,b
1  V   h
1  V  h
2
20, w
2
20, w
This relationship only holds true if changing conditions
(temperature or buffer conditions) have not significantly affected
the shape or hydration property of the molecule. Conversely, if it
is found that the sedimentation coefficient changes, then it can be
concluded that one of those properties has changed
By measuring the sedimentation
coefficient, diffusion coefficient and partial
specific volume, we can calculate the
molecular mass of any particle under any
experimental conditions and follow how it
changes (e.g. dimerization).
Standard Sedimentation Coefficient
Example: The following data have been gathered for ribosomes
obtained from a paramecium
s20,w  82.6S; D20,w  152
.  10 7 cm2 / s;V2  0.61cm3 / g
We can calculate the molar weight of the ribosome by substituting
the diffusion coefficient in place of the frictional coefficient:
m  s 20, w
k BT
1  V  D
2
 82.6 x10
13
20, w
20, w
1.38 x10 23 J / Kx293K
s
 3.4 x10 6 g / mole
7
2
2
1  0.61x11.52 x10 cm / s(1m / 100cm)
Boundary Sedimentation
In a first method to measure sedimentation coefficients, a
homogeneous solution is spun in a ultracentrifuge. As the
macromolecule moves down the centrifugal field, a solutionsolvent boundary is generated. We can estimate s by following
the movement of the boundary with time. By generating a
boundary we also generate a concentration gradient and
therefore we would expect the molecule to begin diffusing;
however, if the macromolecule is large or the field very large
(high spinning speed), then the boundary will be very sharp
because transport by sedimentation will be much larger than
transport by diffusion. If diffusion is significant, then the
boundary broadens as it shifts towards the bottom of the cell
with time.
Boundary Sedimentation
Boundary Sedimentation
If we assume transport by diffusion can be neglected and rewrite:
dr
 sw 2 r
dt
Then we can find a solution:
 r (t ) 
  sw 2 t  t 0 
ln 
 r0 (t 0 ) 
Boundary Sedimentation
 r (t ) 
  sw 2 t  t 0 
ln 
 r0 (t 0 ) 
At zero time, the concentration is uniform throughout the cell;
as time increases, a sharp boundary is generated, with solvent to
the left and solute to the right; the concentration of solute will be
constant on either side of the boundary
This equation means that as centrifugation proceeds, the solute
concentration boundary, with position r relative to the spinning
axis proceeds from an initial position r(t0) to r(t). Rearranging
the equation for r(t), we obtain:
ln r (t )  ln r0 (t 0 )  sw 2 (t  t 0 )
Boundary Sedimentation
ln r (t )  ln r0 (t 0 )  sw 2 (t  t 0 )
A plot of ln r(t) versus elapsed time t-t0 is a straight line with
slope sw2. The concentration of solute at the right of the
boundary is not the same as the starting concentration (uniform)
C0. It can also be shown that:
C b (t )  r0 
 

C0
 r (t ) 
2
Boundary Sedimentation
ln r (t )  ln r0 (t 0 )  sw 2 (t  t 0 )
Zone Sedimentation
A second way to measure sedimentation is called zone
sedimentation. A thin layer of a macromolecular solution is
placed at the top of the solvent at the beginning of the
centrifugation (left, below). As the centrifugation progresses the
macromolecule moves through the solvent as a band or zone
(right, below). To prevent mixing of the dense macromolecular
band with the solvent, a density gradient is created so that the
net density increases in the direction of the centrifugal field.
Typically, a linear sucrose concentration gradient is used.
Alternatively, one could use a concentrated salt solution (e.g.
CsCl), in which case the density gradient will be generated by
the sedimentation of the salt itself.
Zone Sedimentation
The macromolecule band can become broadened due to
diffusion, thus reducing resolution of the macromolecular bands.