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Lecture 17: Application of Sedimentation concept and
o Collisions amongst molecules
o Model of random Walk
o Friction and it’s relation to molecular structure
o Fick’s laws
o Sedimentation
o Sedimentation in centrifuge
o Density gradient centrifugation (application to
DNA problems)
o Concept of viscosity
o Electrophoresis
o Gel electrophoresis
o DNA sequence analysis
o Pulsed field gradient electrophoresis
o Application to DNA and Proteins
Density Gradient Centrifugation
Using salt or sucrose solution where it’s difficult to
overcome effects due diffusion it is possible to create
density gradient across a tube in a centrifuge. Since
sedimentation coefficient depends on:
s  (1   v)
and (x)=top+(d/dx)x, it is possible to find a location
where =1. At this location forces due buoyancy and
centrifugation exactly cancel leading to zero mobility.
This is where the molecular migration stops and can be
used to achieve separation as shown below
Consider laminar flow, generated in figure below.
Liquid in contact with moving wall will move with
velocity of the wall while the liquid at the bottom wall
will be stationary. This creates a momentum gradient
along y.
The consequence of the momentum gradient is that
there is net momentum flux transferred in the opposite
direction. Each of these laminar layers creates an
effective friction amongst layer whose magnitude
depends on the pressure gradient along the x direction.
The viscosity is therefore defined as,
J mu  
du y
Note that the frictional coefficient f is directly
proportional to the viscosity coefficient.
Viscosity (Continued)
To measure viscosity coefficient, we can determine the
terminal velocity of sphere and relate it to the viscosity of
the fluid. Generally, same sphere can be used to compare
viscosities of different fluids. However, more commonly an
Oswald viscometer is used. Here a fixed volume of liquid is
allowed to run through a glass capillary and time required
is measured. The viscosity of the
fluid is calculated by comparing it to
the fluid of known viscosity.
Measured viscosity also depends on
the density of the fluid, since the
pressure difference is directly related
to it.
1 1t1 . This method is generally
 2 1t1 suitable for reasonably
low viscosity fluids.
However, for a highly viscous fluid, a
cone viscometer is commonly used.
In this method, a spindle is immersed in viscous fluid and
the force required to maintain certain rotational frequency
is measured. This allows measurement of the viscosity as a
function of rotational speed. Generally, polymer solutions
show a dramatic dependence on the rotational speed. Hence
they are termed as non-Newtonian
fluids. By measuring the viscosity
as a function of concentration one
can attempt to relate the structural
changes occurring under dynamic
Just as in
processes, we
exploited the
balancing of
forces involving
gravity and
friction. It is
possible to
extend this idea
where we replace
forces with
electrical forces.
In this way,
molecules that
have charge can
be imparted with
terminal velocity,
The quantify u/E is termed as an electrophoretic
mobility and the method is called as electrophoresis.
Since DNA molecules have negatively charged PO4
groups, single strands of DNA molecules were
sequenced using a clever technique.
ZeE  fu  u 
Gel Electrophoresis
Actually, most of the electrophoresis studies use gel
media as opposed to solutions. Gels can be made with
special polymers such as gelatin, agar, or polyacrylamide. The common features of gel that makes
them valuable for these studies are:
1. Convection or accidental mixing is avoided.
2. Owing to their micro-porous structure they slow
the speed of migration significantly depending on
the size of the protein or DNA.
3. Polymer-bio-molecule interactions can be
influenced by selecting the size of the network mesh
(concentration) and/or charges on the gel forming
4. Owing to the obstructive nature of the of polymer,
the actual path taken by bio-molecules is much
longer than the length of the gel allowing for better
separation. (Think about the resolution obtained
on a chromatographic column)
As shown before, one of the clever methods to sequence
DNA in seventies was to subject single stranded DNA to
specific enzymes that cleave a specific base in DNA. As
there are only 4 bases, this method allowed structural
sequence of DNA to be determined using radio-labeled
DNA. The trick here was to use 7m urea. It disables the
base pairing interactions and leaves the charged
phosphate groups unaffected. So the DNA migrates
electrophoretically. To improve resolution and extend
the range of the technique to higher molecular weights,
a pulsed field gradient electrophoresis was invented.
Applications to Proteins
Fundamentally, the same ideas can be used to separate
and identify new proteins. The frictional coefficients of
the proteins depend on their size and shape. Also charge
on the proteins is dependent on their basic amino acid
sequence. The net charge depends on the PK and
therefore on the pH of the buffer solution. Since
different proteins have different isoelectric points (i.e.
where the net charge on the protein is zero), a method
of isoelectric focusing has been developed. Different
buffers are used to establish a pH gradient in a gel. So,
when a protein enters a region of pH corresponding to
its isoelectric point, its mobility vanishes allowing for
separation based on the net charge on the protein.
Conceptually, this is similar to the density gradient
method employed in sedimentation.
Pulsed field Gradient Electrophoresis
Protein Molecular weight
Unlike DNA, which has fixed charge per base pair
due to phosphate group, proteins can have variable
charges depending on the amino acid configuration. To
create a uniform charge density, proteins are denatured
and treated with Sodium dodecyl sulphate and
mercapto-ethanol. The latter cleaves the S-S thiol
bonds. The former, when used in concentrations of 1
mM or above, binds strongly to the denatured protein
(1SDS per two amino acid groups) leading to a uniform
charge density per unit length. This SDS-PAGE method
allows one determine molecular weight of the proteins
based on their electrophoretic mobility as shown above.