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Lecture 12 – Electrophoresis
Ch 24
pages 650-652
Summary of Lecture 11
 The rate at which equilibrium is reached depends on
hydrodynamic properties such as the diffusion coefficient
 The equilibrium concentration profile only depends on
thermodynamic properties of the system and we derived that
equation using either Boltzmann distribution function or
imposing that the chemical potential does not depend on r
Summary of Lecture 11
 Equilibrium sedimentation can be used to separate, purify and
analyze all kind of cellular components and to measure the
absolute molecular weight of biological molecules
 The concentration profile at equilibrium is determined by the
balancing of diffusion and concentration and is described by the
following expression:


C ( r )  2 M 2 1  V2  2

ln

r  r02 
C0
2 RT
Summary of Lecture 11


C ( r )  2 M 2 1  V2  2

ln

r  r02 
C0
2 RT
ln(C) versus r^2
3
2.5
ln(C)
2
1.5
1
0.5
0
46
47
48
49
r*r
(from the homework)
50
51
Summary of Lecture 11


C ( r )  2 M 2 1  V2  2

ln

r  r02 
C0
2 RT
Concentration (arb
units)
C versus r at equilibrium
40
35
30
25
20
15
10
5
0
small protein
(x5)
large protein
sum
1 2 3 4 5 6 7 8
distance
(from the homework)
Summary of Lecture 11
 Sedimentation in a density gradient is a common technique used
to separate biomolecules
A salt solution is spun at very high speed to generate a density
gradient (the density of the solution increases with the salt
concentration); the concentration of CsCl will reach equilibrium
as described by the equilibrium centrifugation equation:


CCsCl
M CsCl  2 1  VCsCl  2

ln

r  r02 
CCsCl ,0
2 RT
 The biomolecule (e.g. DNA) will sediment at a point r’ where
the density of the solution matches the partial specific volume of
the DNA. The concentration profile around r’ is given by:
  2 M DNA V DNA d
2
C DNA ( r )  C DNA ( r ' ) exp  
r ' r  r '  
2 RT
dr


Summary of Lecture 11
 The biomolecule (e.g. DNA) will sediment at a point r’ where
the density of the solution matches the partial specific volume of
the DNA. The concentration profile around r’ is given by:
  2 M DNA V DNA d
2
C DNA ( r )  C DNA ( r ' ) exp  
r ' r  r '  
2 RT
dr


 This is a bell-shaped curve with standard deviation:
RT
  2
 r' M DNAV DNA d / dr 
2
Electrophoresis
Electrophoresis is a primary technique to separate and
analyze biological molecules
It takes advantage of the fact that proteins and nucleic acids
are generally charged and therefore move in an electric field
towards the positive or negative electrode depending on their
charge
The velocity of motion can be derived in complete analogy to
what was done for sedimenation by ultracentrifugation, i.e.
by imposing that all the forces acting on the molecule, under
steady state conditions, balance each other out
Electrophoresis
The velocity of motion can be derived in complete analogy to
what was done for sedimentation by ultracentrifugation, i.e.
by imposing that all the forces acting on the molecule, under
steady state conditions, balance each other out
Fe  F f  0
ZeE  fu  0
u
ZeE
f
Where E is the electric field applied externally, e the electron
charge and f the frictional coefficient. The quantity:

is called electrophoretic mobility.
u Ze

E
f
Electrophoresis
This expression was used to measure the electron charge at
the turn of the century, but biological molecules have complex
electrostatic properties, because they are surrounded by
counterions (e.g. mono and divalent ions for nucleic acids)
that shields the electrostatic field in a complex way. As it
moves, the molecule also drags its ionic atmosphere along
with it, thereby affecting the frictional coefficient that
depends in complex ways on the shape and charge of the
molecule and on the nature of the electrophoretic medium.
For these reasons, it is very difficult to measure absolute
properties of biological molecules by electrophoresis.
However, because the technique is so sensitive, it is used very
effectively to separate molecules that differ very little in
charge and/or mass
Gel electrophoresis of nucleic acids
Gels are three-dimensional polymer networks dissolved in a
solvent. In acrylamide gel electrophoresis, the main technique
for nucleic acids separation, the network is generated by
cross-linking a copolymer of acrylamide and bisacrylamide to
form a net-like structure. The degree of cross-linking can be
controlled by the ratio of the bis-compound (the cross-linker)
and acrylamide (that forms long linear polymers). Although
most of the matrix is occupied by aqueous buffered medium,
the presence of the network prevents diffusion and
convectional forces and allows the separation of DNA
molecules that differ even by a single base
Gel electrophoresis of nucleic acids
The path traveled by the molecule through the porous gel is
very long, much greater than the length of the gel
The gel imposes additional frictional forces on the molecule
The macromolecules interact with charged groups on the gel
network
The pore size may be too small for certain molecules to
penetrate the gel matrix
All of these factors allow separation to be conducted with
exquisite sensitivity to very small differences in mass, charge
and shape
DNA sequencing
The most impressive application of gel electrophoresis
concerns the ability to determine the sequence of singlestranded nucleic acids by fractionating DNA based on its size
under denaturing conditions
The electrophoretic mobility of nucleic acids is determined by
the number of phosphate groups
Each phosphate groups carries one negative charge at and
around neutral pH, though this is largely shielded by positive
ions so that the effective charge is more like 0.24e per
phosphate)
DNA sequencing
High concentrations of a denaturant (like urea) and
temperature (the power at which the gel is run) are used to
break all secondary structure (disrupts W-C base pairs)
Because gel mobility is so sensitive to differences in charge of
even one e (or 0.24e), polynucleotides chains that differ by
even a single base can be separated by running gels at
different concentrations of acrylamide depending on the size
of the molecule one wishes to separate
DNA sequencing
How does one then apply this technique to the problem of
DNA sequencing?
One could either use a chemical reaction selective for each
type of base (e.g. G) to modify the polynucleotide chain so
that it is broken after every guanine (Gilbert)
Alternatively, one could use an enzymatic procedure based
on a DNA polymerase and 4 nucleotide analogues (ddN’s)
that cause termination of chain elongation by a polymerase
(Sanger)
DNA sequencing
The enzyme adds dNTPs as the chain elongates, but if the
nucleotide has been modified to include H instead of OH at
the 3’-position, where polymerization takes place, then the
chain will terminate
This is done only a fraction of the time: the solution will
contain 90% of dNTPs (which can be elongated) and 10% of
ddNTPs (which cannot) so that not all chains are stopped at
the first G (for example) in the sequence
DNA sequencing
If you run 4 separate reactions with analogues of A, C, T and
G, each will contain a mixture of molecule that will terminate
after each base, and by running the four lanes side by side,
one can sequence DNA by labeling each chain with 32P and
monitoring the position of the electrophoretic band on the gel
by autoradiography
If one wants to be clever, it is possible to avoid using
radioactivity by using ddNTP analogues that carry a
fluorescent group, a different chemical group fluorescing at a
different color for each of the 4 bases, so that a single reaction
and single lane (instead of 4) can be used to completely
sequence a DNA molecule
Electrophoresis of DNA
Electrophoresis under native conditions in either agarose (a
mixture of a polysaccharide derived from algae) or
acrylamide can be used not only to separate nucleic acids
based on their size but also based on their conformation
Double stranded DNA - can be separated according to their
size under native conditions; in water, the elecrophoretic
mobility of DNA is independent of molecular weight because
the charge density is constant); however, as the molecules
wander through the pores of the gel, their mobility strongly
depends on molecular weight for sizes of 10 (ten!)-100,000
base pairs
Electrophoresis of DNA
Topoisomers - Nucleic acids with the same molecular weight
but different shape will also migrate differently under
electrophoretic conditions; for example, DNA can be linear or
circular: the circular DNA is more compact than its linear
topoisomer and therefore travels faster. Different DNA’s can
have different topologies (think of a figure 8) and they can be
separated on a gel according to their topological properties
(shape). This is used to study enzymes such as topoisomerase
I and II which play critical roles in DNA replication and are
targets of anticancer drugs
Electrophoresis of DNA
DNA bending - DNAs of a few hundred base pairs behave
essentially as rigid rods; however, certain sequences (AT-rich
sequences), certain chemical modifications induced by drugs
that covalently modify DNA (e.g. platinated compounds used
to cure various forms of cancer), induce bending in the DNA
itself. These can be separated on a gel under native conditions
RNA structure - RNA molecules are synthesized as single
strands, but then, like proteins, fold into complex secondary
and tertiary structures that are essential for its function.
These structures can be studied and separated by gel
electrophoresis (acrylamide in this case)
Electrophoresis of DNA
Nucleic acid-protein interactions – gels can be used to study
protein-DNA or protein-RNA interactions. Under native
conditions, the mobility of a DNA differs depending on
whether a protein is bound to it or not; if the exchange is slow
compared to the time needed for separation, the two species
will migrate with different mobility and the equilibrium
constant can be measured by estimating the amount of DNA
in each band. This technique can be used to study all sort of
kinetic and thermodynamic properties of the interaction of
proteins with nucleic acids.
Gel electrophoresis of proteins
Unlike nucleic acids, proteins are not uniformly charged and
their net charge depends not just on the sequence of the
proteins, but also on the pH of the solution
Furthermore, like RNA molecules or topoisomers, proteins
will adopt different structures and therefore shapes, which
will determine the mobility of the protein under
electrophoretic conditions
One could use these properties to study the shape of proteins
but, most often, electrophoresis of proteins is used to
determine the molecular weight of protein samples and is
therefore conducted under conditions where proteins are not
structured (high concentrations of a surfactant, SDS, that
causes proteins to denature)
Gel electrophoresis of proteins
An additional advantage of having SDS is that at
concentrations higher than mM, most proteins will bind a
nearly constant amount of SDS per amino acid
(approximately 0.5 molecules of SDS per amino acid, on
average)
Under these conditions, the charge of the SDS/protein
complex is determine primarily by the surfactant itself,
making the charge per unit weight independent of the protein
sequence and therefore the same for every protein. Under
these conditions, the mobility of SDS-treated proteins is
determined only by the protein molecular weight;
experimentally, there is a linear relationship between the Log
of molecular weight and distance x traveled in the gel:
Gel electrophoresis of proteins
The mobility of SDS-treated proteins is determined only by
the protein molecular weight; experimentally, there is a linear
relationship between the Log of molecular weight and
distance x traveled in the gel:
log M  a  bx
Where a and b are constant determined by the electric field
strength and gel matrix
Gel electrophoresis of proteins
log M  a  bx
This property can be used to analyze protein molecular
masses, although for some proteins that are highly charged
(e.g. histones) or that binds unusual amounts of SDS
(glycoproteins) or heavily modified (phosphorylated or
methylated or acetylated proteins), this relationship is not
true. Deviations from this behavior can therefore be used to
monitor the modification state of a protein (e.g. its
phosphorylation!).
Gel electrophoresis of proteins
Under native conditions, the mobility of a protein depends on
its charge, which in turn depends in most cases on pH
(ionizable groups on the surface of a protein have different
charges at different pH)
At low pH, all proteins are positively charged bacuse the
carboxy groups of Asp and Glu are neutral (COOH) while the
amino groups of Lys and Arg are charged (NH3+), and so on
for His and other ionizable groups
At high pH, all proteins are negatively charged instead (Lys
and Arg are neutral, Asp and Glu are negatively charged).
Thus, for each protein, there will be a pH value at which the
protein is neutral (isoelectric point)
Gel electrophoresis of proteins
By creating a pH gradient in a gel, proteins can be separated not
only based on their size but also based on their isoelectric
properties
At the isoelectric point, the charge is zero and therefore the
electrophoretic mobility is also zero
If one establishes a pH gradient so that the pH is high towards the
negative electrode and low at the positive electrode, then proteins
will move until they find their isoelectric point
If we then perform SDS-PAGE at a right angle, we will separate
each spot on the gel composed of proteins of similar charge (but
different mass) according to their mass. This is exploited in twodimensional gel electrophoresis to separate even hundreds of
proteins on a single gel.