Biophysics II
By
A/Prof. Xiang Yang Liu
Biophysics Lab
Department of Physics,
NUS
Announcement
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Term Test – Mar 2, 2007, Fri
􀁼 Venue: S13-0507.
􀁼 Time: 8:30-9:30am (1 hr)
Closed book.
One A4 “cheat sheet” is allowed.
Outline
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ELECTROPHORESIS
Discussion: you are supposed to prepare
your questions to be discussed in the lecture.
Example
Example
Example
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If the temperature of the dissolution of sugar
crystals in water is not very far from the
melting temperature (Tm), the solubility (xi
mole fraction) of sugar can be described in
terms of the dissolution enthalpy (Hm). Treat
the dissolution equilibrium as a special
chemical equilibrium. Derive the relationship
between xi and Hm.
ELECTROPHORESIS
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Most of the remarkable advances in
molecular biology over the past few decades
would have been impossible without
electrophoretic methods
ELECTROPHORESIS
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The great majority of the polymers of
biological interest are electrically charged.
Polyelectrolytes are somewhat arbitrarily
classified as “strong” or “weak,” depending on
the ionization constants of the acidic or basic
groups.
They may be strong polyacids, such as the
nucleic acids; weak polybases, such as polyl-lysine; or polyampholytes, such as the
proteins.
ELECTROPHORESIS
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electric charge differences can be used to
separate and analyze mixtures of
biopolymers: electrophoretic methods are
used in every area of biochemistry and
molecular charged: most important physical
technique available to scientists working in
these fields.
Electrophoresis: General Principles
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Electrophoresis: The transport of particles by
an electrical field.
The charged molecule is not alone, but in the
presence of many other charged particles,
and these will both influence the local field
and interact with the macromolecule, making
analysis difficult.
Diffusion through a solvent
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The Diffusion coefficient and the fraction coefficient
Diffusion coefficient introduced Albert Einstein:
D = kT/f
f: friction coefficient-measures the resistance encountered by
the molecule in moving through the solvent.
Stokes’ Law for a sphere of radius a
fo = 6a
: the viscosity of the solvent
Do = kT/6a
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Electrophoresis: General Principles
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An idealized, simplified situation: an isolated charged
particle in a nonconducting medium.
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The force experienced by a particle in an electrical
field is given by Coulomb’s law,
F = ZeE (E-electric field: potential per unit length)
The viscous resistance of the medium to the motion:
-fv (f: the frictional factor)
The viscous resistance of the medium just balances
the driving force.
fv = F = ZeE
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Electrophoresis: General Principles
Electrophoretic mobility U (the ratio of velocity to the
strength of the driving field)
U = v/E = Ze/f
 If the particle happens to be spherical, Stokes’s law
applies
U = Ze/6a
 The zonal techniques: In these methods, a thin layer or
zone of the macromolecule solution is electrophoresed
through some kind of matrix. 
 The matrix provides stability against convection. In
addition, in many cases the matrix acts as a molecular
sieve to aid in the separation of molecules on the basis
of size.
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Electrophoresis: General Principles
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The kind of supporting matrix used depends on the type of
molecules to be separated and on the desired basis for
separation: charge, molecular weight, or both.
Almost all electrophoresis of biological macromolecules is at
present carried out on either polyacrylamide or agarose gels
Electrophoresis
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Each macromolecular solution is applied in a
thin layer in one well.
If several components of different mobility are
present, they will separate during
electrophoresis, just as the zones of
molecules of different sedimentation rate
separate in zonal centrifugation.
Usually, a dye of high mobility is added; its
migration serves to mark the progress of the
experiment.
Electrophoresis
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The dye also serves as a convenient
measure of mobility; the relative mobility Uri
of each component i is defined by
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Ud is the dye mobility and di and dd are the
distances that component i and dye,
respectively, have moved by the conclusion
of the experiment
Ferguson plots
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A very simple relationship between relative mobility
and gel concentration,
logUri = logUrio - kiC
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where C is the gel concentration and is the relative
mobility of component i when C = 0, that is, the
relative mobility in free electrophoresis. The
constant ki: large molecules will have large values of
k, whereas very small molecules will have small
values, and hence will behave almost the same way
in a gel as they do in free electrophoresis.
Electrophoresis
Ferguson plots for a number of commonly encountered
solutions.
Example
Analysis of multisubunit structures by
SDS gel electrophoresis
a very widely used technique for the estimation of the
molecular weights of polypeptide chains.
 the protein to be studied is first heated in a dilute
solution of a detergent such as sodium dodecyl sulfate
(SDS). This breaks down all native quaternary, tertiary,
and secondary structures in the protein.
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Usually, a reducing agent such as -mercaptoethanol is also
added to reduce any disulfide bonds.
The protein is then electrophoresed in the presence of SDS.
The separation proceeds on the basis of polypeptide-chain
weight, and is nearly independent of the charge on the
polypeptide.
Analysis of multisubunit structures by
SDS gel electrophoresis
General principles:
 First, SDS at a given solution concentration binds to
many different proteins at a constant weight-weight
ratio: there is a defined number of bound SDS charges
per amino acid residue; therefore, the charge
contributed by SDS is proportional to protein molecular
weight.
 the complexes between SDS and proteins are
extended structures: molecules with both charge and
friction proportional to molecular weight. As in that
case, this predicts that the free mobility will be
essentially independent of molecular weight, and that
separation will be by the effect of sieving.
Analysis of multisubunit structures by
SDS gel electrophoresis
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As in the case of DNA,
there exists, for each
particular gel type and
concentration, an
approximately linear
relationship between
the logarithm of the
protein molecular
weight and mobility.
logUri = logUrio - kiC
DNA samples (open squares) are restriction fragments from a bacterial
plasmid. Proteins are polymers of the globular domain of histone H5,
cross- linked with either glutaraldehyde (squares) or dithiobis
(succinimidyl propionate) (circles).
References
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Section 5.4 in Principles of Physical
Biochemistry