Electrophoresis in practice
Gel electrophoresis
Physical Chemistry


Uses an acrylamide or agarose gel
Apply electric field for a given time
After electrophoresis, the gel is
visualized with a stain


Lecture 4
Electrophoresis and light
scattering

From J. Vinocur,
Wikimedia
Commons.
Various dyes can be added
Fluorescent molecules can be
detected directly in ultraviolet light
Exposure of film to radioactive
materials
Determination of the distance
traveled in a set time
Run multiple samples in one
experiment


Unknowns
Standard materials for comparison
Capillary zone electrophoresis



Motion of charged particles
In an electric field E a
charged particle (Ze) moves,
the force being proportional
to the electric field (for an
isotropic medium)
The movement is resisted by
the viscous drag of the fluid
Drag force is proportional to
the speed
At steady state, the
molecule moves with a
speed determined by the
balance of the drag and
electric forces


Similar experiment
Uses a capillary tube as the path
Interaction with surface of tube
important
Electromagnetic radiation
Electromagnetic radiation,
including visible light, is
described by a traveling wave


Felectric
 ZeE
Fviscous


fv
At steady state
Felectric  Fviscous
vss


Ze
E
f
Magnetic, B, and electric, E,
field vectors are always
perpendicular
Satisfies Poisson’s equation
Frequency, , and wave length,
, are related
Frequency described in
 Cycles per second (), or
 Radians per second ()
Time-dependent electric and
magnetic fields (such as
electromagnetic radiation)
interact with charges to produce
time-dependent changes in a
charged system

Example: force on a charged
macromolecule in a static
electric field
Electrophoretic mobility
The proportionality coefficient, ,
between steady-state speed and
electric field is the electrophoretic
mobility
Assumption of a spherical particle of
radius r gives an equation for




Friction coefficient from Stokes-Einstein
theory
Depends on charge on particle
Depends on “size” of particle
Depends on viscosity of the medium
v  E
Ze

E
f

Difficult to make quantitative

Ionic environment




Reduction of effective charge by bond ions
Reduction of electric field by local ions that
also contribute to the electric field
Viscous effect of oppositely charged
particles movement in the opposite
direction in the field – electrophoretic effect



Mobility is directly proportional to Z
Mobility is inversely proportional to the
friction coefficient
Found from Maxwell’s
equations for an
electromagnetic field
Proportional to the square
of the electric field
magnitude
Proportionality coefficient is
called the permittivity, 
   0 E02
 0 = permittivity of a
vacuum
Effects of shape
Used as a semiquantitative tool
  2
In discussing radiation, field
energy density, , is an
important parameter
Ze
6r
x

B( x, t )  B 0 cos2 t  


Intensity

 
x

E( x, t )  E 0 cos 2 t  


The rate of change of the
energy density is the
intensity, I

I
  c  c 0 E02
Light travels at c
1
Molar masses determined by
laser light scattering
Electric dipoles
Dynamic light scattering
can determine molar
masses in the range
from a few kilograms to
thousands of kilograms
Can also determine
structure through the
radius of gyration
Dipoles describe a separation of
positive and negative charge

Two kinds of dipole
 Permanent
 Induced


Simple model: two equal (but
opposite sign) charges
separated by a distance r
For an atom or molecule,
induced separation of charge
occurs because of the opposite
forces on the nucleus and the
electrons in an electric field
In a time-dependent field, the
average induced dipole is also
time-dependent

d  Zer
Proportionality between the
induced dipole moment and the
electric field is the polarizability,
 d   E  E 0 cos t

An electric dipole produces
an electric field in the
surrounding space

The magnitude of the
electric field is proportional
to the magnitude of the
dipole
For an oscillating dipole, the
field is oscillating
Light intensity is proportional
I scattered
to the square of the electric
field
I

scattered , unpolarized
Scattered intensity is
proportional to the inverse
 2
 2 2 4
fourth power of the
wavelength
 2 0 R 


The sky is blue in the day
The sky is red at sunset
 Eds

 1  cos 2  s  2 I 0



Scattering from solutions
The scattering depends
on the concentration of
solute molecules
Measurement of
scattering as a function
of concentration gives
the molar mass, M, of
the solute
Particularly useful for
molecules of high molar
mass
Gives the massaveraged molar mass,
MW
AC
2

 MW
AC
 a collection of constants
2
0
Serum albumin
Myosin
DNA
36.0
70.0
493.0
4000
Polystyrene
Radius of
Gyration (nm)
46.8
117.0
1550.0
Tobacco
mosaic virus
39000
Starch
amylopectin
80000
92.4
Taken from K. E. Van Holde, Physical Biochemistry,
Prentice-Hall: Engelwood Cliffs, New Jersey, 1971
and C. Tanford, Physical Chemistry of
Macromolecules, John Wiley and Sons: New York,
1961.
The scattered intensity
has some dependence
on the frequency for a
fixed orientation of the
detector
The half width of the
line is determined by
the diffusion coefficient
and the scattering
vector
Measurement of the line
width gives the
diffusion coefficient
I (0   )  I 0
Dq 2
2
( Dq 2 ) 2    0 
 16 2 D  2
 sin  s
  
2
  
Example: bovine serum albumin
 n 
2
n 
 1  cos  s C
4  C C 0
I
I0
Used for biologically
derived molecules
Used for whole particles
such as viruses
Used to analyze
synthetic polymers
-Lactoglobulin
Mass-averaged
Molar Mass
(kg)
Shape of the scattered line and
diffusion measurements
Electric field of a dipole

Very large particles

Material

Translational diffusion in
bovine serum albumin


From a paper by T. Raj and
W. Flygare, Biochemistry,
1974, 13, 3336 – 3340.
Easily allows monitoring
effects of changing
parameters on the diffusion
The diffusion coefficient
varies as a function of



pH
Ionic strength
Concentration
Explained by changes of
structure of BSA with
conditions
2
Summary
Movement of molecules under an electric field

Electrophoresis
 Qualitative tool
 Electrophoretic mobility
 Often used in comparison mode
Light scattering



Fluctuations of density
Concentration dependence depends on particle
mass
Useful for a wide variety of materials
Both depend on molar mass


Used as a separation device
Measurement of molar mass
3