Electrophoresis

1
Electrophoresis
Electrophoresis is a class of separations methods
based on the transport of species through a
conductive medium it involves separation due to
differential transport of charged species due to
an electric field. Until recently,
electrophoresis was used mostly as an analytical
tool. One example includes DNA testing. Lately,
it has been gaining importance as a preparative
separation method, particularly for biotech
applications.
Basic Configuration
V
V
At t0 a pulse of a mixtureis injected into the
system.
At tt1 the species in the mixtureare are
separated into bands.
2
Electrophoresis
The electric field creates a force on cations
towards the cathode and anions towards the anode.
The rate of transport depends on many factors
including the charge on the ions, the size and
mass of theions and conditions of the medium.
Free-Solution Method
Other configurations include supporting media
Gels Packing  Paper Capillaries Like
chromatography buttransport due to electric
fieldrather than mobile phase.
The sample
Buffered aqueous solution
V
Tiselius 1948 for his development of
electrophoresis
3
Forces and Fluxes
Differential transport, which is the key
principle behind all separations processes, is
induced by the electric field acting on charged
species in the mixture to produce different
average velocities.
The total change in concentration with time
J is the flux and R is the the rate ofreaction.
The divergenceof the fluxes
The rate of reaction
The number of species in a small volume element
changebecause the fluxes into the element are
different than the fluxes out of the element, or
because species are being converted.
R
In electrophoresis the set up is such that we
have no convective driving forces (no bulk flows)
andno reactions.
Thus the change in concentration at a position in
our system is due to only diffusion and Coulombic
forces.
4
Non-Convective Fluxes
If we have no reaction or convective driving
forces the change in concentration with time
reduces to
The flux is just the sum of the flux due to
diffusion and that caused by the electric field
The flux due to diffusion is given by Ficks
First Law
The flux due to diffusion isthe negative of the
diffusion constant times the gradient of
concentration
c
J
x
c(x)
c(xdx)
The flux due to the electric field is given by
The flux due to the electricfield is the
mobility, timesthe concentration times thefield.
V
x
So the total flux is just given by
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Mobility
The mobility constant used in the flux equation
is the electrophoretic mobility. It is a measure
ofthe velocity a species obtains under a given
field in a particular environment.
What are the molecular origins of the mobility?


Stokes Lawfor a sphericalparticle
Faradays constant Charge on a mole of
electrons
The molecules reach steadystate quickly, and the
drag willbalance the Coulombic force
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Mobility
The effective charge on an ion in a liquid is not
the ionic charge z because ions are solvated. A
Gouy- Chapman double-layer (Debye-Huckel Theory)
of thickness h forms around the ion of ionic
radius a
a
The effective charge z
h
Notice the dependence on ionic strength s, and
the dielectric constant ?.
The double-layer thickness h
h o (3 to 1000Å)
The double-layer reduces the effective charge on
a species being pulled by an electric field
through a dielectic , since it drags along a
cloud of counterion which screens the ion charge.
The flux due to the field
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Diffusion
If only a concentration gradient exists, then
We know how the chemical potential ? depends on
concentration for an ideal mixture
The spreading of a dropdepends on thermal
energyfor diffusion and the drag.
Therefore
Using the relationshipbetween flux,
concentrationand velocity
kT
v/b
We obtain Ficks First Law (The flux due to
diffusion)
Thermal energyavailable for random motion.
Where the diffusion constant is given by
Resistance tomoving due to drag.
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Transport Equation for Electrophoresis
Substituting in our expression for flux derived
from diffusion and Coulombic driving forces we
obtain
Diffusion
Field
In one-dimension this becomes
Note that the second term looks like a convective
term with a constant velocity mE.
We can non-dimensionalize this equation using the
characteristic lengths, concentration,driving
forces and time for this system
the ratio of driving force duethe electric field
to the drivingforce of diffusion
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Boundary Conditions
To solve this second order linear partial
differential equation we will need to know the
boundary andinitial conditions c(x,0)
0 xgt0 c(0,t) c0 0lttltt0 c(8,t) finite (bounded
solution) For the non-dimensional
equation C(X,0) 0 Xgt0 C(0,?) 1 0lt ? lt ?
0 C(8, ?) finite (bounded solution)
Initial Condition
C
1
X
Using these boundary conditions we can use
LaPlace Transforms
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Solution
The solution is a moving Gaussian peak. That is,
the injected peak migrates down the
electrophoretic tubeas a Gaussian peak. Notice
that as it migrates, not only does its center
move, but it also broadens
The peak moves with velocity mE This increases
with higher mobilityand higher fields.
The peak height decreases with time.
The peak width increases with timeas diffusion
broadens the distribution.
c
The total area under the peak mustbe constant
(conservation of mass)so if the peak broadens,
it must alsobecome diluted.
x
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Electrophoretic Separation
Notice that the peak will move and broaden
according to the individual molecular properties
of thecomponents in the mixture the diffusivity
D, and the mobility m. Separation is due to
differences in mobility. If the diffusivities
are large, the peaks may overlap, even for
relatively large differences of m.
The peaks move with velocity miE This increases
with higher mobilityand causes differential
transport.
c
x
c
x
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Paper Electrophoresis
One electrophoresis method which uses a 2-D
support is paper electrophoresis
Sample
Paper saturated with bufferingsolution
DC voltage (50V to 1000V)
V
Result after drying and staining (if necessary)
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Paper Electrochromatography
If an perpendicular electric field is added to
the paper electrophoresis configuration the
process can be made continuous
Second DC voltage source to create orthogonal
field
Sample
V
Paper saturated with bufferingsolution
Collector
DC voltage (50V to 1000V)
V
Result after drying and staining (if necessary)
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Continuous-Flow Electrophoresis
Protein Separation by Continuous-Flow
Electrophoresis Microgravity Clifton et al.
AICHE Journal 42, 1996
Sample injection
Carrier Solution
Continuous flow operation High sensitivity
Preparative quantities  Natural
convection  Electrohydrodynamic spread Joule
heating
Anode
Cathode
Fraction collector
Electrode buffer
Electrode buffer
Ion exchange membranes
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Capillary Electrophoresis
Capillary Electrophoresis (CE) is a free-solution
technique and the most active area of
electrophoresis development
Capillary tube filled with conducting buffer
Internal diameter 50? Preparative quantities
Both analytical and quantitative analysis
Reduces Joule heating
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Capillary Electrophoresis
Species move either because of the force due to
the electric field or because they aredragged
along with the buffer solution which is
responding to the electric field.
Electrophoretic mobility the mobility of an
ion in an electric field Electrosmotic mobility
the mobility due to a species being swept along
in a flow arising from a buffer solutions
response to an applied electric field.
The electrosmotic mobility can cause anions and
neutrals to have a net migration towards the
cathode since usually the buffer solution has a
net positive charge.


17
Capillary Electrophoresis
Negatively charged sidewalls (positive buffer)
With short inner diametershydrodynamic flow does
notdevelop and sample moves through capillary
as a plug.
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Electrophoretic and Electroosmotic Mobility
In the case of Capillary Electrophoresis the
electrophoretic mobility depends on the same
properties of the buffer, and the analyte as in
thegeneral electrophoresis case. Consequently we
can use the same equationsin the case of CE as
we developed previously for the general case
In the case CE, negative charges on the capillary
wall create a double layer of charge. The outer
layer is rich in mobile, solvated cations which
movetowards the cathode and drag along anions
and neutrals.
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Electroosmotic Mobility
Potential drop across double layer


V
Buffer dielectric constant
Potential drop across double layer (the zeta
potential)
Viscosity of solution
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Electroosmotic Mobility
The zeta potential increases proportionally with
the charge on the capillary walls. The condition
of the buffer, such as the pH can change the
wall charges. The zeta potential also depends
on the thickness of the double layer. The
thinner the layer, the larger the potentials. So
if the ionic strength of the buffer increases,
the increased number of cations will reduce
the thickness of the double layer.
?
?
pH
Ionic strength
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Total Mobility
The total mobility of a solute will be just the
sum of the individual mobilities
Usually, the mobility of the cations will be
higher than the electroosmotic mobility, while
the anion mobility will be less than the
electroosmotic mobility. The neutral mobility
will be the same as the electroosmotic
flow mobility.



veof
vep
So the cations emerge first in order of their
charge to mass ratios, then neutrals, and finally
the anions elute in reverse order of their charge
to mass ratios. The order can be reversed by
adding ions which cause the capillary walls to be
positively charged.
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Migration Time
The time for a solute to traverse the tube
depends on its average velocity and the length
of the tube
Of course the field E is just the applied voltage
divided by the distance over which the voltage is
dropped.
To reduce the elution time the tube length can be
decreased, or the applied voltage increased.
Another choice is to increase the mobility by
changing the conditions of the buffer solution.
Selectivity is obtained by the ratios of the
mobility between solutes.
Selectivity
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Capillary Electrophoresis (CE)
In CE the problem of Joule heating is reduced by
using a thick tube wall and a small diameter
inner bore (20-100 ?m) For the same potential
drop (applied voltage) the currentflowing
through the sample is reduced. The larger outer
diameter also allows more heat dissipation.
Inner bore
Resin Coating
Fused silica
The inner bore is often filled with a buffer
which is conducting. If the inner bore is
verynarrow very large voltages can be applied.
Larger applied voltages  Increase migration
rate and thus reduce analysis time  Lead to
larger separations and thus high resolutions.
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Sample Introduction and Detection
The sample can be introduced several
ways Electrokinetic injection The sample can
be introduced by applying an electric field to
causethe sample to migrate into the tube.
Hydrodynamic injection The sample is
introduced using a pressure drop, or siphoning.
Detection of the analytes can be done using
several methods, such as Fluorescence and
Laser fluorescence Absorbance UV Mass
spectroscopy Amperometric  Conductometric  Rad
iometric
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Capillary Zone Electrophoresis
Capillary Zone Electrophoresis (CZE) is a
free-solution technique that we have just
described
Capillary tube filled with conducting buffer
Internal diameter 50? Preparative quantities
Both analytical and quantitative analysis
Reduces Joule heating
Inner bore (buffer filled)
Resin Coating
Fused silica
26
Capillary Zone Electrophoresis
Capillary Zone Electrophoresis (CZE) is a
free-solution technique that we have just
described
Capillary tube filled with conducting buffer
Internal diameter 50? Preparative quantities
Both analytical and quantitative analysis
Reduces Joule heating
Inner bore (buffer filled)
Resin Coating
Fused silica
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Capillary Isoelectric Focusing
Capillary isoelectric focusing uses a technique
for separating amphoteric species using a
pH gradient. The buffer includes zwitterions
which have both a positive and negative charge
onthe same group of atoms. In the presence of
the electric field H and OH- are separated and
bind to the zwitterions to create a pH gradient.
Amphoteric species such as proteins migrate
against diffusion to the optimum pH position and
thus in the pH gradient are focused to one
positioin along the tube.
Optimum pH for protein or other amphoteric species
Field
OH
H
Net basic zwitterions
Net acidic zwitterions
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Micellar Electrokinetic Capillary Chromatography
Neutral species in EC elute out of the tube in a
single band since the mobility of neutrals is
all the same. In order to separate neutrals one
can use chromatrography to introduce a mobile
phase which moves under the presence of the field
and which preferentially partition the solutes.
Neutral partioning between micell and buffer
Micell with net negative charge
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Micellar Electrokinetic Capillary Chromatography
Since micelles are usually negative, they move
towards the cathode slower than neutrals and thus
neutrals which partition preferentially into the
micelle will be separated fromthose that dont
and which are moving along due to electroosmotic
flow.
Neutral partioning between micelle and buffer
Electroosmotic force
Electrophoretic force
This neutral moves faster since it experiencesan
electrophoretic force.
Micelle with net negative charge
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Capillary Gel Electrophoresis
This is a combination of CE and size exclusion
chromatography.
Inner bore filled with Gel
Resin Coating
Fused silica
Solutes move through the capillary due to their
electrophorectic mobility. However, the gel slows
down the larger species. This technique can be
used to separate species with similar charge to
size ratios, but different sizes (for example
DNA and other oligonucleotides).