Biomedical Engineering Reference
In-Depth Information
In other words, out of the framework of the simplistic approximations pre-
sented above, electrophoresis becomes rapidly a very complicated phenomenon and
it should be kept in mind that the practical interpretation of these experiments is
often largely empirical.
One last word in this rapid theoretical introduction, we have considered a par-
ticle in an infinite medium at rest. However, the suspension is contained in a physi-
cal cell. In the general case, the walls of this cell are not passive but the charge they
bear responds to the external electric field by developing electro-osmotic flows (see
Section 10.1.2). These induced flows superimpose a plug flow to the electrophoretic
motion of the particles. They can dramatically affect the performances of the de-
vices and should be well controlled.
Double-stranded DNA is the molecule most commonly separated by electro-
phoresis. We will first focus on this case. However, there are many objects on which
electrophoretic separation is used: proteins or single-stranded DNA are molecular
examples. Cells or organelles are other more macroscopic examples.
10.1.4 Electrophoresis of DNA
DNA is a polyelectrolyte (a polymer chain whose monomers bear a charge). On
top of the complexity of charged objects we have just discussed, we must add the
one inherent to polymers. We will shortly present it and infer from these results the
main characteristics of DNA electrophoresis.
10.1.4.1 Polymer Chains in Solution
We have seen in Chapter 8 that, in dilute solutions, DNA chains adopt a coil con-
figuration whose radius, called the radius of gyration
R
g
, is directly related to the
size of the monomers b and their number N through the relation:
1/ 2
(10.17)
R
= ×
b N
To understand the behavior of a polyelectrolyte chain in an electric field, we can
model it by a succession of charged beads of radius a connected together by springs
(Rouse model) [6]. The Stokes friction coefficient of each bead with the solvent is
6
ph
a. Without getting into the full calculation, it turns out that the coil is trans-
parent to the hydrodynamic flow and the friction of the chain in the liquid comes
exclusively from the individual frictions of the beads [7]. The effective friction over
the whole length of the chain is then proportional to the number of beads and thus
to its length. As the electric force applied to the chain is also proportional to its
length, the net result is that the mobility of a long polyelectrolyte is independent of
its length [8].
Now, we know that a polymer chain is not a succession of independent
beads. However, more refined models and in particular the ones derived from the
Zimm description where the hydrodynamic interactions between beads are taken
into account, show that the added terms induce only small deviations to this
law [8].
Practically, we can conclude that no size separation of long DNA will occur by
simply applying an electric field to a solution of these molecules.
