Principles of Electrophoresis

Active fractions isolated by a preparative fractionation  procedure may be subjected to a number of analytical  fractionation  procedures to determine their purity.  Analytical fractionations  are distinguished from preparative fractionations by the criteria shown in Table 1.

In an analytical fractionation, therefore,  a small amount of sample is sacrificed in order to  gain information  about the  state  of purity  of the material being analyzed.  Of the  many physic-chemical techniques which have contributed to our knowledge of proteins (and nucleic acids), electrophoretic techniques occupy a position of primary importance. Electrophoresis finds its greatest usefulness in the analysis of mixtures and in the  determination  of purity,  although  certain  forms  of electrophoresis may be applied on a preparative scale.

Electrophoresis may be defined as the migration of charged ions in an electric field.  In  metal  conductors, electric current is carried by the movement of electrons, largely along the surface of the metal. In solutions, the the “PA NIC”  - Positive  Anode Negative Cathode (NI) Not the Ions electric current flows between electrodes and is carried by ions.  The negative electrode  - the cathode  - donates electrons and the positive electrode - the anode - takes up electrons  to  complete  the  circuit.  The ions that  result from the take  up of electrons  from  the  cathode  will be negatively charged and will thus migrate towards the positive anode. Because of their anodic migration, negative ions are called “anions”.

Ions which result from the  donation of an  electron  to  the  electron-deficient (i.e.  positively  charged)  anode will themselves  be electron deficient, and thus positively charged.  These  will migrate  to  the  cathode and are thus called cations.

Figure 1.  Electrophoresis: the movement of ions in an electric field.

 There is a potential difference (voltage) between the anode and the cathode and if the solution between these is of constant  composition  and constant cross-section (i.e. constant resistance), the  voltage  gradient between them (dV/dx) will be linear, with units of volts cm^-1. An ion placed in such an electric field will experience a force:-

Where,

 F = electrophoretic force

K =  a  constant  (embodying  the  Faraday  constant  and Avogadro's number

q = net charge on the protein (atomic charges/protein molecule)

This force will cause the protein  to  accelerate towards either the cathode or the anode, depending on the sign of its charge. As the protein moves it will experience a retarding frictional force  (hydrodynamic drag), which at the speeds involved is proportional  to  the speed of movement.

Where,

It will be recalled that this situation is very  similar to  that  obtaining during centrifugation  ,  and the  frictional  coefficient  can  be determined in the same way.

Hence,

The proteins very soon reach terminal velocity, at which point the electrophoretic (propelling) force equals the frictional (retarding) force, i.e. from equations 1 and 2:

The free electrophoretic mobility, (µ),  with units of (cm² volt^-1 sec^-1)  can be defined as the velocity per unit of voltage gradient, i.e.:

µ =  velocity (voltage gradient)^-1

Hence, from equation.3,

The electrophoretic mobility is thus a function  of the charge on the protein ion and the medium through which it is travelling. Electrophoretic techniques exploit the fact that different ions have different mobilities in an electric  field and so can be separated by electrophoresis.

The flow of electricity in electrophoresis is subject to the same physical laws as other forms of electricity.  For example,  Ohm's law applies:

Where

I = current (amps)

V =  potential difference (volts)

R =  resistance (ohms).

The unit of electrical charge is the coulomb and the unit of current [the ampere (amp)] may be defined as coulombs sec^-1, i.e.,

The flow- of electricity  involves  work,  which generates  heat,  and the work (W, in joules) done in transferring a charge of q coulombs between a potential difference of V volts is

And, since, from equ 5.,

Then,

From equ .7

Which means that I²Rt joules  of heat  will  be  developed  in  the  conductor. The power (in watts) (defined as the rate of work) gives the rate of heating (joules sec^-1).

Thus,

The effect of the buffer

The buffer in which electrophoresis is conducted, has a large influence on the migration of proteins.  Firstly, the  buffer pH will influence the charge (q) on the  protein  and hence the  direction  and  speed  of its migration. Secondly, the buffer ionic strength  influences the  proportion of the current carried by the proteins - at low ionic  strength the  proteins will carry a relatively  large proportion  of the  current  and so will have  a relatively fast migration.  At high  ionic  strength,  most  of the  current  will be carried by the  buffer ions and so the  proteins  will migrate  relatively slowly.

An analogy might be useful in visualizing  this  effect  of ionic  strength. Imagine a bank where there  are two counters  - one for deposits  the anode) and one for withdrawals  (= the  cathode),  with electrons  being the money. The ions may be considered as customers waiting to be served at either  counter,  which one  can visualize as being at opposite  ends  of the banking hall.

In Fig. 2, the  circles represent customers queuing for service.  In electrophoresis, these queues would be along the so-called field lines, which are usually  (but not necessarily)  straight lines.  The lighter coloured circles represent buffer ion “customers” and the dark circles represent protein “customers”. When the “customer” at the counter is served, they move  away, creating  a  “hole”.  This  “hole”  is filled by  the  next customer in line, and so on, and so the “hole”  moves backwards along the line. No matter how far away from a counter any customer is, they will be drawn towards the counter by the periodic appearance of a “hole” in the queue, immediately in front of them.  If the counter assistants were very energetic (giving a high current) these “holes” would appear frequently and the customers would all progress quickly.  On  the  other hand, if the counter assistants were lethargic  (giving a low current)  the “holes” would appear infrequently and progress of the customers would be slow.

Figure 2. A banking hall analogy of electrophoresis.

In Fig. 75, the  relative proportions  of protein  ions to  buffer ions shown is such that there is one protein ion in each queue.  However, if we have the counter assistants working at the same rate (i.e. with the same current) but increase the number of customers (i.e.  increase the  ionic strength), then we will get the situation shown in Fig. 3.

With more buffer ions present, they  will get most  of the  service  (carry most of the current) and the progress of all ions in their respective queues, including the protein ions, will be slower.

In electrophoresis,  therefore,  a low ionic  strength  is preferred  as it increases the rate  of migration  of proteins.  A low ionic strength  is also preferred as it gives a lower heat generation.  Assuming a constant voltage, if the ionic strength is increased, the electrical resistance decreases but the  current  will increase.  According  to  Eqn  8,  heating  is proportional to I², but is only linearly affected by changes in resistance.

A high ionic strength buffer will therefore lead to greater heat generation, and so a low ionic strength is preferred.

Figure 3.  Illustration of the effect of ionic strength in electrophoresis.

Strictly speaking, it is not the  ionic  strength  per se  which is the important factor in electrophoresis, but the mobility of the buffer ions. Thus at equivalent ionic strengths (i.e.  at comparable buffering capacities), large buffer ions will migrate more slowly than  small buffer ions (because of their greater frictional coefficient, f).  Large buffer ions will thus lead to  less heat generation  and a faster  migration  of  the proteins. For example, barbitone (I) has a mobility about one quarter of that of Tris (II), and can therefore be used at four times the concentration of Tris - at which concentration  it will be roughly four times more effective as a buffer.

The effect of ionic strength  is actually more complex than indicated in the  simplistic model given above.  The  reason  is that  ionic  strength also has an effect on the  electrical  double layer which surrounds proteins in solution.  The  ions  in  the  electrical  double  layer  have  the  effect  of decreasing the  apparent  charge  on  the  protein.  As the  protein  moves under electrophoresis, it takes with it a part of the electrical  double layer. As the  ionic  strength  increases,  the  thickness  of the  electrical  double layer decreases and more of the  counterions  are drawn along with the migrating protein,  effectively reducing its charge.  The  mobility  of the protein thus decreases with increasing ionic strength.  A more complete discussion of this effect is given by Kyte .

References 

Dennison, C. (2002). A guide to protein isolation . School of Molecular mid Cellular Biosciences, University of Natal . Kluwer Academic Publishers new york, Boston, Dordrecht, London, Moscow .