Some Basic Theoretical Concepts

Here some basic equations governing the IEF process will be considered. The most important is the one governing the distribution profile of an ampholyte about its isoelectric point. Under steady-state conditions (obtained by balancing the simultaneous electrophoretic and diffusional mass transports), Svensson derived the following differential equation describing the concentration profile of a focused zone:

sional mass flows. If eqn [1] is re-written in the form:

it is seen that it is possible to integrate it if p is known as a function of pH and D as a function of C. Specifically, if the conductance, the diffusion coefficient, and the derivative:

(where p is the ratio between the protein titration curve and the slope of the pH gradient over the separation axis) can be regarded as constant within the focused zone, then p = —px and one obtains the following analytical solution:






where x is now defined as being zero at the concentration maximum C0. This is a Gaussian concentration distribution with inflection points at:

where C is the concentration of a component in arbitrary mass units per arbitrary volume unit; p is the electric mobility in cm2 V-1 s"1 of ion constituent except H+ and OH", with positive sign for cationic and negative sign for anionic migration; i is the electric current in A; q is the cross-sectional area in cm2 of electrolytic medium, measured perpendicularly to the direction of current; k is the conductance of the medium, in Q 1 cm"1; D is the diffusion coefficient in cm2 s "1 of a given ionic component with mobility p; and x is the coordinate along the direction of current increasing from 0 to the anode towards the cathode.

Each term in eqn [1] expresses the mass flow per second and square centimetre of the cross-section: to the left being the electric and to the right the diffu-

where xi represents the width of the Gaussian distribution of the focused zone measured from the top of the distribution of the focused ampholyte to the inflection point (one standard deviation). The course of the pH gradient is d(pH)/dx and dp/d(pH) represents the titration curve of the ampholyte. It should be kept in mind that this Gaussian profile holds only if and as long as the conductivity of the bulk solution within the zone is constant. Constant conductivity along a pH gradient is quite difficult to maintain, especially as one approaches pH extremes (below pH 4 and above pH 10), if for no other reason, because the non-negligible concentration of H+ and OH" present in the bulk liquid begins to contribute strongly.

Another important equation regards the resolving power in IEF, expressed in A(pI) units, i.e. in the minimum difference of surface charge between two adjacent proteins that the IEF technique is able to resolve. If two adjacent zones of equal mass have a peak-to-peak distance three times greater than the distance from the peak to inflection point there will be a concentration minimum approximating the two outer inflection points. Taking this criterion for resolved adjacent proteins, Rilbe derived the following equation for minimally but definitely resolved zones:

This equation shows that good resolution should be obtained with substances with a low diffusion coefficient (D) and a high mobility slope [d^/d(pH)j at the isoelectric point - conditions that are satisfied by all proteins. Good resolution is also favoured by a high field strength (E) and a shallow pH gradient [d(pH)/dxj. It will be seen that, whereas in conventional IEF the limit to the resolving power is approximately 0.01, in IPGs it is 0.001 pH units.

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