COMSOL 6.4 - Isoelectric Separation

This modeling example applies the Electrophoretic Transport and the Laminar Flow interfaces to model isoelectric separation in a free-flow electrophoresis device. A stream containing four different proteins is divided into separated component streams by means of migrative transport in an electric field.

Free flow electrophoresis can be used to separate macromolecules, such as proteins perpendicular to the flow of the carrier fluid. If a pH and potential gradient is applied across the carrier flow, then molecules can be focused along their isoelectric points. The isoelectric point is the pH at which a molecule has zero net charge. The concept of isoelectric focusing is illustrated in Figure 1.

Figure 1: Ampholytic molecules can be focused around their isoelectric point by means of migrative transport in an electric field.

Molecules with a positive net charge travel in the direction of the electric field, along the pH gradient, until they reach the isoelectric point. At this instance the migrative transport is switched off as the molecules net charge is zero. Similarly, negative net charge species travel in the direction opposite of the electric field.

Model Definition

The model geometry is shown in Figure 2. It represents the separation region in an isoelectric focusing chip. A laminar carrier stream transports a mixture of four proteins, one weak acid and one weak base, injected at the bottom of the cell.

Figure 2: Model geometry.

The Electrophoretic Transport interface supports ionic species transport by diffusion, convection, and migration in electric fields. The mass balance that is solved in the interface is as follows:

In the equation, ci denotes the concentration of species i (SI unit: mol/m3), Di is the diffusion coefficient of species i (SI unit: m2/s), u is the fluid velocity (SI unit: m/s), F refers to Faraday’s constant (SI unit: s·A/mol), ϕ denotes the electric potential (SI unit: V), zi is the charge number of the ionic species (unitless), and um,i its ionic mobility (SI unit: s·mol/kg). The Electrophoretic Transport interface also adds an equation for the charge transport in the electrolyte, based on an assumption of electroneutrality, and a set of chemical equilibria describing the water self- ionization reaction and the dissociation reactions of weak acids and bases.

The fluid flow is set up with a Laminar Flow interface, solving for the Navier–Stokes equations.

Results and Discussion

Figure 3 shows the pH in the cell. The pH gradients in the x direction increase toward the outlet.

Figure 3: Surface plot of pH in the cell.

Figure 4 shows the electrolyte conductivity. The conductivity gets lower close to the electrode surfaces and toward the outlet due to depletion of charge carriers.

Figure 4: Surface plot of electrolyte conductivity in the cell.

Figure 5 shows the electrolyte potential. Outside the electrode gap, the potential gradients are low, which means that the migrative flux close to the inlet and outlet is low.

Figure 5: Surface plot of electrolyte potential in the cell.

Figure 6 shows the concentration of Protein 1, which has an isoelectric point of 4.7. The protein is concentrated toward the right electrode.

Figure 6: Surface plot of molar concentration of Protein 1 in the cell.

Figure 7 shows the concentration of Protein 2, with an isoelectric point of 6.1. This protein reaches its maximum outlet concentration somewhere between the center and the right electrode.

Figure 7: Surface plot of molar concentration of Protein 2 in the cell.

Figure 8 and Figure 9 show the weak acid and base concentrations, respectively. The weak acid, with a negative average charge, is transported to the right and the base, with a positive average charge, is transported to the left in the electric field.