# Interdisciplinary Applied Mathematics

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Moving-boundary electrophoresis is a widely used technique in commercial and laboratory setups, where the solution containing positively and negatively charged particles is subjected to electric fields, and the particles move toward the oppositely charged electrode. This results in motion of the solution boundary, which is commonly detected using Schleiren optical techniques.

Steady-state electrophoresis is obtained when the positions of separated components do not change in time. Steady-state electrophoresis is commonly observed in isoelectric focusing (IEF) applications. In IEF, charged particles migrate under electrophoretic forcing and pH gradients to a location in the buffer, where they experience zero net charge. This location

FIGURE 7.21. Isoelectric focusing of proteins PE, APC, and GFP in a 2 cm x300 pm x5 pm PDMS microchannel. Three proteins are completely resolved with band thicknesses below 100 im, and the GFP is subfractionated into two bands. (Courtesy of P. Dutta and C.F. Ivory.)

is known as the isoelectric point (Righetti, 1983; Macounova et al., 2000; Macounova et    al.,    2001; Cabrera et    al.,    2001).    In    Figure    7.21    we    present

isoelectric focusing of three different proteins in a polydimethyl siloxane (PDMS) microchannel (Horiuchi et al., 2003). The results, obtained in 5 minutes in a 25 V/cm electric field, show separation of phycoerythrin (PE), allophycocyanin (APC), and green fluorescent protein (GPF) mixture with band thickness below 100 pm. The GFP has three constituents with very close focusing points, and the figure shows that the method enables subfractionation of GFP into two bands (on the right side of the figure). Overall, the IEF can be used to separate as well as concentrate charged species under pH gradients. The design shown in (Horiuchi et al., 2003), has the advantage of having approximately 4,500 theoretical bands of 300 pm in a 2 cm channel, enabling detection and concentration of a large number of species.

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