(5a) DNA Electrophoresis in Inverse Opals

We investigate theoretically the electrophoretic motion of a long DNA molecule inside an inverse opal, a class of photonic crystals that consists of a face-centered cubic array of spherical cavities, connected through narrow pores. Our model is based on Zimm's lakes-straits (LS) model whereby the DNA chain is distributed over a fluctuating number of cavities, or lakes, and moves by transferring mass through the narrow pores, or straits. In the present case, the LS model is modified to account for the spherical confinement inside the cavities and the discrete set of allowable exit points from a given cavity. Our results agree with biased reptation theory in the limiting cases of low and high fields. The model also predicts a new regime at the transition between the low and high field reptation regimes that is not observed in gel electrophoresis. In addition to faster separation rates, the range of molecular weights in this regime extends well beyond values of gel electrophoresis. The gain in performance results from the well-defined confinement and limited connectivity of the spherical cavities in an inverse opal, contrasting with the weak confinement and high porosity of an agarose gel.