Theory of band broadening during cycling temperature capillary electrophoresis

A two-state transport model is presented for cycling temperature CE. In this high-throughput method of mutation detection, the temperature oscillates in time, causing the DNA to periodically transit between an annealed state and a partially melted (denatured) state. The change in state alters the electrophoretic mobility, and the presence of a mutation changes the temperature dependence of the denaturing/annealing kinetics. Asymptotic formulae for the mean velocity and effective diffusivity (dispersivity) of the DNA are computed by a multiple-time scales scheme in the limit where the DNA have experienced many temperature cycles before reaching the detector. Explicit analytical results are presented for the case where the temperature cycle consists of one interval with irreversible annealing, followed by a second interval with an infinitely fast, irreversible denaturation. The lag in the annealing leads to a reduction in the mean velocity and an enhanced dispersion compared to the idealized case where the DNA respond instantaneously to the changes in temperature, with the dispersion scaling quadratically with the electric field. The predicted plate height scales linearly with the electric field, and the optimal separation resolution is predicted for moderate values of the cycle frequency that allow the DNA to relax during each temperature oscillation.