Theory of end-labeled free-solution electrophoresis: is the end effect important?

In the theory of free-solution electrophoresis of a polyelectrolyte (such as the DNA) conjugated with a "drag-tag," the conjugate is divided into segments of equal hydrodynamic friction and its electrophoretic mobility is calculated as a weighted average of the mobilities of individual segments. If all the weights are assumed equal, then for an electrically neutral drag-tag, the elution time t is predicted to depend linearly on the inverse DNA length 1/M. While it is well-known that the equal-weights assumption is approximate and in reality the weights increase toward the ends, this "end effect" has been assumed to be small, since in experiments the t(1/M) dependence seems to be nearly perfectly linear. We challenge this assumption pointing out that some experimental linear fits do not extrapolate to the free (i.e. untagged) DNA elution time in the limit 1/M→0, indicating nonlinearity outside the fitting range. We show that a theory for a flexible polymer taking the end effect into account produces a nonlinear curve that, however, can be fitted with a straight line over a limited range of 1/M typical of experiments, but with a "wrong" intercept, which explains the experimental results without additional assumptions. We also study the influence of the flexibilities of the charged and neutral parts.