Cyclic migration of DNA in gels: DNA stretching and electrophoretic mobility

Available data from spectroscopic and microscopy studies of electrophoretic orientation of long DNA (above 40 kbp) in agarose gels is analyzed on the basis of the fact that the migration in constant fields is cyclic in nature. Defining a cycle period as the time between two consecutive compact states, a simple model is used to obtain data on the average time period (< T >) and the step length (< L >) of the migration cycle from spectroscopic measurements of the dynamics of helix orientation and center-of-mass velocity. Furthermore, the degree of orientation is used to analyze tube-orientation and DNA stretching contributions to < L > and < T >. Finally, the average electrophoretic velocity v = < L >/< T > is analyzed in terms of < L > and < T > for different DNA sizes (Lc), field strengths (E), and gel concentrations (A). The main results of the analysis are: (i) the increase and saturation of the electrophoretic mobility with increasing E is mainly governed by < L > via the degree of DNA stretching, (ii) DNA molecules of different sizes migrate with the same velocity because < L > and < T > both increase approximately linearly with Lc, and (iii) migration in a denser gel is slower mainly because < T > increases, while the step length is approximately constant. Assuming the charge Q of DNA is the same as in free solution, these results suggest that the reason the fundamental reptation equation for the electrophoretic mobility mu = (Q/zeta) < (hx/Lt)2 > also applies in the presence of strong fluctuations in the tube length Lt, and end-to-end distance hx, is that the friction coefficient zeta for motion along the tube is lower the more stretched the DNA is.