Modeling ssDNA electrophoretic migration with band broadening in an entangled or cross-linked network

We use a coarse-grained model proposed by Graham and Larson based on the temporary network model by Schieber et al.. [1] to simulate the electrophoretic motion of ssDNA and corresponding band broadening due to dispersion. With dimensionless numbers reflecting the experimental physical properties, we are able to simulate ssDNA behavior under weak to moderate electric field strengths for chains with 8-50 entanglements per chain ( approximately 1000-8500 base pairs), and model smoothly the transition from reptation to oriented reptation. These results are fitted with an interpolation equation, which allows the user to calculate dimensionless mobilities easily from input parameters characterizing the gel matrix, DNA molecules, and field strengths. Dimensionless peak widths are predicted from mobility fluctuations using the central limit theorem and the assumption that the mobility fluctuations are Gaussian. Using results from previous studies of ssDNA physical properties (effective charge xiq and Kuhn step length b(K)) and sieving matrix properties (pore size or tube diameter a), we give scaling factors to convert the dimensionless values to "real" experimental values, including the mobility, migration distance, and time. We find that the interpolation equation fits well the experimental data of ssDNA mobilities and peak widths, supporting the validity of the coarse-grained model. The model does not account for constraint release and hernia formation, and assumes that the sieving network is a homogeneous microstructure with no temperature gradients and no peak width due to injection. These assumptions can be relaxed in future work for more accurate prediction.