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Maxwell-Stefan electrophoresis simulation of equal mass type A catenanes and supercoiled dimers Kadomatsu Hermosa, Maridian José


The analysis of two topological DNA families, type A catenanes (CatAs) and supercoiled dimers (Dims) of a bacterial plasmid by two-dimensional agarose gel electrophoresis (2Dgels) was used to show that the number of crossings is not the only variable that determines electrophoretic mobility in agarose gels run under different conditions. To find out other parameters that could explain these differences in mobility, we consider DNA in the gel as a two-phase fluid model in a porous media, using conservation law models for the mass and the Maxwell-Stefan equation as a constitutive relation between the velocity of topoisomers and the electrostatic gradient of the electrophoresis experiment. The velocity of topoisomers was obtained experimentally considering velocity as a function of the electrophoretic variables. From the modeling, a nonlinear hyperbolic partial differential equation was obtained which was subsequentially solved using a Lax-Friedrich finite difference scheme. Comparisons between experimental 2Dgels and simulations showed that the number of crossing was not the only determinant factor affecting mobility and indicated that molecular deformability also played a crucial role. This observation explains the differences in electrophoretic mobility experimentally observed for CatAs and Dims of the same mass. The numerical results also showed that the drag force of ions in the buffer has a strong influence in the velocity of topoisomers. The results obtained so far encouraged us to improve the modeling as well as to develop faster numerical schemes. This work was partially supported by CONACyT-Paraguay and Spanish BFU2011- 22489. Work in collaboration with Maridian J. Kadomatsu-Hermosa, Jorge Cebrián, María José Fernández-Nestosa, Christian E. Schaerer, Dora B. Krimer and Jorge B. Schvartzman

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