We examine the effect of attractive analyte-gel interactions within the framework of our recently developed lattice model of gel electrophoresis. We show that it is possible to take into account such interactions and still calculate exact mobilities for various analytes and gel structures. Our study then focuses on two main issues: (i) the effect of these interactions on the separation efficiency of the Ogston regime; and (ii) the presence of inflection points (changes of curvature) in Ferguson plots. We establish some general principles, and we describe the results for selected two- and three-dimensional model systems. Numerous practical problems, such as chiral separations and affinity electrophoresis, can be treated using this approach.