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We study the effects of the genetic sequence on the propagation of nonlinear excitations in simple models of DNA in which we incorporate actual data from the human genome. We show that kink propagation requires forces over a certain threshold, a phenomenon already found for aperiodic sequences [F. Domínguez-Adame , Phys. Rev. E 52, 2183 (1995)]. For forces below threshold, the final stop positions are highly dependent on the specific sequence. Contrary to the conjecture advanced by Domínguez-Adame and co-workers, we find no evidence supporting the dependence of the kink dynamics on the information content of the genetic sequences considered. We discuss possible reasons for that result as well as its practical consequences. Physically, the results of our model are consistent with the stick-slip dynamics of the unzipping process observed in experiments. We also show that the effective potential, a …