Growing experimental evidence indicates that iron-sulfur proteins play key roles in DNA repair and replication. In particular, charge transport between [Fe₄ S₄ ] clusters, mediated by proteins and DNA, may convey signals to coordinate enzyme action. Human primase is a well studied [Fe₄ S₄ ] protein, and its p58c domain (which contains an [Fe₄ S₄ ] cluster) plays a role in the initiation of DNA replication. The Y345C mutation in p58c is linked to gastric tumors and may influence the protein-mediated charge transport. The complexity of protein-DNA systems, and the intricate electronic structure of [Fe₄ S₄ ] clusters, have impeded progress into understanding functional charge transport in these systems. In this study, we built force fields to describe the high potential [Fe₄ S₄ ] cluster in both oxidation states. The parameterization is compatible with AMBER force fields and enabled well-balanced molecular dynamics simulations of the p58c-RNA/DNA complex relevant to the initiation of DNA replication. Using the molecular mechanics Poisson-Boltzmann and surface area solvation method on the molecular dynamics trajectories, we find that the p58c mutation induces a modest change in the p58c-duplex binding free energy in agreement with recent experiments. Through kinetic modeling and analysis, we identify key features of the main charge transport pathways in p58c. In particular, we find that the Y345C mutation partially changes the composition and frequency of the most efficient (and potentially relevant to the biological function) charge transport pathways between the [Fe₄ S₄ ] cluster and the duplex. Moreover, our approach sets the stage for a deeper understanding of functional charge transfer in [Fe₄ S₄ ] protein-DNA complexes.