The closing conformational transition of wild-type polymerase P bound to DNA template/primer before the chemical step (nucleotidyl transfer reaction) is simulated using the stochastic difference equation (in length version, "SDEL") algorithm that approximates long-time dynamics. The order of the events and the intermediate states during pol beta's closing pathway are identified and compared to a separate study of pol beta using transition path sampling (TPS) (Radhakrishnan, R.; Schlick, T. Proc. Natl. Acad. Sci. USA 2004, 101, 5970-5975). Results highlight the cooperative and subtle conformational changes in the polp active site upon binding the correct substrate that may help explain DNA replication and repair fidelity. These changes involve key residues that differentiate the open from the closed conformation (Asp192, Arg258, Phe272), as well as residues contacting the DNA template/primer strand near the active site (Tyr271, Arg283, Thr-292, Tyr296) and residues contacting the beta and gamma phosphates of the incoming nucleotide (Ser180, Arg183, Gly189). This study compliments experimental observations by providing detailed atomistic views of the intermediates along the polymerase closing pathway and by suggesting additional key residues that regulate events prior to or during the chemical reaction. We also show general agreement between two sampling methods (the stochastic difference equation and transition path sampling) and identify methodological challenges involved in the former method relevant to large-scale biomolecular applications. Specifically, SDEL is very quick relative to TPS for obtaining an approximate path of medium resolution and providing qualitative information on the sequence of events; however, associated free energies are likely very costly to obtain because this will require both successful further refinement of the path segments close to the bottlenecks and large computational time.