  Describing the kinetics of polymer reactions, such as the formation of loops
and hairpins in nucleic acids or polypeptides, is complicated by the structural
dynamics of their chains. Although both intramolecular reactions, such as
cyclization, and intermolecular reactions have been studied extensively, both
experimentally and theoretically, there is to date no exact explicit analytical
treatment of transport-limited polymer reaction kinetics, even in the case of
the simplest (Rouse) model of monomers connected by linear springs. We
introduce a new analytical approach to calculate the mean reaction time of
polymer reactions that encompasses the non-Markovian dynamics of monomer
motion. This requires that the conformational statistics of the polymer at the
very instant of reaction be determined, which provides, as a by-product, new
information on the reaction path. We show that the typical reactive
conformation of the polymer is more extended than the equilibrium conformation,
which leads to reaction times significantly shorter than predicted by the
existing classical Markovian theory.
