Krapivsky, P. L. and S. Redner
We introduce an aggregation process that is based on templating, where a specified number of constituent clusters must assemble on a larger scaffold aggregate for a reaction to occur. A simple example is a dimer scaffold, upon which two monomers meet and create another dimer, while dimers and larger clusters irreversibly join at mass-independent rates. In the mean-field approximation, templating aggregation has unusual kinetics in which the monomer density ?(?) and the density ?(?) of all clusters heavier than monomers decay with time as ?∼?2∼?−2/3. These strongly contrast with the corresponding behaviors in conventional aggregation, where ?∼?1/2∼?−1. We also treat three natural extensions of templating: (a) the reaction in which ? monomers meet and react on an ?-mer scaffold to create two ?-mers, (b) multistage scaffold reactions, and (c) templated ligation, in which clusters of all masses serve as scaffolds and binary aggregation do