Templating Aggregation

We introduce an aggregation process based on \emph{templating}, where a specified number of constituent clusters must assemble on a larger aggregate, which serves as a scaffold, 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 aggregates undergo in irreversible aggregation with mass-independent rates. In the mean-field approximation, templating aggregation has unusual kinetics in which the cluster and monomer densities, $c(t)$ and $m(t)$ respectively, decay with time as $c\sim m^2\sim t^{-2/3}$. These starkly contrast to the corresponding behaviors in conventional aggregation, $c\sim \sqrt{m}\sim t^{-1}$. We then treat three natural extensions of templating: (a) the reaction in which $L$ monomers meet and react on an $L$-mer scaffold to create two $L$-mers, (b) multistage scaffold reactions, and (c) templated ligation, in which clusters of all masses serve as scaffolds and binary aggregation is absent.