Templating aggregation

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 m(t) and the density c(t) of all clusters heavier than monomers decay with time as c∼m^{2}∼t^{-2/3}. These strongly contrast with the corresponding behaviors in conventional aggregation, where c∼m^{1/2}∼t^{-1}. We also 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 does not occur.