The Templator model is governed by the equations
. Modified ribozyme ligases show growth rates that depend linearly on the concentration of the self-replicator. The Templator model considers this particular behavior and includes a quadratic reactant dependence (
). Therefore, a mechanist's step could be represented as
. Finally, the system is coupled with an enzymatic removal. As a result, the model shows periodic changes in the concentrations, commonly called limit cycles. The
terms are necessary but not sufficient for the existence of a limit cycle. The last term in the second equation represents an enzymatic removal of the self-replicating structure, and it is necessary for complex behavior. For some values of
, there is an interval of
values that show the periodic behavior.
In Rebek's experiments
might represent the scaled concentrations of adenine ribose (AR) and/or biphenyl imide (BI), which are the components of the self-replicating molecule ARBI represented by
. In the case of Joyce's ribozyme system,
are the scaled concentrations of RNAs in units of micro molar.