Templator Model of Chemical Self-Replication

The Templator model is governed by the equations and . 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, and are the scaled concentrations of RNAs in units of micro molar.

For more information see:

E. Peacock-Lopez, "Chemical Oscillations: The Templator Model," The Chemical Educator, 6(4), 2001 pp. 202-209.

K. M. Beutel and E. Peacock-Lopez, "Chemical Oscillations and Turing Patterns in a Generalized Two-Variable Model of Chemical Self-Replication," Journal of Chemical Physics, 125(2), 2006 pp. 024908 1-7.

J. Rebek Jr., "Synthetic Self-Replicating Molecules," Scientific American, 271(1), 1994.

N. Paul and G. F. Joyce, "A Self-Replicating Ligase Ribozyme," Proceedings of the National Academy of Science, 99(20), 2002 pp. 12733-12740.