Wolfram Demonstrations Project

For the last twenty years, chemists have been searching for chemical self-replicating molecules. This Demonstration shows plots of the concentrations of a self-replicating molecule and its components according to a proposed model called the Templator model. The parameter

is the ratio between the external reactant influx and the enzymatic output maximum rate. Thus, it is always less than unity.

is the ratio between the uncatalyzed rate constant and the templator rate constant, so it measures the effectiveness of the catalyst. From experiments it is known that

is very small. Finally,

characterizes the enzymatic reaction that removes the templator from the reacting system.

Contributed by: Enrique Peacock-López

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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