Templator Model of Chemical Self-Replication
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
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 (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
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.
Permanent Citation
Hopf Bifurcation in the Brusselator
Judit Várdai and János Tóth
Reactor Steady States
Brian G. Higgins
Chemical Reactions Described by the Lorenz Equations
Clay Gruesbeck
Simple Arrhenius Model for Activation Energy and Catalysis
S. M. Blinder
Simulation of a Simple Gas Pressure Model
Jon McLoone
Estimating Kinetic Parameters from a Batch Reactor Experiment
Housam Binous, Ahmed Bellagi, and Brian G. Higgins
Cubic Autocatalysis by Successive Bimolecular Steps
Brian G. Higgins and Housam Binous
Polymerization in a Batch Reactor
Rachael L. Baumann and Nathan S. Nelson
Idealized Belousov-Zhabotinsky Reaction
Luca Zammataro
Generalized Arrhenius Function
Georgii Alexandrov
