Chemical Oscillations:
The Templator Model
Introduction
The Template model is a simplified version of the Rebek's experiments on self-replicating molecules. Also it has been modified to study DNA replications via a triple stranded complex. The simplified version due to Peacock-Lopez is discussed in the Chemical Educator.
Linear Stability Analysis
of the
Templator Model
MATHEMATICA Ver. 4.0
Template mechanism
Steady states
Jacobian or relaxation matrix
Minimal Template, ku = 0.
Steady States
Trace's zeros
Discriminat's zeros
Templator model
Steady states
Second order approximation
From our analytic study of the Templator
Brute Force Calculation of the trace's zeros
Comparison betwwen brute force and other methods
Some other figures for the Templator
Time series
ODE's
First we define the differential equations
![[Graphics:Images/templator_gr_129.gif]](Images/templator_gr_129.gif)
Second we define the substitution to use NDSolve
![[Graphics:Images/templator_gr_130.gif]](Images/templator_gr_130.gif)
Define the parameter values used inthe integration. Also we Plot the solutions
Trajectories
Final figures
Converted by Mathematica
November 14, 2000