Repressilator
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
This Demonstration implements a mathematical model of the "repressilator" gene network. The repressilator consists of three genes, each of which represses the following gene. Because of the odd number of components in the circuit, there is a net negative feedback, which can give rise to oscillatory behavior (i.e. a limit cycle) for certain parameter values. The behavior can be visualized either as a function of time or in concentration phase space, where the three coordinates of each point represent the three repressor concentrations at a particular time.
Contributed by: Simon Mochrie (May 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The repressilator was described and implemented in E. coli in [1]. A simplified version of Elowitz and Leibler's mathematical model is implemented here; we omit consideration of mRNA and focus exclusively on the protein (repressor) concentrations. The parameters of this implementation are: the ratio 
of the repressor production rate at a concentration of 1 to the repressor degradation rate, and the Hill function exponent 
, which specifies the cooperativity of the repressor activity. It is possible to show that sustained oscillations occur for values of 
approximately greater than 
. This implies that sustained oscillations can be achieved at small values of 
for large values of 
, but only at large values of 
for smaller values of 
. Interestingly, it is not possible to achieve sustained oscillations at all for 
, irrespective of the values of 
, which is borne out in the Demonstration.
Reference
[1] M. B. Elowitz and S. Leibler, "A Synthetic Oscillatory Network of Transcriptional Regulators," Nature, 403, 2000 pp. 335–338.
Permanent Citation
"Repressilator"
http://demonstrations.wolfram.com/Repressilator/
Wolfram Demonstrations Project
Published: May 2 2011
Marcus Theory for Electron Transfer in Photosystem II
Rebecca Brown and Aaron Walker
Factors Affecting Blood Flow
Juliet Foote and Mihir Surapaneni
Transdermal Drug Delivery by Diffusion
Benjamin Pinsky and Elizabeth Le
Diffusion of Oxygen through the Placenta
Colleen Tacubao, Patrick Chen and Hazel Wong
Steady-State Operation of the Cardiovascular System
Christopher B. Arena
Windkessel Model for Hemodynamics in Arterial Systems
Mikel Landajuela
Heart Electrophysiology
Mikel Landajuela
Effect of Altitude on Alveolar Oxygen Pressure
Natalie Gurevich and Kaitlyn Kuder
Hair and Relative Humidity
Anna Kang, Elaine Kim and Jong Hyun Lee
Diffusion of Oxygen Molecules across a Membrane Using Fick's Law
Neha Paruchuri and Carla Obeid
