Citation |
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Elowitz MB, Leibler S (2000)
A synthetic oscillatory network of transcriptional regulators. Nature.403 : 335 - 338. http:// www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v403/n6767/full/ 403335a0_fs.html |
Description |
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This file describes the deterministic version of the repressilator system. The authors of this model (see reference) use three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network that they called the repressilator. The model system was induced in Escherichia coli. In this system, LacI (variable X is the mRNA, variable PX is the protein) inhibits the tetracycline-resistance transposon tetR (Y, PY describe mRNA and protein). Protein tetR inhibits the gene Cl from phage Lambda (Z, PZ: mRNA, protein),and protein Cl inhibits lacI expression. With appropriate parameter values this system oscillates. The model is based upon the equations in Box 1 of the paper; however, these equations as printed are dimensionless, and the correct dimensions have been returned to the equations, and the parameters set to reproduce Figure 1C (left). |
The original Model was Generated by B.E. Shapiro using Cellerator Version 1.0 update 2.1127 using Mathematica 4.2 for Mac OS X (June 4, 2002), November 27, 2002 12:15:32, using (PowerMac,PowerPC, Mac OS X,MacOSX,Darwin)
Nicolas Le Novere: Corrected version generated by SBMLeditor on Sun Aug 20 00:44:05 BST 2006. Removal of EmptySet species. Ran fine on COPASI 4.0 build 18
Bruce Shapiro: Revised with SBML editor 23 October 2006 20:39 PST. Define default units and correct reactions. The original cellerator reactions while being mathematically correct did not accurately reflect the intent of the authors.' The original notes were mostly removed because they were mostly incorrect in the revised version. Tested with MathSBML 2.6.0
Nicolas Le Novere: changed the volume to 1 cubic micrometre, to allow for stochastic simulation.
Changed by Lukas Endler to use the average livetime of mRNA instead of its halflife and a corrected value of alpha and alpha0.
To clarify the equations used in this model:
The equations given in box 1 the original publication are rescaled in three respects (lowercase letters denote the rescaled, uppercase letters the unscaled number of molecules per cell):
promotor strength (repressed) (tps_repr): | 5*10^{-4} | transcripts/(promotor*s) |
promotor strength (full) (tps_active): | 0.5 | transcripts/(promotor*s) |
mRNA half life, τ_{1/2,mRNA}: | 2 | min |
protein half life, τ_{1/2,prot}: | 10 | min |
K_{M}: | 40 | monomers/cell |
Hill coefficient n: | 2 |
average mRNA lifetime (t_ave): | τ_{1/2,mRNA}/ln(2) | = 2.89 min |
mRNA decay rate (kd_mRNA): | ln(2)/ τ_{1/2,mRNA} | = 0.347 min^{-1} |
protein decay rate (kd_prot): | ln(2)/ τ_{1/2,prot} | |
transcription rate (a_tr): | tps_active*60 | = 29.97 transcripts/min |
transcription rate (repressed) (a0_tr): | tps_repr*60 | = 0.03 transcripts/min |
translation rate (k_tl): | eff*kd_mRNA | = 6.93 proteins/(mRNA*min) |
α : | a_tr*eff*τ_{1/2,prot}/(ln(2)*K_{M}) | = 216.4 proteins/(promotor*cell*Km) |
α_{0} : | a0_tr*eff*τ_{1/2,prot}/(ln(2)*K_{M}) | = 0.2164 proteins/(promotor*cell*Km) |
β : | k_dp/k_dm | = 0.2 |
To reproduce the simulations run published by the authors, the model has to be simulated with any of two different approaches. First, one could use a deterministic method (KISAO:0000035) with continuous variables (KISAO:0000018). One sample algorithm to use is the CVODE solver (KISAO:0000019). Second, one could simulate the system using Gillespie's direct method (KiSAO:0000029) - which is a stochastic method (KISAO:0000036) supporting adaptive timesteps (KISAO:0000041) and using discrete variables (KISAO:0000016).
This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2010 The BioModels.net Team.
For more information see the terms of use.
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.
lacI inhibitor
Tet repressor protein
lambda repressor
ratio of protein to mRNA decay rates
Leakiness in protein copies per promoter and cell
Protein copies per promoter and cell
Average number of proteins per transcript
Hill coefficient
Number of repressor molecules per cell giving half maximal repression, in monomers per cell
mRNA decay rate constant
Protein decay rate costant
Translation rate constant
Transcription rate from free promotor minus a0_tr
Transcrition from free promotor in transcripts per second and promotor
Transcrition from fully repressed promotor in transcripts per second and promotor
Transcription rate from fully repressed promotor