The Repressilator

Introduction

The Repressilator is one the first implemented synthetic genetic circuits. It was developed by Michael B. Elowitz and Stanislas Leibler [Elowitz2000] . It has been used as a canonical example in synthetic biology in various P system studies [Gheorghe2009].

The Repressilator consists of three genes codifying three repressors. Namely, the operon lactose repressor, lacI, the repressor form the tetracycline transposon, tetR, and a repressor from the λ phage virus, cI. These genes are conected in a synthetic gene regulatory network such that LacI represses the expression of the tetR gene, which in turn represses the cI gene. Finally the cycle is closed as CI represses the expression of the lacI gene.

The Model

Our model of the Repressilator consists of a single bacterial cell modelled as a SP-system identified with the name repressilatorCell. The molecular interactions in this SP-system are defined in a modular manner by using the modules in the library basicLibrary:

libraryOfModules basicLibrary

   Const({X},{c_1},{l}) =
   {
       r1: [ geneX ]_l -c_1-> [ geneX + rnaX ]_l
   }

   CoopNegReg({X,Y},{c_1,c_2,c_3,c_4,c_5,c_6},{l}) =
   {
       r1: [ proteinX + geneY ]_l -c_1-> [ proteinX_geneY ]_l
       r2: [ proteinX_geneY ]_l -c_2-> [ proteinX + geneY ]_l
       r3: [ proteinX + proteinX_geneY ]_l -c_3-> [ proteinX2_geneY ]_l
       r4: [ proteinX2_geneY ]_l -c_4-> [ proteinX + proteinX_geneY ]_l
       r5: [ proteinX_geneY ]_l -c_5-> [ proteinX_geneY + rnaY ]_l
       r6: [ proteinX2_geneY ]_l -c_6-> [ proteinX2_geneY + rnaY ]_l
   }

   PostTransc({X},{c_1,c_2,c_3},{l}) =
   {
       r1: [ rnaX ]_l -c_1-> [ ]_l
       r2: [ rnaX ]_l -c_2-> [ rnaX + proteinX ]_l
       r3: [ proteinX ]_l -c_3-> [ ]_l
   }

endLibraryOfModules

The modules in this library model the following basic gene regulatory mechanisms:

• Const({X},{c_1},{l}): This module describes the constitutive expression of a gene $X$ which produces the corresponding messenger at a rate of c_1

SP-system:

SPsystem repressilatorCell

   alphabet
       geneCI
       geneLacI
       geneTetR
       proteinCI
       proteinCI2_geneLacI
       proteinCI_geneLacI
       proteinLacI
       proteinLacI2_geneTetR
       proteinLacI_geneTetR
       proteinTetR
       proteinTetR2_geneCI
       proteinTetR_geneCI
       rnaCI
       rnaLacI
       rnaTetR
   endAlphabet

   compartments
       bacterium
   endCompartments

   initialMultisets
      initialMultiset bacterium
         geneLacI      1
         geneCI         1
         geneTetR     1
      endInitialMultiset
   endInitialMultisets

   ruleSets
      ruleSet bacterium

         CoopNegReg({CI,LacI},{1,224,1,9,0.0005,0.0005},{bacterium}) from basicLibrary.plb
         Const({LacI},{0.5},{bacterium}) from basicLibrary.plb
         PostTransc({LacI},{0.00578,0.167,0.00116},{bacterium}) from basicLibrary.plb

         CoopNegReg({LacI,TetR},{1,224,1,9,0.0005,0.0005},{bacterium}) from basicLibrary.plb
         Const({TetR},{0.5},{bacterium}) from basicLibrary.plb
         PostTransc({TetR},{0.00578,0.167,0.00116},{bacterium}) from basicLibrary.plb

         CoopNegReg({TetR,CI},{1,224,1,9,0.0005,0.0005},{bacterium}) from basicLibrary.plb
         Const({CI},{0.5},{bact}) from basicLibrary.plb
         PostTransc({CI},{0.00578,0.167,0.00116},{bacterium}) from basicLibrary.plb

      endRuleSet
   endRuleSets
endSPsystem

Simulations