The Repressilator

Intro

The Repressilator is a seminal early-implemented synthetic genetic circuit, developed by Michael B. Elowitz and Stanislas Leibler [Elowitz2000].

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 connected 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. Thus, the repressilator consists of mutually repressing repressors and, as a result, none of the promoter activation states remains stable and the operons sequentially activate and inactivate each other - resulting in continued global oscillations.

IBL Modelling

Outlined below is the IBL model for the Repressilator circuit, while the corresponding IBL file can be downloaded here.

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     define RepressilatorCell typeof CELL()
     {
             Plac    = PROMOTER(URI="http://parts.igem.org/Part:BBa_R0010")
             Plambda = PROMOTER(URI="http://parts.igem.org/Part:BBa_R0051")
             Ptet    = PROMOTER(URI="http://parts.igem.org/Part:BBa_R0040")

             cI      = GENE(URI="http://parts.igem.org/Part:BBa_K105004")
             lacI    = GENE(URI="http://parts.igem.org/Part:BBa_C0012")
             tetR    = GENE(URI="http://parts.igem.org/Part:BBa_C0040")
             gfp     = GENE(URI="http://parts.igem.org/Part:BBa_E0040")

             LacI   = PROTEIN()
             CI     = PROTEIN()
             TetR   = PROTEIN()
             GFP    = PROTEIN()

             RULE lac_dimerization : LacI + LacI <-> LacI~LacI
             lac_dimerization.forwardRate = 1e0 min-1
             lac_dimerization.backwardRate = 125 min-1

             RULE cI_dimerization : CI + CI <-> CI~CI
             cI_dimerization.forwardRate = 1e0 min-1
             cI_dimerization.backwardRate = 125 min-1

             RULE tetR_dimerization : TetR + TetR <-> TetR~TetR
             tetR_dimerization.forwardRate = 1e0 min-1
             tetR_dimerization.backwardRate = 125 min-1

             // cI degradation
             RULE cI_degradation : CI ->
             cI_degradation.forwardRate = 13.2e-1 min-1

             // LacI degradation
             RULE lac_degradation : LacI ->
             lac_degradation.forwardRate = 13.2e-1 min-1

             // TetR degradation
             RULE tetR_degradation : TetR ->
             tetR_degradation.forwardRate = 13.2e-1 min-1

             // GFP degradation
             RULE gfp_degradation : GFP ->
             gfp_degradation.forwardRate = 13.2e-2 min-1 // 13.216397448e-3 min-1 from Gardner data // 2.5e-2 min-1 // from Andersen et al. Appl Env Microbiol (1998) 64(6):2240-2246

             operon1 = DEVICE(
                     parts=[Plac,tetR],
                     input=[LacI~LacI],
                     output=[TetR]
             )
             {
                     rna = RNA()

                     // repression
                     RULE repression : Plac + LacI~LacI <-> Plac~LacI~LacI
                     repression.forwardRate = 1e0 min-1
                     repression.backwardRate = 10 min-1

                     // transcription
                     RULE transcription : Plac -> Plac + rna
                     transcription.forwardRate = 1.e0 min-1

                     // translation
                     RULE translation : rna -> rna + TetR
                     translation.forwardRate = 100 min-1

                     // rna degradation
                     RULE rna_degradation : rna ->
                     rna_degradation.forwardRate = 1e-1 min-1
             }

             operon_2 = DEVICE(
                     parts=[Plambda,lacI],
                     input=[CI~CI],
                     output=[LacI]
             )
             {
                     rna = RNA()

                     // repression
                     RULE repression : Plambda + CI~CI <-> Plambda~CI~CI
                     repression.forwardRate = 1e0 min-1
                     repression.backwardRate = 10 min-1

                     // transcription
                     RULE transcription : Plambda -> Plambda + rna
                     transcription.forwardRate = 1.e0 min-1

                     // translation
                     RULE translation : rna -> rna + LacI
                     translation.forwardRate = 100 min-1

                     // rna degradation
                     RULE rna_degradation : rna ->
                     rna_degradation.forwardRate = 1e-1 min-1
             }

             operon_3 = DEVICE(
                     parts=[Ptet,cI],
                     input=[TetR~TetR],
                     output=[CI]
             ) {
                     rna = RNA()

                     // repression
                     RULE repression : Ptet + TetR~TetR <-> Ptet~TetR~TetR
                     repression.forwardRate = 1e0 min-1
                     repression.backwardRate = 10 min-1

                     // transcription
                     RULE transcription : Ptet -> Ptet + rna
                     transcription.forwardRate = 1.e0 min-1

                     // translation
                     RULE translation : rna -> rna + CI
                     translation.forwardRate = 100 min-1

                     // rna degradation
                     RULE rna_degradation : rna ->
                     rna_degradation.forwardRate = 1e-1 min-1
             }
     }

     define site typeof REGION() {
             CELL cell = new RepressilatorCell()
     }

Simulation

In order to analyse the trends in the concentration of the various molecular species, stochastic simulation has been performed, using the following parameters:

  • Max Time: 97,200 seconds (27 hours);
  • Interval: 500 seconds;
  • Number of runs: 5;
  • Gillespie algorithm: Tau Leaping

As depicted in the screenshot below, the result of the stochastic simulation confirms continued oscillations of the regulating proteins LacI (yellow), CI (green) and TetR (red):

The Repressilator Simulation Results

Verification

Given below is a series of properties that have been used for validating the system behaviour:

  1. The LacI concentration repeatedly falls below 1.25 uM, with a probability of 56%;
  2. The LacI concentration repeatedly rises over 1.25 uM, with a probability of 61%;
  3. The steady state concentration of CI is between 0.1 uM and 2 uM, with a probability of 96%.
# Verification Statement Result
1 VERIFY [LacI <= 1.25 uM] HOLDS INFINITELY OFTEN WITH PROBABILITY ? 0.56
2 VERIFY [LacI > 1.25 uM] HOLDS INFINITELY OFTEN WITH PROBABILITY ? 0.61
3 VERIFY [[CI >= 0.1 uM] AND [CI < 2 uM]] HOLDS IN STEADY-STATE WITH PROBABILITY ? 0.96

Biocompilation

Depicted below is the biocompilation result of the Repressilator model:

The Repressilator Biocompilation Results