AND Gate

Intro

AND Gate is a genetic logic circuit, presented by Hasan Baig and Jan Madsen in [Baig2017].

The AND Gate genetic circuit represents a gene regulatory network that is triggered by a combination of external input signals. More specifically, P1 and P2 are promoters, which are the regions of DNA that initiate the process of transcription of a particular gene. When the LacI and TetR input proteins are present in significant amounts within the cell, they inhibit promoters P1 and P2 to produce the output gene CI. When the concentration of CI falls below a certain level, promoter P3 is activated and produces the output protein GFP (green fluorescent protein).

IBL Modelling

Outlined below is the resulted IBL representation, after importing the corresponding SBML model into IBW. The AND Gate IBL file can be downloaded here.

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     define Cell typeof CELL() {

             // Species
             CI = MOLECULE(concentration=20.0 molecules)
             LacI = MOLECULE(concentration=0.0 molecules)
             GFP = MOLECULE(concentration=30.0 molecules)
             TetR = MOLECULE(concentration=0.0 molecules)
             Promoter_GFP = MOLECULE(concentration=2.0 molecules)
             P1 = MOLECULE(concentration=4.0 molecules)
             P3 = MOLECULE(concentration=2.0 molecules)
             P3_mRNA = MOLECULE(concentration=0.0 molecules)
             P2 = MOLECULE(concentration=2.0 molecules)

             // Rules
             RULE Degradation_GFP : GFP ->
             Degradation_GFP.forwardRate = '0.0075*[GFP]'

             RULE Degradation_CI : CI ->
             Degradation_CI.forwardRate = '0.0075*[CI]'

             RULE R_abstracted_production_P1 :  -> CI + CI + CI + CI + CI + CI + CI + CI + CI + CI
             R_abstracted_production_P1.forwardRate = '0.05*4.0*0.033*30.0/((1+0.033*30.0)+(0.5*[LacI])^2.0)'

             RULE R_abstracted_production_P2 :  -> CI + CI + CI + CI + CI + CI + CI + CI + CI + CI
             R_abstracted_production_P2.forwardRate = '0.05*2.0*0.033*30.0/((1+0.033*30.0)+(0.5*[TetR])^2.0)'

             RULE R_abstracted_production_Promoter_GFP :  -> GFP + GFP + GFP + GFP + GFP + GFP + GFP + GFP + GFP + GFP
             R_abstracted_production_Promoter_GFP.forwardRate = '0.05*2.0*0.033*30.0/((1+0.033*30.0)+(0.5*[CI])^2.0)'

             EVENT [TetR = 15 molecules] WHEN [TIME >= 250.0 s]

             EVENT [TetR = 0 molecules] WHEN [TIME >= 450.0 s]

             EVENT [LacI = 15 molecules] WHEN [TIME >= 475.0 s]

             EVENT [LacI = 0 molecules] WHEN [TIME >= 1175.0 s]

             EVENT [LacI = 15 molecules] WHEN [TIME >= 1250.0 s]

             EVENT [TetR = 15 molecules] WHEN [TIME >= 1375.0 s]
     }

     define and typeof REGION () {
             CELL Cell = new Cell()
     }

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: 2,400 seconds;
  • Interval: 10 seconds;
  • Number of runs: 10;

As depicted in the screenshot below, the result of the stochastic simulation shows that, after both TetR and LacI inputs are triggered to 15 molecules (the high threshold), the GFP protein exceeds the 15 molecules (high) threshold, with respect to a propagation delay of approximately 700 seconds. This result confirms the behaviour of the AND gate.

The AND Gate Simulation Results