NOR Gate

Intro

NOR Gate is a genetic logic circuit, presented by Hasan Baig and Jan Madsen in [Baig2017].

The NOR Gate genetic circuit represents a gene regulatory network that is triggered by a combination of external input signals. More specifically, when LacI and/or TetR input proteins are present in significant amounts within the cell, they inhibit promoter P1 to produce 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 NOR Gate IBL file can be downloaded here.

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     define Cell typeof CELL() {

             // Species
             LacI = MOLECULE(concentration=0.0 molecules)
             TetR = MOLECULE(concentration=0.0 molecules)
             GFP = MOLECULE(concentration=0.0 molecules)
             P1 = MOLECULE(concentration=2.0 molecules)

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

             RULE Degradation_TetR : TetR ->
             Degradation_TetR.forwardRate = '0.0075*[TetR]'

             RULE Degradation_LacI : LacI ->
             Degradation_LacI.forwardRate = '0.0075*[LacI]'

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

             EVENT [LacI = 20 molecules] WHEN [TIME >= 120 s]

             EVENT [TetR = 20 molecules] WHEN [TIME >= 1300 s]
     }

     define nor 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: 1,800 seconds;
  • Interval: 10 seconds;
  • Number of runs: 10;

As depicted in the screenshot below, the result of the stochastic simulation shows that, after either one or both TetR and LacI inputs are triggered to 20 molecules (the high threshold), the GFP protein falls below the 20 molecules (high) threshold, with respect to a propagation delay of approximately 140 seconds. This result confirms the behaviour of the NOR gate.

The NOR Gate Simulation Results