Pulse Generator¶
Introduction¶
The pulse generator example consists of the synthetic bacterial colony designed by Ron Weiss’ group in [Basu2005]. This model implements the propagation of a wave of gene expression in a bacterial colony. The complete model can be downloaded from this link.
The pulse generator consists of two different bacterial strains, sender cells and pulsing cells:
- Sender cells contain the gene luxI from Vibrio fischeri. This gene codifies the enzyme LuxI responsible for the synthesis of the molecular signal 3OC6-HSL. The luxI gene is expressed constitutively under the regulation of the promoter PLtetO1 from the tetracycline resistance transposon.
- Pulsing cells contain the luxR gene from Vibrio fischeri that codifies the 3OC6-HSL receptor protein LuxR. This gene is under the constitutive expression of the promoter PluxL from Vibrio fischeri. It also contains the gene cI from lambda phage codifying the repressor CI under the regulation of the promoter PluxR that is activated upon binding of the transcription factor LuxR_3OC6_2. Finally, this bacterial strain carries the gene GFP that codifies the green fluorescent protein under the regulation of the synthetic promoter PluxPR combining the Plux promoter (activated by the transcription factor LuxR_3OC6_2) and the PR promoter from lambda phage (repressed by the transcription factor CI).
The Model¶
Our model of the Pulse Generator uses a module library describing the regulation of the different promoters used in the two bacterial strains. This library is presented below:
# This module library describes the regulation of the gene promoters used in the #
# pulse generator circuit developed by Ron Weiss' group #
libraryOfModules promoterLibrary
# This module represents the constitutive expression of a gene X under the regulation #
# of the promoter PLtetO1 from the tetracycline resistance transposon #
PLtetO1({X},{c_1},{l}) =
{
rules:
r1: [ PLtetO1_geneX ]_l -c1-> [ PLtetO1_geneX + rnaX_RNAP ]_l
}
# This module represents the constitutive expression of a gene X under the regulation #
# of the promoter PluxL from Vibrio fischeri #
PluxL({X},{c_1},{l}) =
{
rules:
r1: [ PluxL_geneX ]_l -c1-> [ PluxL_geneX + rnaX_RNAP ]_l
}
# This module represents the positively regulated expression of a gene X under the control #
# of the promoter PluxR which is activated by LuxR_2 #
PluxR({X},{c_1, c_2, c_3},{l}) =
{
rules:
r1: [ LuxR2 + PluxR_geneX ]_l -c_1-> [ PluxR_LuxR2_geneX ]_l
r2: [ PluxR_LuxR2_geneX ]_l -c_2-> [ LuxR2 + PluxR_geneX ]_l
r3: [ PluxR_LuxR2_geneX ]_l -c_3-> [ PluxR_LuxR2_geneX + rnaX_RNAP ]_l
}
# This module represents the positivele/negatively regulated expression of a gene X under the control #
# of the synthetic promoter PluxPR that combines the activation by LuxR2 with the repression by CI2 #
PluxPR({X},{c_1,c_2,c_3,c_4,c_5,c_6,c_7,c_8,c_9},{l}) =
{
rules:
r1: [ LuxR2 + PluxPR_geneX ]_l -c_1-> [ PluxPR_LuxR2_geneX ]_l
r2: [ PluxPR_LuxR2_geneX ]_l -c_2-> [ LuxR2 + PluxPR_geneX ]_l
r3: [ LuxR2 + PluxPR_CI2_geneX ]_l -c_3-> [ PluxPR_LuxR2_CI2_geneX ]_l
r4: [ PluxPR_LuxR2_CI2_geneX ]_l -c_4-> [ LuxR2 + PluxPR_CI2_geneX ]_l
r5: [ CI2 + PluxPR_geneX ]_l -c_5-> [ PluxPR_CI2_geneX ]_l
r6: [ PluxPR_CI2_geneX ]_l -c_6-> [ CI2 + PluxPR_geneX ]_l
r7: [ CI2 + PluxPR_LuxR2_geneX ]_l -c_7-> [ PluxPR_LuxR2_CI2_geneX ]_l
r8: [ PluxPR_LuxR2_CI2_geneX ]_l -c_8-> [ CI2 + PluxPR_LuxR2_geneX ]_l
r9: [ PluxPR_LuxR2_geneX ]_l -c_9-> [ PluxPR_LuxR2_geneX + rnaX_RNAP ]_l
}
endLibraryOfModules
An additional module library describing several post-transcriptional regulatory mechanisms is also used in our model:
# This module library describes some general post-transcriptional regulatory mechanisms #
libraryOfModules postTrasncriptionalRegulation
# This module represents transcription termination, translation, rna and protein degradation #
PostTransc({X},{c_1,c_2,c_3,c_4,c_5},{l}) =
{
rules:
r1: [ rnaX_RNAP ]_l -c_1-> [ rnaX ]_l
r2: [ rnaX ]_l -c_2-> [ rnaX + proteinX_Rib ]_l
r3: [ rnaX ]_l -c_3-> [ ]_l
r4: [ proteinX_Rib ]_l -c_4-> [ proteinX ]_l
r5: [ proteinX ]_l -c_5-> [ ]_l
}
# This module represents the dimerisation of a protein X #
Dim({X,Y},{c_1,c_2},{l}) =
{
rules:
r1: [ proteinX + proteinX ]_l -c_1-> [ Y ]_l
r2: [ Y ]_l -c_2-> [ ]_l
}
# This module represents the dimerisation of a protein X in the presence of a signal S #
DimSig({X,S,Y},{c_1,c_2,c_3,c_4},{l}) =
{
rules:
r1: [ proteinX + signalS ]_l -c_1-> [ proteinX_S ]_l
r2: [ proteinX_S ]_l -c_2-> [ ]_l
r3: [ proteinX_S + proteinX_S ]_l -c_3-> [ Y ]_l
r4: [ Y ]_l -c_4-> [ ]_l
}
# This module represents the free diffusion of a singal X in a rectangular latice #
Diffusion({X},{c_1},{l}) =
{
rules:
r1: [ signalX ]_l =(1,0)=[ ] -c_1-> [ ]_l =(1,0)=[ signalX ]
r2: [ signalX ]_l =(-1,0)=[ ] -c_1-> [ ]_l =(-1,0)=[ signalX ]
r3: [ signalX ]_l =(0,1)=[ ] -c_1-> [ ]_l =(0,1)=[ signalX ]
r4: [ signalX ]_l =(0,-1)=[ ] -c_1-> [ ]_l =(0,-1)=[ signalX ]
}
endLibraryOfModules
The two different bacterial strains, sender cells and pulsing cells, are represented using the following two SP-system models:
SPsystem senderCell
alphabet
Pconst_geneLuxI
proteinLuxI
proteinLuxI_Rib
rnaLuxI
rnaLuxI_RNAP
signal3OC6
endAlphabet
compartments
cell
endCompartments
initialMultisets
initialMultiset cell
Pconst_geneLuxI 1
endInitialMultiset
endInitialMultisets
ruleSets
ruleSet cell
Pconst({LuxI},{0.001},{cell}) from promoterLibrary.plb
PostTransc({LuxI},{3.36,0.0667,0.004,3.78,0.0667},{cell}) from promoterLibrary.plb
r1: [ proteinLuxI ]_cell -c1-> [ proteinLuxI + signal3OC12 ]_cell c1 = 5
Diffusion({3OC6},{2},{cell}) from postTranscriptional.plb
r2: [ signal3OC12 ]_cell =(1,0)=[ ] -c2-> [ ]_cell =(1,0)=[ signal3OC12 ] c2 = 2
r3: [ signal3OC12 ]_cell =(-1,0)=[ ] -c3-> [ ]_cell =(-1,0)=[ signal3OC12 ] c3 = 2
r4: [ signal3OC12 ]_cell =(0,1)=[ ] -c2-> [ ]_cell =(0,1)=[ signal3OC12 ] c4 = 2
r5: [ signal3OC12 ]_cell =(0,-1)=[ ] -c2-> [ ]_cell =(0,-1)=[ signal3OC12 ] c5 = 2
endRuleSet
endRuleSets
endSPsystem
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
