Team:Imperial College/Model

This year our team created a mathematical representation of our Genetically Engineered Artificial Ratio (G.E.A.R.) system. This representation, or model, informed the wet lab on the timescales of the three modules of GEAR: communication, comparator and growth regulator. It also helped develop assembly strategies thanks to a thorough analysis of parameter scans and sensitivities. After a series of experiments in the wet lab, we were able to finesse our parameters making them more accurate. This process, presented below, can be seen as a continuous feedback between the wet lab and the dry lab of Ecolibrium.


We developed our models with two main goals in mind:

  1. We wanted our model to be able to aid the team in the wetlab. Especially for optimizing the assembly process and balancing the circuit.
  2. We wanted to develop an in silico version of our circuit at single cell and population level. This allowed us to test the viability of the system in both normal and abnormal conditions. It also allows us to plan future experiments and used for the system.

The following pages will show how we implemented modelling approaches to achieve our goals.


The Single Cell Model

  • Communication Module - We constructed the four quorum systems that we considered viable choices for our system (cin, rhl, lux and las)to allow us to directly compare the expected behaviour and plan our growth module experiments accordingly.
  • Comparator Module - We used RNAstruct developed by Matthews Lab to help aid the development of the ANTISTAR. We modeled STAR and ANTISTAR behaviour in silico
  • Growth Regulator Module - We modelled 4 different growth regulator systems in silico in order to assess the speed and effectiveness of each case.

Population Model
  • Matlab population model with GP2 growth regulation in two population
  • We used the GRO programming language to model a simplified version of our circuit with GP0.4 growth regulation into two populations of E.Coli.

Table 1: Universal Species Table
Species Name Description
C4 AHLs produced by RhlI synthase
C14 AHLs produced by CinI synthase
g_C4R Copy number for plasmid backbone housing C4R
mC4R mRNA for RhlR
C4R RhlR transcriptional regulator
C4Comp Complex by C4 AHL and RhlR transcriptional regulator
g_STARC4Comp Complex formed between plasmid backbone for STAR (pRhl) and c4 Comp
g_C14R Copy number for plasmid backbone housing C14R
mC14R mRNA for CinR
C14R CinR transcriptional regulator
C14Comp Complex by C14 AHL and CinR transcriptional regulator
g_ANTISTARC14Comp Complex formed between plasmid backbone for ANTISTAR (pCin) and C14 Comp
g_STAR Copy number for plasmid backbone housing STAR
STAR Short transcription activating RNA (STAR)
g_ANTISTAR Copy number for plasmid backbone housing ANTISTAR
ANTISTAR Anti Short transcription activating RNA (ANTISTAR)
STAR:ANTISTAR STAR:ANTISTAR Complex
STAR_Target Star Target plasmid (AD1 terminator)
Table 2: Unique Species for GP0.4 model Table
Species Name Description
g_GP0.4 Plasmid hosting STAR Target and growth regulating protein GP2
mGP0.4 mRNA for GP0.4
pre_GP0.4 Unfolded GP0.4
GP0.4 GP0.4 (Gene Product 0.4) sequesters FtsZ and stops cell division.
FtsZ FtsZ is a protein that influences cell division
GP0.4:FtsZ GP0.4:FtsZ Complex
Table 3: Unique Species for GP2 model Table
Species Name Description
g_GP2 Plasmid hosting STAR Target and growth regulating protein GP2
mGP2 mRNA for GP2
pre_GP2 Unfolded GP2
GP2 GP2 (Gene Product 2) sequesters RNA Polymerase
RNAP RNA Polymerase
GP2:RNAP GP2:RNAP Complex
Table 4: Unique Species for CAT and LeuB
Species Name Description
mTet mRNA for Tetracycline
Tet Tetracycline
pTet Promoter that is repressed by Tetracycline
Tet:pTet Tetracycline:pTet complex
mLeuB mRNA for Leucine B
LeuB Leucine B
mCAT mRNA for Chloramphenicol Acetyltransferase
CAT Chloramphenicol Acetyltransferase
Table 5: General Numbers Table
Parameter name Description Value Unit Source
Cell Volume 6.70E-16 L Neidhardt F.C. Escherichia coli and Salmonella: Cellular and Molecular Biology. Vol 1. pp. 15, ASM Press 1996.
Transcription rate 28 Nucleotides/s was used 28-89 Nucleotides/s Vogel U, Jensen KF. The RNA chain elongation rate in Escherichia coli depends on the growth rate. J Bacteriol. 1994 May176(10):2807-13 p.2811 table 2
Translation rate 12 Amino acid/s was used 12-21 Amino acids/s Bremer, H., Dennis, P. P. (1996) Modulation of chemical composition and other parameters of the cell by growth rate. Neidhardt, et al. eds. Escherichia coli and Salmonella typhimurium: Cellular and Molecular Biology, 2nd ed. chapter 97, p. 1559, Table 3
d_prot Protein degradation 1.39E-05 1/min Biomolecular Systems by Del Vecchio
k_mat Protein maturation rate 0.16 1/min Megerle JA, Fritz G, Gerland U, Jung K, Rädler JO. Timing and dynamics of single cell gene expression in the arabinose utilization system. Biophys J. 2008 Aug95(4):2103-15. p.2106 right column bottom of paragraph
D Dilution rate 0.048 1/min A synthetic Escherichia coli predator–prey ecosystem
d_mRNA mRNA degradation rate constant 0.139 1/min Taken from 5 min mRNA degradation time
Copy number for 3K3 and 3C3 Copy number 20-30 molecules http://parts.igem.org/Part:pSB3K3
Copy number for 1K3 and 1C3 Copy number 100-300 molecules http://parts.igem.org/Part:pSB1C3
Table 6: Quorum Module Numbers Table
Parameter name Description Value Unit Source
k_C4 Rhl/C4 Production Rate Constant
  • 8.00E-07
  • 5.36E-13
  • 5.36E-22
  • 3.22E02
  • M/min
  • nMol/min
  • mol/min
  • molecules/min
 Optimal tuning of bacterial sensing potential - Anand Pai & Lingchong You
k_C14 Cin/C14 Production Rate Constant
  • 5.00E-08
  • 3.35E-14
  • 3.35E-23
  • 2.00E01
  • M/min
  • nMol/min
  • mol/min
  • molecules/min
 Optimal tuning of bacterial sensing potential - Anand Pai & Lingchong You
k_mC4R Transcription rate of C4R
  • 2.23
  • 5.51E-09
  • 3.69E-24
  • mRNA/min
  • nMol/min
  • Mol/min
 Calculated from Bionumbers average transcription rate - RNA polymerase transcription
k_mC14R Transcription rate of C14R
  • 2.23
  • 3.69E-15
  • 3.69E-24
  • mRNA/min
  • nMol/min
  • Mol/min
 Calculated from Bionumbers average transcription rate - RNA polymerase transcription
k_C4R Translation rate of C4R
  • 2.99
  • 4.96E-24
  • Protein/min
  • Mol/min
 Calculated from Bionumbers average translation rate : Bremer et al
k_C14R Translation rate of C14R
  • 2.99
  • 4.96E-24
  • Protein/min
  • Mol/min
 Calculated from Bionumbers average translation rate : Bremer et al
kf_C4Comp C4 - C4R Complex formation
  • 1.00E08
  • 2.50E-01
  • 1/M.min
  • 1/complexes.min
 Dynamics of quorum sensing switch - Weber
kr_C4Comp C4:C4R Complex dissassociation 10 1/min Dynamics of quorum sensing switch - Weber
kf_C14Comp C4 - C4R Complex formation
  • 1.00E08>/sup>
  • 2.50E-01
  • 1/M.min
  • 1/complexes.min
 Dynamics of quorum sensing switch - Weber
kr_C14Comp C4:C4R Complex dissassociation 10 1/min Dynamics of quorum sensing switch - Weber
kf_DimC4 C4:C4R complex dimerization 5.00E07 M/min Dynamics of quorum sensing switch - Weber
kr_DimC4 C4:C4R complex reverse dimerization 1 1/min Dynamics of quorum sensing switch - Weber
kf_DimC14 C14:C14R complex dimerization 5.00E07 M/min Dynamics of quorum sensing switch - Weber
kr_DimC14 C14:C14R complex reverse dimerization 1 1/min Dynamics of quorum sensing switch - Weber
d_C4 C4 degradation rate constant 2.21E-04 1/min Optimal tuning of bacterial sensing potential - Anand Pai & Lingchong You
d_C14 C14 degradation rate constant 2.83E-04 1/min Optimal tuning of bacterial sensing potential - Anand Pai & Lingchong You
d_C4R C4R degradation rate constant 0.002 1/min Optimal tuning of bacterial sensing potential - Anand Pai & Lingchong You
d_C14R C14R degradation rate constant 0.002 1/min Optimal tuning of bacterial sensing potential - Anand Pai & Lingchong You
Table 7: STAR Module Numbers Table
Parameter name Description Value Unit Source
kf_gSTARC4Comp gSTAR-C4 comple association 0.25 1/molecules.min Assumed same as quorum complex formation
kr_gSTARC4Comp gSTAR-C4 complex disassociation 10 1/min Assumed same as quorum complex formation
kf_gANTISTARC14Comp gANTISTAR-C14 complex association 0.25 1/molecules.min Assumed same as quorum complex formation
kr_gANTISTARC14Comp gANTISTAR - C14 complex disassociation 10 1/min Assumed same as quorum complex formation
k_STAR Basal Rate of STAR production (without C4:C4R induction)
  • 1.91E-01
  • 3.08E-23
  • mRNA/min
  • mol/min
 Calculated from Bionumbers average transcription rate - RNA polymerase transcription
k_iSTAR Rate of STAR production (after induction of C4:C4R)
  • 18.57
  • 3.08E-23
  • mRNA/min
  • mol/min
 Calculated from Bionumbers average transcription rate - RNA polymerase transcription
k_ANTISTAR Basal Rate of ANTISTAR production (without C14:C14R induction) 1.91E-01 mRNA/min Calculated from Bionumbers average transcription rate - RNA polymerase transcription
k_iANTISTAR Rate of ANTI STAR production (after induction of C14:C14R) 18.57 mRNA/min Calculated from Bionumbers average transcription rate - RNA polymerase transcription
kf_STARANTISTAR STAR:ANTISTAR complex formation 62 complexes/min Calculated using DNA strand displacement (Winfree et al)
kr_STARANTISTAR STAR:ANTISTAR complex dissociation 2 1/min Calculated using DNA strand displacement (Winfree et al)
kf_STARAD1 STAR:AD1 Complex formation 62 complexes/min Calculated using DNA strand displacement (Winfree et al)
kr_STARAD1 STAR:AD1 Complex dissociation 2 1/min Calculated using DNA strand displacement (Winfree et al)
Table 8: Gp0.4 Module Numbers Table
Parameter name Description Value Unit Source
k_mGP0.4 Transcription of mGP0.4 before STAR induction 0.086 mRNA/min Calculated from Bionumbers average transcription rate - RNA polymerase transcription
k_imGP0.4 Transcription of mGP0.4 after STAR induction 8.08 mRNA/min Calculated from Bionumbers average transcription rate - RNA polymerase transcription
kf_GP0.4Ftsz GP0.4:Ftsz complex formation 9.44E03 1/molecules.min
kr_GP0.4Ftsz GP0.4:Ftsz complex dissociation 30 1/min
k_GP0.4 Translation of GP0.4 13.86 Protein/min Calculated from Bionumbers average translation rate : Bremer et al
Table 9: Tet Module Numbers Table
Parameter name Description Value Unit Source
k_mTET Basal transcription of TET 0.028 mRNA/min Calculated from experimental results for STAR activation (94 fold activation)
k_imTET Induced transcription of TET 2.7 mRNA/min
k_TET:pTET TET:pTET complex formation 120 1/molecules.min https://2009.igem.org/Team:Aberdeen_Scotland/parameters/invest_1
k_-TET:pTET TET:pTET complex dissassociation 8.40E05 1/min https://2009.igem.org/Team:Aberdeen_Scotland/parameters/invest_1
Table 10: LeuB Module Numbers Table
Parameter name Description Value Unit Source
k_mLeuB Basal transcription of LeuB transcription 1.538 mRNA/min Calculated from Bionumbers average transcription rate - RNA polymerase transcription
k_imLeuB Induced transcription of LeuB transcription 0.015 mRNA/min 99% Repression from tet was assumed
k_LeuB Translation of LeuB 0.0218 molecule/min http://biocyc.org/gene?orgid=ECOLI&id=3-ISOPROPYLMALDEHYDROG-MONOMER#tab=FTRS
Table 11: CAT Module Numbers Table
Parameter name Description Value Unit Source
k_mCAT Basal transcription of CAT transcription 1.875 mRNA/min Calculated from Bionumbers average transcription rate - RNA polymerase transcription
k_imCAT Induced transcription of CAT transcription 0.018 mRNA/min 99% Repression from CAT was assumed
k_CAT Translation of CAT 0.03568 molecule/min http://www.uniprot.org/uniprot/P62577
Table 12: GP2 Module Numbers Table
Parameter name Description Value Unit Source
k_mGP2 Transcription of mGP2 before STAR induction - Basal 0.07 mRNA/min Calculated using 94 fold activation
k_imGP2 Transcription of mGP2 after STAR induction (7.2 kDa) 6.56 mRNA/min Calculated from Bionumbers average transcription rate - RNA polymerase transcription
k_GP2RNAP GP2:RNAP complex formation 1/Mole.min Intracellular Kinetics of a Growing Virus: A Genetically Structured Simulation for Bacteriophage T7
k_-GP2RNAP GP2:RNAP complex dissociation 1/min Intracellular Kinetics of a Growing Virus: A Genetically Structured Simulation for Bacteriophage T7
k_GP2 Translation of GP2 11.2 Protein/min Intracellular Kinetics of a Growing Virus: A Genetically Structured Simulation for Bacteriophage T7
RNA Total RNA pol 1800 molecules/cell Intracellular Kinetics of a Growing Virus: A Genetically Structured Simulation for Bacteriophage T7
k_mRNAP Transcription of RNA pol 2400 nucleotides/min.RNAP Intracellular Kinetics of a Growing Virus: A Genetically Structured Simulation for Bacteriophage T7