Team:KULeuven/Modeling

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KULeuven iGEM 2011

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overview     Freeze     Antifreeze     Cell Death


Modeling Overview


1. Description of the whole system

To make predictions for are plasmid transformed E.coli, a structured segregated model is designed in Simbiology. A graphical representation of the model was build in the block diagram editor . Afterwards reaction equations and parameters were added. We designed one model for the whole system and 3 models for 3 subsystems. The 3 subsystems are antifreeze, freeze and cell death. For more information about these 3 subsystems, we refer to the extended project description and the 3 modelling pages: freeze, antifreeze and cell death.


2. Full Model

There are in total 5 different kinetic equations we used in the model Transcription equation For most promoters, hill kinetics is used, it is a way of quantitatively describing cooperative binding processes, it was developed for hemoglobin in 1913. A Hill coefficient (n) is a measure for the cooperativity. Translation equation RNA degradation Protein degration Assimiliation FULL MODEL

3. Simulation tests

In the table below the parameters for our full model are displayed. However it was hard to find accurate parameters, because databases for kinetic parameters are limiting.

The parameters used in this model are:

Parameter Value Description Reference
0 NA Notation convention
dRNA_LuxR 0.00227 did not find this value [1]
dLuxR 1e-3 - 1e-4 [per sec+D4] (used in model: 0,0005) http://parts.mit.edu/igem07/index.php/ETHZ/Engineering [2]
dRNA_LuxR 0.00227 s-1 did not find this value[1]
dLuxR1e-3 - 1e-4 [per sec+D4] (used in model: 0,0005)http://parts.mit.edu/igem07/index.php/ETHZ/Engineering[2]
dLuxI2.31e-3 [per sec] http://parts.mit.edu/igem07/index.php/ETHZ/Engineering[3]
dHSL 1.02E-6 s-1 very stable in the medium, average lifetime of 185h [4]
dLuxR_HSL 0.0010 s-1 complex of HSL and LuxR degrades, giving back HSL (estimation)
Association/Dissociation/Reaction Rates
kass (HSL+LuxR) 0.002372 s-1 (used in model 100= 0,002372*42100, why? to remove molar dimension)association rate of HSL with LuxR (estimate from KM but recalculated to remove molar dimension) [5]
kdiss (HSL-LuxR) 1.0 s-1 (used in model 42100, why?)dissociation rate of the HSL-LuxR complex (estimate from KM) [5]
kass (HSL+lactonase) 0.002372 s-1 (used in model 0,1, why?)association rate of HSL with lactonase (estimate from KM but recalculated to remove molar dimension) [6]
kdiss (HSL-lactonase) 4470.0 s-1 (used in model 188428.3, why?)dissociation rate of the HSL-lactonase complex (estimate from Kd) [6]
kcat (HSL>>hydroxy-acid) 29 s-1 (same in model)lactonase catalyzed transformation of HSL to a hydroxy-acid [6]
Dissociation Constants
KHSL_LuxR 1E-6 [M] HSL binding to LuxR[5]
Transcription Rates
kmRNA_luxR0.025estimation ( constitutive promotor ?)
kmRNA_ompA_AFP0.025
kmRNA_luxI0.025
kmRNA_cIrep0.025
kmRNA_melA0.025
Translation Rates
kluxR translation0.556 s-1 (0.03888888 in model?)Translation rate for LuxR, B0034 RBS (relative efficiency 1.0) [6]
kluxI translation0.167 s-1translation rate for B0032 RBS (0.3 relative efficiency) (https://2008.igem.org/Team:KULeuven/Model/Inverter)[7]
Hill cooperativity
nluxR (luxR activator)2http://parts.mit.edu/igem07/index.php/ETHZ/Engineering[2]
nAHL (AHL-luxR activator)1http://parts.mit.edu/igem07/index.php/ETHZ/Engineering[8]
nHSL_LuxR 2.08
CeaB transcription0,025
CeaB mRNA degradation0,002311
hybrid promotor kinetics[9]
k_transcr0.003
Km0.1099
vol0,000000000000001
N6,023E+29
hill2.08hil coefficient
Km_luxR0.00000405
k_l0.000504
other: protein degradations0.001estimation
other: mRNA degrade0.0025estimation
all other translation0.167same as kLuxI translation[7]
all other transcription0.025constitutive promotor value[9]
luxRk_transcr*Gene_LuxR*power(Km_CIIP22,2)/(power(Km_CIIP22,2)+power(CIIP22,2))*(power(HSL_LuxR_complex/(vol*N),hill)/(power(Km_LuxR,hill)+power(HSL_LuxR_complex/(vol*N),hill))+k_l/k_transcr)
ccdBf_stop*k_transcr*Gene_ccdB*power(Km_CIIP22,2)/(power(Km_CIIP22,2)+power(CIIP22,2))*(power(HSL_LuxR_complex/(vol*N),hill)/(power(Km_LuxR,hill)+power(HSL_LuxR_complex/(vol*N),hill))+k_l/k_transcr)
dRNA_LuxR 0.00227 s-1 did not find this value[1]
dLuxR1e-3 - 1e-4 [per sec+D4] (used in model: 0,0005)http://parts.mit.edu/igem07/index.php/ETHZ/Engineering[2]
dLuxI2.31e-3 [per sec] http://parts.mit.edu/igem07/index.php/ETHZ/Engineering[3]
dHSL 1.02E-6 s-1 very stable in the medium, average lifetime of 185h [4]
dLuxR_HSL 0.0010 s-1 complex of HSL and LuxR degrades, giving back HSL (estimation)
Association/Dissociation/Reaction Rates
kass (HSL+LuxR) 0.002372 s-1 (used in model 100= 0,002372*42100, why? to remove molar dimension)association rate of HSL with LuxR (estimate from KM but recalculated to remove molar dimension) [5]
kdiss (HSL-LuxR) 1.0 s-1 (used in model 42100, why?)dissociation rate of the HSL-LuxR complex (estimate from KM) [5]
kass (HSL+lactonase) 0.002372 s-1 (used in model 0,1, why?)association rate of HSL with lactonase (estimate from KM but recalculated to remove molar dimension) [6]
kdiss (HSL-lactonase) 4470.0 s-1 (used in model 188428.3, why?)dissociation rate of the HSL-lactonase complex (estimate from Kd) [6]
kcat (HSL>>hydroxy-acid) 29 s-1 (same in model)lactonase catalyzed transformation of HSL to a hydroxy-acid [6]
Dissociation Constants
KHSL_LuxR 1E-6 [M] HSL binding to LuxR[5]
Transcription Rates
kmRNA_luxR0.025estimation ( constitutive promotor ?)
kmRNA_ompA_AFP0.025
kmRNA_luxI0.025
kmRNA_cIrep0.025
kmRNA_melA0.025
Translation Rates
kluxR translation0.556 s-1 (0.03888888 in model?)Translation rate for LuxR, B0034 RBS (relative efficiency 1.0) [6]
kluxI translation0.167 s-1translation rate for B0032 RBS (0.3 relative efficiency) (https://2008.igem.org/Team:KULeuven/Model/Inverter)[7]
Hill cooperativity
nluxR (luxR activator)2http://parts.mit.edu/igem07/index.php/ETHZ/Engineering[2]
nAHL (AHL-luxR activator)1http://parts.mit.edu/igem07/index.php/ETHZ/Engineering[8]
nHSL_LuxR 2.08
CeaB transcription0,025
CeaB mRNA degradation0,002311
hybrid promotor kinetics[9]
k_transcr0.003
Km0.1099
vol0,000000000000001
N6,023E+29
hill2.08hil coefficient
Km_luxR0.00000405
k_l0.000504

References

  1. J.A. Bernstein et al., “Global analysis of mRNA decay and abundance in Escherichia coli at single-gene resolution using two-color fluorescent DNA microarrays,” Proceedings of the National Academy of Sciences of the United States of America, vol. 99, Jul. 2002, pp. 9697–9702.
  2. "Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants", Biosystems 83(2-3):178-187, 2004
  3. Tuttle L.M., Salis H., Tomshine J., and Kaznessis Y.N., "Model-Driven Designs of an Oscillating Gene Network", Biophysical Journal, vol. 89, no. 6, pp. 3873--3883, 2005.
  4. Y. Wang and J.R. Leadbetter, “Rapid Acyl-Homoserine Lactone Quorum Signal Biodegradation in Diverse Soils,” Appl. Environ. Microbiol., vol. 71, Mar. 2005, pp. 1291-1299.
  5. N. Qin et al., “Analysis of LuxR Regulon Gene Expression during Quorum Sensing in Vibrio fischeri,” J. Bacteriol., vol. 189, Jun. 2007, pp. 4127-4134.
  6. L. Wang et al., “Specificity and enzyme kinetics of the quorum-quenching AHL-lactonase,” J. Biol. Chem., Jan. 2004, p. M311194200.
  7. http://partsregistry.org/Part:BBa_B0032
  8. Parameter Estimation for Two Synthetic Gene Networks: A Case Study", ICASSP 5:769-772, 2005
  9. https://2008.igem.org/Team:KULeuven/Model/CellDeath


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