Team:KULeuven/Modeling

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

Different amounts of lactose and arabinose are used to check the efficiency of the model. Lactose is the inducing compound involved in the freeze system, which can result in the production of ice nucleating protein (INP), while antifreeze system is repressed by lactose. On the other hand, L-arabinose is repressing the system by inducing the production of LuxI, and yet, in the antifreeze model, AFP production is induced by it. The results reveal that the kinetics of synthesis of AFP and CeaB are much higher than that of INP formation, for example, the difference of the concentrations of AFP and INP can reach 10E15 in Fig. 1. The main reason is the efficiency of the formation of AHL complex. From mathematical modeling, we can find INP gene functions after AHL complex, and they are in same series reaction. Therefore, the low activity of AHL directly leads to the limited amount of INP formation. To stimulate the INP production, we can increase the amount of lactose, e.g. 100 for lactose and 1 for arabinose (Fig.2). As a result, the INP production dramatically increases by 10E14.

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4. Sensitivity Analysis

5. Kinetic Constants

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]
dLuxR	1e-3 - 1e-4 [per sec+D4] (used in model: 0,0005)	http://parts.mit.edu/igem07/index.php/ETHZ/Engineering	[2]
dLuxI	2.31e-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_luxR	0.025	estimation ( constitutive promotor ?)
kmRNA_ompA_AFP	0.025
kmRNA_luxI	0.025
kmRNA_cIrep	0.025
kmRNA_melA	0.025
Translation Rates
kluxR translation	0.556 s-1 (0.03888888 in model?)	Translation rate for LuxR, B0034 RBS (relative efficiency 1.0)	[6]
kluxI translation	0.167 s-1	translation rate for B0032 RBS [11]	[7]
Hill cooperativity
nluxR (luxR activator)	2	[10]	[2]
nAHL (AHL-luxR activator)	1	[10]	[8]
nHSL_LuxR	2.08
CeaB transcription	0,025
CeaB mRNA degradation	0,002311
hybrid promotor kinetics			[9]
k_transcr	0.003
Km	0.1099
vol	0,000000000000001
N	6,023E+29
hill	2.08	hil coefficient
Km_luxR	0.00000405
k_l	0.000504
other: protein degradations	0.001	estimation
other: mRNA degrade	0.0025	estimation
all other translation	0.167	same as kLuxI translation	[7]
all other transcription	0.025	constitutive promotor value	[9]