User:Jaroslaw Karcz/Modelling Sandbox

Model Development

The process of modelling consists of a number of layers; the following is a description of the modelling workflow:

1. Definition of the problem
2. Verification of information available
3. Selection of model structure
4. Establishing a simple model
5. Sensitivity analysis
6. Experimental tests of the model predictions
7. Stating the agreements and divergences between experimental and modelling results, including any emergent behaviour
8. Iterative refinement of model

[math]\displaystyle{ f_{obj}(k) = \sum_{i=1}^q (f_{obs}(i) - f_{per}(i,k))^2 }[/math]

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Introduction

The real world is dominated by complexity, especially biological systems
Mathematical modelling and computer simulations provide a means of understanding the innate funtioning of system - dynamics, and to arrive at well-founded predictions about their future development and the effect of interactions with the environment. So what is a model? A model is an abstract representation of objects and processes that explain the features/nature of these objects or processes. We present the model of our construct, as a system of differential equations to describe the dynamics of that network.

Model Parameters

Parameter	Value	Description	Comments		Parameter	Value	Description	Comments
c1max	0.01 [mM/h]	max. transcription rate of constitutive promoter (per gene)	promoter no. J23105; Estimate		c2max	0.01 [mM/h]	max. transcription rate of luxR-activated promoter (per gene)	Estimate
lhi	25	high-copy plasmid number	Estimate		llo	5	low-copy plasmid number	Estimate
a	1%	basic production levels	Estimate
Degradation constants
dlacI	2.31e-3 [1/s]	degradation of lacI	Ref. [10]		dtetR	1e-5 [1/s] 2.31e-3 [1/s]	degradation of tetR	Ref. [9] Ref. [10]
dluxR	1e-3 - 1e-4 [1/s]	degradation of luxR	Ref: [6]
dcI	7e-4 [1/s]	degradation of cI	Ref. [7]		dp22cII		degradation of p22cII
dYFP	6.3e-3 [1/min]	degradation of YFP	suppl. mat. to Ref. [8] corresponding to a half life of 110min		dGFP	6.3e-3 [1/min]	degradation of GFP	in analogy to YFP
dRFP	6.3e-3 [1/min]	degradation of RFP	in analogy to YFP		dCFP	6.3e-3 [1/min]	degradation of CFP	in analogy to YFP
Dissociation constants
KlacI	0.1 - 1 [pM]	lacI repressor dissociation constant	Ref. [2]		KIPTG	1.3 [µM]	IPTG-lacI repressor dissociation constant	Ref. [2]
KtetR	179 [pM]	tetR repressor dissociation constant	Ref. [1]		KaTc	893 [pM]	aTc-tetR repressor dissociation constant	Ref. [1]
KluxR	55 - 520 [nM]	luxR activator dissociation constant	Ref: [6]		KAHL	0.09 - 1 [µM]	AHL-luxR activator dissociation constant	Ref: [6]
KcI	8 [pM] 50 [nM]	cI repressor dissociation constant	Ref. [12] starting with values of Ref. [6] and using Ref. [3]		Kp22cII	0.577 [µM]	p22cII repressor dissociation constant	Ref. [11]. Note that they use a protein cII and we have p22cII. Does that match?
Hill cooperativity
nlacI	1	lacI repressor Hill cooperativity	Ref. [5]		nIPTG	2	IPTG-lacI repressor Hill cooperativity	Ref. [5]
ntetR	3	tetR repressor Hill cooperativity	Ref. [3]		naTc	2 (1.5-2.5)	aTc-tetR repressor Hill cooperativity	Ref. [3]
nluxR	2	luxR activator Hill cooperativity	Ref: [6]		nAHL	1	AHL-luxR activator Hill cooperativity	Ref. [3]
ncI	2	cI repressor Hill cooperativity	Ref. [12]		np22cII	4	p22cII repressor Hill cooperativity	Ref. [11]. Note that they use a protein cII and we have p22cII. Does that match?