User:Jaroslaw Karcz/Modelling Sandbox

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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.
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.
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 ==
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{| class="wikitable" border="1" cellspacing="0" cellpadding="2" style="text-align:left; margin: 1em 1em 1em 0; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse;"
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! Parameter                       
 +
! Value
 +
! Description
 +
! Comments
 +
!
 +
! Parameter                       
 +
! Value
 +
! Description
 +
! Comments
 +
|-
 +
| c<sub>1</sub><sup>max</sup>
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| 0.01 [mM/h]
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| max. transcription rate of constitutive promoter (per gene)
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| promoter no. J23105; Estimate
 +
|
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| c<sub>2</sub><sup>max</sup>
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| 0.01 [mM/h]
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| max. transcription rate of luxR-activated promoter (per gene)
 +
| Estimate
 +
|-
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| l<sup>hi</sup>
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| 25
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| high-copy plasmid number
 +
| Estimate
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|
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| l<sup>lo</sup>
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| 5
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| low-copy plasmid number
 +
| Estimate
 +
|-
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| a
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| 1%
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| basic production levels
 +
| Estimate
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|-
 +
| Degradation constants
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|-
 +
| d<sub>lacI</sub>
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| 2.31e-3 [1/s]
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| degradation of lacI
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| Ref. [10]
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|
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| d<sub>tetR</sub>
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|
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*1e-5 [1/s]
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*2.31e-3 [1/s]
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| degradation of tetR
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|
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*Ref. [9]
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*Ref. [10]
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|-
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| d<sub>luxR</sub>
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| 1e-3 - 1e-4 [1/s]
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| degradation of luxR
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| Ref: [6]
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|
 +
|
 +
|
 +
|
 +
|
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|-
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| d<sub>cI</sub>
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| 7e-4 [1/s]
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| degradation of cI
 +
| Ref. [7]
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|
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| d<sub>p22cII</sub>
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|
 +
| degradation of p22cII
 +
|
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|-
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| d<sub>YFP</sub>
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| 6.3e-3 [1/min]
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| degradation of YFP
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| suppl. mat. to Ref. [8] corresponding to a half life of 110min
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|
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| d<sub>GFP</sub>
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| 6.3e-3 [1/min]
 +
| degradation of GFP
 +
| in analogy to YFP
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|-
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| d<sub>RFP</sub>
 +
| 6.3e-3 [1/min]
 +
| degradation of RFP
 +
| in analogy to YFP
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|
 +
| d<sub>CFP</sub>
 +
| 6.3e-3 [1/min]
 +
| degradation of CFP
 +
| in analogy to YFP
 +
|-
 +
| Dissociation constants
 +
|
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|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|-
 +
| K<sub>lacI</sub>
 +
| 0.1 - 1 [pM]
 +
| lacI repressor dissociation constant
 +
| Ref. [2]
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|
 +
| K<sub>IPTG</sub>
 +
| 1.3 [&#181;M]
 +
| IPTG-lacI repressor dissociation constant
 +
| Ref. [2]
 +
|-
 +
| K<sub>tetR</sub>
 +
| 179 [pM]
 +
| tetR repressor dissociation constant
 +
| Ref. [1]
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|
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| K<sub>aTc</sub>
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| 893 [pM]
 +
| aTc-tetR repressor dissociation constant
 +
| Ref. [1]
 +
|-
 +
| K<sub>luxR</sub>
 +
| 55 - 520 [nM]
 +
| luxR activator dissociation constant
 +
| Ref: [6]
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|
 +
| K<sub>AHL</sub>
 +
| 0.09 - 1 [&#181;M]
 +
| AHL-luxR activator dissociation constant
 +
| Ref: [6]
 +
|-
 +
| K<sub>cI</sub>
 +
|
 +
*8 [pM]
 +
*50 [nM]
 +
| cI repressor dissociation constant
 +
|
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*Ref. [12]
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*starting with values of Ref. [6] and using Ref. [3]
 +
|
 +
| K<sub>p22cII</sub>
 +
| 0.577 [&#181;M]
 +
| p22cII repressor dissociation constant
 +
| Ref. [11]. Note that they use a protein cII and we have p22cII. Does that match?
 +
|-
 +
|Hill cooperativity
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|
 +
|-
 +
| n<sub>lacI</sub>
 +
| 1
 +
| lacI repressor Hill cooperativity
 +
| Ref. [5]
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|
 +
| n<sub>IPTG</sub>
 +
| 2
 +
| IPTG-lacI repressor Hill cooperativity
 +
| Ref. [5]
 +
|-
 +
| n<sub>tetR</sub>
 +
| 3
 +
| tetR repressor Hill cooperativity
 +
| Ref. [3]
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|
 +
| n<sub>aTc</sub>
 +
| 2 (1.5-2.5)
 +
| aTc-tetR repressor Hill cooperativity
 +
|Ref. [3]
 +
|-
 +
| n<sub>luxR</sub>
 +
| 2
 +
| luxR activator Hill cooperativity
 +
| Ref: [6]
 +
|
 +
| n<sub>AHL</sub>
 +
| 1
 +
| AHL-luxR activator Hill cooperativity
 +
| Ref. [3]
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|-
 +
| n<sub>cI</sub>
 +
| 2
 +
| cI repressor Hill cooperativity
 +
| Ref. [12]
 +
|
 +
| n<sub>p22cII</sub>
 +
| 4
 +
| p22cII repressor Hill cooperativity
 +
| Ref. [11]. Note that they use a protein cII and we have p22cII. Does that match?
 +
|-
 +
|}
 +
 +
<br>

Revision as of 09:50, 20 October 2007

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


f_{obj}(k) = \sum_{i=1}^q (f_{obs}(i) - f_{per}(i,k))^2


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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?


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