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 == | ||
+ | {| 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;" | ||
+ | ! Parameter | ||
+ | ! Value | ||
+ | ! Description | ||
+ | ! Comments | ||
+ | ! | ||
+ | ! Parameter | ||
+ | ! Value | ||
+ | ! Description | ||
+ | ! Comments | ||
+ | |- | ||
+ | | c<sub>1</sub><sup>max</sup> | ||
+ | | 0.01 [mM/h] | ||
+ | | max. transcription rate of constitutive promoter (per gene) | ||
+ | | promoter no. J23105; Estimate | ||
+ | | | ||
+ | | c<sub>2</sub><sup>max</sup> | ||
+ | | 0.01 [mM/h] | ||
+ | | max. transcription rate of luxR-activated promoter (per gene) | ||
+ | | Estimate | ||
+ | |- | ||
+ | | l<sup>hi</sup> | ||
+ | | 25 | ||
+ | | high-copy plasmid number | ||
+ | | Estimate | ||
+ | | | ||
+ | | l<sup>lo</sup> | ||
+ | | 5 | ||
+ | | low-copy plasmid number | ||
+ | | Estimate | ||
+ | |- | ||
+ | | a | ||
+ | | 1% | ||
+ | | basic production levels | ||
+ | | Estimate | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | |- | ||
+ | | Degradation constants | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | |- | ||
+ | | d<sub>lacI</sub> | ||
+ | | 2.31e-3 [1/s] | ||
+ | | degradation of lacI | ||
+ | | Ref. [10] | ||
+ | | | ||
+ | | d<sub>tetR</sub> | ||
+ | | | ||
+ | *1e-5 [1/s] | ||
+ | *2.31e-3 [1/s] | ||
+ | | degradation of tetR | ||
+ | | | ||
+ | *Ref. [9] | ||
+ | *Ref. [10] | ||
+ | |- | ||
+ | | d<sub>luxR</sub> | ||
+ | | 1e-3 - 1e-4 [1/s] | ||
+ | | degradation of luxR | ||
+ | | Ref: [6] | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | |- | ||
+ | | d<sub>cI</sub> | ||
+ | | 7e-4 [1/s] | ||
+ | | degradation of cI | ||
+ | | Ref. [7] | ||
+ | | | ||
+ | | d<sub>p22cII</sub> | ||
+ | | | ||
+ | | degradation of p22cII | ||
+ | | | ||
+ | |- | ||
+ | | d<sub>YFP</sub> | ||
+ | | 6.3e-3 [1/min] | ||
+ | | degradation of YFP | ||
+ | | suppl. mat. to Ref. [8] corresponding to a half life of 110min | ||
+ | | | ||
+ | | d<sub>GFP</sub> | ||
+ | | 6.3e-3 [1/min] | ||
+ | | degradation of GFP | ||
+ | | in analogy to YFP | ||
+ | |- | ||
+ | | d<sub>RFP</sub> | ||
+ | | 6.3e-3 [1/min] | ||
+ | | degradation of RFP | ||
+ | | in analogy to YFP | ||
+ | | | ||
+ | | d<sub>CFP</sub> | ||
+ | | 6.3e-3 [1/min] | ||
+ | | degradation of CFP | ||
+ | | in analogy to YFP | ||
+ | |- | ||
+ | | Dissociation constants | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | |- | ||
+ | | K<sub>lacI</sub> | ||
+ | | 0.1 - 1 [pM] | ||
+ | | lacI repressor dissociation constant | ||
+ | | Ref. [2] | ||
+ | | | ||
+ | | K<sub>IPTG</sub> | ||
+ | | 1.3 [µM] | ||
+ | | IPTG-lacI repressor dissociation constant | ||
+ | | Ref. [2] | ||
+ | |- | ||
+ | | K<sub>tetR</sub> | ||
+ | | 179 [pM] | ||
+ | | tetR repressor dissociation constant | ||
+ | | Ref. [1] | ||
+ | | | ||
+ | | K<sub>aTc</sub> | ||
+ | | 893 [pM] | ||
+ | | aTc-tetR repressor dissociation constant | ||
+ | | Ref. [1] | ||
+ | |- | ||
+ | | K<sub>luxR</sub> | ||
+ | | 55 - 520 [nM] | ||
+ | | luxR activator dissociation constant | ||
+ | | Ref: [6] | ||
+ | | | ||
+ | | K<sub>AHL</sub> | ||
+ | | 0.09 - 1 [µM] | ||
+ | | AHL-luxR activator dissociation constant | ||
+ | | Ref: [6] | ||
+ | |- | ||
+ | | K<sub>cI</sub> | ||
+ | | | ||
+ | *8 [pM] | ||
+ | *50 [nM] | ||
+ | | cI repressor dissociation constant | ||
+ | | | ||
+ | *Ref. [12] | ||
+ | *starting with values of Ref. [6] and using Ref. [3] | ||
+ | | | ||
+ | | K<sub>p22cII</sub> | ||
+ | | 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 | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | | | ||
+ | |- | ||
+ | | n<sub>lacI</sub> | ||
+ | | 1 | ||
+ | | lacI repressor Hill cooperativity | ||
+ | | Ref. [5] | ||
+ | | | ||
+ | | n<sub>IPTG</sub> | ||
+ | | 2 | ||
+ | | IPTG-lacI repressor Hill cooperativity | ||
+ | | Ref. [5] | ||
+ | |- | ||
+ | | n<sub>tetR</sub> | ||
+ | | 3 | ||
+ | | tetR repressor Hill cooperativity | ||
+ | | Ref. [3] | ||
+ | | | ||
+ | | 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] | ||
+ | |- | ||
+ | | 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:
- Definition of the problem
- Verification of information available
- Selection of model structure
- Establishing a simple model
- Sensitivity analysis
- Experimental tests of the model predictions
- Stating the agreements and divergences between experimental and modelling results, including any emergent behaviour
- Iterative refinement of model
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 | |
---|---|---|---|---|---|---|---|---|
c_{1}^{max} | 0.01 [mM/h] | max. transcription rate of constitutive promoter (per gene) | promoter no. J23105; Estimate | c_{2}^{max} | 0.01 [mM/h] | max. transcription rate of luxR-activated promoter (per gene) | Estimate | |
l^{hi} | 25 | high-copy plasmid number | Estimate | l^{lo} | 5 | low-copy plasmid number | Estimate | |
a | 1% | basic production levels | Estimate | |||||
Degradation constants | ||||||||
d_{lacI} | 2.31e-3 [1/s] | degradation of lacI | Ref. [10] | d_{tetR} |
| degradation of tetR |
| |
d_{luxR} | 1e-3 - 1e-4 [1/s] | degradation of luxR | Ref: [6] | |||||
d_{cI} | 7e-4 [1/s] | degradation of cI | Ref. [7] | d_{p22cII} | degradation of p22cII | |||
d_{YFP} | 6.3e-3 [1/min] | degradation of YFP | suppl. mat. to Ref. [8] corresponding to a half life of 110min | d_{GFP} | 6.3e-3 [1/min] | degradation of GFP | in analogy to YFP | |
d_{RFP} | 6.3e-3 [1/min] | degradation of RFP | in analogy to YFP | d_{CFP} | 6.3e-3 [1/min] | degradation of CFP | in analogy to YFP | |
Dissociation constants | ||||||||
K_{lacI} | 0.1 - 1 [pM] | lacI repressor dissociation constant | Ref. [2] | K_{IPTG} | 1.3 [µM] | IPTG-lacI repressor dissociation constant | Ref. [2] | |
K_{tetR} | 179 [pM] | tetR repressor dissociation constant | Ref. [1] | K_{aTc} | 893 [pM] | aTc-tetR repressor dissociation constant | Ref. [1] | |
K_{luxR} | 55 - 520 [nM] | luxR activator dissociation constant | Ref: [6] | K_{AHL} | 0.09 - 1 [µM] | AHL-luxR activator dissociation constant | Ref: [6] | |
K_{cI} |
| cI repressor dissociation constant |
| K_{p22cII} | 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 | ||||||||
n_{lacI} | 1 | lacI repressor Hill cooperativity | Ref. [5] | n_{IPTG} | 2 | IPTG-lacI repressor Hill cooperativity | Ref. [5] | |
n_{tetR} | 3 | tetR repressor Hill cooperativity | Ref. [3] | n_{aTc} | 2 (1.5-2.5) | aTc-tetR repressor Hill cooperativity | Ref. [3] | |
n_{luxR} | 2 | luxR activator Hill cooperativity | Ref: [6] | n_{AHL} | 1 | AHL-luxR activator Hill cooperativity | Ref. [3] | |
n_{cI} | 2 | cI repressor Hill cooperativity | Ref. [12] | n_{p22cII} | 4 | p22cII repressor Hill cooperativity | Ref. [11]. Note that they use a protein cII and we have p22cII. Does that match? |