The context of this example is given in :
J. Guespin, G. Bernot, J.-P. Comet, A. Mérieau, A. Richard, C. Hulen and B. Polack.
Epigenesis and dynamic similarity in two regulatory networks in Pseudomonas aeruginosa.
Acta Biotheoretica, in press. (2004).
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The following regulatory networks are possible simplified networks
controlling the mucoidy and the cytotoxicity of Pseudomonas
aeruginosa :
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networks 1
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networks 2
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Acquisition of both phenotype (mucoidy and cytotoxicity) may be due to an epigenetic
modification. This epigenetic hypothesis can be translated into the following CTL
formula :
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((x=0)->AG(x‹2)) & (x=2)->AX(AF(x=2))
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When (x=2) the bacteria products mucus and is cytotoxic.
When (x=0) it has not both phenotypes. Thus the formula
expresses that :
- if the bacteria has not the phenotypes,
in all futures (AG) it has not the phenotypes.
- if the bacteria has the phenotypes,
in all strict futures there is a time (AX AF) where it has the phenotypes.
SMBioNet shows that for both networks 4 models (values of logical
parameters) fulfill the epigenetic hypothesis (to obtain this result,
we use the Snoussi constraints and we set Kx,{}=0
and Ky,{}=0).
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Models satisfying the epigenetic hypothesis
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Parameter table of networks 1
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Parameter table of networks 2
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| x | y |
Kx | Ky |
| 0 | 0 | Kx,{y} | Ky,{} |
| 0 | 1 | Kx,{} | Ky,{} |
| 1 | 0 | Kx,{y} | Ky,{x} |
| 1 | 1 | Kx,{} | Ky,{x} |
| 2 | 0 | Kx,{xy} | Ky,{x} |
| 2 | 1 | Kx,{x} | Ky,{x} |
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| x | y |
Kx | Ky |
| 0 | 0 | Kx,{y} | Ky,{} |
| 0 | 1 | Kx,{} | Ky,{} |
| 1 | 0 | Kx,{xy} | Ky,{} |
| 1 | 1 | Kx,{x} | Ky,{} |
| 2 | 0 | Kx,{xy} | Ky,{x} |
| 2 | 1 | Kx,{x} | Ky,{x} |
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Models of network 1
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Models of network 2
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Model 1
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Model 1
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| Kx,{} | Kx,{y} | Kx,{x} | Kx,{xy} | Ky,{} | Ky,{x} |
| 0 | 0 | 2 | 2 | 0 | 0 |
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| Kx,{} | Kx,{y} | Kx,{x} | Kx,{xy} | Ky,{} | Ky,{x} |
| 0 | 0 | 1 | 2 | 0 | 0 |
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State graph of model 1
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State graph of model 1
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Model 2
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Model 2
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| Kx,{} | Kx,{y} | Kx,{x} | Kx,{xy} | Ky,{} | Ky,{x} |
| 0 | 1 | 2 | 2 | 0 | 0 |
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| Kx,{} | Kx,{y} | Kx,{x} | Kx,{xy} | Ky,{} | Ky,{x} |
| 0 | 0 | 2 | 2 | 0 | 0 |
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State graph of model 2
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State graph of model 2
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Model 3
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Model 3
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| Kx,{} | Kx,{y} | Kx,{x} | Kx,{xy} | Ky,{} | Ky,{x} |
| 0 | 0 | 2 | 2 | 0 | 1 |
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| Kx,{} | Kx,{y} | Kx,{x} | Kx,{xy} | Ky,{} | Ky,{x} |
| 0 | 0 | 1 | 2 | 0 | 1 |
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State graph of model 3
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State graph of model 3
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Model 4
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Model 4
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| Kx,{} | Kx,{y} | Kx,{x} | Kx,{xy} | Ky,{} | Ky,{x} |
| 0 | 1 | 2 | 2 | 0 | 1 |
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| Kx,{} | Kx,{y} | Kx,{x} | Kx,{xy} | Ky,{} | Ky,{x} |
| 0 | 0 | 2 | 2 | 0 | 1 |
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State graph of model 4
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State graph of model 4
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Among this 8 models, SMBioNet automatically shows (with the observability constraints) that 2 models, the model 4 of
network 1 and the model 3 of networks 2, are such that all interactions
of the networks are active : the two corresponding state graphs cannot be
associated to simplest networks (with less interactions).
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- G. Bernot, J.-P. Comet, A. Richard, J. Guespin, "A Fruitful Application of Formal Methods to Biological Regulatory Networks: Extending Thomas' Asynchronous Logical Approach with Temporal Logic", J.T.B., 229(3):339-347, 2004.
- J. Guespin, G. Bernot, J.-P. Comet, A. Mérieau, A. Richard, C. Hulen and B. Polack.
Epigenesis and dynamic similarity in two regulatory networks in Pseudomonas aeruginosa.
Acta Biotheoretica. 52 (4): 379-390, 2004.
The result of the modeling, obtained with SMBioNet
and not given in this paper, is presented in the
example of modeling page.
- G. Bernot, J. Guespin-Michel, J.-P. Comet, P. Amar,
A. Zemirline, F. Delaplace, P. Ballet and A. Richard.
Modelling, observability and experiment: a case study. In Proc. of the Dieppe Spring school on Modelling and simulation of biological processes in the context of genomics (eds. P. Amar, F. Képés, V. Norris and P. Tracqui) pp. 49-55, Publisher Frontier group, ISBN : 2 84704 036 6, 2003.
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