Jérôme Feret Laboratoire d'Informatique de l'École Normale Supérieure

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SAS 2011 Formal model reduction Jérôme Feret Laboratoire d'Informatique de l'École Normale Supérieure INRIA, ÉNS, CNRS Friday, September the 16th

laboratoire d'informatique de l'ecole normale

abstract interpretation

formal model

msb4100014-e2 molecularsystemsbiology2005

abstract semantics

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Publié par

pefav

Nombre de lectures

Langue

Français

Poids de l'ouvrage

4 Mo

SAS 2011

Formal model reduction

Jérôme Feret Laboratoire d’Informatique de l’École Normale Supérieure INRIA, ÉNS, CNRS

Friday, September the 16th

Joint-work with...

Walter Fontana Harvard Medical School

Jérôme Feret

Russ Harmer Harvard Medical School

Vincent Danos Edinburgh

Ferdinanda Camporesi Bologna / ÉNS

Jean Krivine Paris VII

Friday, September the 16th

Overview

1.Context and motivations 2. Handmade ODEs 3. Abstract interpretation framework 4. Kappa 5. Concrete semantics 6. Abstract semantics 7. Conclusion

Jérôme Feret

Friday, September the 16th

Jérôme Feret

Signalling

Pathways

Eikuch, 2007

Friday, September the 16th

Jérôme Feret

Pathway

maps

Oda, Matsuoka, Funahashi, Kitano, Molecular Systems Biology, 2005

Friday, September the 16th

Differential models

dtxd1= −k1∙x1∙x2+k−1∙x3 ddxt2= −k1∙x1∙x2+k−1∙x3 − xddtxdtd43==kk12∙∙xx123∙−x2k2−∙xk4−1+∙pxv443∙+xx+552−∙(kk32∙∙xx43∙−x3k−3k∙−x52∙)x4 dx 5=∙ ∙ ∙ dt . ddxtn= −k1∙x1∙c2+k−1∙x3

−do not describe the structure of molecules; −combinatorial explosion:forces choices that are not principled; −a nightmare to modify.

Jérôme Feret

Friday, September the 16th

A gap between two worlds

Two levels of description: 1. Databases of proteins interactions in natural language + documented and detailed description + transparent description −cannot be interpreted 2. ODE-based models + can be integrated −opaque modelling process, models can hardly be modiﬁed −there are also some scalability issues.

Jérôme Feret

Friday, September the 16th

Rule-based approach

We use site graph rewrite systems

1. The description level matches with both •the observation level •and the intervention level of the biologist.

We can tune the model easily. 2. Model description is very compact.

Jérôme Feret

Friday, September the 16th

Several

semantics

Y68

Y48

Sh Interaction map

Jérôme Feret

Semantics

(qualititative

and/or

CTMC

quantitative)

can

deﬁned.

= − ddxt1k1∙x1∙x2+k−1∙x3 dx2 = −k1∙x1∙x2+k−1∙x3 dt ddxt3=k1∙x1∙x2−k−1∙x3+2∙k2∙x3∙x3−k−2∙x4) dtdx4=k2∙x32−k2∙x4+pv44+∙xx55− (k3∙x4−k−3∙x5) dx5= ∙ ∙ ∙ dt . dxdtn= −k1∙x1∙c2+k−1∙x3 ODEs

Friday, September the 16th

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