no. 11
Systèmes dynamiques/Informatique théorique
Complexity of gene circuits, Pfaffian functions and the morphogenesis problem
[Complexité de réseaux de gènes, fonctions de Pfaff et le problème de morphogenèse]

Présenté par : Christophe Soulé

Vakulenko, Sergey1 ; Grigoriev, Dmitry2
1 Institute of Mechanical Engineering Problems, St Petersburg, Russia
2 IRMAR, Université de Rennes, Beaulieu, 35042 Rennes, France
Comptes Rendus. Mathématique, Tome 337 (2003) no. 11, pp. 721-724.

On considère un modèle de réseaux de gènes. Nous démontrons que ces réseaux peuvent engendrer toutes les structures spatio–temporelles et nous obtenons des bornes inférieures du nombre de gènes du réseau qui engendrent une structure prescrite.

We consider a model of gene circuits. We show that these circuits are capable to generate any spatio–temporal patterns. We give lower bounds on the number of genes required to create a given pattern.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.10.021
Vakulenko, Sergey 1 ; Grigoriev, Dmitry 2

1 Institute of Mechanical Engineering Problems, St Petersburg, Russia
2 IRMAR, Université de Rennes, Beaulieu, 35042 Rennes, France 
@article{CRMATH_2003__337_11_721_0,
     author = {Vakulenko, Sergey and Grigoriev, Dmitry},
     title = {Complexity of gene circuits, {Pfaffian} functions and the morphogenesis problem},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {721--724},
     publisher = {Elsevier},
     volume = {337},
     number = {11},
     year = {2003},
     doi = {10.1016/j.crma.2003.10.021},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2003.10.021/}
}
TY  - JOUR
AU  - Vakulenko, Sergey
AU  - Grigoriev, Dmitry
TI  - Complexity of gene circuits, Pfaffian functions and the morphogenesis problem
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 721
EP  - 724
VL  - 337
IS  - 11
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2003.10.021/
DO  - 10.1016/j.crma.2003.10.021
LA  - en
ID  - CRMATH_2003__337_11_721_0
ER  - 
%0 Journal Article
%A Vakulenko, Sergey
%A Grigoriev, Dmitry
%T Complexity of gene circuits, Pfaffian functions and the morphogenesis problem
%J Comptes Rendus. Mathématique
%D 2003
%P 721-724
%V 337
%N 11
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2003.10.021/
%R 10.1016/j.crma.2003.10.021
%G en
%F CRMATH_2003__337_11_721_0
Vakulenko, Sergey; Grigoriev, Dmitry. Complexity of gene circuits, Pfaffian functions and the morphogenesis problem. Comptes Rendus. Mathématique, Tome 337 (2003) no. 11, pp. 721-724. doi : 10.1016/j.crma.2003.10.021. http://www.numdam.org/articles/10.1016/j.crma.2003.10.021/

[1] Barron, A. Universal approximation bounds for superpositions of a sigmoidal functions, IEEE Trans. Inform. Theory, Volume 39 (1993), pp. 930-945

[2] Grigoriev, D.; Vorobjov, N. Complexity lower bounds for computation trees with elementary transcendental functions gates, Theoret. Comput. Sci., Volume 157 (1996), pp. 185-214

[3] Hartwell, L.H.; Hopfield, J.J.; Leibler, S.; Murray, A.W. From molecular to modular cell biology, Nature, Volume 402 (1999), p. C47-C52

[4] Hopfield, J.J. Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. USA, Volume 79 (1982), pp. 2554-2558

[5] Khovanskii, A. Fewnomials, Transl. Math. Monographs, 88, American Mathematical Society, 1991

[6] Meinhardt, H. Mathematical Models for Biological Pattern Formation (Maini, P.K.; Othmer, H.G., eds.), IMA Vol. Math. Appl., 121, Springer, 2000

[7] Mjolness, E.; Sharp, D.H.; Reinitz, J. A connectionist model of development, J. Theor. Biol., Volume 152 (1991), pp. 429-453

[8] Reinitz, J.; Sharp, D.H. Mechanism of formation of eve stripes, Mechanisms of Developments, Volume 49 (1995), pp. 133-158

[9] Turing, A.M. The chemical basis of morphogenesis, Philos. Trans. Roy. Soc. London Ser. B, Volume 237 (1952), pp. 37-72

[10] Wolpert, L.; Beddington, R.; Jessell, T.; Lawrence, P.; Meyerowitz, E.; Smith, J. Principles of Development, Oxford University Press, 2002

[11] Vakulenko, S. Dissipative systems generating any structurally stable chaos, Adv. Differential Equations, Volume 5 (2000), pp. 1139-1178

[12] S. Vakulenko, D. Grigoriev, Complexity of patterns generated by genetic circuits and Pfaffian functions, Preprint IHES, 2003

Cité par Sources :