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2015 | OriginalPaper | Buchkapitel

Symbolic Dynamics of Biochemical Pathways as Finite States Machines

verfasst von : Ovidiu Radulescu, Satya Swarup Samal, Aurélien Naldi, Dima Grigoriev, Andreas Weber

Erschienen in: Computational Methods in Systems Biology

Verlag: Springer International Publishing

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Abstract

We discuss the symbolic dynamics of biochemical networks with separate timescales. We show that symbolic dynamics of monomolecular reaction networks with separated rate constants can be described by deterministic, acyclic automata with a number of states that is inferior to the number of biochemical species. For nonlinear pathways, we propose a general approach to approximate their dynamics by finite state machines working on the metastable states of the network (long life states where the system has slow dynamics). For networks with polynomial rate functions we propose to compute metastable states as solutions of the tropical equilibration problem. Tropical equilibrations are defined by the equality of at least two dominant monomials of opposite signs in the differential equations of each dynamic variable. In algebraic geometry, tropical equilibrations are tantamount to tropical prevarieties, that are finite intersections of tropical hypersurfaces.

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Andrieux, G., Fattet, L., Le Borgne, M., Rimokh, R., Théret, N.: Dynamic regulation of Tgf-B signaling by Tif1\(\gamma \): a computational approach. PloS One 7(3), e33761 (2012)CrossRef

Chiavazzo, E., Karlin, I.: Adaptive simplification of complex multiscale systems. Phys. Rev. E 83(3), 036706 (2011)CrossRef

Gorban, A., Karlin, I.: Invariant Manifolds for Physical and Chemical Kinetics. Lecture Notes in Physics, vol. 660. Springer, Heidelberg (2005)MATH

Gorban, A., Radulescu, O.: Dynamic and static limitation in reaction networks, revisited. In: Guy B. Marin, D.W., Yablonsky, G.S. (eds.) Advances in Chemical Engineering - Mathematics in Chemical Kinetics and Engineering. Advances in Chemical Engineering, vol. 34, pp. 103–173. Elsevier, Amsterdam (2008)

Grigoriev, D.: Complexity of solving tropical linear systems. Comput. Complex. 22(1), 71–88 (2013)MathSciNetCrossRefMATH

Grigoriev, D., Podolskii, V.V.: Complexity of tropical and min-plus linear prevarieties. Comput. Complex. 24, 31–64 (2015)MathSciNetCrossRef

Haller, G., Sapsis, T.: Localized instability and attraction along invariant manifolds. SIAM J. Appl. Dyn. Syst. 9(2), 611–633 (2010)MathSciNetCrossRefMATH

Maas, U., Pope, S.B.: Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space. Combust. Flame 88(3), 239–264 (1992)CrossRef

Noel, V., Grigoriev, D., Vakulenko, S., Radulescu, O.: Tropical geometries and dynamics of biochemical networks application to hybrid cell cycle models. In: Feret, J., Levchenko, A. (eds.) Proceedings of the 2nd International Workshop on Static Analysis and Systems Biology (SASB 2011). Electronic Notes in Theoretical Computer Science, vol. 284, pp. 75–91. Elsevier (2012)

10.

Noel, V., Grigoriev, D., Vakulenko, S., Radulescu, O.: Tropicalization and tropical equilibration of chemical reactions. In: Topical and Idempotent Mathematics and Applications, vol. 616. American Mathematical Society (2014)

11.

Palis, J.: A global view of dynamics and a conjecture on the denseness of finitude of attractors. Astérisque 261, 339–351 (2000)

12.

Radulescu, O., Gorban, A.N., Zinovyev, A., Lilienbaum, A.: Robust simplifications of multiscale biochemical networks. BMC Syst. Biol. 2(1), 86 (2008)CrossRef

13.

Radulescu, O., Gorban, A.N., Zinovyev, A., Noel, V.: Reduction of dynamical biochemical reactions networks in computational biology. Front. Genet. 3(131) (2012)

14.

Radulescu, O., Vakulenko, S., Grigoriev, D.: Model reduction of biochemical reactions networks by tropical analysis methods. Mathematical Model of Natural Phenomena (2015, in press)

15.

Samal, S.S., Radulescu, O., Grigoriev, D., Fröhlich, H., Weber, A.: A tropical method based on newton polygon approach for algebraic analysis of biochemical reaction networks. In: 9th European Conference on Mathematical and Theoretical Biology (2014)

16.

Soliman, S., Fages, F., Radulescu, O.: A constraint solving approach to model reduction by tropical equilibration. Algorithms Mol. Biol. 9(1), 24 (2014)CrossRef

17.

Theobald, T.: On the frontiers of polynomial computations in tropical geometry. J. Symbolic Comput. 41(12), 1360–1375 (2006)MathSciNetCrossRefMATH

18.

Tsuda, I.: Chaotic itinerancy as a dynamical basis of hermeneutics in brain and mind. World Futures: J. Gen. Evol. 32(2–3), 167–184 (1991)CrossRef

Titel: Symbolic Dynamics of Biochemical Pathways as Finite States Machines
verfasst von: Ovidiu Radulescu
Satya Swarup Samal
Aurélien Naldi
Dima Grigoriev
Andreas Weber
Verlag: Springer International Publishing
Buch: Computational Methods in Systems Biology
Print ISBN: 978-3-319-23400-7

Electronic ISBN: 978-3-319-23401-4

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-23401-4_10

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