Abstract
Reaction systems are a formal model for processes inspired by the functioning of the living cell. These processes are determined by the iteration of the state transition functions of reaction systems, also called rs functions. In this paper we provide mathematical characterisations of rs functions implemented/defined by “minimal reaction systems”, ı.e., reaction systems with reactions using the minimal number of reactants, or the minimal number of inhibitors, or the minimal number of resources (ı.e., reactants and inhibitors together).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baldan, P., Cocco, N., Marin, A., Simeoni, M.: Petri nets for modelling metabolic pathways: a survey. Natural Computing 9(4), 955–989 (2010)
Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Troina, A.: A calculus of looping sequences for modelling microbiological systems. Fundam. Inform. 72(1-3), 21–35 (2006)
Brijder, R., Ehrenfeucht, A., Main, M.G., Rozenberg, G.: A tour of reaction systems. Int. J. Found. Comput. Sci. 22(7), 1499–1517 (2011)
Brijder, R., Ehrenfeucht, A., Rozenberg, G.: A note on causalities in reaction systems. ECEASST 30 (2010)
Brijder, R., Ehrenfeucht, A., Rozenberg, G.: Reaction Systems with Duration. In: Kelemen, J., Kelemenová, A. (eds.) Pǎun Fetschrift. LNCS, vol. 6610, pp. 191–202. Springer, Heidelberg (2011)
Ciocchetta, F., Hillston, J.: Bio-PEPA: A framework for the modelling and analysis of biological systems. Theor. Comput. Sci. 410(33-34), 3065–3084 (2009)
Desel, J., Reisig, W., Rozenberg, G. (eds.): Lectures on Concurrency and Petri Nets. LNCS, vol. 3098. Springer, Heidelberg (2004)
Ehrenfeucht, A., Kleijn, J., Koutny, M., Rozenberg, G.: Qualitative and quantitative aspects of a model for processes inspired by the functioning of the living cell. In: Katz, E. (ed.) Biomolecular Computing: From Logic Systems to Smart Sensors and Actuators. Wiley-VCH Verlag GmbH & Co. KGaA (2012)
Ehrenfeucht, A., Main, M.G., Rozenberg, G.: Combinatorics of life and death for reaction systems. Int. J. Found. Comput. Sci. 21(3), 345–356 (2010)
Ehrenfeucht, A., Main, M.G., Rozenberg, G.: Functions defined by reaction systems. Int. J. Found. Comput. Sci. 22(1), 167–178 (2011)
Ehrenfeucht, A., Rozenberg, G.: Events and modules in reaction systems. Theor. Comput. Sci. 376(1-2), 3–16 (2007)
Ehrenfeucht, A., Rozenberg, G.: Reaction systems. Fundam. Inform. 75(1-4), 263–280 (2007)
Ehrenfeucht, A., Rozenberg, G.: Introducing time in reaction systems. Theor. Comput. Sci. 410(4-5), 310–322 (2009)
Heiner, M., Gilbert, D.: How Might Petri Nets Enhance Your Systems Biology Toolkit. In: Kristensen, L.M., Petrucci, L. (eds.) PETRI NETS 2011. LNCS, vol. 6709, pp. 17–37. Springer, Heidelberg (2011)
Heiner, M., Gilbert, D., Donaldson, R.: Petri Nets for Systems and Synthetic Biology. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 215–264. Springer, Heidelberg (2008)
Hirvensalo, M.: On probabilistic and quantum reaction systems. Theor. Comput. Sci. 429, 134–143 (2012)
Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Prentice Hall (2006)
Kleijn, J., Koutny, M., Rozenberg, G.: Modelling reaction systems with Petri nets. In: BioPPN 2011, International Workshop on Biological Processes & Petri Nets. CEUR-WS Workshop Proceedings, vol. 724, pp. 36–52 (2011)
Lehninger, A.L.: Bioenergetics: The Molecular Basis of Biological Energy Transformations. W.A. Benjamin, Inc., New York (1965)
Priami, C., Regev, A., Shapiro, E.Y., Silverman, W.: Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Inf. Process. Lett. 80(1), 25–31 (2001)
Salomaa, A.: On State Sequences Defined by Reaction Systems. In: Constable, R.L., Silva, A. (eds.) Kozen Festschrift. LNCS, vol. 7230, pp. 271–282. Springer, Heidelberg (2012)
Schlosser, G., Wagner, G.P. (eds.): Modularity in Development and Evolution. The University of Chicago Press, Chicago (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ehrenfeucht, A., Kleijn, J., Koutny, M., Rozenberg, G. (2012). Minimal Reaction Systems. In: Priami, C., Petre, I., de Vink, E. (eds) Transactions on Computational Systems Biology XIV. Lecture Notes in Computer Science(), vol 7625. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35524-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-35524-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35523-3
Online ISBN: 978-3-642-35524-0
eBook Packages: Computer ScienceComputer Science (R0)