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Warianty tytułu
Języki publikacji
Abstrakty
Models of complex biological systems can be built using different types of Petri nets. Qualitative nets, for example, can be successfully used to obtain a model of such a system and on its basis a structure-based analysis can be performed. Time is an important factor influencing a whole biological system behaviour and in many cases it should be considered during building a model of such a system. In this paper various types of time Petri nets have been described and methods for studying corresponding models have been discussed. In particular, an algorithm using time parameters to enhance t-invariants based analysis is proposed. This algorithm allows for calculation of the minimal and maximal numbers of tokens (respectively, for an optimistic and pessimistic case) in particular places necessary to assure that all transitions from a given t-invariant support will be able to fire. Additionally, to address the problem of the proper assignment of time values to transitions, the known methods for calculation and evaluation of such time parameters based on the net structure have also been discussed.
Rocznik
Tom
Strony
67--78
Opis fizyczny
Bibliogr. 29 poz., rys., tab.
Twórcy
autor
- Institute of Computing Science, Poznan University of Technology, ul. Piotrowo 2, 60-965 Poznan, Poland
- Lhasa Limited, Granary Wharf House, 2 Canal Wharf, Holbeck, Leeds LS11 5PY, U.K.
autor
- Institute of Computing Science, Poznan University of Technology, ul. Piotrowo 2, 60-965 Poznan, Poland
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, ul. Z. Noskowskiego 12/14, 61-704 Poznan, Poland
autor
- Institute of Computing Science, Poznan University of Technology, ul. Piotrowo 2, 60-965 Poznan, Poland
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, ul. Z. Noskowskiego 12/14, 61-704 Poznan, Poland
Bibliografia
- [1] Z. Szallasi, J. Stelling, and V. Periwal, System Modeling in Cellural Biology. From Concepts to Nuts and Bolts, MIT Press Cambridge, Massachusetts, 2006.
- [2] P. Formanowicz, “On the border between biology, mathematics and computer science”, BioTechnologia 92, 217–220 (2011).
- [3] E. Klipp, W. Liebermeister, C. Wierling, A. Kowald, H. Lehrach, and R. Herwig, Systems Biology: A Textbook, Wiley-VCH, Weinheim, 2009.
- [4] T. Murata, “Petri nets: Properties, analysis and applications”, Proceedings of the IEEE, 77, 541–580 (1989).
- [5] C. Chaouiya, “Petri net modelling of biological networks”, Briefings in Bioinformatics, 8(4), 210–219 (2007).
- [6] I. Koch, W. Reisig, and F. Schreiber (Eds.), Modeling in Systems Biology. The Petri Net Approach, Springer-Verlag, London, 2011.
- [7] P. Baldan, N. Cocco, A. Marin and M. Simeoni, “Petri nets for modelling metabolic pathways: a survey”, Natural Computing, 9(4), 955–989 (2010).
- [8] A. Sackmann, M. Heiner, and I. Koch, “Application of Petri net based analysis techniques to signal transduction pathway”, BMC Bioinformatics, 7, 482 (2006).
- [9] E. Grafahrend-Belau, F. Schreiber, M. Heiner, A. Sackmann, B.H. Junker, S. Grunwald, A. Speer, K. Winder, and I. Koch, “Modularization of biochemical networks based on classification of Petri net t-invariants”, BMC Bioinformatics 9, 90 (2008).
- [10] D. Formanowicz, M. Radom, P. Zawierucha, and P. Formanowicz, “Petri net-based approach to modeling and analysis of selected aspects of the molecular regulation of angiogenesis”, PLOS ONE 12(3), e0173020 (2017).
- [11] R. David and H. Alla, Discrete, Continuous and Hybrid Petri Nets, Springer Verlag, Berlin Heidelberg, 2010.
- [12] L. Popova, “On time Petri nets”, Journal of Information Processing and Cybernetics 27(4), 227–244 (1991).
- [13] W.M. Zuberek, “Timed Petri nets definitions, properties, and applications”, Microelectronics Reliability, 31(4), 627–644 (1991).
- [14] L. Popova, Time and Petri Nets, Springer Verlag, Berlin Heidelberg, 2013.
- [15] L. Popova and M. Heiner, and I. Koch, “Time Petri nets for modelling and analysis of biochemical networks”, Fundamenta Informaticae, 67, 149–162 (2005).
- [16] C. Li, Q.-W. Ge, M. Nakata, H. Matsuno, and S. Miyano S, “Modelling and simulation of signal transduction in an apoptosis pathway by using timed Petri nets”, Journal of Biosciences 32 (1), 113–127 (2007).
- [17] J. Błażewicz, D. Formanowicz, P. Formanowicz, A. Sackmann, and M. Sajkowski, “Modeling the process of human body iron homeostasis using a variant of timed Petri nets”, Discrete Applied Methematics 157, 2221–2231 (2009).
- [18] L. Popova and E. Pelz, “Studying steady states in biochemical reaction systems by time Petri nets”, Proceedings of the 2nd International Workshop on Biological Processes & Petri Nets, 71–86 (2011).
- [19] M. Heiner, D. Gilbert, and R. Donaldson, “Petri nets for systems and synthetic biology”, Lecture Notes in Computer Science, 5016, 215–264 (2008).
- [20] M. Heiner, “Understanding network behavior by structured representations of transition invariants”, Algorithmic Bioprocesses, 367–389 (2009).
- [21] D. Formanowicz, A. Kozak, T. Głowacki, M. Radom, and P. Formanowicz, “Hemojuvelin-hepcidin axis modeled and analyzed using Petri nets”, Journal of Biomedical Informatics 46(6), 1030–1043 (2013).
- [22] S. Schuster and C. Hilgetag, “On elementary flux modes in biochemical reaction systems at steady state”, Journal of Biological Systems 2, 165–182 (1994).
- [23] I. Zevedei-Oancea and S. Schuster. “Topological analysis of metabolic networks based on Petri net theory”, In Silico Biology 3(3), 323–245 (2003).
- [24] J. Behre, L.F. de Figueiredo, S. Schuster, and C. Kaleta, “Detecting structural invariants in biological reaction networks”, Methods in Molecular Biology 804, 377–407 (2012).
- [25] J. Wang, Timed Petri Nets, Kluwer Academic Publishers, Dordrecht, Netherlands, 1998.
- [26] M. Radom, J. Olszak, and P. Formanowicz, “Metody analizy modeli systemów biologicznych opartych na czasowych sieciach Petriego”, In: A. Świerniak, J. Krystek (eds.), Automatyzacja procesów dyskretnych. Teoria i zastosowania. Vol. II, Wydawnictwo Pracowni Komputerowej Jacka Skalmierskiego, Gliwice, 189‒203 (2016).
- [27] INA – Integrated Net Analyzer, http://www2.informatik.huberlin.de/starke/ina.html.
- [28] P.J. Delves, S.J. Martin, D.R. Burton, and I.M. Roitt, Roitt’s Essential Immunology, 13th Edition. Wiley-Blackwell, Chichester 2017.
- [29] Y. Miwa, C. Li, Q.-W. Ge, H. Matsuno, and S. Miyano, “On determining firing delay time of transitions for Petri net based signaling pathways by introducing stochastic decision rules”, In Silico Biology 10(1), 49–66 (2010).
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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