Hybrid semantics for Bio-PEPA. (English) Zbl 1300.68035
Summary: This paper investigates the stochastic, continuous and instantaneous (hybrid) modelling of systems defined in Bio-PEPA, a quantitative process algebra for biological modelling. This is achieved by mapping a Bio-PEPA model to a model in stochastic HYPE, a process algebra that models these three behaviour types in a compositional and structured manner. The novel mapping between process algebras provides another method of analysis for Bio-PEPA models and presents the modeller with a well-structured stochastic HYPE model which can itself be easily modified and is only a small constant larger in size than the Bio-PEPA model. The structure of the stochastic HYPE model generated has desirable properties and also gives a general framework for modelling biochemical systems where the advantages of both stochastic and deterministic simulation are required. Thresholds are introduced for each reaction, and when all values are above these thresholds, the reaction is treated deterministically. However, if a relevant value is below a threshold, the reaction is treated stochastically (as are the changes in species quantities as a result of that reaction). It is proved that in the purely deterministic case and in the purely stochastic case, the stochastic HYPE model has the same behaviour as the Bio-PEPA model when considered purely deterministically and purely stochastically, respectively. Furthermore, addition of instantaneous events in the style of Bio-PEPA with events is illustrated, and a proposal for mapping Bio-PEPA with delays (Bio-PEPAd) to stochastic HYPE is presented.
MSC:
| 68Q85 | Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.) |
| 92C42 | Systems biology, networks |
Keywords:
process algebra; biological modeling; events; hybrid modeling; stochastic modeling; deterministic simulation; continuous modeling; discrete behavior; instantaneous simulationReferences:
| [1] | Akman, O.; Ciocchetta, F.; Degasperi, A.; Guerriero, M., Modelling biological clocks with Bio-PEPA: stochasticity and robustness for the Neurospora Crassa circadian network, (Proceedings of the 7th International Conference on Computational Models in Systems Biology. Proceedings of the 7th International Conference on Computational Models in Systems Biology, CMSB 2009. Proceedings of the 7th International Conference on Computational Models in Systems Biology. Proceedings of the 7th International Conference on Computational Models in Systems Biology, CMSB 2009, Lect. Notes Comput. Sci., vol. 5688 (2009), Springer), 52-67 |
| [2] | Akman, O.; Guerriero, M.; Loewe, L.; Troein, C., Complementary approaches to understanding the plant circadian clock, (Proceedings of FBTC’10. Proceedings of FBTC’10, Electron. Proc. Theor. Comp. Sci., vol. 19 (2010)) |
| [3] | Alfonsi, A.; Cancès, E.; Turinici, G.; Ventura, B. D.; Huisinga, W., Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems, ESAIM Proc., 1-13 (2005) · Zbl 1070.92019 |
| [4] | Barbuti, R.; Caravagna, G.; Maggiolo-Schettini, A.; Milazzo, P., Delay stochastic simulation of biological systems: a purely delayed approach, (Transactions on Computational Systems Biology XIII. Transactions on Computational Systems Biology XIII, Lect. Notes Comput. Sci., vol. 6575 (2011)), 61-84 · Zbl 1326.92026 |
| [5] | Barrio, M.; Burrage, K.; Leier, A.; Tian, T., Oscillatory regulation of hes1: discrete stochastic delay modelling and simulation, PLoS Comput. Biol., 2, 9, e177 (2006) |
| [6] | Blossey, R.; Cardelli, L.; Phillips, A., A compositional approach to the stochastic dynamics of gene networks, (Transactions on Computational Systems Biology IV. Transactions on Computational Systems Biology IV, Lect. Notes Comput. Sci., vol. 3939 (2006), Springer), 99-122 · Zbl 1179.92021 |
| [7] | Bortolussi, L.; Galpin, V.; Hillston, J., HYPE with stochastic events, (Proceedings of the Ninth Workshop on Quantitative Aspects of Programming Languages. Proceedings of the Ninth Workshop on Quantitative Aspects of Programming Languages, QAPL 2011. Proceedings of the Ninth Workshop on Quantitative Aspects of Programming Languages. Proceedings of the Ninth Workshop on Quantitative Aspects of Programming Languages, QAPL 2011, Electron. Proc. Theor. Comp. Sci., vol. 57 (2011), Saarbrücken), 120-133 · Zbl 1457.68179 |
| [8] | Bortolussi, L.; Galpin, V.; Hillston, J., Hybrid performance modelling of opportunistic networks, (Proceedings of the Tenth Workshop on Quantitative Aspects of Programming Languages. Proceedings of the Tenth Workshop on Quantitative Aspects of Programming Languages, QAPL 2012, Tallinn. Proceedings of the Tenth Workshop on Quantitative Aspects of Programming Languages. Proceedings of the Tenth Workshop on Quantitative Aspects of Programming Languages, QAPL 2012, Tallinn, Electron. Proc. Theor. Comp. Sci., vol. 85 (2012)), 106-121 · Zbl 1458.68026 |
| [10] | Bortolussi, L.; Galpin, V.; Hillston, J.; Tribastone, M., Hybrid semantics for PEPA, (Proceedings of QEST 2010 (2010)), 181-190 |
| [11] | Bortolussi, L.; Policriti, A., Hybrid semantics of stochastic programs with dynamic reconfiguration, (Proceedings of the Second International Workshop on Computational Models for Cell Processes. Proceedings of the Second International Workshop on Computational Models for Cell Processes, COMPMOD 2009. Proceedings of the Second International Workshop on Computational Models for Cell Processes. Proceedings of the Second International Workshop on Computational Models for Cell Processes, COMPMOD 2009, Electron. Proc. Theor. Comp. Sci., vol. 6 (2009)), 63-76 |
| [12] | Bortolussi, L.; Policriti, A., Hybrid dynamics of stochastic programs, Theor. Comput. Sci., 411, 2052-2077 (2010) · Zbl 1198.68175 |
| [13] | Bortolussi, L.; Policriti, A., (Hybrid) automata and (stochastic) programs: The hybrid automata lattice of a stochastic program, J. Log. Comput., 23, 761-798 (2013) · Zbl 1272.68289 |
| [14] | Bortolussi, L.; Policriti, A., Hybrid approximation of stochastic process algebras for systems biology, (IFAC World Congress (July 2008)) |
| [15] | Box, G.; Draper, N., Empirical Model-Building and Response Surfaces (1987), Wiley · Zbl 0614.62104 |
| [16] | Bratsun, D.; Volfson, D.; Tsimring, L.; Hasty, J., Delay-induced stochastic oscillations in gene regulation, Proc. Natl. Acad. Sci. USA, 102, 14593-14598 (2005) |
| [17] | Brugnano, L.; Mazzia, F.; Trigiante, D., Fifty years of stiffness, (Recent Advances in Computational and Applied Mathematics (2011), Springer), 1-21 · Zbl 1216.65083 |
| [18] | Cao, Y.; Gillespie, D.; Petzold, L., Accelerated stochastic simulation of the stiff enzyme-substrate reaction, J. Chem. Phys., 123, 14, 144917 (2005) |
| [19] | Cao, Y.; Gillespie, D.; Petzold, L., Avoiding negative populations in explicit Poisson tau-leaping, J. Chem. Phys., 123, 054104 (2005) |
| [20] | Cao, Y.; Gillespie, D.; Petzold, L., The slow-scale stochastic simulation algorithm, J. Chem. Phys., 122, 1, 14116 (2005) |
| [21] | Caravagna, G., Formal modeling and simulation of biological systems with delays (2011), University of Pisa, PhD thesis |
| [22] | Caravagna, G.; Antoniotti, M.; Mauri, G.; Graudenzi, A.; d’Onofrio, A., Effects of delayed immune-response in tumor immune-system interplay, (Proceedings of the First International Workshop on Hybrid Systems and Biology. Proceedings of the First International Workshop on Hybrid Systems and Biology, HSB. Proceedings of the First International Workshop on Hybrid Systems and Biology. Proceedings of the First International Workshop on Hybrid Systems and Biology, HSB, Electron. Proc. Theor. Comp. Sci., vol. 92 (2012)), 106-121 |
| [23] | Caravagna, G.; Graudenzi, A.; d’Onofrio, A., Distributed delays in a hybrid model of tumor-immune system interplay, Math. Biosci. Eng., 10, 37-57 (2013) · Zbl 1259.92035 |
| [24] | Caravagna, G.; Hillston, J., Bio-PEPAd: A non-markovian extension of Bio-PEPA, Theor. Comput. Sci., 419, 26-49 (2012) · Zbl 1232.68090 |
| [25] | Ciocchetta, F., Bio-PEPA with SBML-like events, (Proceedings of the Workshop on Computational Models for Cell Processes (2008)), 11-22 |
| [26] | Ciocchetta, F., Bio-PEPA with events, (Transactions on Computational Systems Biology XI. Transactions on Computational Systems Biology XI, Lect. Notes Comput. Sci., vol. 5750 (2009), Springer), 45-68 · Zbl 1260.92021 |
| [27] | Ciocchetta, F.; Degasperi, A.; Heath, J.; Hillston, J., Modelling and analysis of the NF-\(κB\) pathway in Bio-PEPA, (Transactions on Computational Systems Biology XII. Transactions on Computational Systems Biology XII, Lect. Notes Comput. Sci., vol. 5945 (2010), Springer), 229-262 |
| [28] | Ciocchetta, F.; Hillston, J., Bio-PEPA: a framework for the modelling and analysis of biological systems (2008), School of Informatics, University of Edinburgh, Tech. Rep. EDI-INF-RR-1231 |
| [29] | Ciocchetta, F.; Hillston, J., Calculi for biological systems, (Formal Methods for Computational Systems Biology. Formal Methods for Computational Systems Biology, SFM08. Formal Methods for Computational Systems Biology. Formal Methods for Computational Systems Biology, SFM08, Lect. Notes Comput. Sci., vol. 5016 (2008)), 265-312 |
| [30] | 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) · Zbl 1173.68041 |
| [31] | Culshaw, R.; Ruan, S., A delay-differential equation model of HIV infection of CD4+T-cells, Math. Biosci., 165, 27-39 (2000) · Zbl 0981.92009 |
| [32] | Curtiss, C.; Hirschfelder, J., Integration of stiff equations, Proc. Natl. Acad. Sci. USA, 38, 235 (1952) · Zbl 0046.13602 |
| [33] | Danos, V.; Laneve, C., Formal molecular biology, Theor. Comput. Sci., 325, 69-110 (2004) · Zbl 1071.68041 |
| [34] | Davis, M., Markov Models and Optimization (1993), Chapman & Hall · Zbl 0780.60002 |
| [35] | Ellavarason, K., An automatic mapping from the Systems Biology Markup Language to the Bio-PEPA process algebra (2008), University of Trento, Master’s thesis |
| [36] | Gadgil, C., Stochastic modeling of biological reactions, J. Indian Inst. Sci., 88, 45-55 (2008) |
| [37] | Galpin, V., Equivalences for a biological process algebra, Theor. Comput. Sci., 412, 6058-6082 (2011) · Zbl 1402.92201 |
| [38] | Galpin, V., Modelling trafficking of proteins within the mammalian cell using Bio-PEPA, (Proceedings of the 10th International Conference on Computational Methods in Systems Biology. Proceedings of the 10th International Conference on Computational Methods in Systems Biology, CMSB 2012. Proceedings of the 10th International Conference on Computational Methods in Systems Biology. Proceedings of the 10th International Conference on Computational Methods in Systems Biology, CMSB 2012, Lect. Notes Comput. Sci., vol. 7605 (2012)), 374-377 |
| [39] | Galpin, V.; Bortolussi, L.; Hillston, J., HYPE: a process algebra for compositional flows and emergent behaviour, (Proceedings of CONCUR 2009. Proceedings of CONCUR 2009, Lect. Notes Comput. Sci., vol. 5710 (2009), Springer), 305-320 · Zbl 1254.68170 |
| [40] | Galpin, V.; Bortolussi, L.; Hillston, J., HYPE: Hybrid modelling by composition of flows, Form. Asp. Comput., 25, 503-541 (2013) · Zbl 1298.68191 |
| [41] | Gandin, I., Integrating continuous and discrete dynamic for Bio-PEPA models of biological systems (2011), University of Trieste, Master’s thesis |
| [42] | Gillespie, D., Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81, 25, 2340-2361 (1997) |
| [43] | Gillespie, D., Approximate accelerated stochastic simulation of chemically reacting systems, J. Chem. Phys., 115, 1716-1733 (2001) |
| [44] | Guerriero, M., Qualitative and quantitative analysis of a Bio-PEPA model of the gp130/JAK/STAT signalling pathway, (Transactions on Computational Systems Biology XI. Transactions on Computational Systems Biology XI, Lect. Notes Comput. Sci., vol. 5750 (2009), Springer), 90-115 |
| [45] | Harris, L.; Clancy, P., A “partitioned leaping” approach for multiscale modeling of chemical reaction dynamics, J. Chem. Phys., 125, 144107 (2006) |
| [46] | Harris, L.; Piccirilli, A.; Majusiak, E.; Clancy, P., Quantifying stochastic effects in biochemical reaction networks using partitioned leaping, Phys. Rev. E, 79, 051906 (2009) |
| [47] | Herajy, M.; Heiner, M., Hybrid representation and simulation of stiff biochemical networks, Nonlinear Anal. Hybrid Syst., 6, 942-959 (2012) · Zbl 1269.93061 |
| [48] | Hillston, J., A Compositional Approach to Performance Modelling (1996), Cambridge University Press |
| [49] | Kalantzis, G., Hybrid stochastic simulations of intracellular reaction-diffusion systems, Comput. Biol. Chem., 33, 205 (2009) · Zbl 1403.92098 |
| [50] | Keizer, J., Statistical Thermodynamics of Nonequilibrium Processes (1987), Springer |
| [51] | Kummer, U.; Olsen, L.; Dixon, C.; Green, A.; Bornberg-Bauer, E.; Baier, G., Switching from simple to complex oscillations in calcium signaling, Biophys. J., 79, 1188-1195 (2000) |
| [52] | Kurtz, T., The relationship between stochastic and deterministic models for chemical reactions, J. Chem. Phys., 57, 2976-2978 (1972) |
| [53] | Kwiatkowska, M.; Norman, G.; Parker, D., PRISM 4.0: Verification of probabilistic real-time systems, (23rd International Conference on Computer Aided Verification (CAV’11). 23rd International Conference on Computer Aided Verification (CAV’11), Lect. Notes Comput. Sci., vol. 6806 (2011)), 585-591 |
| [54] | Kwiatkowski, M.; Stark, I., The continuous \(π\)-calculus: A process algebra for biochemical modelling, (Proceedings of CMSB 2008. Proceedings of CMSB 2008, Lect. Notes Comput. Sci., vol. 5307 (2008)), 103-122 |
| [55] | McKane, A.; Nagy, J.; Newman, T.; Stefanini, M., Amplified biochemical oscillations in cellular systems, J. Stat. Phys., 128, 165-191 (2007) · Zbl 1158.92309 |
| [56] | Michaelis, L.; Menten, M., Die Kinetik der Invertinwirkung, Biochemistry Zeitung, 49, 333-369 (1913) |
| [57] | Nisbet, R.; Gurney, W., A simple mechanism for population cycles, Nature, 263, 319-320 (1976) |
| [58] | Pahle, J., Biochemical simulations: stochastic, approximate stochastic and hybrid approaches, Brief. Bioinform., 10, 53-64 (2009) |
| [59] | Pedersen, M.; Plotkin, G., A language for biochemical systems: design and formal specification, (Transactions on Computational Systems Biology XII. Transactions on Computational Systems Biology XII, Lect. Notes Comput. Sci., vol. 5945 (2010)), 77-145 · Zbl 1275.92020 |
| [60] | Priami, C.; Quaglia, P., Beta binders for biological interactions, (Proceedings of the International Conference on Computational Methods in Systems Biology. Proceedings of the International Conference on Computational Methods in Systems Biology, CMSB 2004. Proceedings of the International Conference on Computational Methods in Systems Biology. Proceedings of the International Conference on Computational Methods in Systems Biology, CMSB 2004, Lect. Notes Comput. Sci., vol. 3082 (2004), Springer), 20-33 · Zbl 1088.68646 |
| [61] | Priami, C.; Regev, A.; Shapiro, E.; Silverman, W., Application of a stochastic name-passing calculus to representation and simulation of molecular processes, Inf. Process. Lett., 80, 25-31 (2001) · Zbl 0997.92018 |
| [62] | Regev, A.; Panina, E.; Silverman, W.; Cardelli, L.; Shapiro, E., BioAmbients: an abstraction for biological compartments, Theor. Comput. Sci., 325, 141-167 (2004) · Zbl 1069.68569 |
| [63] | Regev, A.; Shapiro, E., Cellular abstractions: Cells as computation, Nature, 419, 343 (2002) |
| [64] | Samoilov, M.; Arkin, A., Deviant effects in molecular reaction pathways, Nat. Biotechnol., 24, 1235-1240 (2006) |
| [65] | Smith, H., An Introduction to Delay Differential Equations with Applications to the Life Sciences (2011), Springer · Zbl 1227.34001 |
| [66] | Tribastone, M.; Duguid, A.; Gilmore, S., The PEPA Eclipse Plugin, SIGMETRICS Perform. Eval. Rev., 36, 28-33 (2009) |
| [67] | Troein, C.; Corellou, F.; Dixon, L.; van Ooijen, G.; O’Neill, J.; Bouget, F.-Y.; Millar, A., Multiple light inputs to a simple clock circuit allow complex biological rhythms, Plant J., 66, 375-385 (2011) |
| [68] | Vasudeva, K.; Bhalla, U., Adaptive stochastic-deterministic chemical kinetic simulations, Bioinformatics, 20, 78-84 (2004) |
| [69] | Vellela, M.; Qian, H., A quasistationary analysis of a stochastic chemical reaction: Keizer’s paradox, Bull. Math. Biol., 69, 1727-1746 (2007) · Zbl 1298.92129 |
| [70] | Wolkenhauer, O.; Ullah, M.; Kolch, W.; Cho, K.-H., Modeling and simulation of intracellular dynamics: choosing an appropriate framework, IEEE Trans. Nanobiosci., 3, 200-207 (2004) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
