Bio-PEPAd: A non-Markovian extension of Bio-PEPA
Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting in more compact models. In this paper, we enrich the stochastic process algebra Bio-PEPA, with the possibility o...
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| Abstract | Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting in more compact models. In this paper, we enrich the stochastic process algebra Bio-PEPA, with the possibility of assigning delays to actions, yielding a new non-Markovian stochastic process algebra: Bio-PEPAd. This is a conservative extension meaning that the original syntax of Bio-PEPA is retained and the delay specification which can now be associated with actions may be added to existing Bio-PEPA models. The semantics of the firing of the actions with delays is the delay-as-duration approach, earlier presented in papers on the stochastic simulation of biological systems with delays. This semantics of the algebra is given in the Starting–Terminating style, meaning that the state and the completion of an action are observed as two separate events, as required by delays. We formally define the encoding of Bio-PEPAd systems in Generalized Semi-Markov Processes (GSMPs), as input for a Delay Stochastic Simulation Algorithm (DSSA) and as sets of Delay Differential Equations (DDEs), the deterministic framework for modeling of biological systems with delays. Finally, we prove theorems stating the relation between Bio-PEPA and Bio-PEPAd models. We end the paper with an example model of biological systems with delays to illustrate the approach. |
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| AbstractList | Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting in more compact models. In this paper, we enrich the stochastic process algebra Bio-PEPA, with the possibility of assigning delays to actions, yielding a new non-Markovian stochastic process algebra: Bio-PEPAd. This is a conservative extension meaning that the original syntax of Bio-PEPA is retained and the delay specification which can now be associated with actions may be added to existing Bio-PEPA models. The semantics of the firing of the actions with delays is the delay-as-duration approach, earlier presented in papers on the stochastic simulation of biological systems with delays. This semantics of the algebra is given in the Starting–Terminating style, meaning that the state and the completion of an action are observed as two separate events, as required by delays. We formally define the encoding of Bio-PEPAd systems in Generalized Semi-Markov Processes (GSMPs), as input for a Delay Stochastic Simulation Algorithm (DSSA) and as sets of Delay Differential Equations (DDEs), the deterministic framework for modeling of biological systems with delays. Finally, we prove theorems stating the relation between Bio-PEPA and Bio-PEPAd models. We end the paper with an example model of biological systems with delays to illustrate the approach. |
| Author | Hillston, Jane Caravagna, Giulio |
| Author_xml | – sequence: 1 givenname: Giulio surname: Caravagna fullname: Caravagna, Giulio email: caravagn@di.unipi.it organization: Dipartimento di Informatica, Università di Pisa, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy – sequence: 2 givenname: Jane surname: Hillston fullname: Hillston, Jane email: jane.hillston@ed.ac.uk organization: Laboratory for Foundations of Computer Science, The University of Edinburgh, Edinburgh EH8 9AB, Scotland, United Kingdom |
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| CitedBy_id | crossref_primary_10_1016_j_entcs_2013_02_016 crossref_primary_10_1088_1478_3975_abc2ab crossref_primary_10_1016_j_peva_2016_09_001 crossref_primary_10_1016_j_ic_2014_01_010 crossref_primary_10_1016_j_tcs_2015_03_051 crossref_primary_10_1186_1752_0509_9_S3_S8 crossref_primary_10_1016_j_ic_2014_01_016 crossref_primary_10_1080_17445760_2025_2527713 |
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| Keywords | DDEs Delay-as-duration GSMPs Non-Markovian process algebra DSSA Bio-PEPA |
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