TY - JOUR
T1 - Hybrid semantics for Bio-PEPA
AU - Galpin, Vashti
N1 - Special Issue on Hybrid Systems and Biology
PY - 2014/8
Y1 - 2014/8
N2 - 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.
AB - 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.
KW - Simulation
U2 - 10.1016/j.ic.2014.01.016
DO - 10.1016/j.ic.2014.01.016
M3 - Article
VL - 236
SP - 122
EP - 145
JO - Information and Computation
JF - Information and Computation
SN - 0890-5401
IS - 0
ER -