Adam Duguid

The PEPA eclipse plugin

The PEPA Eclipse Plug-in supports the creation and analysis of performance models, from small-scale Markov models to large-scale simulation studies and differential equation systems. Whichever form of analysis is used, models are expressed in a single highlevel language for quantitative modelling, Performance Evaluation Process Algebra (PEPA).

Stronger computational modelling of signalling pathways using both continuous and discrete-state methods

Starting from a biochemical signalling pathway model expressed in a process algebra enriched with quantitative information we automatically derive both continuous-space and discrete-state representations suitable for numerical evaluation. We compare results obtained using implicit numerical differentiation formulae to those obtained using approximate stochastic simulation thereby exposing a flaw in the use of the differentiation procedure producing misleading results.

The Bio-PEPA Tool Suite

Bio-PEPA is a timed process algebra designedspecifically for the description of biological phenomena and theiranalysis through quantitative methods such asstochastic simulation and probabilistic model-checking.Two software tools are available for modelling with Bio-PEPA, theBio-PEPA Workbench and the Bio-PEPA Eclipse Plugin. The Bio-PEPAWorkbench is the research prototype tool which allows us to try outnew language features and new types of analysis through rapidprototyping. The Bio-PEPA Eclipse Plugin is a polished modellingenvironment which targets end-users who wish to do Bio-PEPA modellingsupported by a comprehensive integrated development environment. Bothmodelling tools allow the user to analyse their model both in thediscrete stochastic regime and in the sure continuous regime whilemaintaining only a single source in the Bio-PEPA language.

Design and development of software tools for Bio-PEPA

This paper surveys the design of software tools for the Bio-PEPA process algebra. Bio-PEPA is a high-level language for modelling biological systems such as metabolic pathways and other biochemical reaction networks. Through providing tools for this modelling language we hope to allow easier use of a range of simulators and model-checkers thereby freeing the modeller from the responsibility of developing a custom simulator for the problem of interest. Further, by providing mappings to a range of different analysis tools the Bio-PEPA language allows modellers to compare analysis results which have been computed using independent numerical analysers, which enhances the reliability and robustness of the results computed.

Coping with the parallelism of bittorrent: conversion of PEPA to ODEs in dealing with state space explosion

The Performance Evaluation Process Algebra (PEPA) language is a stochastic process algebra, generating Continuous Time Markov Chains (CTMC) to allow quantitative analysis. Protocols such as BitTorrent are highly parallel in nature, and represent one area where CTMC analysis is limited by the well-known state space problem. The number of unique states each client can exist in, and the number of clients required to accurately model a typical BitTorrent network preclude the use of CTMCs. Recent work has shown that PEPA models also allow the derivation of an activity matrix, from which ODE and stochastic simulation models, as alternative forms of analysis, are possible. Using this technique, a BitTorrent network is created, analysed, and the results compared against previous BitTorrent models.

A compartmental model of the cAMP/PKA/MAPK pathway in Bio-PEPA

The vast majority of biochemical systems involve the exchange of information between different compartments, either in the form of transportation or via the intervention of membrane proteins which are able to transmit stimuli between bordering compartments. The correct quantitative handling of compartments is, therefore, extremely important when modelling real biochemical systems. The Bio-PEPA process algebra is equipped with the capability of explicitly defining quantitative information such as compartment volumes and membrane surface areas. Furthermore, the recent development of the Bio-PEPA Eclipse Plug-in allows us to perform a correct stochastic simulation of multi-compartmental models. Here we present a Bio-PEPA compartmental model of the cAMP/PKA/MAPK pathway. We analyse the system using the Bio-PEPA Eclipse Plug-in and we show the correctness of our model by comparison with an existing ODE model. Furthermore, we perform computational experiments in order to investigate certain properties of the pathway. Specifically, we focus on the system response to the inhibition and strengthening of feedback loops and to the variation in the activity of key pathway reactions and we observe how these modifications affect the behaviour of the pathway. These experiments are useful to understand the control and regulatory mechanisms of the system.

Partial Evaluation of PEPA Models for Fluid-Flow Analysis

We present an application of partial evaluationto performance models expressed in the PEPA stochastic process algebra [1]. We partially evaluate the state-space of a PEPA model in order to remove uses of the cooperation and hiding operators and compile an arbitrary sub-model into a single sequential component. This transformation is applied to PEPA models which are not in the correct form for the application of the fluid-flow analysis for PEPA [2]. The result of the transformation is a PEPA model which is amenable to fluid-flow analysis but which is strongly equivalent[1] to the input PEPA model and so, by an application of Hillstons theorem, performance results computed from one model are valid for the other. We apply the method to a Markovian model of a key distribution centre used to facilitate secure distribution of cryptographic session keys between remote principals communicating over an insecure network.

Deriving Differential Equations from Process Algebra Models in Reagent-Centric Style

The reagent-centric style of modeling allows stochastic process algebra models of biochemical signaling pathways to be developed in an intuitive way. Furthermore, once constructed, the models are amenable to analysis by a number of different mathematical approaches including both stochastic simulation and coupled ordinary differential equations. In this chapter, we give a tutorial introduction to the reagent-centric style, in PEPA and Bio-PEPA, and the way in which such models can be used to generate systems of ordinary differential equations.

Integrated Analysis from Abstract Stochastic Process Algebra Models

Bio-PEPA is a novel stochastic process algebra which has been recently developed for modelling biochemical pathways [5,6]. In Bio-PEPA a reagent-centric style of modelling is adopted, and a variety of analysis techniques can be applied to a single model expression. Such an approach facilitates easy validation of analysis results when the analyses address the same issues [3] and enhanced insight when the analyses are complementary [4]. Currently supported analysis techniques include stochastic simulation at the molecular level, ordinary di..erential equations, probabilistic model checking and numerical analysis of a continuous time Markov chain.