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44
BioPEPA: a framework for the modelling and analysis of biological systems
, 2008
"... In this work we present BioPEPA, a process algebra for the modelling and the analysis of biochemical networks. It is a modification of PEPA, originally defined for the performance analysis of computer systems, in order to handle some features of biological models, such as stoichiometry and the use ..."
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Cited by 94 (25 self)
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In this work we present BioPEPA, a process algebra for the modelling and the analysis of biochemical networks. It is a modification of PEPA, originally defined for the performance analysis of computer systems, in order to handle some features of biological models, such as stoichiometry and the use of general kinetic laws. The domain of application is the one of biochemical networks. BioPEPA may be seen as an intermediate, formal, compositional representation of biological systems, on which different kinds of analysis can be carried out. BioPEPA is enriched with some notions of equivalence. Specifically, the isomorphism and strong bisimulation for PEPA have been considered. Finally, we show the translation of three biological models into the new language and we report some analysis results.
On process rate semantics
 Theoretical Computer Science
, 2008
"... We provide translations between process algebra and systems of chemical reactions. We show that the translations preserve discretestate (stochastic) and continuousstate (concentration) semantics, and in particular that the continuousstate semantics of processes corresponds to the differential equ ..."
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Cited by 53 (11 self)
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We provide translations between process algebra and systems of chemical reactions. We show that the translations preserve discretestate (stochastic) and continuousstate (concentration) semantics, and in particular that the continuousstate semantics of processes corresponds to the differential equations of chemistry based on the law of mass action. The novel semantics of processes so obtained equates processes that have the same state occupation dynamics, but that may have different interaction interfaces. 1
Stronger computational modelling of signalling pathways using both continuous and discretestate methods
 In To appear in Computational Methods in Systems Biology 2006, LNCS
, 2006
"... Abstract. Starting from a biochemical signalling pathway model expressed in a process algebra enriched with quantitative information we automatically derive both continuousspace and discretestate representations suitable for numerical evaluation. We compare results obtained using implicit numerica ..."
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Cited by 28 (15 self)
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Abstract. Starting from a biochemical signalling pathway model expressed in a process algebra enriched with quantitative information we automatically derive both continuousspace and discretestate 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. 1
Using Probabilistic Model Checking in Systems Biology
"... Probabilistic model checking is a formal verification framework for systems which exhibit stochastic behaviour. It has been successfully applied to a wide range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we demonstrate i ..."
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Cited by 25 (0 self)
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Probabilistic model checking is a formal verification framework for systems which exhibit stochastic behaviour. It has been successfully applied to a wide range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we demonstrate its applicability to the analysis of biological pathways and show how it can yield a better understanding of the dynamics of these systems. Through a case study of the MAP (MitogenActivated Protein) Kinase cascade, we explain how biological pathways can be modelled in the probabilistic model checker PRISM and how this enables the analysis of a rich selection of quantitative properties. 1.
From processes to ODEs by Chemistry
 in TCS 2008, Fifth IFIP International Conference on Theoretical Computer Science
, 2004
"... We investigate the collective behavior of processes in terms of differential equations, using chemistry as a stepping stone. Chemical reactions can be converted to ordinary differential equations, and also to processes in a stochastic process algebra. Conversely, certain stochastic processes (in Che ..."
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Cited by 21 (0 self)
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We investigate the collective behavior of processes in terms of differential equations, using chemistry as a stepping stone. Chemical reactions can be converted to ordinary differential equations, and also to processes in a stochastic process algebra. Conversely, certain stochastic processes (in Chemical Parametric Form, or CPF) can be converted to chemical reactions. CPF is a subset of πcalculus, but is already more powerful that what is strictly needed to represent chemistry: it supports also parameterization and compositional reuse of models. The mapping of CPF to chemistry thus induces a parametric and compositional mapping of CPF to differential equations; the indirect mapping through chemistry is easier to define and understand than a direct mapping. As an example, we derive a quantitative interleaving law from the differential equations. 1
The dynamic systems approach to control and regulation of intracellular networks
 FEBS Letters
, 2005
"... Abstract Systems theory and cell biology have enjoyed a long relationship that has received renewed interest in recent years in the context of systems biology. The term ÔsystemsÕ in systems biology comes from systems theory or dynamic systems theory: systems biology is defined through the applicati ..."
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Cited by 16 (2 self)
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Abstract Systems theory and cell biology have enjoyed a long relationship that has received renewed interest in recent years in the context of systems biology. The term ÔsystemsÕ in systems biology comes from systems theory or dynamic systems theory: systems biology is defined through the application of systemsand signaloriented approaches for an understanding of interand intracellular dynamic processes. The aim of the present text is to review the systems and control perspective of dynamic systems. The biologistÕs conceptual framework for representing the variables of a biochemical reaction network, and for describing their relationships, are pathway maps. A principal goal of systems biology is to turn these static maps into dynamic models, which can provide insight into the temporal evolution of biochemical reaction networks. Towards this end, we review the case for differential equation models as a ÔnaturalÕ representation of causal entailment in pathways. Blockdiagrams, commonly used in the engineering sciences, are introduced and compared to pathway maps. The stimulusresponse representation of a molecular system is a necessary condition for an understanding of dynamic interactions among the components that make up a pathway. Using simple examples, we show how biochemical reactions are modelled in the dynamic systems framework and visualized using blockdiagrams.
Strand Algebras for DNA Computing
, 2009
"... We present a process algebra for DNA computing, discussing compilation of other formal systems into the algebra, and compilation of the algebra into DNA structures. ..."
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Cited by 12 (1 self)
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We present a process algebra for DNA computing, discussing compilation of other formal systems into the algebra, and compilation of the algebra into DNA structures.
Artificial biochemistry
 In Algorithmic Bioproceses, LNCS
, 2008
"... Chemical and biochemical systems are presented as collectives of interacting stochastic automata: each automaton represents a molecule that undergoes state transitions. This framework constitutes an artificial biochemistry, where automata interact by the equivalent of the law of mass action. We anal ..."
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Cited by 10 (2 self)
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Chemical and biochemical systems are presented as collectives of interacting stochastic automata: each automaton represents a molecule that undergoes state transitions. This framework constitutes an artificial biochemistry, where automata interact by the equivalent of the law of mass action. We analyze several example systems and networks, both by stochastic simulation and by ordinary dif‐ ferential equations. 1 Stochastic Automata Collectives This paper is an empirical investigation of an artifi‐ cial biochemistry obtained by the interactions of sto‐ chastic automata. The study of such artificial frame‐ works has been advocated before [2]; we explore a modern version based on a theory of concurrent processes that obeys the equivalent of the law of mass action. Foundations for this work have been investigated elsewhere [1]; here we aim to give a self‐contained and accessible presentation of the framework, and to explore by means of examples the richness of “emergent ” and unexpected behavior that can be represented by combinations of simple building blocks. By a collective we mean a large set of interacting, finite state automata. This is not quite the situation we have in classical automata theory, because we are interested in the behavior of a large set of auto‐ mata acting together. It is also not quite the situation with cellular automata, because our automata are interacting, but not necessarily on a regular grid. It is also not quite the situation in process algebra, be‐ cause again we are interested in the behavior of col‐ lectives, not of individuals. Similar frameworks have been investigated under the headings of collectives [12], sometimes including stochasticity [6]. By stochastic we mean that automata interactions have rates. Stochastic rates induce a quantitative semantics for the behavior of collectives. Collective behavior cannot be considered quite discrete, be‐ cause it can be the result of hundreds or thousands individual contributions. But it is not quite continu‐ ous either, because of the possibility of non‐trivial stochastic effects. And it is also not hybrid: there is no switching between discrete and continuous re‐ gimes.
Process algebras in systems biology
"... Abstract. In this chapter we introduce process algebras, a class of formal modelling techniques developed in theoretical computer science, and discuss their use within systems biology. These formalisms have a number of attractive features which make them ideal candidates to be intermediate, formal, ..."
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Abstract. In this chapter we introduce process algebras, a class of formal modelling techniques developed in theoretical computer science, and discuss their use within systems biology. These formalisms have a number of attractive features which make them ideal candidates to be intermediate, formal, compositional representations of biological systems. As we will show, when modelling is carried out at a suitable level of abstraction, the constructed model can be amenable to analysis using a variety of different approaches, encompassing both individualsbased stochastic simulation and populationbased ordinary differential equations. We focus particularly on BioPEPA, a recently defined extension of the PEPA stochastic process algebra, which has features to capture both stoichiometry and general kinetic laws. We present the definition of the language, some equivalence relations and the mappings to underlying mathematical models for analysis. We demonstrate the use of BioPEPA on two biological examples.
An alternative to Gillespie’s algorithm for simulating chemical reactions
 Computational Methods in Systems Biology (CMSB’05
, 2005
"... Abstract. We introduce a probabilistic algorithm for the simulation of chemical reactions, which can be used as an alternative to the wellestablished stochastic algorithm proposed by D.T. Gillespie in the ’70s. We show that the probabilistic evolution of systems derived by means of our algorithm can ..."
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Cited by 7 (4 self)
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Abstract. We introduce a probabilistic algorithm for the simulation of chemical reactions, which can be used as an alternative to the wellestablished stochastic algorithm proposed by D.T. Gillespie in the ’70s. We show that the probabilistic evolution of systems derived by means of our algorithm can be compared to the stochastic time evolution of chemical reactive systems described by Gillespie. Moreover, we use our algorithm in the definition of a formal model based on multiset rewriting, and we show some simulation results of enzymatic activity, which we compare with results of real experiments. 1