## A Graphical Representation for Biological Processes in the Stochastic pi-calculus (2006)

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Venue: | Transactions in Computational Systems Biology |

Citations: | 33 - 15 self |

### BibTeX

@ARTICLE{Phillips06agraphical,

author = {Andrew Phillips and Luca Cardelli},

title = {A Graphical Representation for Biological Processes in the Stochastic pi-calculus},

journal = {Transactions in Computational Systems Biology},

year = {2006},

volume = {4230},

pages = {2006}

}

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### Abstract

Abstract. This paper presents a graphical representation for the stochastic π-calculus, which is formalised by defining a corresponding graphical calculus. The graphical calculus is shown to be reduction equivalent to stochastic π, ensuring that the two calculi have the same expressive power. The graphical representation is used to model a couple of example biological systems, namely a bistable gene network and a mapk signalling cascade. One of the benefits of the representation is its ability to highlight the existence of cycles, which are a key feature of biological systems. Another benefit is its ability to animate interactions between system components, in order to visualise system dynamics. The graphical representation can also be used as a front end to a simulator for the stochastic π-calculus, to help make modelling and simulation of biological systems more accessible to non computer scientists. 1

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Citation Context ...on to ensure that fn(Pi) ⊆ mi, and renaming process definitions where necessary to ensure that all top-level definitions are distinct. The transformations are based on standard encodings presented in =-=[21,11,20]-=-. A core syntax of the SPiM programming language is presented in Appendix A. The implementation can display a process of the graphical stochastic πcalculus by exporting to an open graph syntax such as... |

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Citation Context ...on to ensure that fn(Pi) ⊆ mi, and renaming process definitions where necessary to ensure that all top-level definitions are distinct. The transformations are based on standard encodings presented in =-=[21,11,20]-=-. A core syntax of the SPiM programming language is presented in Appendix A. The implementation can display a process of the graphical stochastic πcalculus by exporting to an open graph syntax such as... |

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Citation Context ...ore syntax of the SPiM programming language is presented in Appendix A. The implementation can display a process of the graphical stochastic πcalculus by exporting to an open graph syntax such as DOT =-=[5]-=-. DOT is a textual syntax for representing directed graphs, which can be rendered using the Graphviz DOT layout engine. A symbolic core syntax for DOT graphs is described in Definition 9. An encoding ... |

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Citation Context ...e modelling and simulation of biological systems more accessible to non computer scientists. 1 Introduction The stochastic π-calculus has been used to model and simulate a range of biological systems =-=[9,17,19]-=-. One of the main benefits of the calculus is its ability to model large systems incrementally, by composing simpler models of subsystems in an intuitive way [2]. Various stochastic simulators have be... |

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Citation Context ...e modelling and simulation of biological systems more accessible to non computer scientists. 1 Introduction The stochastic π-calculus has been used to model and simulate a range of biological systems =-=[9,17,19]-=-. One of the main benefits of the calculus is its ability to model large systems incrementally, by composing simpler models of subsystems in an intuitive way [2]. Various stochastic simulators have be... |

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Citation Context ... corresponding graphical calculus. The papersis structured as follows. Section 2 presents a variant of the stochastic π-calculus that supports internal transitions and recursive definitions, based on =-=[18]-=-. Section 3 presents a graphical representation for the stochastic π-calculus, and explains why additional syntax constraints are needed to define a corresponding graphical execution model. Section 4 ... |

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Citation Context ...on to ensure that fn(Pi) ⊆ mi, and renaming process definitions where necessary to ensure that all top-level definitions are distinct. The transformations are based on standard encodings presented in =-=[21,11,20]-=-. A core syntax of the SPiM programming language is presented in Appendix A. The implementation can display a process of the graphical stochastic πcalculus by exporting to an open graph syntax such as... |

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Citation Context ... simply the rate r of the delay, while the apparent rate of an interaction on a given channel x is equal to the number of possible combinations of inputs and outputs on x, multiplied by the rate of x =-=[15]-=-. The function R(x, P ) calculates the apparent rate of channel x in process P and is defined by: R(x, P ) = rate(x) × (Inx(P ) × Outx(P ) − Mixx(P )) (12) 3sα Description fn(α) bn(α) ?x(n) Receive a ... |

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Citation Context ...te a range of biological systems [9,17,19]. One of the main benefits of the calculus is its ability to model large systems incrementally, by composing simpler models of subsystems in an intuitive way =-=[2]-=-. Various stochastic simulators have been developed for the calculus [19,14], in order to perform virtual experiments on biological system models. Such in silico experiments can be used to formulate t... |

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Citation Context ...ec. 2, ensuring that the two calculi have the same expressive power. Section 5 uses the graphical stochastic π-calculus to model a couple of example biological systems, namely a bistable gene network =-=[4]-=- and a mapk signalling cascade [8]. Finally, Section 6 shows how the graphical representation can be used as a front end to a simulator for the stochastic π-calculus. 2 The Stochastic π-calculus This ... |

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Citation Context ... scalable, selfcontained graphical representation of concurrent systems. More recent work proposed a synchronous variant to Statecharts, in which concurrent processes can synchronise on shared labels =-=[1]-=-. Our graphical representation uses a similar principle, in contrast with foundational work on graphical representations for the π-calculus [10], which uses more elaborate rules for graph re-writing. ... |

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Citation Context ...P !x(y) −→ P ′ ⇒ νy P !x(νy) −→ P ′ x /∈ fn(α) ∪ bn(α) P α −→ P ′ ⇒ νx P α −→ νx P ′ M α −→ P ′ ⇒ π.P + M α −→ P ′ bn(α) ∩ fn(Q) = ∅ P α −→ P ′ ⇒ P | Q α X(m)=P P{n/m} α −→ P ′ ⇒ X(n) (4) (6) (7) (8) =-=(9)-=- −→ P ′ | Q (10) α −→ P ′ Definition 3. Reduction in Sπ. An output !x(n).P can send the value n on channel x and then execute process P (1). An input ?x(m).P can receive a value n on channel x and the... |

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Citation Context ...esentations for the π-calculus [10], which uses more elaborate rules for graph re-writing. In general, graphical representations for process calculi are still an active area of research. For example, =-=[12]-=- describes an automata-based representation for the π-calculus, in which each state of the system is represented as a node in the graph of an automaton. In this paper we adopt a less ambitious but per... |

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Citation Context ...li have the same expressive power. Section 5 uses the graphical stochastic π-calculus to model a couple of example biological systems, namely a bistable gene network [4] and a mapk signalling cascade =-=[8]-=-. Finally, Section 6 shows how the graphical representation can be used as a front end to a simulator for the stochastic π-calculus. 2 The Stochastic π-calculus This section presents a variant of the ... |

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Citation Context ...e r, such as a stochastic delay or an interaction on a private channel. !x(n).P + M !x(n) −→ P (1) ?x(m).P + M ?x(n) −→ P{n/m} (2) τr.P + M P !x(n) −→ P ′ Q ?x(n) −→ Q ′ ⇒ P | Q x −→ P ′ | Q ′ r −→ P =-=(3)-=- n /∈ fn(Q) P !x(νn) −→ P ′ Q ?x(n) −→ Q ′ ⇒ P | Q x −→ νn (P ′ | Q ′ ) (5) P x −→ P ′ R(x,P ) ⇒ νx P −→ νx P ′ x �= y P !x(y) −→ P ′ ⇒ νy P !x(νy) −→ P ′ x /∈ fn(α) ∪ bn(α) P α −→ P ′ ⇒ νx P α −→ νx ... |

9 | A Graphical Representation for the Stochastic Pi-calculus. Concurrent models in molecular biology
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Citation Context ... ideas to produce a novel representation, in which different node types are used to distinguish between stochastic choice and parallel composition. An extended abstract for this paper is presented in =-=[16]-=-. The reduction semantics of [15] relies on a notion of structural congruence for the re-ordering of processes. Although this gives rise to a simplified definition of reduction, it cannot be used in t... |

7 |
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Citation Context ...ch concurrent processes can synchronise on shared labels [1]. Our graphical representation uses a similar principle, in contrast with foundational work on graphical representations for the π-calculus =-=[10]-=-, which uses more elaborate rules for graph re-writing. In general, graphical representations for process calculi are still an active area of research. For example, [12] describes an automata-based re... |

3 |
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Citation Context ...the calculus is its ability to model large systems incrementally, by composing simpler models of subsystems in an intuitive way [2]. Various stochastic simulators have been developed for the calculus =-=[19,14]-=-, in order to perform virtual experiments on biological system models. Such in silico experiments can be used to formulate testable hypotheses on the behaviour of biological systems, as a guide to fut... |

1 |
Akira Funahashi1, and Hiroaki Kitano. A comprehensive pathway map of epidermal growth factor receptor signaling. Molecular Systems Biology, 1:E1–E17
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Citation Context ...ms could be built on top of the stochastic π-calculus, as discussed in Sec. 5. It would be interesting to define high-level graphical representations for these libraries, inspired by diagrams such as =-=[13]-=- that are currently being used by biologists. Another area for future work is to explore ways of minimising the occurrence of substitution labels in the graphical representation of a given process. Su... |