A Graphical Representation for Biological Processes in the Stochastic pi-Calculus

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]  Corrado Priami,et al.  Stochastic pi-Calculus , 1995, Comput. J..

[2]  Marco Pistore,et al.  History-Dependent Automata: An Introduction , 2005, SFM.

[3]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[4]  Chi-Ying F. Huang,et al.  Ultrasensitivity in the mitogen-activated protein kinase cascade. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[5]  David N. Turner,et al.  The polymorphic Pi-calculus : theory and implementation , 1996 .

[6]  Luca Cardelli,et al.  A Compositional Approach to the Stochastic Dynamics of Gene Networks , 2006, Trans. Comp. Sys. Biology.

[7]  Luca Cardelli,et al.  A Correct Abstract Machine for the Stochastic Pi-calculus , 2004 .

[8]  Robin Milner.  Pi-Nets: A Graphical Form of pi-Calculus , 1994, ESOP.

[9]  David Harel,et al.  Statecharts: A Visual Formalism for Complex Systems , 1987, Sci. Comput. Program..

[10]  H. Kitano,et al.  A comprehensive pathway map of epidermal growth factor receptor signaling , 2005, Molecular systems biology.

[11]  Luca Cardelli.  A Compositional Approach to the Stochastic Dynamics of Gene Networks , 2005, CONCUR.

[12]  Corrado Priami,et al.  Application of a stochastic name-passing calculus to representation and simulation of molecular processes , 2001, Inf. Process. Lett..

[13]  C. Petri.  Kommunikation mit Automaten , 1962 .

[14]  M. Elowitz,et al.  A synthetic oscillatory network of transcriptional regulators , 2000, Nature.

[15]  V. Hakim,et al.  Design of genetic networks with specified functions by evolution in silico. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Emden R. Gansner,et al.  An open graph visualization system and its applications to software engineering , 2000 .

[17]  Robin Milner,et al.  Communicating and mobile systems - the Pi-calculus , 1999 .

[18]  Davide Sangiorgi,et al.  Communicating and Mobile Systems: the π-calculus, , 2000 .

[19]  Luca Cardelli,et al.  A Graphical Representation for the Stochastic Pi-calculus , 2005 .

[20]  Raheel Ahmad,et al.  The π-Calculus: A theory of mobile processes , 2008, Scalable Comput. Pract. Exp..

[21]  Marco Bernardo,et al.  Formal Methods for Mobile Computing, 5th International School on Formal Methods for the Design of Computer, Communication, and Software Systems, SFM-Moby 2005, Bertinoro, Italy, April 26-30, 2005, Advanced Lectures , 2005, SFM.

[22]  Paola Lecca,et al.  Cell Cycle Control in Eukaryotes: A BioSpi model , 2007, Electron. Notes Theor. Comput. Sci..

[23]  Emden R. Gansner,et al.  An open graph visualization system and its applications to software engineering , 2000, Softw. Pract. Exp..

[24]  Stephen Gilmore,et al.  Modelling the Influence of RKIP on the ERK Signalling Pathway Using the Stochastic Process Algebra PEPA , 2006, Trans. Comp. Sys. Biology.

[25]  Ch. Andre,et al.  Synccharts: A visual representation of reactive behaviors , 1995 .

[26]  Aviv Regev,et al.  Representation and Simulation of Biochemical Processes Using the pi-Calculus Process Algebra , 2000, Pacific Symposium on Biocomputing.

[27]  Davide Sangiorgi,et al.  The Pi-Calculus - a theory of mobile processes , 2001 .