From Biochemistry to Stochastic Processes

The nano@k calculus is a formalism that models biochemical systems by defining its set of reactions. We study the implementation of nano@k into the Stochastic Pi Machine where biochemical systems are defined by regarding molecules as processes, and deriving the overall behaviour by means of communication rules. Our implementation complies with the stochastic behaviors of systems, thus allowing one to use nano@k as an intelligible front-end for a process-oriented simulator. This study also permits to reuse, in nano@k, the theories and tools already developed for process calculi.

[1]  Alan Bundy,et al.  Constructing Induction Rules for Deductive Synthesis Proofs , 2006, CLASE.

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

[3]  Luca Cardelli,et al.  On process rate semantics , 2008, Theor. Comput. Sci..

[4]  Luca Cardelli,et al.  On the Computational Power of Biochemistry , 2008, AB.

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

[6]  Vincent Danos,et al.  Computational self-assembly , 2008, Theor. Comput. Sci..

[7]  Ramon Puigjaner,et al.  Proceedings of the 10th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools , 1998 .

[8]  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.

[9]  Stephen Gilmore,et al.  The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling , 1994, Computer Performance Evaluation.

[10]  Vincent Danos,et al.  Scalable Simulation of Cellular Signaling Networks , 2007, APLAS.

[11]  Paolo Milazzo,et al.  A Calculus of Looping Sequences for Modelling Microbiological Systems , 2006, Fundam. Informaticae.

[12]  Cosimo Laneve,et al.  Formal molecular biology , 2004, Theor. Comput. Sci..

[13]  Cosimo Laneve,et al.  Modelization and Simulation of Nano Devices in $\mathtt{nano}\kappa$ Calculus , 2007, CMSB.

[14]  Jane Hillston,et al.  Bio-PEPA: An Extension of the Process Algebra PEPA for Biochemical Networks , 2007, FBTC@CONCUR.

[15]  Marco Bernardo,et al.  A Survey of Markovian Behavioral Equivalences , 2007, SFM.

[16]  Catuscia Palamidessi,et al.  Model Checking Probabilistic and Stochastic Extensions of the π-Calculus , 2009, IEEE Transactions on Software Engineering.

[17]  Luca de Alfaro,et al.  Symbolic Model Checking of Probabilistic Processes Using MTBDDs and the Kronecker Representation , 2000, TACAS.

[18]  Gordon D. Plotkin,et al.  A structural approach to operational semantics , 2004, J. Log. Algebraic Methods Program..

[19]  François Fages,et al.  BIOCHAM: an environment for modeling biological systems and formalizing experimental knowledge , 2006, Bioinform..

[20]  Jane Hillston,et al.  Bio-PEPA: A framework for the modelling and analysis of biological systems , 2009, Theor. Comput. Sci..

[21]  Marta Z. Kwiatkowska,et al.  Probabilistic model checking of complex biological pathways , 2008, Theor. Comput. Sci..

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