Attractor Equivalence: An Observational Semantics for Reaction Networks

We study observational semantics for networks of chemical reactions as used in systems biology. Reaction networks without kinetic information, as we consider, can be identified with Petri nets. We present a new observational semantics for reaction networks that we call the attractor equivalence. The main idea of the attractor equivalence is to observe reachable attractors and reachability of an attractor divergence in all possible contexts. The attractor equivalence can support powerful simplifications for reaction networks as we illustrate at the example of the Tet-On system. Alternative semantics based on bisimulations or traces, in contrast, do not support all needed simplifications.

[1]  Sylvain Soliman,et al.  Invariants and Other Structural Properties of Biochemical Models as a Constraint Satisfaction Problem , 2012, Algorithms for Molecular Biology.

[2]  T Murata,et al.  Reduction and expansion of live and safe marked graphs. , 1979 .

[3]  Sylvain Soliman,et al.  A Constraint Solving Approach to Tropical Equilibration and Model Reduction , 2014, 1401.6337.

[4]  Grzegorz Rozenberg,et al.  Advances in Petri Nets 1985 , 1985, Lecture Notes in Computer Science.

[5]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[6]  Ian Stark,et al.  The Continuous pi-Calculus: A Process Algebra for Biochemical Modelling , 2008, CMSB.

[7]  Andrew M. Pitts,et al.  Operational Semantics and Program Equivalence , 2000, APPSEM.

[8]  Serge Haddad,et al.  A reduction theory for coloured nets , 1988, European Workshop on Applications and Theory in Petri Nets.

[9]  Carla Simone,et al.  A survey of equivalence notions for net based systems , 1992, Advances in Petri Nets: The DEMON Project.

[10]  René Thomas.  Regulatory networks seen as asynchronous automata: A logical description , 1991 .

[11]  F. Fages,et al.  Long-term model predictive control of gene expression at the population and single-cell levels , 2012, Proceedings of the National Academy of Sciences.

[12]  Robert Valette,et al.  Analysis of Petri Nets by Stepwise Refinements , 1979, J. Comput. Syst. Sci..

[13]  Grzegorz Rozenberg.  Advances in Petri Nets 1991 , 1990, Lecture Notes in Computer Science.

[14]  M. Gossen,et al.  Tight control of gene expression in mammalian cells by tetracycline-responsive promoters. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Joseph Sifakis,et al.  Fairness and related properties in transition systems — a temporal logic to deal with fairness , 1983, Acta Informatica.

[16]  Grzegorz Rozenberg.  Advances in Petri Nets 1992 , 1992, Lecture Notes in Computer Science.

[17]  C. A. R. Hoare,et al.  A Model for Communicating Sequential Processes , 1980, On the Construction of Programs.

[18]  Aurélien Naldi,et al.  Efficient Handling of Large Signalling-Regulatory Networks by Focusing on Their Core Control , 2012, CMSB.

[19]  M. Gossen,et al.  Transcriptional activation by tetracyclines in mammalian cells. , 1995, Science.

[20]  Joachim Niehren,et al.  Observational Semantics for a Concurrent Lambda Calculus with Reference Cells and Futures , 2007, MFPS.

[21]  Davide Sangiorgi,et al.  Environmental Bisimulations for Higher-Order Languages , 2007, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007).

[22]  François Fages,et al.  The Biochemical Abstract Machine BIOCHAM , 2004, CMSB.

[23]  Alexander N. Gorban,et al.  Robust simplifications of multiscale biochemical networks , 2008, BMC Systems Biology.

[24]  N P Smith,et al.  Development of models of active ion transport for whole-cell modelling: cardiac sodium-potassium pump as a case study. , 2004, Progress in biophysics and molecular biology.

[25]  Larry L. Kinney,et al.  REDUCTION OF PETRI NETS. , 1976 .

[26]  François Fages,et al.  Formal Cell Biology in Biocham , 2008, SFM.

[27]  Tadao Murata,et al.  Additional methods for reduction and expansion of marked graphs , 1981 .

[28]  Joël Favrel,et al.  Hierarchical reduction method for analysis and decomposition of Petri nets , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[29]  Paolo Milazzo,et al.  The Calculus of Looping Sequences , 2008, SFM.

[30]  Ichiro Suzuki,et al.  A Method for Stepwise Refinement and Abstraction of Petri Nets , 1983, J. Comput. Syst. Sci..

[31]  Manuel Silva Suárez,et al.  Top-down synthesis of live and bounded free choice nets , 1990, Applications and Theory of Petri Nets.

[32]  Joachim Niehren,et al.  Observational program calculi and the correctness of translations , 2015, Theor. Comput. Sci..

[33]  Zuyi Huang,et al.  Using the Tet-On system to develop a procedure for extracting transcription factor activation dynamics. , 2010, Molecular bioSystems.

[34]  Robert H. Sloan,et al.  Reduction rules for time Petri nets , 1996, Acta Informatica.

[35]  Rob J. van Glabbeek,et al.  The Linear Time - Branching Time Spectrum II , 1993, CONCUR.

[36]  Gordon D. Plotkin,et al.  A Calculus of Chemical Systems , 2013, In Search of Elegance in the Theory and Practice of Computation.

[37]  Joachim Niehren,et al.  Biochemical Reaction Rules with Constraints , 2011, ESOP.

[38]  Hsu-Chun Yen,et al.  A Taxonomy of Fairness and Temporal Logic Problems for Petri Nets , 1988, Theoretical Computer Science.

[39]  Manfred Schmidt-Schauß,et al.  Conservative Concurrency in Haskell , 2012, 2012 27th Annual IEEE Symposium on Logic in Computer Science.

[40]  Gérard Berthelot,et al.  Checking properties of nets using transformation , 1985, Applications and Theory in Petri Nets.

[41]  Jörg Desel,et al.  Reduction and Design of Well-behaved Concurrent Systems , 1990, CONCUR.

[42]  L. Aarons,et al.  Proper lumping in systems biology models. , 2009, IET systems biology.

[43]  Jane Hillston,et al.  Equivalence and Discretisation in Bio-PEPA , 2009, CMSB.

[44]  Aurélien Naldi,et al.  Dynamically consistent reduction of logical regulatory graphs , 2011, Theor. Comput. Sci..

[45]  François Fages,et al.  A graphical method for reducing and relating models in systems biology , 2010, Bioinform..

[46]  François Lemaire,et al.  Symmetry-Based Model Reduction for Approximate Stochastic Analysis , 2012, CMSB.

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

[48]  James Cheney,et al.  Toward a Theory of Self-explaining Computation , 2013, In Search of Elegance in the Theory and Practice of Computation.

[49]  Monika Heiner,et al.  Petri Nets for Systems and Synthetic Biology , 2008, SFM.

[50]  R. J. vanGlabbeek.  The linear time - branching time spectrum , 1990 .

[51]  Tadao Kasami,et al.  Decidable Problems on the Strong Connectivity of Petri Net Reachability Sets , 1977, Theor. Comput. Sci..

[52]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[53]  Antoni Mazurkiewicz.  Mathematical Foundations of Computer Science 1976 , 1976, Lecture Notes in Computer Science.

[54]  Michael L. Mavrovouniotis,et al.  Petri Net Representations in Metabolic Pathways , 1993, ISMB.

[55]  Matthias Jantzen.  Language theory of Petri nets , 1986 .

[56]  Jane Hillston,et al.  A semi-quantitative equivalence for abstracting from fast reactions , 2011, CompMod.

[57]  Brian Campbell,et al.  Amortised Memory Analysis Using the Depth of Data Structures , 2009, ESOP.