IDD-based model validation of biochemical networks

This paper presents efficient techniques for the qualitative and quantitative analysis of biochemical networks, which are modeled by means of qualitative and stochastic Petri nets, respectively. The analysis includes standard Petri net properties as well as model checking of the Computation Tree Logic and the Continuous Stochastic Logic. Efficiency is achieved by using Interval decision diagrams to alleviate the well-known problem of state space explosion, and by applying operations exploiting the Petri structure and the principle of locality. All presented techniques are implemented in our tool IDD-MC which is available on our website.

[1]  Gianfranco Ciardo,et al.  Efficient Reachability Set Generation and Storage Using Decision Diagrams , 1999, ICATPN.

[2]  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.

[3]  Zohar Manna,et al.  The Temporal Logic of Reactive and Concurrent Systems , 1991, Springer New York.

[4]  Timothy Kam.  State minimization of finite state machines using implicit techniques , 1996 .

[5]  Gianfranco Ciardo,et al.  SMART: stochastic model-checking analyzer for reliability and timing , 2002, Proceedings International Conference on Dependable Systems and Networks.

[6]  Masahiro Fujita,et al.  Multi-Terminal Binary Decision Diagrams: An Efficient Data Structure for Matrix Representation , 1997, Formal Methods Syst. Des..

[7]  Christel Baier,et al.  Model Checking Continuous-Time Markov Chains by Transient Analysis , 2000, CAV.

[8]  Martin Schwarick,et al.  Snoopy: a tool to design and animate/simulate graph-based formalisms , 2008, SimuTools.

[9]  Martin Schwarick,et al.  DSSZ-MC - A Tool for Symbolic Analysis of Extended Petri Nets , 2009, Petri Nets.

[10]  Kwang-Hyun Cho,et al.  Mathematical Modeling of the Influence of RKIP on the ERK Signaling Pathway , 2003, CMSB.

[11]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

[12]  Emmanuelle Encrenaz-Tiphène,et al.  Data Decision Diagrams for Petri Net Analysis , 2002, ICATPN.

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

[14]  J. Cheney,et al.  A sequent calculus for nominal logic , 2004, LICS 2004.

[15]  Kurt Lautenbach,et al.  A Completion of the S–invariance Technique by means of Fixed Point Algorithms , 2007 .

[16]  Monika Heiner,et al.  From Petri Nets to Differential Equations - An Integrative Approach for Biochemical Network Analysis , 2006, ICATPN.

[17]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[18]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[19]  Lothar Thiele,et al.  Symbolic model checking using interval diagram techniques , 1998 .

[20]  Jehoshua Bruck,et al.  Scaffold proteins may biphasically affect the levels of mitogen-activated protein kinase signaling and reduce its threshold properties. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Shin-ichi Minato,et al.  Zero-Suppressed BDDs for Set Manipulation in Combinatorial Problems , 1993, 30th ACM/IEEE Design Automation Conference.

[22]  Monika Heiner,et al.  Snoopy - a unifying Petri net framework to investigate biomolecular networks , 2010, Bioinform..

[23]  Monika Heiner,et al.  A Unifying Framework for Modelling and Analysing Biochemical Pathways Using Petri Nets , 2007, CMSB.

[24]  Martin Schwarick,et al.  CSL Model Checking of Biochemical Networks with Interval Decision Diagrams , 2009, CMSB.

[25]  Susanna Donatelli,et al.  Verifying Stochastic Well-formed Nets with CSL Model-Checking Tools , 2006, Sixth International Conference on Application of Concurrency to System Design (ACSD'06).

[26]  David Anthony Parker,et al.  Implementation of symbolic model checking for probabilistic systems , 2003 .

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

[28]  Tomohiro Yoneda,et al.  BDDs vs. Zero-Suppressed BDDs: for CTL Symbolic Model Checking of Petri Nets , 1996, FMCAD.

[29]  Randal E. Bryant,et al.  Efficient implementation of a BDD package , 1991, DAC '90.

[30]  William J. Stewart,et al.  Introduction to the numerical solution of Markov Chains , 1994 .

[31]  Peter A. Beerel,et al.  Efficient state classification of finite state Markov chains , 1998, DAC.

[32]  Marta Simeoni,et al.  Petri nets for modelling metabolic pathways: a survey , 2010, Natural Computing.

[33]  Henrik Reif Andersen,et al.  Difference Decision Diagrams , 1999, CSL.

[34]  David Gilbert,et al.  Analysis of signalling pathways using the prism model checker , 2005 .

[35]  Martin Schwarick.  Transient Analysis of Stochastic Petri Nets With Interval Decision Diagrams , 2008, AWPN.

[36]  Stephan Merz,et al.  Model Checking , 2000 .