Logical Modeling and Dynamical Analysis of Cellular Networks

The logical (or logic) formalism is increasingly used to model regulatory and signaling networks. Complementing these applications, several groups contributed various methods and tools to support the definition and analysis of logical models. After an introduction to the logical modeling framework and to several of its variants, we review here a number of recent methodological advances to ease the analysis of large and intricate networks. In particular, we survey approaches to determine model attractors and their reachability properties, to assess the dynamical impact of variations of external signals, and to consistently reduce large models. To illustrate these developments, we further consider several published logical models for two important biological processes, namely the differentiation of T helper cells and the control of mammalian cell cycle.

[1]  Yangyang Zhao,et al.  BioModels: ten-year anniversary , 2014, Nucleic Acids Res..

[2]  Jacky L. Snoep,et al.  Reproducible computational biology experiments with SED-ML - The Simulation Experiment Description Markup Language , 2011, BMC Systems Biology.

[3]  D. Irons,et al.  Logical analysis of the budding yeast cell cycle. , 2009, Journal of theoretical biology.

[4]  Giovanni De Micheli,et al.  Modeling stochasticity and robustness in gene regulatory networks , 2009, Bioinform..

[5]  R. Thomas,et al.  Logical analysis of systems comprising feedback loops. , 1978, Journal of theoretical biology.

[6]  Maxim Teslenko,et al.  A SAT-Based Algorithm for Finding Short Cycles in Shift Register Based Stream Ciphers , 2016, IACR Cryptol. ePrint Arch..

[7]  Xin Liu,et al.  Dynamical and Structural Analysis of a T Cell Survival Network Identifies Novel Candidate Therapeutic Targets for Large Granular Lymphocyte Leukemia , 2011, PLoS Comput. Biol..

[8]  Steffen Klamt,et al.  Hypergraphs and Cellular Networks , 2009, PLoS Comput. Biol..

[9]  R. Thomas,et al.  Boolean formalization of genetic control circuits. , 1973, Journal of theoretical biology.

[10]  Alex Madrahimov,et al.  The Cell Collective: Toward an open and collaborative approach to systems biology , 2012, BMC Systems Biology.

[11]  James R Faeder,et al.  The Duration of T Cell Stimulation Is a Critical Determinant of Cell Fate and Plasticity , 2013, Science Signaling.

[12]  J. Tyson,et al.  Models in biology: lessons from modeling regulation of the eukaryotic cell cycle , 2015, BMC Biology.

[13]  Jean-Luc Gouzé,et al.  Comparing Boolean and Piecewise Affine Differential Models for Genetic Networks , 2010, Acta biotheoretica.

[14]  M Sugita,et al.  Functional analysis of chemical systems in vivo using a logical circuit equivalent. II. The idea of a molecular automation. , 1963, Journal of theoretical biology.

[15]  Emmanuel Barillot,et al.  Mathematical Modelling of Molecular Pathways Enabling Tumour Cell Invasion and Migration , 2015, PLoS Comput. Biol..

[16]  D. Lauffenburger,et al.  Discrete logic modelling as a means to link protein signalling networks with functional analysis of mammalian signal transduction , 2009, Molecular systems biology.

[17]  Andrew Hinton,et al.  PRISM: A Tool for Automatic Verification of Probabilistic Systems , 2006, TACAS.

[18]  Claudine Chaouiya,et al.  Quantification of reachable attractors in asynchronous discrete dynamics , 2014, ArXiv.

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

[20]  Aurélien Naldi,et al.  Diversity and Plasticity of Th Cell Types Predicted from Regulatory Network Modelling , 2010, PLoS Comput. Biol..

[21]  Claudine Chaouiya,et al.  A Discrete Model of Drosophila Eggshell Patterning Reveals Cell-Autonomous and Juxtacrine Effects , 2014, PLoS Comput. Biol..

[22]  Steffen Klamt,et al.  SBML qualitative models: a model representation format and infrastructure to foster interactions between qualitative modelling formalisms and tools , 2013, BMC Systems Biology.

[23]  Nir Friedman,et al.  Mapping Differentiation under Mixed Culture Conditions Reveals a Tunable Continuum of T Cell Fates , 2013, PLoS biology.

[24]  Elena R. Alvarez-Buylla,et al.  A minimal regulatory network of extrinsic and intrinsic factors recovers observed patterns of CD4+ T cell differentiation and plasticity , 2015 .

[25]  Julio Saez-Rodriguez,et al.  Fuzzy Logic Analysis of Kinase Pathway Crosstalk in TNF/EGF/Insulin-Induced Signaling , 2007, PLoS Comput. Biol..

[26]  Martin Gebser,et al.  Learning Boolean logic models of signaling networks with ASP , 2015, Theor. Comput. Sci..

[27]  É. Remy,et al.  A Modeling Approach to Explain Mutually Exclusive and Co-Occurring Genetic Alterations in Bladder Tumorigenesis. , 2015, Cancer research.

[28]  Aurélien Naldi,et al.  Decision Diagrams for the Representation and Analysis of Logical Models of Genetic Networks , 2007, CMSB.

[29]  Luis Mendoza,et al.  A network model for the control of the differentiation process in Th cells. , 2006, Bio Systems.

[30]  Mahbubul Majumder,et al.  Systems Perturbation Analysis of a Large-Scale Signal Transduction Model Reveals Potentially Influential Candidates for Cancer Therapeutics , 2015, Front. Bioeng. Biotechnol..

[31]  Aurélien Naldi,et al.  Logical modelling of gene regulatory networks with GINsim. , 2012, Methods in molecular biology.

[32]  Steffen Klamt,et al.  A Logical Model Provides Insights into T Cell Receptor Signaling , 2007, PLoS Comput. Biol..

[33]  Tomáš Helikar,et al.  Ergodic Sets as Cell Phenotype of Budding Yeast Cell Cycle , 2012, PloS one.

[34]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[35]  L. Glass,et al.  The logical analysis of continuous, non-linear biochemical control networks. , 1973, Journal of theoretical biology.

[36]  S. Kauffman,et al.  Cancer attractors: a systems view of tumors from a gene network dynamics and developmental perspective. , 2009, Seminars in cell & developmental biology.

[37]  Steffen Klamt,et al.  Transforming Boolean models to continuous models: methodology and application to T-cell receptor signaling , 2009, BMC Systems Biology.

[38]  Tomáš Helikar,et al.  A Comprehensive, Multi-Scale Dynamical Model of ErbB Receptor Signal Transduction in Human Mammary Epithelial Cells , 2013, PloS one.

[39]  Réka Albert,et al.  Boolean modeling: a logic‐based dynamic approach for understanding signaling and regulatory networks and for making useful predictions , 2014, Wiley interdisciplinary reviews. Systems biology and medicine.

[40]  R. Thomas,et al.  Dynamical behaviour of biological regulatory networks--II. Immunity control in bacteriophage lambda. , 1995, Bulletin of mathematical biology.

[41]  Michael Hucka,et al.  The Systems Biology Markup Language (SBML) Level 2 Version 2 , 2007 .

[42]  Dov M. Gabbay.  The Reduction Method , 1976 .

[43]  Shankar P. Bhattacharyya,et al.  Robustness And Fragility , 2009 .

[44]  Aurélien Naldi,et al.  Model Checking to Assess T-Helper Cell Plasticity , 2014, bioRxiv.

[45]  Assieh Saadatpour,et al.  A Reduction Method for Boolean Network Models Proven to Conserve Attractors , 2013, SIAM J. Appl. Dyn. Syst..

[46]  Madalena Chaves,et al.  Robustness and fragility of Boolean models for genetic regulatory networks. , 2005, Journal of theoretical biology.

[47]  Luis Mendoza,et al.  A Minimal Regulatory Network of Extrinsic and Intrinsic Factors Recovers Observed Patterns of CD4+ T Cell Differentiation and Plasticity , 2015, PLoS Comput. Biol..

[48]  Emmanuel Barillot,et al.  Continuous time boolean modeling for biological signaling: application of Gillespie algorithm , 2012, BMC Systems Biology.

[49]  Luis Mendoza,et al.  The regulatory network that controls the differentiation of T lymphocytes , 2013, Biosyst..

[50]  J. Monod,et al.  Teleonomic mechanisms in cellular metabolism, growth, and differentiation. , 1961, Cold Spring Harbor symposia on quantitative biology.

[51]  Giovanni De Micheli,et al.  Synchronous versus asynchronous modeling of gene regulatory networks , 2008, Bioinform..

[52]  N. Novère.  Quantitative and logic modelling of molecular and gene networks , 2015, Nature Reviews Genetics.

[53]  Claudine Chaouiya,et al.  Efficient Verification for Logical Models of Regulatory Networks , 2012, PACBB.

[54]  D. Thieffry,et al.  Segmenting the fly embryo: logical analysis of the role of the segment polarity cross-regulatory module. , 2008, The International journal of developmental biology.

[55]  Alexander Bockmayr,et al.  Computing maximal and minimal trap spaces of Boolean networks , 2015, Natural Computing.

[56]  Ioannis Xenarios,et al.  A method for the generation of standardized qualitative dynamical systems of regulatory networks , 2005, Theoretical Biology and Medical Modelling.

[57]  David L. Robertson,et al.  A logical model of HIV-1 interactions with the T-cell activation signalling pathway , 2015, Bioinform..

[58]  Lubos Brim,et al.  Model Checking of Biological Systems , 2013, SFM.

[59]  Peter K. Sorger,et al.  Logic-Based Models for the Analysis of Cell Signaling Networks† , 2010, Biochemistry.

[60]  Hugh D. Spence,et al.  Minimum information requested in the annotation of biochemical models (MIRIAM) , 2005, Nature Biotechnology.

[61]  Denis Thieffry,et al.  Integrative Modelling of the Influence of MAPK Network on Cancer Cell Fate Decision , 2013, PLoS Comput. Biol..

[62]  T. Helikar,et al.  Dynamics of Influenza Virus and Human Host Interactions During Infection and Replication Cycle , 2013, Bulletin of mathematical biology.

[63]  Julio Saez-Rodriguez,et al.  CellNOptR: a flexible toolkit to train protein signaling networks to data using multiple logic formalisms , 2012, BMC Systems Biology.

[64]  Beatriz Peñalver Bernabé,et al.  State–time spectrum of signal transduction logic models , 2012, Physical biology.

[65]  S. Bornholdt,et al.  The transition from differential equations to Boolean networks: a case study in simplifying a regulatory network model. , 2008, Journal of theoretical biology.

[66]  Oliver Sawodny,et al.  ON/OFF and Beyond - A Boolean Model of Apoptosis , 2009, PLoS Comput. Biol..

[67]  Ioannis Xenarios,et al.  Hard-wired heterogeneity in blood stem cells revealed using a dynamic regulatory network model , 2013, Bioinform..

[68]  S. Klamt,et al.  Modeling approaches for qualitative and semi-quantitative analysis of cellular signaling networks , 2013, Cell Communication and Signaling.

[69]  Denis Thieffry,et al.  Dynamical roles of biological regulatory circuits , 2007, Briefings Bioinform..

[70]  R. Albert,et al.  Network model of survival signaling in large granular lymphocyte leukemia , 2008, Proceedings of the National Academy of Sciences.

[71]  Denis Thieffry,et al.  Logical modelling of the role of the Hh pathway in the patterning of the Drosophila wing disc , 2008, ECCB.

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

[73]  Aurélien Naldi,et al.  Cooperative development of logical modelling standards and tools with CoLoMoTo , 2014, bioRxiv.

[74]  Kayoko Sato,et al.  Helper T cell diversity and plasticity. , 2014, Circulation journal : official journal of the Japanese Circulation Society.

[75]  R Thomas,et al.  A complex control circuit. Regulation of immunity in temperate bacteriophages. , 1976, European journal of biochemistry.

[76]  David A. Rosenblueth,et al.  "Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis , 2011, BMC Bioinformatics.

[77]  Stefan Bornholdt,et al.  Boolean network models of cellular regulation: prospects and limitations , 2008, Journal of The Royal Society Interface.

[78]  Aurélien Naldi,et al.  Model checking to assess T-helper cell plasticity , 2014 .

[79]  Tomáš Helikar,et al.  Design, Assessment, and in vivo Evaluation of a Computational Model Illustrating the Role of CAV1 in CD4+ T-lymphocytes , 2014, Front. Immunol..

[80]  François Fages,et al.  Symbolic Model Checking of Biochemical Networks , 2003, CMSB.

[81]  Laurent Trilling,et al.  Applications of a formal approach to decipher discrete genetic networks , 2010, BMC Bioinformatics.

[82]  Hiroaki Kitano,et al.  The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models , 2003, Bioinform..

[83]  John J Tyson,et al.  A model for restriction point control of the mammalian cell cycle. , 2004, Journal of theoretical biology.

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

[85]  Daniel C Kirouac,et al.  Computational Modeling of ERBB2-Amplified Breast Cancer Identifies Combined ErbB2/3 Blockade as Superior to the Combination of MEK and AKT Inhibitors , 2013, Science Signaling.

[86]  Edward R. Dougherty,et al.  Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks , 2002, Bioinform..

[87]  Pedro T. Monteiro,et al.  Dynamical modeling and analysis of large cellular regulatory networks. , 2013, Chaos.

[88]  J. Monod,et al.  Genetic regulatory mechanisms in the synthesis of proteins. , 1961, Journal of Molecular Biology.

[89]  Réka Albert,et al.  An effective network reduction approach to find the dynamical repertoire of discrete dynamic networks. , 2013, Chaos.

[90]  Holger Fröhlich,et al.  Modeling ERBB receptor-regulated G1/S transition to find novel targets for de novo trastuzumab resistance , 2009, BMC Systems Biology.

[91]  M. Aldana,et al.  Floral Morphogenesis: Stochastic Explorations of a Gene Network Epigenetic Landscape , 2008, PloS one.

[92]  Isaac Crespo,et al.  Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states , 2012, Nucleic acids research.

[93]  Andreas Zell,et al.  Coordinating Role of RXRα in Downregulating Hepatic Detoxification during Inflammation Revealed by Fuzzy-Logic Modeling , 2016, PLoS Comput. Biol..

[94]  M Sugita,et al.  Functional analysis of chemical systems in vivo using a logical circuit equivalent. 3. Analysis using a digital circuit combined with an analogue computer. , 1963, Journal of theoretical biology.

[95]  J. Saez-Rodriguez,et al.  Large-scale models of signal propagation in human cells derived from discovery phosphoproteomic data , 2015, Nature Communications.

[96]  Denis Thieffry,et al.  Logical modeling of the mammalian cell cycle , 2015 .

[97]  Julio Saez-Rodriguez,et al.  Training Signaling Pathway Maps to Biochemical Data with Constrained Fuzzy Logic: Quantitative Analysis of Liver Cell Responses to Inflammatory Stimuli , 2011, PLoS Comput. Biol..

[98]  Alessio Lomuscio,et al.  Automatic Verification of Knowledge and Time with NuSMV , 2007, IJCAI.

[99]  Axel Legay,et al.  Statistical Model Checking in BioLab: Applications to the Automated Analysis of T-Cell Receptor Signaling Pathway , 2008, CMSB.

[100]  Radu Mateescu,et al.  Validation of qualitative models of genetic regulatory networks by model checking: analysis of the nutritional stress response in Escherichia coli , 2005, ISMB.

[101]  E. R. de Arantes e Oliveira.  The Discrete Model , 1975 .

[102]  D. Thieffry,et al.  Modular logical modelling of the budding yeast cell cycle. , 2009, Molecular bioSystems.

[103]  Denis Thieffry,et al.  Discovery of Drug Synergies in Gastric Cancer Cells Predicted by Logical Modeling , 2015, PLoS Comput. Biol..

[104]  T. Helikar,et al.  A Cell Simulator Platform: The Cell Collective , 2013, Clinical pharmacology and therapeutics.

[105]  Aurélien Naldi,et al.  The Systems Biology Markup Language (SBML) Level 3 Package: Qualitative Models, Version 1, Release 1 , 2015, J. Integr. Bioinform..

[106]  Marco Pistore,et al.  NuSMV 2: An OpenSource Tool for Symbolic Model Checking , 2002, CAV.

[107]  Claudine Chaouiya,et al.  Modelling the onset of senescence at the G1/S cell cycle checkpoint , 2014, BMC Genomics.

[108]  Denis Thieffry,et al.  A description of dynamical graphs associated to elementary regulatory circuits , 2003, ECCB.

[109]  Hidde de Jong,et al.  Symbolic reachability analysis of genetic regulatory networks using discrete abstractions , 2008, Autom..

[110]  Aurélien Naldi,et al.  Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle , 2006, ISMB.

[111]  Denis Thieffry,et al.  Dynamical behaviour of biological regulatory networks—II. Immunity control in bacteriophage lambda , 1995 .

[112]  Q. Ouyang,et al.  The yeast cell-cycle network is robustly designed. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[113]  J. Ferrell,et al.  Modeling the Cell Cycle: Why Do Certain Circuits Oscillate? , 2011, Cell.

[114]  S. Kauffman.  Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[115]  Denis Thieffry,et al.  Logical modelling of cell cycle control in eukaryotes: a comparative study. , 2009, Molecular bioSystems.

[116]  Maxim Teslenko,et al.  A SAT-Based Algorithm for Finding Attractors in Synchronous Boolean Networks , 2011, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[117]  Jim A. Rogers,et al.  ChemChains: a platform for simulation and analysis of biochemical networks aimed to laboratory scientists , 2009, BMC Systems Biology.

[118]  J. Monod,et al.  Genetic regulatory mechanisms in the synthesis of proteins. , 1961, Journal of molecular biology.