Reasoning over Biological Networks Using Maximum Satisfiability

Systems biology is with no doubt one of the most compelling fields for a computer scientist. Modelling such systems is per se a major challenge, but the ultimate goal is to reason over those systems. We focus on modelling and reasoning over biological networks using Maximum Satisfiability (MaxSAT). Biological networks are represented by an influence graph whose vertices represent the genes of the network and edges represent interactions between genes. Given an influence graph and an experimental profile, the first step is to check for mutual consistency. In case of inconsistency, a repair is suggested. In addition, what is common to all solutions/optimal repairs is also provided. This information, named prediction, is of particular interest from a user's point of view. Answer Set Programming (ASP) has been successfully applied to biological networks in the recent past. In this work, we give empirical evidence that MaxSAT is by far more adequate for solving this problem. Moreover, we show how concepts well studied in the fields of MaxSAT and CP, such as backbones and unsatisfiable subformulas, can be naturally related to this practical problem.

[1]  Martin Gebser,et al.  The Conflict-Driven Answer Set Solver clasp: Progress Report , 2009, LPNMR.

[2]  Martin Gebser,et al.  The BioASP Library: ASP Solutions for Systems Biology , 2010, 2010 22nd IEEE International Conference on Tools with Artificial Intelligence.

[3]  Wolfgang Faber,et al.  Logic Programming and Nonmonotonic Reasoning , 2011, Lecture Notes in Computer Science.

[4]  Carito Guziolowski,et al.  Checking Consistency Between Expression Data and Large Scale Regulatory Networks: A Case Study , 2007 .

[5]  Laurent Trilling,et al.  Connections and Integration with SAT Solvers: A Survey and a Case Study in Computational Biology , 2011 .

[6]  Barry O'Sullivan,et al.  Finding Diverse and Similar Solutions in Constraint Programming , 2005, AAAI.

[7]  João P. Marques Silva.  Minimal Unsatisfiability: Models, Algorithms and Applications (Invited Paper). , 2010, ISMVL 2010.

[8]  Daniel G. Bobrow,et al.  Qualitative Reasoning about Physical Systems: An Introduction , 1984, Artif. Intell..

[9]  Martin Gebser,et al.  Repair and Prediction (under Inconsistency) in Large Biological Networks with Answer Set Programming , 2010, KR.

[10]  Niklas Sörensson,et al.  An Extensible SAT-solver , 2003, SAT.

[11]  Hans Kleine Büning,et al.  Theory and Applications of Satisfiability Testing - SAT 2008, 11th International Conference, SAT 2008, Guangzhou, China, May 12-15, 2008. Proceedings , 2008, SAT.

[12]  Vasco M. Manquinho,et al.  Towards More Effective Unsatisfiability-Based Maximum Satisfiability Algorithms , 2008, SAT.

[13]  Mikolás Janota,et al.  On Computing Backbones of Propositional Theories , 2010, ECAI.

[14]  Joao Marques-Silva,et al.  Minimal Unsatisfiability: Models, Algorithms and Applications (Invited Paper) , 2010, 2010 40th IEEE International Symposium on Multiple-Valued Logic.

[15]  Sharad Malik,et al.  SAT-based techniques for determining backbones for post-silicon fault localisation , 2011, 2011 IEEE International High Level Design Validation and Test Workshop.

[16]  Laurent Trilling,et al.  A declarative constraint-based method for analyzing discrete genetic regulatory networks , 2009, Biosyst..

[17]  Marius Thomas Lindauer,et al.  Potassco: The Potsdam Answer Set Solving Collection , 2011, AI Commun..

[18]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[19]  Julio Collado-Vides,et al.  RegulonDB (version 6.0): gene regulation model of Escherichia coli K-12 beyond transcription, active (experimental) annotated promoters and Textpresso navigation , 2007, Nucleic Acids Res..

[20]  Martin Gebser,et al.  Detecting inconsistencies in large biological networks with answer set programming , 2008, Theory and Practice of Logic Programming.

[21]  Christian J. Muise,et al.  Probabilistically Estimating Backbones and Variable Bias: Experimental Overview , 2008, CP.

[22]  A. D. de Koning,et al.  Effects of Fis on Escherichia coli gene expression during different growth stages. , 2007, Microbiology.

[23]  Sylvain Soliman,et al.  Constraint Programming for the Dynamical Analysis of Biochemical Systems – A Survey , 2011 .

[24]  Weixiong Zhang,et al.  Backbone Guided Local Search for Maximum Satisfiability , 2003, IJCAI.

[25]  Lakhdar Sais,et al.  Extracting MUCs from Constraint Networks , 2006, ECAI.

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

[27]  Maria Fox,et al.  A New Empirical Study of Weak Backdoors , 2008, CP.

[28]  A Siegel,et al.  Qualitative analysis of the relation between DNA microarray data and behavioral models of regulation networks. , 2006, Bio Systems.

[29]  Rémi Monasson,et al.  Determining computational complexity from characteristic ‘phase transitions’ , 1999, Nature.

[30]  Toby Walsh,et al.  Backbones in Optimization and Approximation , 2001, IJCAI.

[31]  Martin Gebser,et al.  Detecting Inconsistencies in Large Biological Networks with Answer Set Programming , 2008, ICLP.

[32]  Jeremy D. Glasner,et al.  Genome-Scale Analysis of the Uses of the Escherichia coli Genome: Model-Driven Analysis of Heterogeneous Data Sets , 2003, Journal of bacteriology.

[33]  Christophe Soulé,et al.  Mathematical approaches to differentiation and gene regulation. , 2005, Comptes rendus biologies.

[34]  Hidde de Jong,et al.  Modeling and Simulation of Genetic Regulatory Systems: A Literature Review , 2002, J. Comput. Biol..

[35]  L. Krippahl,et al.  Bioinformatics: A Challenge to Constraint Programming , 2011 .

[36]  Toby Walsh,et al.  Backbones and Backdoors in Satisfiability , 2005, AAAI.

[37]  Mohamed El Bachir Menai.  A Two-Phase Backbone-Based Search Heuristic for Partial MAX-SAT - An Initial Investigation , 2005, IEA/AIE.