An integer optimization approach for reverse engineering of gene regulatory networks

Gene regulatory networks are a common tool to describe the chemical interactions between genes in a living cell. This paper considers the Weighted Gene Regulatory Network (WGRN) problem, which consists in identifying a reduced set of interesting candidate regulatory elements which can explain the expression of all other genes. We provide an integer programming formulation based on a graph model and derive from it a branch-and-bound algorithm which exploits the Lagrangian relaxation of suitable constraints. This allows to determine lower bounds tighter than CPLEX on most benchmark instances, with the exception of the sparser ones. In order to determine feasible solutions for the problem, which appears to be a hard task for general-purpose solvers, we also develop and compare two metaheuristic approaches, namely a Tabu Search and a Variable Neighborhood Search algorithm. The experiments performed on both of them suggest that diversification is a key feature to solve the problem.

[1]  Fred W. Glover,et al.  Tabu Search , 1997, Handbook of Heuristics.

[2]  Satoru Miyano,et al.  Inferring Gene Regulatory Networks from Time-Ordered Gene Expression Data of Bacillus Subtilis Using Differential Equations , 2002, Pacific Symposium on Biocomputing.

[3]  Steven Skiena,et al.  Identifying gene regulatory networks from experimental data , 2001, Parallel Comput..

[4]  Satoru Miyano,et al.  Inferring Gene Regulatory Networks from Time-Ordered Gene Expression Data Using Differential Equations , 2002, Discovery Science.

[5]  M. Reinders,et al.  Genetic network modeling. , 2002, Pharmacogenomics.

[6]  P. Camerini,et al.  On improving relaxation methods by modified gradient techniques , 1975 .

[7]  Ting Chen,et al.  Modeling Gene Expression with Differential Equations , 1998, Pacific Symposium on Biocomputing.

[8]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[9]  Martin Romauch,et al.  A mathematical program to refine gene regulatory networks , 2009, Discret. Appl. Math..

[10]  Michal Linial,et al.  Using Bayesian Networks to Analyze Expression Data , 2000, J. Comput. Biol..

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

[12]  Vladimir Filkov,et al.  Identifying Gene Regulatory Networks from Gene Expression Data , 2005 .

[13]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[14]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[15]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

[16]  Henry Horng-Shing Lu,et al.  Statistical methods for identifying yeast cell cycle transcription factors. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Xinkun Wang,et al.  An effective structure learning method for constructing gene networks , 2006, Bioinform..

[18]  B. E. Davidson,et al.  TyrR protein of Escherichia coli and its role as repressor and activator , 1991, Molecular microbiology.

[19]  A. Gartel,et al.  Lost in transcription: p21 repression, mechanisms, and consequences. , 2005, Cancer research.

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

[21]  Steven Skiena,et al.  Analysis techniques for microarray time-series data , 2001, RECOMB.

[22]  Martin A. Nowak,et al.  Inferring Cellular Networks Using Probabilistic Graphical Models , 2004 .

[23]  N. Lee,et al.  Genomic approaches for reconstructing gene networks. , 2005, Pharmacogenomics.