Bilevel integer programming on a Boolean network for discovering critical genetic alterations in cancer development and therapy

Abstract Boolean network is a modeling tool that describes a dynamic system with binary variables and their logical transition formulas. Recent studies in precision medicine use a Boolean network to discover critical genetic alterations that may lead to cancer or target genes for effective therapies to individuals. In this paper, we study a logical inference problem in a Boolean network to find all such critical genetic alterations in a minimal (parsimonious) way. We propose a bilevel integer programming model to find a single minimal genetic alteration. Using the bilevel integer programming model, we develop a branch and bound algorithm that effectively finds all of the minimal alterations. Through a computational study with eleven Boolean networks from the literature, we show that the proposed algorithm finds solutions much faster than the state-of-the-art algorithms in large data sets.

[1]  Roded Sharan,et al.  Reconstructing Boolean Models of Signaling , 2012, RECOMB.

[2]  Tatsuya Akutsu,et al.  Integer Programming-Based Approach to Attractor Detection and Control of Boolean Networks , 2012, IEICE Trans. Inf. Syst..

[3]  Steffen Klamt,et al.  A methodology for the structural and functional analysis of signaling and regulatory networks , 2006, BMC Bioinformatics.

[4]  Michelle L. Wynn,et al.  Logic-based models in systems biology: a predictive and parameter-free network analysis method. , 2012, Integrative biology : quantitative biosciences from nano to macro.

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

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

[7]  Julian D. Schwab,et al.  Concepts in Boolean network modeling: What do they all mean? , 2020, Computational and structural biotechnology journal.

[8]  J. Lindberg,et al.  Cell-free DNA profiling of metastatic prostate cancer reveals microsatellite instability, structural rearrangements and clonal hematopoiesis , 2018, Genome Medicine.

[9]  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..

[10]  Alan Veliz-Cuba,et al.  Identification of control targets in Boolean molecular network models via computational algebra , 2015, BMC Systems Biology.

[11]  Satoru Miyano,et al.  Identification of gene regulatory networks by strategic gene disruptions and gene overexpressions , 1998, SODA '98.

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

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

[14]  Ted K. Ralphs,et al.  A branch-and-cut algorithm for mixed integer bilevel linear optimization problems and its implementation , 2020, Mathematical Programming Computation.

[15]  Ruth Nussinov,et al.  Structure and dynamics of molecular networks: A novel paradigm of drug discovery. A comprehensive review , 2012, Pharmacology & therapeutics.

[16]  Matteo Fischetti,et al.  On the use of intersection cuts for bilevel optimization , 2017, Mathematical Programming.

[17]  Pierre Hansen,et al.  Links Between Linear Bilevel and Mixed 0–1 Programming Problems , 1995 .

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

[19]  Réka Albert,et al.  Cell Fate Reprogramming by Control of Intracellular Network Dynamics , 2014, PLoS Comput. Biol..

[20]  Ioannis Xenarios,et al.  Efficient computation of minimal perturbation sets in gene regulatory networks , 2013, Front. Physiol..

[21]  Jonathan F. Bard,et al.  The Mixed Integer Linear Bilevel Programming Problem , 1990, Oper. Res..

[22]  Massimiliano Caramia,et al.  Enhanced exact algorithms for discrete bilevel linear problems , 2015, Optim. Lett..

[23]  Erik Kropat,et al.  Modeling, inference and optimization of regulatory networks based on time series data , 2011, Eur. J. Oper. Res..

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

[25]  Pan Xu,et al.  An exact algorithm for the bilevel mixed integer linear programming problem under three simplifying assumptions , 2014, Comput. Oper. Res..

[26]  Pierre-Louis Poirion,et al.  Algorithms and applications for a class of bilevel MILPs , 2020, Discret. Appl. Math..

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

[28]  Hans A. Kestler,et al.  BoolNet - an R package for generation, reconstruction and analysis of Boolean networks , 2010, Bioinform..

[29]  Martin Schmidt,et al.  A Survey on Mixed-Integer Programming Techniques in Bilevel Optimization , 2021, EURO J. Comput. Optim..

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

[31]  Adrien Richard,et al.  Number of Fixed Points and Disjoint Cycles in Monotone Boolean Networks , 2016, SIAM J. Discret. Math..

[32]  Alan Veliz-Cuba.  Reduction of Boolean network models. , 2011, Journal of theoretical biology.

[33]  Steffen Klamt,et al.  The Logic of EGFR/ErbB Signaling: Theoretical Properties and Analysis of High-Throughput Data , 2009, PLoS Comput. Biol..

[34]  Ted K. Ralphs,et al.  A Branch-and-cut Algorithm for Integer Bilevel Linear Programs , 2009 .

[35]  Denis Thieffry,et al.  Mathematical Modelling of Cell-Fate Decision in Response to Death Receptor Engagement , 2010, PLoS Comput. Biol..

[36]  S. Schnell,et al.  Predicting neuroblastoma using developmental signals and a logic-based model. , 2018, Biophysical chemistry.

[37]  Pan Xu,et al.  The Watermelon Algorithm for The Bilevel Integer Linear Programming Problem , 2017, SIAM J. Optim..

[38]  Aurélien Naldi,et al.  MaBoSS 2.0: an environment for stochastic Boolean modeling , 2017, Bioinform..

[39]  Franck Delaplace,et al.  Causal Reasoning on Boolean Control Networks Based on Abduction: Theory and Application to Cancer Drug Discovery , 2019, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[40]  M. L. Martins,et al.  Boolean Network Model for Cancer Pathways: Predicting Carcinogenesis and Targeted Therapy Outcomes , 2013, PloS one.

[41]  Tatsuya Akutsu,et al.  On control of singleton attractors in multiple Boolean networks: integer programming-based method , 2014, BMC Systems Biology.

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

[43]  Jin Niu,et al.  Boolean network modeling in systems pharmacology , 2018, Journal of Pharmacokinetics and Pharmacodynamics.

[44]  Lude Franke,et al.  An integrative approach for building personalized gene regulatory networks for precision medicine , 2018, Genome Medicine.

[45]  Rui-Sheng Wang,et al.  Boolean modeling in systems biology: an overview of methodology and applications , 2012, Physical biology.

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

[47]  É. Remy,et al.  Mapping multivalued onto Boolean dynamics. , 2011, Journal of theoretical biology.

[48]  Matteo Fischetti,et al.  Intersection Cuts for Bilevel Optimization , 2016, IPCO.

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

[50]  Melanie Boerries,et al.  Boolean approach to signalling pathway modelling in HGF-induced keratinocyte migration , 2012, Bioinform..

[51]  Steffen Klamt,et al.  Structural and functional analysis of cellular networks with CellNetAnalyzer , 2007, BMC Systems Biology.

[52]  Ioannis Xenarios,et al.  Angiogenic Activity of Breast Cancer Patients’ Monocytes Reverted by Combined Use of Systems Modeling and Experimental Approaches , 2015, PLoS Comput. Biol..

[53]  Xiangpei Hu,et al.  An enhanced branch-and-bound algorithm for bilevel integer linear programming , 2020, Eur. J. Oper. Res..

[54]  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.

[55]  Matthew N. McCall,et al.  On the underlying assumptions of threshold Boolean networks as a model for genetic regulatory network behavior , 2013, Front. Genet..

[56]  Torsten Schaub,et al.  Minimal intervention strategies in logical signaling networks with ASP , 2013, Theory and Practice of Logic Programming.

[57]  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.

[58]  Steffen Klamt,et al.  Computing Combinatorial Intervention Strategies and Failure Modes in Signaling Networks , 2010, J. Comput. Biol..

[59]  Darrell Whitley,et al.  Computation of Robust Minimal Intervention Sets in Multi-Valued Biological Regulatory Networks , 2019, Front. Physiol..

[60]  Matteo Fischetti,et al.  A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs , 2017, Oper. Res..

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

[62]  Zalmiyah Zakaria,et al.  A review on the computational approaches for gene regulatory network construction , 2014, Comput. Biol. Medicine.