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Boolean function metrics can assist modelers to check and choose logical rules. (English) Zbl 1483.92071

Summary: Computational models of biological processes provide one of the most powerful methods for a detailed analysis of the mechanisms that drive the behavior of complex systems. Logic-based modeling has enhanced our understanding and interpretation of those systems. Defining rules that determine how the output activity of biological entities is regulated by their respective inputs has proven to be challenging. Partly this is because of the inherent noise in data that allows multiple model parameterizations to fit the experimental observations, but some of it is also due to the fact that models become increasingly larger, making the use of automated tools to assemble the underlying rules indispensable. We present several Boolean function metrics that provide modelers with the appropriate framework to analyze the impact of a particular model parameterization. We demonstrate the link between a semantic characterization of a Boolean function and its consistency with the model’s underlying regulatory structure. We further define the properties that outline such consistency and show that several of the Boolean functions under study violate them, questioning their biological plausibility and subsequent use. We also illustrate that regulatory functions can have major differences with regard to their asymptotic output behavior, with some of them being biased towards specific Boolean outcomes when others are dependent on the ratio between activating and inhibitory regulators. Application results show that in a specific signaling cancer network, the function bias can be used to guide the choice of logical operators for a model that matches data observations. Moreover, graph analysis indicates that commonly used Boolean functions become more biased with increasing numbers of regulators, supporting the idea that rule specification can effectively determine regulatory outcome despite the complex dynamics of biological networks.

MSC:

92C42 Systems biology, networks
06E30 Boolean functions
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[1] Wassim Abou-Jaoudé, Pauline Traynard, Pedro T Monteiro, Julio Saez-Rodriguez, Tomáš Helikar, Denis Thieffry, and Claudine Chaouiya. Logical Modeling and Dynamical Analysis of Cellular Networks. Frontiers in genetics, 7: 94, 2016. https://doi.org/10.3389/fgene.2016.00094.
[2] Sara Sadat Aghamiri, Vidisha Singh, Aurélien Naldi, Tomáš Helikar, Sylvain Soliman, and Anna Niarakis. Automated inference of Boolean models from molecular interaction maps using CaSQ. Bioinformatics, 2020. ISSN 1367-4803. https://doi.org/10.1093/bioinformatics/btaa484.
[3] Albert László Barabási and Réka Albert. Emergence of scaling in random networks. Science, 286 (5439): 509-512, Oct 1999. ISSN 00368075. https://doi.org/10.1126/science.286.5439.509. · Zbl 1226.05223
[4] Aldana, Maximino, Boolean dynamics of networks with scale-free topology, Physica D: Nonlinear Phenomena, 185, 1, 45-66 (2003) · Zbl 1039.94016
[5] Maximino Aldana, Enrique Balleza, Stuart Kauffman, and Osbaldo Resendiz. Robustness and evolvability in genetic regulatory networks. Journal of Theoretical Biology, 245 (3): 433-448, Apr 2007. ISSN 00225193. https://doi.org/10.1016/j.jtbi.2006.10.027. · Zbl 1451.92210
[6] Rolf Apweiler, Tim Beissbarth, Michael R Berthold, Nils Blüthgen, Yvonne Burmeister, Olaf Dammann, Andreas Deutsch, Friedrich Feuerhake, Andre Franke, Jan Hasenauer, Steve Hoffmann, Thomas Höfer, Peter LM Jansen. Lars Kaderali, Ursula Klingmüller, Ina Koch, Oliver Kohlbacher, Lars Kuepfer, Frank Lammert, Dieter Maier, Nico Pfeifer, Nicole Radde, Markus Rehm, Ingo Roeder, Julio Saez-Rodriguez, Ulrich Sax, Bernd Schmeck, Andreas Schuppert, Bernd Seilheimer, Fabian J Theis, Julio Vera, and Olaf Wolkenhauer. Whither systems medicine? Experimental & Molecular Medicine, 50 (3): e453, Mar 2018. ISSN 2092-6413. https://doi.org/10.1038/emm.2017.290.
[7] Amel Bekkar, Anne Estreicher, Anne Niknejad, Cristina Casals-Casas, Alan Bridge, Ioannis Xenarios, Julien Dorier, and Isaac Crespo. Expert curation for building network-based dynamical models: a case study on atherosclerotic plaque formation. Database, 2018 (2018): 31, Jan 2018. ISSN 1758-0463. https://doi.org/10.1093/database/bay031.
[8] Veronica V. Rossato, Daner A. Silveira, Shantanu Gupta, and José Carlos M. Mombach. Towards the contribution of the p38MAPK pathway to the dual role of TGFβin cancer: A boolean model approach. Computers in Biology and Medicine, 104: 235-240, Jan 2019. ISSN 0010-4825. https://doi.org/10.1016/J.COMPBIOMED.2018.11.025.
[9] Itai Benjamini, Oded Schramm, and David B. Wilson. Balanced Boolean functions that can be evaluated so that every input bit is unlikely to be read. In Proceedings of the Annual ACM Symposium on Theory of Computing, pages 244-250, New York, USA, 2005. ACM Press. https://doi.org/10.1145/1060590.1060627. · Zbl 1192.68851
[10] Archie Blake. Canonical expressions in boolean algebra. PhD Thesis, 1937. Department of Mathematics, University of Chicago. · Zbl 0018.38601
[11] Bree B. Aldridge, John M. Burke, Douglas A. Lauffenburger, and Peter K. Sorger. Physicochemical modelling of cell signalling pathways. Nature Cell Biology, 8 (11): 1195-1203, Nov 2006. ISSN 1465-7392. https://doi.org/10.1038/ncb1497.
[12] Anna D. Broido and Aaron Clauset. Scale-free networks are rare. Nature Communications, 10 (1): 1-10, Dec 2019. ISSN 20411723. https://doi.org/10.1038/s41467-019-08746-5.
[13] Laurence Calzone, Laurent Tournier, Simon Fourquet, Denis Thieffry, Boris Zhivotovsky, Emmanuel Barillot, and Andrei Zinovyev. Mathematical modelling of cell-fate decision in response to death receptor engagement. PLoS computational biology, 6 (3): e1000702, Mar 2010. ISSN 1553-7358. https://doi.org/10.1371/journal.pcbi.1000702.
[14] Han-Yu Chuang, Matan Hofree, and Trey Ideker. A Decade of Systems Biology. Annual Review of Cell and Developmental Biology, 26 (1): 721-744, Nov 2010. ISSN 1081-0706. https://doi.org/10.1146/annurev-cellbio-100109-104122.
[15] Jacob Cohen. A Coefficient of Agreement for Nominal Scales. Educational and Psychological Measurement, 20 (1): 37-46, Apr 1960. ISSN 0013-1644. https://doi.org/10.1177/001316446002000104.
[16] Crama, Yves, Hammer, Peter L., 2011. Boolean functions: Theory, algorithms, and applications. Cambridge University Press. · Zbl 1237.06001
[17] José E.R. Cury, Pedro T. Monteiro, and Claudine Chaouiya. Partial Order on the set of Boolean Regulatory Functions, Jan 2019. arXiv preprint arXiv:1901.07623.
[18] Åsmund Flobak, Anaïs Baudot, Elisabeth Remy, Liv Thommesen, Denis Thieffry, Martin Kuiper, and Astrid Lægreid. Discovery of Drug Synergies in Gastric Cancer Cells Predicted by Logical Modeling. PLOS Computational Biology, 11 (8): e1004426, Aug 2015. ISSN 1553-7358. https://doi.org/10.1371/journal.pcbi.1004426.
[19] Gherardi, Marco; Rotondo, Pietro, Measuring logic complexity can guide pattern discovery in empirical systems, Complexity, 21, 397-408 (2016)
[20] Enio Gjerga, Panuwat Trairatphisan, Attila Gabor, Hermann Koch, Celine Chevalier, Franceco Ceccarelli, Aurelien Dugourd, Alexander Mitsos, and Julio Saez-Rodriguez. Converting networks to predictive logic models from perturbation signalling data with CellNOpt. Bioinformatics, 2020. ISSN 1367-4803. https://doi.org/10.1093/bioinformatics/btaa561.
[21] Claudine Chaouiya, Ouerdia Ourrad, and Ricardo Lima. Majority Rules with Random Tie-Breaking in Boolean Gene Regulatory Networks. PLoS ONE, 8 (7): 69626, Jul 2013. ISSN 19326203. https://doi.org/10.1371/journal.pone.0069626.
[22] Ronald L Graham, Donald E Knuth, and Oren Patashnik. Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley Longman Publishing Co., Inc, USA, 2nd edition, 1994. ISBN 0201558025. · Zbl 0836.00001
[23] Sam F Greenbury, Iain G Johnston, Matthew A Smith, Jonathan P K Doye, and Ard A Louis. The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks. Journal of Theoretical Biology, 267 (1): 48-61, 2010. ISSN 0022-5193. https://doi.org/10.1016/j.jtbi.2010.08.006. · Zbl 1410.92065
[24] Luca Grieco, Laurence Calzone, Isabelle Bernard-Pierrot, François Radvanyi, Brigitte Kahn-Perlès, and Denis Thieffry. Integrative Modelling of the Influence of MAPK Network on Cancer Cell Fate Decision. PLOS Computational Biology, 9 (10): e1003286, Oct 2013. ISSN 1553-7358. https://doi.org/10.1371/JOURNAL.PCBI.1003286.
[25] Tomáš Helikar, Bryan Kowal, Sean McClenathan, Mitchell Bruckner, Thaine Rowley, Alex Madrahimov, Ben Wicks, Manish Shrestha, Kahani Limbu, and Jim A. Rogers. The Cell Collective: Toward an open and collaborative approach to systems biology. BMC Systems Biology, 6 (1): 96, Aug 2012. ISSN 17520509. https://doi.org/10.1186/1752-0509-6-96.
[26] David Henriques, Alejandro F. Villaverde, Miguel Rocha, Julio Saez-Rodriguez, and Julio R. Banga. Data-driven reverse engineering of signaling pathways using ensembles of dynamic models. PLoS Computational Biology, 13 (2): e1005379, Feb 2017. ISSN 15537358. https://doi.org/10.1371/journal.pcbi.1005379.
[27] Hiroaki Kitano. Computational systems biology. Nature, 420 (6912): 206-210, Nov 2002. ISSN 00280836. https://doi.org/10.1038/nature01254.
[28] J.J. Hopfield. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences of the United States of America, 79 (8): 2554-2558, Apr 1982. ISSN 00278424. https://doi.org/10.1073/pnas.79.8.2554. · Zbl 1369.92007
[29] John Jack, John F. Wambaugh, and Imran Shah. Simulating Quantitative Cellular Responses Using Asynchronous Threshold Boolean Network Ensembles. BMC Systems Biology, 5 (1): 1-13, Jul 2011. ISSN 17520509. https://doi.org/10.1186/1752-0509-5-109.
[30] H. Jeong, B. Tombor, R. Albert, Z.N. Oltval, A.L. Barabási. The large-scale organization of metabolic networks. Nature, 407 (6804): 651-654, Oct 2000. ISSN 00280836. https://doi.org/10.1038/35036627.
[31] Lars Kaderali, Eva Dazert, Ulf Zeuge, Michael Frese, and Ralf Bartenschlager. Reconstructing signaling pathways from RNAi data using probabilistic Boolean threshold networks. Bioinformatics, 25 (17): 2229-2235, Sep 2009. ISSN 1460-2059. https://doi.org/10.1093/bioinformatics/btp375.
[32] S.A. Kauffman. Metabolic stability and epigenesis in randomly constructed genetic nets. Journal of Theoretical Biology, 22 (3): 437-467, Mar 1969. ISSN 10958541. https://doi.org/10.1016/0022-5193(69)90015-0.
[33] Kauffman, Stuart A., 1993. The origins of order: Self-organization and selection in evolution. Oxford University Press, USA.
[34] Raya Khanin and Ernst Wit. How scale-free are biological networks. Journal of Computational Biology, 13 (3): 810-818, Apr 2006. ISSN 10665277. https://doi.org/10.1089/cmb.2006.13.810.
[35] Fangting Li, Tao Long, Ying Lu, Qi Ouyang, and Chao Tang. The yeast cell-cycle network is robustly designed. Proceedings of the National Academy of Sciences of the United States of America, 101 (14): 4781-4786, Apr 2004. ISSN 00278424. https://doi.org/10.1073/pnas.0305937101.
[36] Malvina Marku, Nina Verstraete, Flavien Raynal, Miguel Madrid-Mencía, Marcin Domagala, Jean Jacques Fournié, Loïc Ysebaert, Mary Poupot, and Vera Pancaldi. Insights on TAM formation from a boolean model of macrophage polarization based on in vitro studies. Cancers, 12 (12): 1-23, Dec 2020. ISSN 20726694. https://doi.org/10.3390/cancers12123664.
[37] Mary L. McHugh. Interrater reliability: The kappa statistic. Biochemia Medica, 22 (3): 276-282, Oct 2012. ISSN 13300962. https://doi.org/10.11613/bm.2012.031.
[38] McCulloch, Warren S.; Pitts, Walter, A logical calculus of the ideas immanent in nervous activity, The Bulletin of Mathematical Biophysics, 5, 4, 115-133 (1943) · Zbl 0063.03860
[39] Luis Mendoza and Ioannis Xenarios. A method for the generation of standardized qualitative dynamical systems of regulatory networks. Theoretical Biology and Medical Modelling, 3 (1): 13, Mar 2006. ISSN 17424682. https://doi.org/10.1186/1742-4682-3-13.
[40] Christoph Müssel, Martin Hopfensitz, and Hans A. Kestler. BoolNet - an R package for generation, reconstruction and analysis of Boolean networks. Bioinformatics, 26 (10): 1378-1380, May 2010. ISSN 1460-2059. https://doi.org/10.1093/bioinformatics/btq124.
[41] Aurélien Naldi. BioLQM: A Java Toolkit for the Manipulation and Conversion of Logical Qualitative Models of Biological Networks. Frontiers in Physiology, 9: 1605, Nov 2018. ISSN 1664-042X. https://doi.org/10.3389/fphys.2018.01605.
[42] Naldi, Aurélien, Thieffry, Denis, Chaouiya, Claudine, 2007. Decision Diagrams for the Representation and Analysis of Logical Models of Genetic Networks. In: International Conference on Computational Methods in Systems Biology. Springer, pp. 233-247. https://dl.acm.org/doi/10.5555/1780158.1780174. · Zbl 1211.92024
[43] Aurélien Naldi, Céline Hernandez, Nicolas Levy, Gautier Stoll, Pedro T. Monteiro, Claudine Chaouiya, Tomáš Helikar, Andrei Zinovyev, Laurence Calzone, Sarah Cohen-Boulakia, Denis Thieffry, and Loïc Paulevé. The CoLoMoTo Interactive Notebook: Accessible and Reproducible Computational Analyses for Qualitative Biological Networks. Frontiers in Physiology, 9: 680, Jun 2018. ISSN 1664-042X. https://doi.org/10.3389/fphys.2018.00680.
[44] Barbara Niederdorfer, Vasundra Touré, Miguel Vazquez, Liv Thommesen, Martin Kuiper, Astrid Lægreid, and Åsmund Flobak. Strategies to Enhance Logic Modeling-Based Cell Line-Specific Drug Synergy Prediction. Frontiers in Physiology, 11: 862, Jul 2020. ISSN 1664-042X. https://doi.org/10.3389/fphys.2020.00862.
[45] Panos Oikonomou and Philippe Cluzel. Effects of topology on network evolution. Nature Physics, 2 (8): 532-536, Aug 2006. ISSN 17452481. https://doi.org/10.1038/nphys359.
[46] Réka Albert and Albert László Barabási. Statistical mechanics of complex networks. Reviews of Modern Physics, 74 (1): 47-97, Jan 2002. ISSN 00346861. https://doi.org/10.1103/RevModPhys.74.47. · Zbl 1205.82086
[47] Réka Albert. Scale-free networks in cell biology. Journal of Cell Science, 118 (21): 4947-4957, Nov 2005. ISSN 00219533. https://doi.org/10.1242/jcs.02714.
[48] J. Richard Landis and Gary G. Koch. The Measurement of Observer Agreement for Categorical Data. Biometrics, 33 (1): 159, Mar 1977. ISSN 0006341X. https://doi.org/10.2307/2529310. · Zbl 0351.62039
[49] Roded Sharan and Richard M. Karp. Reconstructing Boolean Models of Signaling. Journal of Computational Biology, 20 (3): 249-257, Mar 2013. ISSN 1066-5277. https://doi.org/10.1089/cmb.2012.0241.
[50] Julio Saez-Rodriguez, Leonidas G Alexopoulos, Jonathan Epperlein, Regina Samaga, Douglas A Lauffenburger, Steffen Klamt, and Peter K Sorger. Discrete logic modelling as a means to link protein signalling networks with functional analysis of mammalian signal transduction. Molecular Systems Biology, 5 (1): 331, Jan 2009. ISSN 1744-4292. https://doi.org/10.1038/msb.2009.87.
[51] Santiago Videla, Julio Saez-Rodriguez, Carito Guziolowski, and Anne Siegel. caspo: a toolbox for automated reasoning on the response of logical signaling networks families. Bioinformatics, 33 (6): 947-950, 2016. ISSN 1367-4803. https://doi.org/10.1093/bioinformatics/btw738.
[52] Stefan Wuchty. Scale-Free Behavior in Protein Domain Networks. Molecular Biology and Evolution, 18 (9): 1694-1702, Sep 2001. ISSN 1537-1719. https://doi.org/10.1093/oxfordjournals.molbev.a003957.
[53] I. Shmulevich, E.R. Dougherty, S. Kim, and W. Zhang. Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics, 18 (2): 261-274, Feb 2002. ISSN 1367-4803. https://doi.org/10.1093/bioinformatics/18.2.261.
[54] Ilya Shmulevich and Stuart A. Kauffman. Activities and sensitivities in Boolean network models. Physical Review Letters, 93 (4): 048701, Jul 2004. ISSN 00319007. https://doi.org/10.1103/PhysRevLett.93.048701.
[55] Maria I. Davidich and Stefan Bornholdt. Boolean Network Model Predicts Cell Cycle Sequence of Fission Yeast. PLoS ONE, 3 (2), Feb 2008. ISSN 1932-6203. https://doi.org/10.1371/journal.pone.0001672. · Zbl 1400.92207
[56] Stefan Bornholdt. Boolean network models of cellular regulation: prospects and limitations. Journal of The Royal Society Interface, 5, Aug 2008. ISSN 1742-5689. https://doi.org/10.1098/rsif.2008.0132.focus.
[57] Camille D.A. Terfve, Edmund H. Wilkes, Pedro Casado, Pedro R. Cutillas, and Julio Saez-Rodriguez. Large-scale models of signal propagation in human cells derived from discovery phosphoproteomic data. Nature Communications 2015 6:1, 6 (1): 1-11, sep 2015. ISSN 2041-1723. https://doi.org/10.1038/ncomms9033.
[58] Touré, Vasundra; Flobak, Åsmund; Vercruysse, Steven; Niarakis, Anna; Kuiper, Martin, The status of causality in biological databases: data resources and data retrieval possibilities to support logical modeling, Briefings in Bioinformatics (2020)
[59] Pauline Traynard, Luis Tobalina, Federica Eduati, Laurence Calzone, and Julio Saez-Rodriguez. Logic Modeling in Quantitative Systems Pharmacology. CPT: Pharmacometrics & Systems Pharmacology, 6 (8): 499-511, Aug 2017. ISSN 21638306. https://doi.org/10.1002/psp4.12225.
[60] Eirini Tsirvouli, Vasundra Touré, Barbara Niederdorfer, Åsmund Flobak, and Martin Kuiper. A middle-out modeling strategy to extend a colon cancer logical model improves drug synergy predictions in epithelial-derived cancer cell lines. Frontiers in Molecular Biosciences, 7: 300, 2020a. ISSN 2296-889X. https://doi.org/10.3389/FMOLB.2020.502573.
[61] Eirini Tsirvouli, Barbara Niederdorfer, John Zobolas, Touré Vasundra, Åsmund Flobak, and Martin Kuiper. CASCADE - CAncer Signaling CAusality DatabasE. Zenodo, Oct 2020b. 10.5281/zenodo.4066665. Retrieved from https://github.com/druglogics/cascade, (1 June 2021, date last accessed).
[62] Andreas Wagner. Evolution of gene networks by gene duplications: A mathematical model and its implications on genome organization. Proceedings of the National Academy of Sciences of the United States of America, 91 (10): 4387-4391, May 1994. ISSN 00278424. https://doi.org/10.1073/pnas.91.10.4387. · Zbl 0795.92019
[63] Wang, Rui-Sheng; Saadatpour, Assieh; Albert, Réka, Boolean modeling in systems biology: an overview of methodology and applications, Physical Biology, 9, 5, 55001 (2012)
[64] Jorge G.T. Zañudo, Maximino Aldana, and Gustavo Martínez-Mekler. Boolean threshold networks: Virtues and limitations for biological modeling. Information Processing and Biological Systems, 11: 113-151, 2011. ISSN 18684394. https://doi.org/10.1007/978-3-642-19621-8_6.
[65] Ranran Zhang, Mithun Vinod Shah, Jun Yang, Susan B. Nyland, Xin Liu, Jong K. Yun, Réka Albert, and Thomas P. Loughran. Network model of survival signaling in large granular lymphocyte leukemia. Proceedings of the National Academy of Sciences, 105 (42): 16308-16313, Oct 2008. ISSN 0027-8424. https://doi.org/10.1073/PNAS.0806447105.
[66] John Zobolas. Gitsbe format documentation, 2020. Retrieved from https://druglogics.github.io/druglogics-doc/gitsbe-config.html#gitsbe-format, (1 June 2021, date last accessed).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.