Computing Minimal Boolean Models of Gene Regulatory Networks
Publication: Journal of Computational Biology
Volume 31, Issue Number 2
Abstract
Models of gene regulatory networks (GRNs) capture the dynamics of the regulatory processes that occur within the cell as a means to understanding the variability observed in gene expression between different conditions. Arguably the simplest mathematical construct used for modeling is the Boolean network, which dictates a set of logical rules for transition between states described as Boolean vectors. Due to the complexity of gene regulation and the limitations of experimental technologies, in most cases knowledge about regulatory interactions and Boolean states is partial. In addition, the logical rules themselves are not known a priori. Our goal in this work is to create an algorithm that finds the network that fits the data optimally, and identify the network states that correspond to the noise-free data. We present a novel methodology for integrating experimental data and performing a search for the optimal consistent structure via optimization of a linear objective function under a set of linear constraints. In addition, we extend our methodology into a heuristic that alleviates the computational complexity of the problem for datasets that are generated by single-cell RNA-Sequencing (scRNA-Seq). We demonstrate the effectiveness of these tools using simulated data, and in addition a publicly available scRNA-Seq dataset and the GRN that is associated with it. Our methodology will enable researchers to obtain a better understanding of the dynamics of GRNs and their biological role.
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REFERENCES
Akaike H. Information theory and an extension of the maximum likelihood principle. In: Springer Series in Statistics. Springer: New York, NY, USA; 1998; pp. 199–213;
Akutsu T, Tamura T, Horimoto K. Completing networks using observed data. In: Lecture Notes in Computer Science. Springer: Berlin Heidelberg; 2009; pp. 126–140;
Arenas E, Denham M, Villaescusa JC. How to make a midbrain dopaminergic neuron. Development 2015;142(11):1918–1936;
Barman S, Kwon Y-K. A boolean network inference from time-series gene expression data using a genetic algorithm. Bioinformatics 2018;34(17):i927–i933;
Geistlinger L, Csaba G, Dirmeier S, et al. A comprehensive gene regulatory network for the diauxic shift in saccharomyces cerevisiae. Nucleic Acids Res 2013;41(18):8452–8463;
Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual; 2023. Available from: https://www.gurobi.com
Han S, Wong RKW, Lee TCM, et al. A full Bayesian approach for Boolean genetic network inference. PLoS One 2014;9(12):e115806;
Hashimoto RF, Kim S, Shmulevich I, et al. Growing genetic regulatory networks from seed genes. Bioinformatics 2004;20(8):1241–1247;
Huang M, Wang J, Torre E, et al. SAVER: Gene expression recovery for single-cell RNA sequencing. Nat Methods 2018;15(7):539–542;
Karlebach G, Shamir R. Modelling and analysis of gene regulatory networks. Nat Rev Mol Cell Biol 2008;9(10):770–780;
Karlebach G, Shamir R. Constructing logical models of gene regulatory networks by integrating transcription factor–DNA interactions with expression data: An entropy-based approach. J Comput Biol 2012;19(1):30–41;
Kauffman SA. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol 1969;22(3):437–467;
Lähdesmäki H, Shmulevich I, Yli-Harja O. On learning gene regulatory networks under the Boolean network model. Mach Learn 2003;52(1/2):147–167;
La Manno G, Gyllborg D, Codeluppi S, et al. Molecular diversity of midbrain development in mouse, human, and stem cells. Cell 2016;167(2):566.e19–580.e19;
Liang S, Fuhrman S, Somogyi R. Reveal, a general reverse engineering algorithm for inference of genetic network architectures. In: Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing; 1998; pp.18–29. ISSN 2335-6936. Copyright: This record is sourced from MEDLINE®/ ®, a database of the U.S. National Library of Medicine.
Liu Z, Lou H, Xie K, et al. Reconstructing cell cycle pseudo time-series via single-cell transcriptome data. Nat Commun 2017;8(1);
Müssel C, Hopfensitz M, Kestler HA. Boolnet—An r package for generation, reconstruction and analysis of Boolean networks. Bioinformatics 2010;26(10):1378–1380.
Ohara T, Hearn TJ, Webb AAR, et al. Gene regulatory network models in response to sugars in the plant circadian system. J Theor Biol 2018;457:137–151;
Ono Y, Nakatani T, Minaki Y, et al. The basic helix-loop-helix transcription factor nato3 controls neurogenic activity in mesencephalic floor plate cells. Development 2010;137(11):1897–1906;
Rissanen J. A universal prior for integers and estimation by minimum description length. Ann Stat 1983;11(2);
Risso D, Cole M. scrnaseq 2017. Available from: https://bioconductor.org/packages/scRNAseq
Sanchez MA, Sullivan GM, Armstrong RC. Genetic detection of sonic hedgehog (shh) expression and cellular response in the progression of acute through chronic demyelination and remyelination. Neurobiol Dis 2018;115:145–156;
Satija R, Farrell JA, Gennert D, et al. Spatial reconstruction of single-cell gene expression data. Nat Biotechnol 2015;33(5):495–502;
Schwarz G. Estimating the dimension of a model. Ann Stat 1978;6(2);
Seth S, Mallik S, Bhadra T, et al. Dimensionality reduction and Louvain agglomerative hierarchical clustering for cluster-specified frequent biomarker discovery in single-cell sequencing data. Front Genet 2022;13;
Shavit Y, Yordanov B, Dunn S-J, et al. Automated synthesis and analysis of switching gene regulatory networks. Biosystems 2016;146:26–34;
Willis SN, Nutt SL. New players in the gene regulatory network controlling late b cell differentiation. Curr Opin Immunol 2019;58:68–74;
Information & Authors
Information
Published In
Journal of Computational Biology
Volume 31 • Issue Number 2 • February 2024
Pages: 117 - 127
PubMed: 37889991
Copyright
Copyright 2024, Mary Ann Liebert, Inc., publishers.
History
Published online: 12 February 2024
Published in print: February 2024
Published ahead of print: 27 October 2023
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Authors' Contributions
The authors contributed to the article equally. Both authors have read and agreed to the published version of the article.
Author Disclosure Statement
The authors declare they have no conflicting financial interests.
Funding Information
This work was supported by internal funding of the Jackson Laboratory.
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