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Inferring sparse genetic regulatory networks based on maximum-entropy probability model and multi-objective memetic algorithm

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Abstract

Maximum-entropy probability models (MEPMs) have been widely used to reveal the structure of genetic regulatory networks (GRNs). However, owing to the inherent network sparsity and small sample size, most of the existing MEPMs use convex optimization to approximate the inference of GRNs which tend to be trapped in less accurate local optimal solutions. Evolutionary algorithms (EAs) can help address this issue thanks to their superior global search capability, yet the conventional EA-based methods cannot handle the sparsity of GRNs efficiently. To overcome this problem, we propose a multi-objective memetic algorithm in this study to infer the sparse GRNs with MEPMs. Particularly, the target inferring problem is formulated as a multi-objective optimization problem where the maximum entropy and the constraints of the MEPM are formulated as two objectives. We employ Graphical LASSO (Glasso) to generate prior knowledge for population initialization. The genetic operators are adopted to ensure the diversity and sparsity of the inferred GRNs. Local search based on the spatial relations among solutions and different Glasso results in the decision space is incorporated into the algorithm to improve the search efficiency. Experimental results on both simulated and real-world data sets suggest that the proposed method outperforms other state-of-the-art GRN inferring methods in terms of effectiveness and efficiency.

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Data availibility

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

References

  1. Butte AJ, Kohane IS (1999) Mutual information relevance networks: functional genomic clustering using pairwise entropy measurements. In: Biocomputing 2000, pp. 418–429. World Scientific

  2. Cantone I, Marucci L, Iorio F, Ricci MA, Belcastro V, Bansal M, Santini S, Di Bernardo M, Di Bernardo D, Cosma MP (2009) A yeast synthetic network for in vivo assessment of reverse-engineering and modeling approaches. Cell 137(1):172–181

    Article  Google Scholar 

  3. Chanda P, Costa E, Hu J, Sukumar S, Van Hemert J, Walia R (2020) Information theory in computational biology: where we stand today. Entropy 22(6):627

    Article  MathSciNet  Google Scholar 

  4. Cheng F, Chu F, Xu Y, Zhang L (2021) A steering-matrix-based multiobjective evolutionary algorithm for high-dimensional feature selection. IEEE transactions on cybernetics

  5. Costantini G, Richetin J, Preti E, Casini E, Epskamp S, Perugini M (2019) Stability and variability of personality networks. a tutorial on recent developments in network psychometrics. Personal Individ Differ 136:68–78

    Article  Google Scholar 

  6. Danaher P, Wang P, Witten DM (2014) The joint graphical lasso for inverse covariance estimation across multiple classes. J Royal Stat Soc: Series B, Stat Methodol 76(2):373

    Article  MathSciNet  MATH  Google Scholar 

  7. De Martino A, De Martino D (2018) An introduction to the maximum entropy approach and its application to inference problems in biology. Heliyon 4(4):e00596

    Article  Google Scholar 

  8. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  9. Fan Z, Fang Y, Li W, Lu J, Cai X, Wei C (2017) A comparative study of constrained multi-objective evolutionary algorithms on constrained multi-objective optimization problems. In: 2017 IEEE congress on evolutionary computation (CEC), pp. 209–216. IEEE

  10. Friedman J, Hastie T, Tibshirani R (2008) Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9(3):432–441

    Article  MATH  Google Scholar 

  11. Friedman N, Linial M, Nachman I, Pe’er D (2000) Using bayesian networks to analyze expression data. J Comput Biol 7(3–4):601–620

    Article  Google Scholar 

  12. Gao X, Pu DQ, Wu Y, Xu H (2012) Tuning parameter selection for penalized likelihood estimation of gaussian graphical model. Statistica Sinica pp. 1123–1146

  13. Grechkin M, Fazel M, Witten D, Lee SI (2015) Pathway graphical lasso. In: Proceedings of the AAAI conference on artificial intelligence, vol. 29

  14. Hurley D, Araki H, Tamada Y, Dunmore B, Sanders D, Humphreys S, Affara M, Imoto S, Yasuda K, Tomiyasu Y et al (2012) Gene network inference and visualization tools for biologists: application to new human transcriptome datasets. Nucleic Acids Res 40(6):2377–2398

    Article  Google Scholar 

  15. Huynh-Thu VA, Irrthum A, Wehenkel L, Geurts P (2010) Inferring regulatory networks from expression data using tree-based methods. PLoS ONE 5(9):e12776

    Article  Google Scholar 

  16. Huynh-Thu VA, Sanguinetti G (2019) Gene regulatory network inference: an introductory survey. In: Gene regulatory networks, pp. 1–23. Springer

  17. Khan A, Mandal S, Pal RK, Saha G (2016) Construction of gene regulatory networks using recurrent neural networks and swarm intelligence. Scientifica. 2016

  18. de Lacerda MGP, de Araujo Pessoa LF, de Lima Neto FB, Ludermir TB, Kuchen H (2021) A systematic literature review on general parameter control for evolutionary and swarm-based algorithms. Swarm Evol Comput 60:100777

    Article  Google Scholar 

  19. Lachmann A, Giorgi FM, Lopez G, Califano A (2016) Aracne-ap: gene network reverse engineering through adaptive partitioning inference of mutual information. Bioinformatics 32(14):2233–2235

    Article  Google Scholar 

  20. Lian S (2016) Duan Y (2016) Smoothing of the lower-order exact penalty function for inequality constrained optimization. J Inequal Appl 1:1–12

    MathSciNet  Google Scholar 

  21. Liu L, Liu J (2018) Inferring gene regulatory networks with hybrid of multi-agent genetic algorithm and random forests based on fuzzy cognitive maps. Appl Soft Comput 69:585–598

    Article  Google Scholar 

  22. Ma X, Liu F, Qi Y, Wang X, Li L, Jiao L, Yin M, Gong M (2015) A multiobjective evolutionary algorithm based on decision variable analyses for multiobjective optimization problems with large-scale variables. IEEE Trans Evol Comput 20(2):275–298

    Article  Google Scholar 

  23. Marbach D, Schaffter T, Mattiussi C, Floreano D (2009) Generating realistic in silico gene networks for performance assessment of reverse engineering methods. J Comput Biol 16(2):229–239

    Article  Google Scholar 

  24. Pant M, Zaheer H, Garcia-Hernandez L, Abraham A et al (2020) Differential evolution: a review of more than two decades of research. Eng Appl Artif Intell 90:103479

    Article  Google Scholar 

  25. Peng J, Wang P, Zhou N, Zhu J (2009) Partial correlation estimation by joint sparse regression models. J Am Stat Assoc 104(486):735–746

    Article  MathSciNet  MATH  Google Scholar 

  26. Perou CM, Sørlie T, Eisen MB, Van De Rijn M, Jeffrey SS, Rees CA, Pollack JR, Ross DT, Johnsen H, Akslen LA et al (2000) Molecular portraits of human breast tumours. Nature 406(6797):747–752

    Article  Google Scholar 

  27. Ramteke M, Ghune N, Trivedi V (2015) Simulated binary jumping gene: a step towards enhancing the performance of real-coded genetic algorithm. Inf Sci 325:429–454

    Article  Google Scholar 

  28. Roudi Y, Nirenberg S, Latham PE (2009) Pairwise maximum entropy models for studying large biological systems: when they can work and when they can’t. PLoS Comput Biol 5(5):e1000380

    Article  MathSciNet  Google Scholar 

  29. Saint-Antoine MM, Singh A (2020) Network inference in systems biology: recent developments, challenges, and applications. Curr Opin Biotechnol 63:89–98

    Article  Google Scholar 

  30. Saldanha AJ, Brauer MJ, Botstein D (2004) Nutritional homeostasis in batch and steady-state culture of yeast. Mol Biol Cell 15(9):4089–4104

    Article  Google Scholar 

  31. Schäfer J, Strimmer K (2005) An empirical bayes approach to inferring large-scale gene association networks. Bioinformatics 21(6):754–764

    Article  Google Scholar 

  32. Schäfer J, Strimmer K (2005) A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Stat Appl Genet Mol Biol. 4(1)

  33. Stein RR, Marks DS, Sander C (2015) Inferring pairwise interactions from biological data using maximum-entropy probability models. PLoS Comput Biol 11(7):e1004182

    Article  Google Scholar 

  34. Stolovitzky G, Monroe D, Califano A (2007) Dialogue on reverse-engineering assessment and methods: the dream of high-throughput pathway inference. Ann N Y Acad Sci 1115(1):1–22

    Article  Google Scholar 

  35. Tian Y, Zhang X, Wang C, Jin Y (2019) An evolutionary algorithm for large-scale sparse multiobjective optimization problems. IEEE Trans Evol Comput 24(2):380–393

    Article  Google Scholar 

  36. Wang L, Feng L (2021) Guest editorial: special issue on memetic algorithms with learning strategy. Memet Comput 13(2):147–148

    Article  Google Scholar 

  37. Wang Y (2020) Evolution strategies for learning sparse matrix representations of gene regulatory networks. Ph.D. thesis, Syracuse University

  38. Wang YK, Hurley DG, Schnell S, Print CG, Crampin EJ (2013) Integration of steady-state and temporal gene expression data for the inference of gene regulatory networks. PLoS ONE 8(8):e72103

    Article  Google Scholar 

  39. Wu N, Huang J, Zhang XF, Ou-Yang L, He S, Zhu Z, Xie W (2019) Weighted fused pathway graphical lasso for joint estimation of multiple gene networks. Front Genet 10:623

    Article  Google Scholar 

  40. Zhang M, Wang H, Cui Z, Chen J (2018) Hybrid multi-objective cuckoo search with dynamical local search. Memet Comput 10(2):199–208

    Article  Google Scholar 

  41. Zhang X, Zhao J, Hao JK, Zhao XM, Chen L (2015) Conditional mutual inclusive information enables accurate quantification of associations in gene regulatory networks. Nucleic Acids Res 43(5):e31–e31

    Article  Google Scholar 

  42. Zhang Y, Tian Y, Zhang X (2021) A comparison study of evolutionary algorithms on large-scale sparse multi-objective optimization problems. In: EMO, pp. 424–437

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Acknowledgements

This work was partially supported by the National Key Research and Development Project [2019YFE0109600], the National Natural Science Foundation of China [61871272], the Shenzhen Fundamental Research Program [JCYJ20190808173617147], and the open project of BGIShenzhen [BGIRSZ20200002].

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Authors and Affiliations

  1. College of Electronics and Information Engineering, Shenzhen University, Shenzhen, 518060, China

    Fu Yin & Weixin Xie

  2. College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, 518060, China

    Zexuan Zhu

  3. BGI-Shenzhen, Shenzhen, 518083, China

    Zexuan Zhu

  4. School of Biosciences, University of Birmingham, Birmingham, B15 2TT, UK

    Jiarui Zhou

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  1. Fu Yin
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Yin, F., Zhou, J., Xie, W. et al. Inferring sparse genetic regulatory networks based on maximum-entropy probability model and multi-objective memetic algorithm. Memetic Comp. 15, 117–137 (2023). https://doi.org/10.1007/s12293-022-00383-8

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