Abstract
One of the most important problems in the context of systems biology is to infer gene regulatory networks from gene expression data, since most of the control of cellular processes are performed by the multivariate activity of genes by means of their transcribed mRNA expression. Although many methods have been proposed to deal with this problem in the last two decades, gene network inference from gene expression data is still considered an open problem, mostly because the huge dimensionality (thousands of genes) and the very limited number of data samples typically available, even considering the fact that the network is sparse (limited number of input genes per target gene). In this work, we propose two variants of a previously published method which alleviates the curse of dimensionality by grouping predictor gene configurations in their respective linear combination values. Such values are assigned to equivalence classes. In this way, the number of instances of predictor values (equivalence classes) grows as a linear function of the dimensionality (number of predictors) instead of increasing as an exponential function when considering the original configurations. Both proposed method and its variants follow the probabilistic gene networks approach, applying local feature selection to achieve a satisfactory predictor gene set for each target gene. Although the results obtained from the aforementioned previous work were very promising, it applies the grouping unconditionally, even in cases where the number of samples is enough to estimate the conditional probabilities of the target given the predictors, which leads to unnecessary information loss. Results from simulated and real data indicate that, despite suffering from information loss, the inference with linear grouping tends to provide networks with better topological similarities than those obtained without grouping in cases where the number of samples is quite limited and the inference involves a larger number of predictors per gene. Besides, the variants proposed here displayed better results in cases where part of the parameters could be properly estimated without grouping, thus achieving better balance between information loss and estimation power gain.
Similar content being viewed by others
References
Akutsu T, Miyano S, Kuhara S (1999) Identification of genetic networks from a small number of gene expression patterns under the boolean network model. Pac Symp Biocomput 4:17–28
Albert R, Othmer HG (2003) The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in drosophila melanogaster. J Theor Biol 223(1):1–18
Angeletti M, Culmone R, Merelli E (2001) An intelligent agents architecture for dna-microarray data integration. Tech. rep., U. of Camerino, Italy
Barabsi AL, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512
Barrera J, Cesar-Jr RM, Martins-Jr DC, Vencio RZN, Merino EF, Yamamoto MM, Leonardi FG, Pereira CAB, del Portillo HA (2007) Constructing probabilistic genetic networks of Plasmodium falciparum from dynamical expression signals of the intraerythrocytic development cycle. In: Methods of Microarray Data Analysis V, chap 2, pp 11–26. Springer (2007)
Bozdech Z, Llins M, Pulliam BL, Wong ED, Zhu J, DeRisi JL (2003) The transcriptome of the intraerythrocytic developmental cycle of Plasmodium falciparum. Plos Biol 1(1)
Brun M, Dougherty ER, Shmulevich I (2005) Steady-state probabilities for attractors in probabilistic boolean networks. Signal Process 85(10):1993–2013
Davidich MI, Bornholdt S (2008) Boolean network model predicts cell cycle sequence of fission yeast. PLoS One 3(2):e1672
D’haeseleer P, Liang S, Somgyi R (1999) Tutorial: Gene expression data analysis and modeling. In: Pacific Symposium on Biocomputing. Hawaii
Dougherty ER (2011) Validation of gene regulatory networks: scientific and inferential. Brief Bioinform 12(3):245–252
Dougherty ER, Barrera J, Mozelle G, Kim S, Brun M (2001) Multiresolution analysis for optimal binary filters. J Math Imaging Vis 14(1):53–72. doi:10.1023/A:1008311431244
Dougherty ER, Brun M, Trent J, Bittner ML (2009) A conditioning-based model of contextual regulation. IEEE/ACM Trans Comput Biol Bioinform 6(2):310–320
Dougherty ER, Kim S, Chen Y (2000) Coefficient of determination in nonlinear signal processing. EURASIP J Signal Process 80(10):2219–2235
Erds P, RTnyi A (1959) On random graphs. Publ Math Debr 6:290–297
Espinosa-Soto C, Padilla-Longoria P, Alvarez-Buylla ER (2004) A gene regulatory network model for cell-fate determination during arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles. Plant Cell 16(11):2923–2939
Faure A, Naldi A, Chaouiya C, Thieffry D (2006) Dynamical analysis of a generic boolean model for the control of the mammalian cell cycle. Bioinformatics 22(14):e124–131
Friedman N, Linial M, Nachman I, Pe’er D (2000) Using bayesian networks to analyze expression data. J Comput Biol 7:601–620
Hecker M, Lambeck S, Toepfer S, van Someren E, Guthke R (2009) Gene regulatory network inference: data integration in dynamic models-a review. Biosystems 96:86–103
Ivanov I, Dougherty ER (2006) Modeling genetic regulatory networks: continuous or discrete? J Biol Syst 14(2):219–229
Jong HD (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol 9(1):67–103
Karlebach G, Shamir R (2008) Modelling and analysis of gene regulatory networks. Nat Rev Mol Cell Biol 9(10):770–780. doi:10.1038/nrm2503
Kauffman SA (1969) Homeostasis and differentiation in random genetic control networks. Nature 224(215):177–178
Kelemen A, Abraham A, Chen Y (2008) Computational Intelligence in Bioinformatics. Springer, Berlin, Heidelberg
Lahdesmaki H, Shmulevich I (2003) On learning gene regulatory networks under the boolean network model. Mach Learn 52:147–167
Li F, Long T, Lu Y, Ouyang Q, Tang C (2004) The yeast cell-cycle network is robustly designed. Proc Natl Acad Sci USA 101(14):4781–4786
Liang S, Fuhrman S, Somogyi R (1998) Reveal, a general reverse engineering algorithm for inference of genetic network architectures. Pac Simpos Biocomput 3:18–29
Lopes FM, Martins-Jr DC, Barrera J, Cesar-Jr RM (2014) A feature selection technique for inference of graphs from their known topological properties: revealing scale-free gene regulatory networks. Inf Sci 272:1–15
Lopes FM, Martins-Jr DC, Cesar-Jr RM (2008) Feature selection environment for genomic applications. BMC Bioinform 9(451)
Lopes FM, Ray SS, Hashimoto RF, Cesar-Jr RM (2014) Entropic biological score: a cell cycle investigation for grns inference. Gene 541:129–137
Marbach D, Prill RJ, Schaffter T, Mattiussi C, Floreano D, Stolovitzky G (2010) Revealing strengths and weaknesses of methods for gene network inference. Proc Nat Acad Sci 107(14):6286–6291
Martins-Jr DC, Braga-Neto U, Hashimoto RF, Dougherty ER, Bittner ML (2008) Intrinsically multivariate predictive genes. IEEE J Sel Top Signal Process 2(3):424–439
Martins-Jr DC, Oliveira EA, Braga-Neto UM, Hashimoto RF, Cesar-Jr RM (2013) Signal propagation in bayesian networks and its relationship with intrinsically multivariate predictive variables. Inf Sci 225:18–34
McCluskey EJ (1956) Minimization of boolean functions. Bell Syst Tech J 35(5):1417–1444
Montoya-Cubas CF, Martins-Jr DC, Santos CS, Barrera J (2014) Gene networks inference through linear grouping of variables. In: 14th IEEE International Conference on Bioinformatics and Bioengineering (BIBE), pp 243–250. Boca Raton, FL
Nam D, Seo S, Kim S (2006) An efficient top-down search algorithm for learning boolean networks of gene expression. Mach Learn 65:229–245
Ristevski B (2013) A survey of models for inference of gene regulatory networks. Nonlinear Anal: Model Control 18(4):444–465
Sánchez L, Thieffry D (2001) A logical analysis of the drosophila gap-gene system. J Theor Biol 211(2):115–141
Shalon D, Smith SJ, Brown PO (1996) A dna microarray system for analyzing complex dna samples using two-color fluorescent probe hybridization. Genome Res pp 639–45
Shmulevich I, Dougherty ER (2007) Genomic signal processing. Princeton University Press, New Jersey
Shmulevich I, Dougherty ER, Kim S, Zhang W (2002) Probabilistic boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 18(2):261–274
Snoep JL, Westerhoff HV (2005) From isolation to integration, a systems biology approach for building the silicon cell. Top Curr Genet 13:13–30
Styczynski MP, Stephanopoulos G (2005) Overview of computational methods for the inference of gene regulatory networks. Comput Chem Eng 29(3):519–534
Theodoridis S, Koutroumbas K (2006) Pattern Recognition. Elsevier, Academic Press, Amsterdam, New York
Velculescu VE, Zhang L, Vogelstein B, Kinzler KW (1995) Serial analysis of gene expression. Science 270:484–487
Wang Z, Gerstein M, Snyder M (2009) Rna-seq: a revolutionary tool for transcriptomics. Nat Rev Genet 10(1):57–63
Zhang Y, Qian M, Ouyang Q, Deng M, Li F, Tang C (2006) Stochastic model of yeast cell-cycle network. Physica D 219(1):35–39
Acknowledgments
We would like to thank FAPESP Grant # 2011/50761-2, CNPq, CAPES and NAP eScience—PRP—USP for the financial support.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare no conflict of interest and that this research did not involve human participants and/or animals.
Rights and permissions
About this article
Cite this article
Cubas, C.F.M., Martins-Jr, D.C., Santos, C.S. et al. Linear grouping of predictor instances to infer gene networks. Netw Model Anal Health Inform Bioinforma 4, 34 (2015). https://doi.org/10.1007/s13721-015-0105-2
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13721-015-0105-2