- Open Access
Using hidden Markov models to investigate G-quadruplex motifs in genomic sequences
© Yano and Kato; licensee BioMed Central Ltd. 2014
- Published: 8 December 2014
G-quadruplexes are four-stranded structures formed in guanine-rich nucleotide sequences. Several functional roles of DNA G-quadruplexes have so far been investigated, where their putative functional roles during DNA replication and transcription have been suggested. A necessary condition for G-quadruplex formation is the presence of four regions of tandem guanines called G-runs and three nucleotide subsequences called loops that connect G-runs. A simple computational way to detect potential G-quadruplex regions in a given genomic sequence is pattern matching with regular expression. Although many putative G-quadruplex motifs can be found in most genomes by the regular expression-based approach, the majority of these sequences are unlikely to form G-quadruplexes because they are unstable as compared with canonical double helix structures.
Here we present elaborate computational models for representing DNA G-quadruplex motifs using hidden Markov models (HMMs). Use of HMMs enables us to evaluate G-quadruplex motifs quantitatively by a probabilistic measure. In addition, the parameters of HMMs can be trained by using experimentally verified data. Computational experiments in discriminating between positive and negative G-quadruplex sequences as well as reducing putative G-quadruplexes in the human genome were carried out, indicating that HMM-based models can discern bona fide G-quadruplex structures well and one of them has the possibility of reducing false positive G-quadruplexes predicted by existing regular expression-based methods. Furthermore, our results show that one of our models can be specialized to detect G-quadruplex sequences whose functional roles are expected to be involved in DNA transcription.
The HMM-based method along with the conventional pattern matching approach can contribute to reducing costly and laborious wet-lab experiments to perform functional analysis on a given set of potential G-quadruplexes of interest. The C++ and Perl programs are available at http://tcs.cira.kyoto-u.ac.jp/~ykato/program/g4hmm/.
- Regular Expression
- Hide State
- Viterbi Algorithm
- Forward Algorithm
- Pattern Match Approach
Deoxyribonucleic acids (DNAs) are macromolecules that hold genetic information in almost all of the organisms. The bulk of existing DNA molecules is assumed to form a right-handed double helical structure called B-DNA , where each constituent bases A and C selectively bind to bases T and G, respectively, between two strands arranged in the antiparallel way. In contrast, several in vitro experiments reveal the existence of non-B-DNA structures caused by particular sequence motifs and DNA-protein interactions. Well investigated examples include G-quadruplex (G4), Z-DNA, cruciform and triplex. Recent advances in providing in vitro evidence of these specific structures develop the hypothesis that these structures are considered to have some functional roles in living cells .
Eukyariotic telomeric sequences include G-rich regions and they can form G4 structures in vitro. However, the question of how many such G-rich regions can actually form G4 structures in vivo has not been resolved. The potential to form G4 structures in telomeric sequences in vivo can be shown by in vitro DNA binding experiments with those sequences . For example, telomere end-binding proteins in ciliates can control the formation of G4 DNA structures at telomeres . Interestingly, however, a recent study suggests that endogenous G4 structures in human cells are present largely outside the telomeres . Another work reports that protruding nucleotides in human telomeric sequences destabilize the G4 structure and overhanging sequences influence the folding of the quadruplex . Other examples of G-rich regions in genomes are transcriptional start sites, mitotic and meiotic double strand break sites. Although G4 structures have stability with higher temperature than that of canonical double helix structures, many functional regions in genomic sequences have not a few G-rich motifs , motivating us to investigate further the functional roles of G4 structures.
Since little is known about the functions of G4 structures and genome-scale wet-lab experiments with nuclear magnetic resonance (NMR) spectroscopy for structural analysis  are not feasible, several computational efforts have been made on identifying the locations of potential G4 sequences in genomic DNAs and inferring their functions by comparative sequence analysis using related genes with known functions [10, 11]. In principle, G4 motifs can be represented by a regular expression G+N ∗G+N∗G+N∗G+, where 'N' shows an arbitrary base including G, '+' denotes at least one repeat of the preceding symbol and '∗' means at least zero repeats. Due to this simple pattern of G4 motifs, several in silico methods have been proposed to detect G4 sequences in genomes using pattern matching with regular expression [12–16]. Moreover, regular expression-based methods that incorporate a simple scoring scheme are proposed [17–19]. Another computational study focuses on thermodynamic stability of G4 structures using Gaussian process regression . Although the pattern matching approaches can detect many G4 motifs in genomic sequences quite fast, it is pointed out that the majority of these motifs may be false positive G4 sequences [21, 22].
In this contribution, we present more elaborate computational models than regular expression to represent G4 motifs, employing hidden Markov models (HMMs). HMMs are so flexible in modeling linear dependence that they are widely used in bioinformatics including protein secondary structure prediction [23, 24] and sequence motif search . To model G4 motifs, we provide four HMM-based models from the viewpoint of the number of hidden states that describe G-runs and loops, and compare with each other in three computational experiments. The first preliminary experiment in predicting G-run regions in a set of 100 real G4 sequences in the literature  indicates that each HMM-based model can represent actual G-run regions well. The subsequent experiment in discriminating real and shuffled G4 sequences by using HMMs shows that the models considering detailed distributions of G-run and loop lengths can outperform the simple probabilistic extension of regular expression. In the third test with statistical analysis in discriminating highly likely G4 structures from putative G4 motifs in the human pre-mRNA sequences , the results show that the HMM-based model that can represent elaborate length distribution of G-run regions outperforms the other three models presented in this work. Moreover, the above model can be specialized to detect G4 sequences whose functional roles are expected to be involved in DNA transcription. Finally, this model in conjunction with pattern search is applied to G4 screening in the whole human genome, producing a considerably smaller number of G4 candidates with statistical significance than that of G4 sequences predicted by pattern matching alone.
Here we would like to emphasize the significance of our research findings as follows:
As compared with the regular expression-based approach, our method can assess G4 motifs quantitatively by a probabilistic measure. Indeed, G4 motifs can be detected first by the "discrete" regular expression-based method and then may be scored to judge their thermodynamic stability using energy parameters for G4 structures. However, to the best of our knowledge, elaborate energy parameters for G4 structures have not been available so far. Under these circumstances, probabilistic models including HMMs are useful in not only evaluating predictions quantitatively but also training the model parameters from experimentally verified data.
Our results show that HMM-based models are statistically reliable enough to detect a more specified motif among general G4 structures in genomic sequences, narrowing down potential G4 sequences predicted by the existing pattern matching method. This means that the combination of the regular expression-based approach and our probabilistic method will help reduce expensive and laborious wet-lab experiments more than the regular expression method alone will do to exhaustively analyze a given set of G4 motifs of interest. We believe that our research findings can boost understanding of functional roles of G4 structures in genomes, as well as helping to design therapeutic drugs that target specific G4 structures.
We develop four HMMs to see how well the models can represent real G4 sequences and can reduce false positive G4 sequences from putative ones. To put it simply, the HMMs developed have four sets of hidden states for G-runs linked by three sets of hidden states for loops (see Methods for details of HMMs). In addition, the parameters of HMMs were trained by experimentally verified data in the literature .
Predicting G-run regions
Stegle et al.  provide a dataset of 260 G4 structures, which were experimentally verified with varying salt concentrations. Note that the corresponding sequences are of the form G+N∗G+N∗G+N∗G+ in regular expression. In our test, we used 100 sequences out of 260 because the original dataset contains duplicate sequences with different salt concentrations.
where SEN, PPV and F denote sensitivity, positive predictive value and F-measure, respectively.
Results of predicting G-run regions in 100 real G4 sequences verified experimentally in .
Discriminating G4 sequences
We first investigate the discriminative performance of the four HMM-based models between real and shuffled G4 sequences. More specifically, we first randomly split the set of 100 real G4 sequences in Stegle et al.'s dataset  into two sets of 50 positive sequences, where one set is for training and the other is for validation. Next, a set of 50 negative sequences for validation was created by doing trinucleotide shuffling  of 50 positive sequences in the validation set. Note that use of trinucleotide shuffling comes from the observation that G4 structures often have at least three consecutive Gs as each G-run to make their structures stable. In total, we have 100 sequences in the validation set where 50 sequences are positive and the other 50 sequences are negative.
where and s denote the average and the standard deviation, respectively, of all validation sequences.
Reducing potential G4 sequences in database
Human genes that include putative non-overlapping G4 sequences used in our experiments.
# putative G4s
# putative G4s
Functional analysis of putative G4 sequences
where G(X) is the number of G4 sequences in the gene X and |X| shows the length of X. For the original G4 candidates in the GRSDB2 database and their reduced G4 sequences computed by the HMM-based models 2 and 4 with the cutoff of lower-tailed 5% point of the standard normal distribution, we calculated G4 density of each gene and converted it into the Z-score in each case. It should be noted that the Z-scores were calculated over all genes in each case. We should also notice that the point here is to make clear which gene can be considered to have significantly many G4 sequences.
G4 density of each gene computed from the results of the HMM-based model 2.
Z(D pred )
Z(D ref )
Z(D pred )
Z(D ref )
G4 density of each gene computed from the results of the HMM-based model 4.
Z(D pred )
Z(D ref )
Z(D pred )
Z(D ref )
Information on genes that have significantly many putative G4 structures.
Function: RNA binding, methyltransferase activity, nucleotide binding.
Process: metabolic process.
Function: ligase activity, metal ion binding, protein binding, ubiquitin-protein, ligase activity, zinc ion binding.
Process: activation of MAPKKK activity, positive regulation of MAPKKK cascade, protein ubiquitination, regulation of apoptosis, regulation of transcription, DNA-dependent, transcription.
Component: ubiquitin ligase complex.
Function: metal ion binding, molecular function.
Process: apoptosis, biological_process, multicellular organismal development.
Component: cellular_component, nucleus.
Function: IMP dehydrogenase activity, catalytic activity, metal ion binding, oxydoreductase activity, potassium ion binding.
Process: GMP biosynthetic process, GTP biosynthetic process, lymphocyte proliferation, metabolic process, purine nucleotide biosynthetic process, response to stimulus, visual perception.
Applying HMM to whole human genome
The third experiment stated above focuses only on pre-mRNA sequences in the human genome, leaving further potential G4 sequences over the whole genome. Thus, we demonstrate here how many potential G4 sequences the regular expression-based method can detect in the whole human genome and how many our method can reduce.
Comparison of the number of G-motifs in the human genome between use of regular expression (RE) alone and that of HMM (model 2) together with RE.
# G4 motifs
RE+HMM with cutoff 1
2m 5.296s + 22.245s
RE+HMM with cutoff 2
2m 5.296s + 22.245s
From our experimental results, the following two points on the constitution of HMMs become clear:
Increasing the hidden states for representing G-runs in an HMM can lead to small variance of the probability distribution over input sequences given the model.
Increasing the hidden states for describing loops can make the HMM flexible.
Here we will look closely at G-runs and loops in G4 sequences. Recall that G-run is a region of consecutive Gs involved in G-quartets and loop is a single strand consisting of arbitrary bases that connect G-runs in front and behind. Since the HMM-based model 2 as well as the model 4 is specialized to represent consecutive Gs, each G in G-runs will be strictly discriminated in the model, affecting the sharpness of the probability distribution over the set of input sequences. On the other hand, the model 3 has more hidden states that can represent any base, and thus it can output an arbitrary sequence in a more flexible framework and show multi-modal probability distribution. Viewed in this light, we may say that the model 4 has the broader distribution of Z-scores due to increase in hidden states for representing loops, and several groups of peaks because of increase in hidden states for describing G-runs (see also Figure 6). Although the different peaks in score distributions may tell us which potential G4 sequence actually forms G4 structure in vitro and/or in vivo, experimental verification in wet-labs is still awaited.
We presented the HMM-based modelings for G4 motifs in anticipation of reducing false positive G4 sequences in genomic DNAs detected by simple pattern matching with regular expression. The discrimination test with the HMMs was indicative of high discriminative power of elaborate models between positive and negative G4 sequences. Our computational experiments with statistical analysis on potential G4 sequences in human genomes make it clear that the HMM-based model that considers detailed distribution of G-run length can discriminate well between G4 sequences that match the model and those that do not. Moreover, another experimental results suggest that the above HMM-based model can be specialized to detect genes whose functional roles are expected to be involved in transcription, which include significantly many G4 sequences. Furthermore, this model in conjunction with use of regular expression can detect a considerably smaller number of G4 candidates in the whole human genome with statistical significance. Therefore, we may reasonably conclude that the HMM-based approach together with the conventional pattern matching method can contribute to reducing costly and laborious wet-lab experiments to exhaustively analyze a given set of G4 motifs of interest.
In this work, we proposed the HMM-based models where each G-run has variable length. In contrast, applying HMMs that deal only with a specific fixed length of G-runs to genomic sequences may yield more accurate discrimination of G4 sequences. In addition, change of the training sequences that should be verified experimentally may have a certain effect on prediction results. In this sense, collaboration between in silico, in vitro and in vivo experiments will be even more important to advance functional analysis of G4 structures in genomes of various organisms.
A G4 sequence comprises alternate G-runs and loops, which can be described as G+N∗G+N∗G+N∗G+ in regular expression. In particular, the majority of existing pattern matching-based methods assume that the length of a G-run is between three and five and that of a loop is between one and seven . To model the G4 motif by HMMs, we focus on which state of G-run and loop each base in a given sequence is decoded into. Advantages of use of HMMs can be summarized as follows:
The most likely state path that corresponds to structural elements in a sequence can be predicted by the Viterbi algorithm.
The probability of a sequence given the parameterized model can be calculated by the forward algorithm.
Optimal probability parameters of the model can be estimated on a set of example sequences by the Baum-Welch algorithm.
The Viterbi algorithm can compute the most probable state path of an HMM for a given sequence in O(m2n) time based on dynamic programming, where m is the number of hidden states in the HMM and n is the sequence length. The forward algorithm and the backward algorithm, which is analogous to the forward algorithm but differs in that a backward recursion starts at the end of a sequence, can compute the probability of a sequence given an HMM by dynamic programming with the same running time of the Viterbi algorithm. Finally, the Baum-Welch algorithm can calculate optimal parameters of an HMM given a set of training sequences, where the forward and backward algorithms are repeatedly used until the change in log likelihood of the sequences is less than some threshold. Details of the algorithms can be found in .
Publication charges were supported by JSPS KAKENHI [#24700296 to YK]
We would like to thank Prof. Shigehiko Kanaya at Nara Institute of Science and Technology for his helpful comments. This work was supported by JSPS KAKENHI [#24700296 to YK].
This article has been published as part of BMC Genomics Volume 15 Supplement 9, 2014: Thirteenth International Conference on Bioinformatics (InCoB2014): Computational Biology. The full contents of the supplement are available online at http://www.biomedcentral.com/bmcgenomics/supplements/15/S9.
- Watson JD, Crick FH: Molecular structure of nucleic acids: a structure for deoxyribose nucleic acid. Nature. 1953, 171: 737-738. 10.1038/171737a0.PubMedView ArticleGoogle Scholar
- Bochman ML, Paeschke K, Zakian VA: DNA secondary structures: stability and function of G-quadruplex structures. Nat Rev Genet. 2012, 13: 770-780. 10.1038/nrg3296.PubMedPubMed CentralView ArticleGoogle Scholar
- Huppert JL: Structure, location and interactions of G-quadruplexes. FEBS J. 2010, 277: 3452-3458. 10.1111/j.1742-4658.2010.07758.x.PubMedView ArticleGoogle Scholar
- Guédin A, Gros J, Alberti P, Mergny JL: How long is too long? Effects of loop size on G-quadruplex stability. Nucleic Acids Res. 2010, 38: 7858-7868. 10.1093/nar/gkq639.PubMedPubMed CentralView ArticleGoogle Scholar
- Takahama K, Sugimoto C, Arai S, Kurokawa R, Oyoshi T: Loop lengths of G-quadruplex structures affect the G-quadruplex DNA binding selectivity of the RGG motif in ewing's sarcoma. Biochemistry. 2011, 50: 5369-5378. 10.1021/bi2003857.PubMedView ArticleGoogle Scholar
- Paeschke K, Simonsson T, Postberg J, Rhodes D, Lipps HJ: Telomere end-binding proteins control the formation of G-quadruplex DNA structures in vivo. Nat Struct Mol Biol. 2005, 12: 847-854. 10.1038/nsmb982.PubMedView ArticleGoogle Scholar
- Biffi G, Tannahill D, McCafferty J, Balasubramanian S: Quantitative visualization of DNA G-quadruplex structures in human cells. Nat Chem. 2013, 5: 182-186. 10.1038/nchem.1548.PubMedPubMed CentralView ArticleGoogle Scholar
- Viglasky V, Bauer L, Tluckova K, Javorsky P: Evaluation of human telomeric G-quadruplexes: the influence of overhanging sequences on quadruplex stability and folding. J Nucleic Acids. 2010, 2010:Google Scholar
- Adrian M, Heddi B, Phan AT: NMR spectroscopy of G-quadruplexes. Methods. 2012, 57: 11-24. 10.1016/j.ymeth.2012.05.003.PubMedView ArticleGoogle Scholar
- Todd AK: Bioinformatics approaches to quadruplex sequence location. Methods. 2007, 43: 246-277. 10.1016/j.ymeth.2007.08.004.PubMedView ArticleGoogle Scholar
- Huppert JL: Hunting G-quadruplexes. Biochimie. 2008, 90: 1140-1148. 10.1016/j.biochi.2008.01.014.PubMedView ArticleGoogle Scholar
- Todd AK, Johnston M, Neidle S: Highly prevalent putative quadruplex sequence motifs in human DNA. Nucleic Acids Res. 2005, 33: 2901-2907. 10.1093/nar/gki553.PubMedPubMed CentralView ArticleGoogle Scholar
- Huppert JL, Balasubramanian S: Prevalence of quadruplexes in the human genome. Nucleic Acids Res. 2005, 33: 2908-2916. 10.1093/nar/gki609.PubMedPubMed CentralView ArticleGoogle Scholar
- Rawal P, Kummarasetti VB, Ravindran J, Kumar N, Halder K, Sharma R, Mukerji M, Das SK, Chowdhury S: Genome-wide prediction of G4 DNA as regulatory motifs: role in Escherichia coli global regulation. Genome Res. 2006, 16: 644-655. 10.1101/gr.4508806.PubMedPubMed CentralView ArticleGoogle Scholar
- Huppert JL, Balasubramanian S: G-quadruplexes in promoters throughout the human genome. Nucleic Acids Res. 2007, 35: 406-413.PubMedPubMed CentralView ArticleGoogle Scholar
- Cao K, Ryvkin P, Johnson FB: Computational detection and analysis of sequences with duplex-derived interstrand G-quadruplex forming potential. Methods. 2012, 57: 3-10. 10.1016/j.ymeth.2012.05.002.PubMedPubMed CentralView ArticleGoogle Scholar
- D'Antonio L, Bagga P: Computational methods for predicting intramolecular G-quadruplexes in nucleotide sequences. Proceedings of the 2004 IEEE Computational Systems Bioinformatics Conference (CSB2004). 2004, Stanford, CA, 561-562. 16-19 August 2004Google Scholar
- Kikin O, D'Antonio L, Bagga PS: QGRS Mapper: a web-based server for predicting G-quadruplexes in nucleotide sequences. Nucleic Acids Res. 2006, 34: 676-682. 10.1093/nar/gkj467.View ArticleGoogle Scholar
- Beaudoin JD, Jodoin R, Perreault JP: New scoring system to identify RNA G-quadruplex folding. Nucleic Acids Res. 2014, 42: 1209-1223. 10.1093/nar/gkt904.PubMedPubMed CentralView ArticleGoogle Scholar
- Stegle O, Payet L, Mergny JL, MacKay DJC, Huppert JL: Predicting and understanding the stability of G-quadruplexes. Bioinformatics. 2009, 25: 374-382. 10.1093/bioinformatics/btp210.View ArticleGoogle Scholar
- Beaudoin JD, Perreault JP: 5'-UTR G-quadruplex structures acting as translational repressors. Nucleic Acids Res. 2010, 38: 7022-7036. 10.1093/nar/gkq557.PubMedPubMed CentralView ArticleGoogle Scholar
- Lorenz R, Bernhart SH, Externbrink F, Qin J, Siederdissen CH, Amman F, Hofacker IL, Stadler PF: RNA folding algorithms with G-quadruplexes. Lect Notes Bioinform. 2012, 7409: 49-60.Google Scholar
- Asai K, Hayamizu S, Handa K: Prediction of protein secondary structure by the hidden Markov model. Comput Appl Biosci. 1993, 9: 141-146.PubMedGoogle Scholar
- Krogh A, Brown M, Mian IS, Sjölander K, Haussler D: Hidden Markov models in computational biology. Applications to protein modeling. J Mol Biol. 1994, 235: 1501-1531. 10.1006/jmbi.1994.1104.PubMedView ArticleGoogle Scholar
- Durbin R, Eddy SR, Krogh A, Mitchison G: Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. 1998, Cambridge University Press, CambridgeView ArticleGoogle Scholar
- Kikin O, Zappala Z, D'Antonio L, Bagga PS: GRSDB2 and GRS_UTRdb: databases of quadruplex forming G-rich sequences in pre-mRNAs and mRNAs. Nucleic Acids Res. 2008, 36: 141-148. 10.1093/nar/gkn705.View ArticleGoogle Scholar
- Jiang M, Anderson J, Gillespie J, Mayne M: uShuffle: a useful tool for shuffling biological sequences while preserving the k-let counts. BMC Bioinform. 2008, 9: 192-10.1186/1471-2105-9-192.View ArticleGoogle Scholar
- Karolchik D, Barber GP, Casper J, Clawson H, Cline MS, Diekhans M, Dreszer TR, Fujita PA, Guruvadoo L, Haeussler M, Harte RA, Heitner S, Hinrichs AS, Learned K, Lee BT, Li CH, Raney BJ, Rhead B, Rosenbloom KR, Sloan CA, Speir ML, Zweig AS, Haussler D, Kuhn RM, Kent WJ: The UCSC Genome Browser database: 2014 update. Nucleic Acids Res. 2014, 42: 764-770. 10.1093/nar/gkt946.View ArticleGoogle Scholar
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