Abnizova, I.

Gilks, W.

Te Boekhorst, R.

English

University of Hertfordshire Research Archive

17COMPUTATIONAL STRUCTURAL AND FUNCTIONAL GENOMICSSOME WAYS TO INFER A DNA FUNCTIONFROM THE SEQUENCE INFORMATIONAbnizova I.*, te Boekhorts R., Gilks W.MRC-BSU Cambridge, University of Hertfordshire Hatfield, UK* Corresponding author: irina.abnizova@mrc-bsu.cam.ac.ukKeywords: regulatory regions, coding DNA, heterogeneity, computational methods,information entropy, long range correlationsSummaryWe present a computational approach to infer DNA function based on eukaryotic  DNA sequenceinformation. Namely, we utilise an observation that exons, regulatory regions and non codingnon regulatory DNA exhibit different statistical information patterns. We suggest to capture andmeasure these patterns with several independent mathematical tools such as rescaled analysis,information entropy, density of low-entropy patches and similarity test.Results: We introduce here a new optimization technique of which the outcome is independent ofthe size of the sliding window and hence avoids averaging. This technique, which takes accountof the heterogeneity in the DNA sequence, performs an unsupervised search, without usingreference sets or cross genome comparison. We also introduce new way of measuring DNA localheterogeneity, and a statistical test for abundance of similar words.A preliminary application of our methods to the set of genes from six different species, namelyhuman, mouse, fugu, sea urchin, drosophila and yeast, reliably identifies the borders of the regionsof interest and thus reveals the potential of our approach.We propose that this combination of established computational statistical methods, augmentedwith our sliding window optimization technique, and our new statistical tests, might create apowerful DNA sequence characterization and annotation tool that optimises the search fordifferences in statistical properties between coding, non-coding and regulatory DNA.Availability: The software is available from the authors on request.IntroductionThe unsupervised search methods for analysing the structure of the genome fall, broadly speaking,in one of two categories: (i) methods for characterizing the composition of the genome and (ii)those used for detecting sequential or serial dependency (i.e. that focus on the actual ordering ofnucleotides).Nucleotide composition is commonly investigated with tools from information theory (i.e. variousways to estimate the entropy of parts of the genome), self-organising maps (Abe et al., 2003),complexity analysis (Wan et al., 2003; Li , 1997) and statistical linguistics (Mantegna et al., 1994).Statistical dependencies between nucleotides/amino acids have been analysed using mutualinformation functions (Azbel, 1995), Markov models (Krogh et al., 1994), spectra (Voss, 1992)and methods derived from random walk dynamics such as detrended fluctuation- and rescaledrange analysis (Peng et al., 1994). In particular the detection of long range correlations (LRCs)has attracted much attention (Li, 1997; Mantegna et al., 1994; Azbel, 1995; Peng et al., 1994;Herzel et al., 1997) and correlations ranging from a few base pairs up to 1000 bp have beenfound.Results from the application of these methods seem to indicate that non-coding and coding DNAhave distinguishable statistical properties: long range correlations have been reported for non-coding, but not for coding regions (Peng et al., 1994; Herzel et al., 1997; but see Voss, 1992).18COMPUTATIONAL STRUCTURAL AND FUNCTIONAL GENOMICS                                                                                                    BGRS 2004Unfortunately, when these techniques are used in the conventional way, their results will behighly dependent on the size of the sliding window.Methods and ResultRandom walks and rescaled range analysis. One way to characterize the succession of nucleotidesis to imagine a “walk” along the DNA string by moving up each time a pyrimidine (a T or C) occursand by moving down whenever a purine (an A or G) is encountered. As a result, one may obtain afractal-looking “landscape”, in which probably long stretches of mainly purine alternate with stretchesthat contain mostly pyrimidine. If the probability of the occurrence of a pyrimidine equals that of apurine and is independent of the position in the string (i.e. P (pyrimidine) = P (purine)), then such a“DNA walk” would actually be a “random walk”. The increments of the walk would form a seriesof independent and identically distributed events with constant mean and finite variance that istherefore stationary and furthermore characterised by a flat spectrum and the absence ofautocorrelations (“white noise”). The random walk itself, being integrated white noise, is typicallynon-stationary. This is manifest in the largely non-vanishing spikes in the autocorrelation functionand the predominance of low frequency components in the power spectrum (Voss, 1992 ).Another way to do find long range correlations in DNA sequence is to calculate the Hurst exponent(H) by means of a “rescaled range analysis”. The Hurst exponent estimates the degree of“persistence” of the system. Rescaled range analysis can be applied to any time or space series.Setting x k = +1 for k = T, C and x k = -1 for k = A, G, the sequence {x k} can be characterised by:  [ ]∑∑==〉〈−==〉〈imnmniin xxniXxnx11),( ,1 ),(min),(max)( niXniXnR nini ≤≤ −= ,2112 ])(1[)( ∑=〉〈−=nini xxnnSfor any 2 ≤ n ≤ N.For scale free data R(n)/S(n) ~ (n/2)H. Hence, the Hurst exponent (H) can be computed from theleast squares fit of the regression of log[R(n)/S(n)] on log[n]. In the above formulas, the test-statistic (H) should be compared with a Hurst exponent obtained under the null-hypothesis thatthe cumulative data (i.e. the time series after integration) are from a random walk and thereforethat the original data are white noise. In other words, Hobserved should be contrasted with Hexpected =0.5 and not with Hexpected = -0.5 (which would be the Hurst exponent of the original data).Obviously, changes in persistence are not accounted for by the conventional application of rescaledrange analysis, i.e. by using a too large, fixed window.  This might be detected as changes in theslope of the log-log plot. We therefore suggest a window that increases until the Hurst exponentreaches a minimum (H < 0.5): this window detects the most probable boards of exons.Entropy-based DNA segmentation  with optimal window method. The conventional procedurefor measuring DNA entropy (Li, 1997) typically consists of calculating a frequency vectordescribing the area’s nucleotide composition for a sufficiently large, but subjectively definedarea, and then subjecting it to the well-known Shannon function:‡”=-=M1iiiM,seq )Plog(PH ,where M is the length of the frequency vector, which in case of single nucleotides is 4, in case of di-nucleotides is 16, etc. The entropy of a frequency vector is maximal when all elements occur withequal probability, in which case H seq, M = log (1/M), and hence measures the “eveness” or the19COMPUTATIONAL STRUCTURAL AND FUNCTIONAL GENOMICS                                                                                                    BGRS 2004“diversity” of the composition. In contrast, low entropy indicates the “dominance” of a few of theelements. Clearly, when increasingly larger fragments of the same stretch of DNA are used, theentropy of the fragments will asymptotically approach the entropy of the entire stretch. Such anoverall estimate does not capture the possibly deviating entropy of small but functionally importantsubparts. Too large and fixed windows therefore overlook local differences in nucleotide composition.For a more powerful method, we therefore must optimise the length of the local windows. To thisaim, we move sliding window of varying length along the DNA sequence, optimising the lengthof the window due to the local maximum of Entropy before it reaches asymptotic value. The mosthigh entropy regions are the most likely locations of exons.Low entropy patches density as heterogeneity measure. There exit two visions of DNAheterogeneity: 1) Heterogeneity is caused by gradual change (bias) of nucleotide composition indifferent parts of the sequence; 2) Heterogeneity is caused by short runs of repetitive (low-entropy)patterns. If you remove them, DNA will be homogeneous again. It is local heterogeneity.To calculate the density of low entropy patches, we first developed an entropy-based algorithmable to fish for these patches; this algorithm occurred to detect very weird patterns, which norepeat masker could find. Thus, we used the density of these low entropy patches as a measure oflocal heterogeneity of DNA.As the result, we present an example of splitting fugu DNA into functional parts due to low-entropypatches: exons typically have minimum density, non coding non regulatory DNA has maximumdensity, and regulatory DNA has intermediate density, as one can see at the table below.In the table, “diverged” denotes non coding non conserved DNA: they were picked up randomlythrough out the Mayfolds fugu whole genome shotgun assembly v.3.0 (August 26, 2002); “cne”(conserved non coding elements) are considered as putative regulatory regions: these elementsare collected due to ClustalW multiple alignment between fugu, mouse, rat and human in thegroup of Greg Elgar (Woolfe et al., submitted 2004), short elements were concatenated together;exons are randomly picked up in Scaffolds1 and 21 fugu whole genome shotgun assembly v.3.0(August 26, 2002), www.ensembl.org (Table).Measure of similar word abundance: similarity-tail test. There is well known observation thatthere are unusually large (unexpectedly due to random multinomial model) number of somesimilar words in the regulatory regions. To quantify this fact, we got the collection of knownfunctional regulatory regions from Drosophila genome. For each region, we computed thedistribution of clusters of similar words inside it, so called similarity-tail test. We calculated thenumber of similar words of length m with few mismatches exhaustively for each m-word in thegiven regulatory region. Due to the presence of unusually high number of over-represented words,we expect to have more “fat” (containing a lot of similar words) clusters in comparison withrandom chance.To sample this random chance, we shuffled our given sequence 200 times keeping its original di-nucleotide content. For each shuffled sequence we plotted the histograms of similar wordsdistribution. We could easily observe that the original sequence “tails” were significantly longerthan all randomised ones.Almost all regulatory regions analysed (currently, 35) exhibit “fluffy” tails, in contrast with exonregions where there is no significant tail exist. This observation gave raise to the algorithm,which distinguish between exons and regulatory regions due to the presence of statisticallysignificant tails in the original distribution. The algorithm currently is applied for Drosophilagenome.Conclusion: Our collection of tools: • Information entropy • Rescaled Range Analysis: Hurstexponent• Density of low entropy patterns• Tests for frequency of similar words might help20COMPUTATIONAL STRUCTURAL AND FUNCTIONAL GENOMICS                                                                                                    BGRS 2004to infer the function of a given not yet annotated DNA stretch, and thus to distinguish betweendifferent DNA functional parts when all the tools are combined.In this work we propose an adaptive optimal windowing technique applied for two popular methodswhich search for short and long range correlations in DNA: rescaled analysis to estimate longdistance dependency by the Hurst exponent, and entropy measurement. Both improvedtechniques are capable to detect putative functional regions in DNA. In addition, we captureDNA homogeneity and presence of repetitive words in other two independent ways: with densityof low-entropy patches, and similar words abundance in the DNA stretch. When we combineresults of these tests with adaptive window methods, we therefore increase likelihood of detectingfunctional DNA regions.ReferencesAbe T., Kanaya S., Kinouchi M, Ichiba Y., Kozuki T., Ikemura T. Informatics for unveiling hidden genomesignatures // Genome Res. 2003. V. 13(4). P. 693–702.Table.Type of sequence Density of low-entropy patterns A + C + G + T Pcg -probability to get cg Pcg/PcPg Pc - probability to get c Length, bp Diverged      Diverged1 0.34 0.29+0.25+0.18+0.26 0.028 0.60 5156 Diverged2 0.44 0.28+0.20+0.21+0.28 0.018 0.41 15221 Diverged3 1.0 0.22+0.36+0.18+0.21 0.03 0.44 755 Diverged4 0.66 0.26+0.18+0.17+0.37 0.02 0.65 1000 Diverged5 0.56 0.30+0.20+0.19+0.30 0.014 0.38 4819 Diverged6 0.62 0.26+0.20+0.20+0.32 0.02 0.48 4750 Diverged7 0.37 0.28+0.20+0.20+0.30 0.02 0.53 8501 Means 0.58 0.28+0.22+0.20+0.29 0.02 0.46  Cnes      Cne2 0.032 0.30+0.21+0.18+0.29 0.018 0.44 14782 Cne3 0.0 0.31+0.19+0.19+0.29 0.012 0.34 3423 Cne5 0.018 0.30+0.18+0.19+0.29 0.012 0.33 18876 Cne6 0.078 0.31+0.18+0.20+0.30 0.01 0.29 14500 Cne7 0.02 0.28+0.20+0.21+0.29 0.017 0.39 23258 Cne8 0.05 0.30+0.18+0.21+0.30 0.013 0.34 10378 Means  0.07 0.30+0.19+0.20+0.30 0.014 0.37  Exons      Ex1_fugu 0.0 0.24+0.27+0.27+0.20 0.048 0.64 4295 Ex2_fugu 0.0 0.27+0.25+0.26+0.22 0.036 0.54 22373 Ex3_fugu 0.03 0.27+0.26+0.26+0.19 0.04 0.57 19940 Ex4_fugu 0 0.25+0.27+0.28+0.20 0.058 0.73 1224 Ex5_fugu 0 0.27+0.26+0.26+0.19 0.045 0.63 3489 Ex6_fugu 0 0.27+0.27+0.26+0.20 0.042 0.58 2835 Ex7_fugu 0.0 0.26+0.27+0.26+0.19 0.043 0.60 3714 Ex8_fugu 0.05 0.27+0.25+0.27+0.20 0.035 0.51 5740 Means  0.007 0.27+0.26+0.27+0.20 0.0412 0.58   21COMPUTATIONAL STRUCTURAL AND FUNCTIONAL GENOMICS                                                                                                    BGRS 2004Abnizova I., Schilstra M., te Boekhorst R., Nehaniv C.L. 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Some ways to infer a DNA function from the sequence information

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