DIGITAL REPRESENTATION AND ANALYSIS OF GENOMIC DATA

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1 1 PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Seies A, OF THE ROMANIAN ACADEMY Volume 5, Numbe 2/2004, pp DIGITAL REPRESENTATION AND ANALYSIS OF GENOMIC DATA Paul Dan CRISTEA Bio-Medical Engineeing Cente "Politehnica" Univesity of Buchaest, Romania Complex epesentation of nucleotides is used to convet sequences of nucleotides into complex digital genomic signals that ae analyzed using signal pocessing methods. Using phase analysis, we establish global and lage scale featues of pokayote and eukayote chomosomes, including all human chomosomes. We show that both the cumulated and unwapped phases of concatenated eoiented ORFs have a linea vaiation along pokayote DNA molecules. A hypothesis on the existence of a pimay ancestal genomic mateial fom which the cuent DNA molecules have evolved is advanced on these bases. Keywods: Genomic signals, Complex epesentation, Phase analysis, Open Reading Fames INTRODUCTION The almost complete sequencing of the human [10,15] and mouse genomes [13] and of othe eukayote and pokayote oganisms [9,11,14], as well as the public access to the genomic databases, offe the oppotunity to exploe in depth this unique infomation depositoy in the attempt to extact useful knowledge fom this vast volume of aw data. Afte the publishing of the fist vesions of the almost complete sequence of the human genome, it has been fomulated the opinion that only the genes, the appoximately five pecent of the genome that contains the infomation to synthesize the poteins was of eal inteest, while the emaining vast majoity of the genome was simply junk DNA. The genes have been consideed the blue-pints of any oganism and the ole of othe endogenous and exogenous factos in the complex ontogeny, function and dysfunction of the living has been diminished, if not ignoed. This eductionist view, eminiscent of the classic concept one gene one tait, efomulated as one gene one potein, has also been motivated by the potential impotance of genes in phamacogenomics, in the hope of leading to the synthesis of poteins, potentially useful as tageted medication [12]. Cetainly, the impotance of poteins fo the living can not be undeestimated. Poteins ae the main contibutos to cell stuctue and, as enzymes, catalyse the chemical eactions specific to the functioning of any cells. Almost eveything in the oganism is made of o by poteins. The genes encode the pimay stuctue of poteins, i.e., the composition of the amino acid sequences that build-up the polypeptide chains. A potein can contain seveal polypeptide chains and its biological functions take place at the level of the vey complex spatial stuctue that esults fom the coiling (seconday stuctue), folding (tetiay stuctue) and aggegation (quatenay stuctue) of the polypeptide chains. The complexity of the poteome the set of poteins existing in a cell, exceeds by fa the complexity of its genome. The total numbe of genes in the human genome is of about 30000, while the poteome compises moe than one million poteins. It became gadually clea that the key to oganism complexity is not in the gene numbe, but in the way pats of genes ae expessed and combined to build diffeent poteins using altenative splicing. The complexity of the phenotype also esults fom pocesses like pleiotopy one gene affecting seveal phenotypic chaacteistics, and polygeny a goup of genes acting togethe to cumulatively poduce a cetain tait. It is to be expected that the egulatoy mechanisms that contol these pocesses ae sensitive to signals fom the extenal envionment and fom the cells, tissues and ogans themselves. Despite the fact that the integenic pat of the human genome contains epetitive, quasi-andom sequences and a lage amount of tansposable elements that bea a close esemblance to the DNA of

2 Paul Dan CRISTEA 2 independent entities like viuses and bacteia, significant pats of the inte-gene chomosomal DNA most likely play an impotant ole in the contol of potein synthesis, conjointly with othe gene egulatoy systems. The standad appoach of symbolically epesenting the genomic infomation by sequences of nitogenous base symbols in the stands of DNA and RNA molecules (a = adenine, c = cytosine, g = guanine, t = thymine / u = uacil), by symbolic codons (tiplets of nucleotides), o by symbolic sequences of amino acids in the coesponding polypeptide chains (fo the genes) limits the methodology of pocessing the genetic infomation to mee patten matching and statistical analysis. Conveting the DNA sequences into digital signals [5] opens the possibility to apply signal pocessing methods to the analysis of genomic data [2-8]. The genomic signal appoach has aleady poven its potential in evealing lage scale featues of DNA sequences maintained ove distances of base pais, including both coding and non-coding egions, i.e., at the scale of whole chomosomes [3]. One of the most conspicuous esults is that the unwapped phase of DNA complex genomic signals vaies almost linealy along all investigated chomosomes, fo both pokayotes and eukayotes. The slope is specific fo vaious taxa and chomosomes. Such a behaviou eveals lage scale second ode statistical ules fo the distibution of pais of successive nucleotides, simila to Chagaff s fist ode ules fo the fequencies of occuence of nucleotides [1]. The existence of this egulaity suppots the view that exta gene DNA sequences, that do not encode poteins, can play impotant functional oles, most likely in the contol of gene expession. This is stongly suppoted by the ecent publications of a high quality daft sequence of the mouse genome [13] that allowed a compaative analysis of the mouse and human genomes. Along with the about genes, the homo sapiens and the mus musculus genomes shae twice as long othe exta gene DNA sequences. These sequences must have impotant functions to explain thei exact consevation ove the 75 million yea divegent evolution of human and mouse lineages. The pape gives a bief oveview of ou cuent wok on digital genomic signal epesentation and analysis and epots seveal new esults obtained by using this appoach. 2. VECTORIAL AND COMPLEX REPRESENTATION OF NUCLEOTIDES The convesion of DNA sequences fom the symbolic fom given in the genomic data bases [12] into digital signals allows using poweful signal pocessing pocedues fo handling and analysing genomic data. We have investigated a lage vaiety of mappings and we have selected the tetahedal (3D) and the complex (2D) epesentations used thoughout ou wok [2-8] based on seveal equiements that must be satisfied by an adequate mapping. Fist of all, the mapping has to be tuthful and un-biased. A tuthful mapping R (puines) S (stong bond) G (guanine) C (cytosine) Y (pyimidines) M (amino ) A (adenine) T (thymine) W (weak bond) Fig. 1. Dichotomies of nitogenous bases K (keto ) expesses the elevant featues of the epesented objects in coesponding mathematical popeties of the digital signal samples. An un-biased mapping does not intoduce atefacts, i.e., popeties of the esulting digital signal without coespondent in the of the featues of the epesented symbolic sequence. On the othe hand, the mapping should allow a fast and computationally effective convesion and should povide an output easy to ead fo humans. The last equest favous epesentations with a low dimensionality of the output, pefeably 1D o 2D. In this section we biefly pesent the digital epesentation of nucleotides stating fom the essential featues of DNA sequences. A detailed study of the symbolic to digital convesion of genomic sequences can be found in [5]. The double helix DNA molecules compises two antipaallel intetwined complementay stands, each a helicoidally coiled heteopolyme [16]. The epetitive units ae the nucleotides which consist each of thee pats linked by stong covalent bounds: a phosphate goup, a suga the deoxyibose, and a nitogenous base. Thee ae fou nucleotides in DNA molecules diffeing by the nitogenous basis they contain: adenine

3 3 Digital Repesentation and Analysis of Genomic Data (A), cytosine (C), guanine (G) o thymine (T). Along the two stands of the DNA double helix, a basis in one chain always faces its complementay basis in the othe chain, and only the base pais T-A and C-G exist. The hydogen bonds within these base pais keep togethe the two stands. The entities in the nucleotide chains that encode polypeptides, i.e., specify the pimay stuctue of poteins, ae called genes. The genes ae made up of seveal exons coding egions sepaated by intons non-coding egions. The potein coding is govened by the Genetic Code (GC) that establishes the mapping of codons tiplets of successive nucleotides in the exons to the 20 amino acids found in the polypeptide chains and to the teminato that maks the end of an encoding segment. Thee is a lage edundancy (degeneation) of the GC as thee ae 4 3 = 64 codons to specify only 21 distinct outputs. The edundancy is distibuted unevenly among the outputs: thee ae amino acids encoded by one (2 instances), two (9 instances), thee (one instance), fou (5 instances) o six (3 instances) distinct codons, while the teminato is encoded by thee codons. When a gene is expessed, the oiginal DNA stand is fist tanscibed into a complementay messenge RNA (mrna) sequence, which is edited by the excision of all intons and the joining of all exons. The numbe of nucleotides in an exon is not necessaily a multiple of thee, i.e., an exon does not necessaily compise an intege numbe of codons. In RNA molecules, thymine is eplaced by uacil a elated nitogenous base, but the GC emains othewise the same. A polypeptide chain is synthesized by ibosomes that tanslate the codon sequence of mrna into an amino acid sequence. Each of the 20 amino acids is bought by a specific tansfe RNA (trna). As schematically shown in Fig. 1, thee ae thee main dichotomies of the nitogenous bases biochemical popeties that allow aanging them in classes: (1) molecula stuctue A and G ae puines (R), while C and T ae pyimidines (Y); (2) stength of links bases A and T ae linked by two hydogen bonds (W - weak bond), while C and G ae liked by thee hydogen bonds (S - stong bond); (3) adical content A and C contain the amino (NH 3 ) goup (M class), while T and G contain the keto (C=O) goup (K class). To conseve the symmety of the nucleotides and to expess thei classification in the couples shown in Fig. 1, we have poposed the nucleotide tetahedal epesentation [5, 8] given in Fig. 2. Amino-Keto (y) Amino Stong Bonds c Puine-Pyimidines (z) Adenine a Puines Pyimidines g Guanine t Keto Weak Bonds Weak-Stong (x) Thymine Keto R Y M G -1 C S Stong bonds Im = R-Y -j j W A 1 T Weak bonds Amino Puines Re =W-S Pyimidines K Cytosine Fig. 2. Nucleotide tetahedon Fig. 3. Nucleotide quadantal epesentation The nucleotides ae mapped to fou vectos oiented towads the vetices of a egula tetahedon. Each of the six edges coesponds to a cetain class compising a pai of nucleotides. The epesentation is theedimensional and the axes chosen in Fig. 2 coespond to the diffeences: x = W S, y = M K, z = R Y. By choosing { ± 1} coodinates fo the vetices of the embedding cube, the vectos that epesent the fou nucleotides take the simple fom: a = i + j + k, c = i + j k, g = i j + k, t = i j k. The dimensionality of the epesentation can be educed by pojecting the nucleotide tetahedon on an adequately chosen plane. This plane can be put in coespondence with the complex plane, so that a complex (1)

4 Paul Dan CRISTEA 4 epesentation of the nucleotides is obtained. The choice of the pojection plane is detemined by the featues that have to be conseved as being most elevant in the given context. Fo the epesentation of DNA sequences, we have found that the pojection on the plane xz is best as it expesses the S-W and Y-R dichotomies. The coesponding quadantal epesentation is given in Fig. 3, in which the pais of nucleotides ae gouped in the six above mentioned classes, while the coesponding complex epesentation of the nucleotides is given by the equations: (2) a = 1 + j, c = 1 j, g = 1+ j, t = 1 j. Fo a codon consisting of the sequence of thee nucleotides X = B 2 B 1 B 0, B i {A, C, G, T}; i = 0, 1, 2, the vecto and the complex epesentations ae obtained using the basis 2 expansions: (3) x = 2 b + 2 b + 2 b ; { a, c, g, t }; i = 0,1, 2, 2 x b + 2 b 2 b b i = ; { a, c, g, t} ; i = 0,1, 2 b i, espectively. Fo example, in the case of methionine, to which coesponds the codon ATG that also stats any gene, the vecto epesentation is M = 5 i + j + 3 k, while the complex epesentation is M = 5 + j 3. Relations (2) and simila ones can be seen as epesenting the nucleotides in two mutually othogonal (bipola) binay systems, each with a complex basis, instead of a system in base fou. Using equation (3) one can build the codon tetahedon on which the Genetic Code is mapped [5]. It is emakable that the diffeent epesentations of an amino acid, esulting fom the edundancy of the Genetic Code, ae mapped in neighbouing points of the codon tetahedon, with the exception of the thee instances of amino acids degeneated of ode six fo which none of the investigated mapping can obtain the full contiguity of the epesentations. Similaly, equation (4) geneates a complex epesentation of the Genetic Code. (4) 3. PHASE ANALYSIS OF GENOMIC SIGNALS Seveal analysis tools have been developed fo extacting local and lage scale featues of genetic signals [2,6]. Phase analysis concepts have been pesented in detail elsewhee [3], but ae biefly eviewed in this section fo convenience. The phase of a complex numbe is peiodic with peiod 2π. The standad mathematical convention, coveing only once all the possible diections in the complex plane. The cumulated phase is the sum of the phases of the complex samples in a sequence, fom the fist to the cuent one. To avoid the bias intoduced by the estiction of the phase, which favous π ove -π fo eal negative samples, a small unifomly distibuted complex noise is added to each sample in the sequence. Fo the epesentation (2), the slope s c of the cumulated phase vaiation is elated to the fequencies of occuence of the nucleotides along the DNA by the equation [3]: esticts the phase of a complex numbe to the domain ( π,π ] s c π = 3 4 [ ( f f ) + ( f f )] G C The unwapped phase is a coected phase of the elements in a complex sequence, in which the absolute value of the diffeence between the phase of each element and the phase of its peceding element is kept smalle than π by adding o subtacting an appopiate multiple of 2π to o fom the phase of the cuent element. Again, a small complex noise has been added to avoid the phase bias descibed above. The unwapped phase is a measue of the fequencies of the nucleotide pais (tansitions) in a sequence. Fo the complex epesentation given in Eq.(2), each positive tansition A G, G C, C T, T A detemines an incease of the unwapped phase with 2 π, each negative tansition A T, T C, C G, G A detemines a simila decease, while all othe tansitions ae neutal and do not change the unwapped phase on the aveage. Coespondingly, the slope s u of the unwapped phase along a DNA stand is elated to the A T (5)

5 5 Digital Repesentation and Analysis of Genomic Data diffeence between the fequency f + of the positive tansitions and the fequency f - of the negative ones by the elation: s = π u ( f + f ). (6) 2 4. LARGE SCALE FEATURES OF GENOMIC SIGNALS Contigs fom seveal eukayote and pokayote genomes have been downloaded fom GenBank of NIH [12] and conveted to genomic signals using the complex epesentation given in Eq. (2). Lage scale featues of the signals have been sought fo at the scale of contigs o concatenated contigs. The cumulated phase and the unwapped phase have well defined long ange tends which ae specific fo the diffeent eukayote and pokayote genomes. Fig. 4 shows the unwapped phase along the cumulated contigs of all homo sapiens chomosomes. The unwapped phase vaies almost linealy o piece-wise linealy, along all chomosomes, with seveal exceptions. Remakable enough, when DNA daft sequences ae efined, passing to highe quality dafts, the lineaity of the unwapped phase impoves. Phase 3 data show best this featue. The aveage slope of the unwapped phase fo all homo sapiens chomosomes ae given in Fig. 4 and Table 1. Table 1. Aveage slope of the unwapped phase of homo sapiens chomosomes Chomosome s u [ad / bp] Chomosome s u [ad / bp] Chomosome s u [ad / bp] X Y The linea incease of the unwapped phase of a sequence of nucleotide complex epesentations along a DNA stand shows that the complex epesentations fom on the aveage a counte clockwise helix that completes a tun ove the spatial peiod: (7) 2π L =, s u whee s u is the slope of the unwapped phase. It is emakable that the tend of vaiation of the unwapped phase is maintained ove distances of tens of millions of bases, evealing a statistical egulaity in the distibution of the succession of bases (base-pais), not only in the distibution of the bases themselves: The diffeence between the fequency of positive nucleotide-to-nucleotide tansitions (A G, G C, C T, T A) and that of negative tansitions (the opposite ones) along a stand of nucleic acid tends to be small, constant and taxon & chomosome specific. Simila long ange behaviou has been found fo the mus musculus (mouse) contigs. Chomosomes 1 and 4 of mus musculus displays each two distinct linea domains of the unwapped phase that suggest a composite stuctue of these chomosomes. Fo both homo sapiens and mus musculus, the cumulated phase has locally a less egula vaiation but, at the scale of epesentation used fo the unwapped phase, emains close to the hoizontal axis showing an oveall appoximate balance of the puines and pyimidines in all chomosomes as stated by the well known Chagaff s law. The behaviou is quite diffeent fo pokayotes. Typically, the cumulated phase vaies piece-wise linealy along the DNA stands, as shown in Fig. 5 fo the complete genome ( bp) of Clostidium pefingens (NC , [12]), an anaeobic flesh-eate bacteia [14]. The unwapped phase pesents the same linea vaiation found fo all taxa and all chomosomes. The chomosomes of both pokayotes and eukayotes have a vey patchy stuctue compising many intetwined coding and non-coding segments oiented in diect and invese sense. Figue 5 also shows the effect of e-oienting all the 2660 coding egions

6 Paul Dan CRISTEA 6 in the genome along the same positive diection. A stiking change is displayed by the cumulated phase which becomes appoximately linea along the whole sequence of bp. The unwapped phase emains almost unchanged, with the exception of the shotening of the sequence esulting fom the emoval of the non-coding egions, fo which thee ae no oientation data. As shown in [4], the diection evesal of a DNA segment is always accompanied by the switching of the antipaallel stands of its double helix. This fact explains why the statistics of fist ode and the cumulated phase change obviously when e-oienting ORFs, while the statistic of second ode and the unwapped phase emain almost unchanged Fig. 4. Unwapped phase along the concatenated contigs of all homo sapiens chomosomes

7 7 Digital Repesentation and Analysis of Genomic Data Figue 6 pesents the same analysis fo the complete genome of anothe pokayote, the hypethemophilic bacteium Aquifex aeolicus [9] (AE [12]). In this case, the cumulated phase has a Fig. 5. Cumulated and unwapped phase of the genomic signals fo the complete nucleotide sequence and the concatenated e-oiented 2660 coding egions of Clostidium pefingens genome [14] (NC [12]). Fig. 6. Cumulated and unwapped phase of the genomic signals fo the complete nucleotide sequence and the concatenated e-oiented 1522 coding egions of Aquifex aeolicus genome [9] (AE [12]). quasi-andom close to zeo vaiation fo the complete genome, and becomes linea when the 1522 coding egions ae e-oiented along the positive sense of the molecule. Again, the unwapped phase conseves its linea vaiation befoe and afte the ORF e-oientation. 5. CONCLUSIONS DNA sequences have been conveted into genomic signals by using a complex quadantal epesentation of the nucleotides that has been deived fom the tetahedal epesentation of nucleotides. The

8 Paul Dan CRISTEA 8 main advantage of genomic signals ove symbolic sequences is that they can be analysed by using signal pocessing methods. The pape pesents esults of the phase analysis of complex genomic signals fo both pokayotes and eukayotes. Specifically, esults of the phase analysis fo all the chomosomes of the human genome and fo two bacteia ae given. The genomic signal cumulated phase and unwapped phase ae put in coespondence with the statistical distibution of bases and base-pais, espectively. Lage scale egulaities, maintained ove distances of base pais, i.e., at the scale of whole chomosomes, ae epoted. This esult contadicts the ovesimplified genomic model that consides exta-genic egions as domains of andomness, ecognizing only the meaningful stuctue of the exons [10,12,15]. In the case of pokayotes, it is shown that the cumulated phase displays eithe a piece-wise linea, o a quasi-andom, close to zeo, vaiation along the DNA molecules, while the unwapped phase has always an almost linea vaiation. In statistical tems, this esult confims the well known Chagaff s laws fo the fis ode distibution of nucleotides, but also eveals a simila law fo the second ode distibution of the nucleotide-to-nucleotide tansitions. The e-odeing in the same (positive) diection of all the coding egions of a chomosome, changes completely the vaiation of the cumulated phase, but leaves unchanged the unwapped phase. The lineaity of the cumulated phase fo the e-odeed ORFs stongly suggests two hypotheses: (1) the existence of a pimay ancestal genomic mateial fom which the cuent DNA molecules have evolved, (2) the functional ole of the paticula oientation of diect and invese ORFs, that geneates specific densities of the fist and second ode epatition of nucleotides along chomosomes. The ole of these lage scale featues in the contol of cossing-ove/ecombination pocesses and the sepaation of species emain to be futhe investigated. REFERENCES 1. CHARGAFF E., Stuctue and function of nucleic acids as cell constituents, Fed. Poc., 10, 1951, pp CRISTEA, P., Genomic signals fo whole chomosomes, SPIE Confeence, BiOS 2003 Intenational Biomedical Optics Symposium, Molecula Analysis and Infomatics, San Jose, USA, BO , Januay 25-31, CRISTEA, P., Lage Scale Featues in DNA Genomic Signals, ELSEVIER, Signal Pocessing, Special Issue on Genomic Signal Pocessing, 83, 2003, pp CRISTEA, P., Genomic Signals of Re-Oiented ORFs, EURASIP JASP, Special Issue on Genomic Signal Pocessing, vol. 2004, 1 Januay 2004, no. 1, pp CRISTEA, P., Convesion of Nitogenous Base Sequences into Genomic Signals, Jounal of Cellula and Molecula Medicine, 6, 2, Apil June 2002, pp CRISTEA, P., Genetic signal epesentation and analysis, SPIE Confeence, BiOS 2002 Intenational Biomedical Optics Symposium, Molecula Analysis and Infomatics, San Jose, USA, BO , Januay 21-24, CRISTEA, P., Genetic Signal Analysis, ISSPA 2001 The Sixth Intenational Symposium on Signal Pocessing and its Applications, Invited Pape, Kuala Lumpu, Malaysia, August 13 16, 2001, pp CRISTEA, P., Genetic Signals, Rev. Roum. Sci. Techn. Electotechn. et Eneg., 46, 2, 2001, pp DECKERT, G. et al, The complete genome of the hypethemophilic bacteium Aquifex aeolicus, Natue, 392 (6674), 1998, pp Intenational Human Genome Sequencing Consotium, Initial sequencing and analysis of the human genome, Natue, 409, Febuay 15, 2001, pp MYERS, E.W. et al., A Whole-Genome Assembly of Dosophila, Science, 287, Mach 24, 2000, pp National Cente fo Biotechnology Infomation, National Institutes of Health, National Libay of Medicine, National Cente fo Biotechnology Infomation, GenBank, RIKEN Genome Exploation Reseach Goup Phase II Team and the FANTOM Consotium, Functional annotation of a fulllength mouse cdna collection, Natue, 409, Febuay 8, 2001, pp SHIMIZU, T. et al, Complete genome sequence of Clostidium pefingens, an anaeobic flesh-eate, Poc. Natl. Acad. Sci. U.S.A., 99, 2002, pp VENTER, J.C. et al., Daft Analysis of the Human Genome by Celea Genomics, Science, 291, Febuay 16, 2001, pp WATSON, J.D., CRICK, F.H.C., A Stuctue fo Deoxyibose Nucleic Acid, Natue, 171, Apil 2, 1953, pp Received Octobe 27, 2003