Precise identification of cascading alpha satellite higher order repeats in T2T-CHM13 assembly of human chromosome 3.

AIM: To precisely identify and analyze alpha-satellite higher-order repeats (HORs) in T2T-CHM13 assembly of human chromosome 3. METHODS: From the recently sequenced complete T2T-CHM13 assembly of human chromosome 3, the precise alpha satellite HOR structure was computed by using the novel high-precision GRM2023 algorithm with global repeat map (GRM) and monomer distance (MD) diagrams. RESULTS: The major alpha satellite HOR array in chromosome 3 revealed a novel cascading HOR, housing 17mer HOR copies with subfragments of periods 15 and 2. Within each row in the cascading HOR, the monomers were of different types, but different rows within the same cascading 17mer HOR contained more than one monomer of the same type. Each canonical 17mer HOR copy comprised 17 monomers belonging to 16 different monomer types. Another pronounced 10mer HOR array was of the regular Willard's type. CONCLUSION: Our findings emphasize the complexity within the chromosome 3 centromere as well as deviations from expected highly regular patterns.

Novel Cascade Alpha Satellite HORs in Orangutan Chromosome 13 Assembly: Discovery of the 59mer HOR-The largest Unit in Primates-And the Missing Triplet 45/27/18 HOR in Human T2T-CHM13v2.0 Assembly.

From the recent genome assembly NHGRI_mPonAbe1-v2.0_NCBI (GCF_028885655.2) of orangutan chromosome 13, we computed the precise alpha satellite higher-order repeat (HOR) structure using the novel high-precision GRM2023 algorithm with Global Repeat Map (GRM) and Monomer Distance (MD) diagrams. This study rigorously identified alpha satellite HORs in the centromere of orangutan chromosome 13, discovering a novel 59mer HOR-the longest HOR unit identified in any primate to date. Additionally, it revealed the first intertwined sequence of three HORs, 18mer/27mer/45mer HORs, with a common aligned "backbone" across all HOR copies. The major 7mer HOR exhibits a Willard's-type canonical copy, although some segments of the array display significant irregularities. In contrast, the 14mer HOR forms a regular Willard's-type HOR array. Surprisingly, the GRM2023 high-precision analysis of chromosome 13 of human genome assembly T2T-CHM13v2.0 reveals the presence of only a 7mer HOR, despite both the orangutan and human genome assemblies being derived from whole genome shotgun sequences.

Novel Concept of Alpha Satellite Cascading Higher-Order Repeats (HORs) and Precise Identification of 15mer and 20mer Cascading HORs in Complete T2T-CHM13 Assembly of Human Chromosome 15.

Unraveling the intricate centromere structure of human chromosomes holds profound implications, illuminating fundamental genetic mechanisms and potentially advancing our comprehension of genetic disorders and therapeutic interventions. This study rigorously identified and structurally analyzed alpha satellite higher-order repeats (HORs) within the centromere of human chromosome 15 in the complete T2T-CHM13 assembly using the high-precision GRM2023 algorithm. The most extensive alpha satellite HOR array in chromosome 15 reveals a novel cascading HOR, housing 429 15mer HOR copies, containing 4-, 7- and 11-monomer subfragments. Within each row of cascading HORs, all alpha satellite monomers are of distinct types, as in regular Willard's HORs. However, different HOR copies within the same cascading 15mer HOR contain more than one monomer of the same type. Each canonical 15mer HOR copy comprises 15 monomers belonging to only 9 different monomer types. Notably, 65% of the 429 15mer cascading HOR copies exhibit canonical structures, while 35% display variant configurations. Identified as the second most extensive alpha satellite HOR, another novel cascading HOR within human chromosome 15 encompasses 164 20mer HOR copies, each featuring two subfragments. Moreover, a distinct pattern emerges as interspersed 25mer/26mer structures differing from regular Willard's HORs and giving rise to a 34-monomer subfragment. Only a minor 18mer HOR array of 12 HOR copies is of the regular Willard's type. These revelations highlight the complexity within the chromosome 15 centromeric region, accentuating deviations from anticipated highly regular patterns and hinting at profound information encoding and functional potential within the human centromere.

The Evolution of Life Is a Road Paved with the DNA Quadruplet Symmetry and the Supersymmetry Genetic Code.

Symmetries have not been completely determined and explained from the discovery of the DNA structure in 1953 and the genetic code in 1961. We show, during 10 years of investigation and research, our discovery of the Supersymmetry Genetic Code table in the form of 2 × 8 codon boxes, quadruplet DNA symmetries, and the classification of trinucleotides/codons, all built with the same physiochemical double mirror symmetry and Watson-Crick pairing. We also show that single-stranded RNA had the complete code of life in the form of the Supersymmetry Genetic Code table simultaneously with instructions of codons' relationship as to how to develop the DNA molecule on the principle of Watson-Crick pairing. We show that the same symmetries between the genetic code and DNA quadruplet are highly conserved during the whole evolution even between phylogenetically distant organisms. In this way, decreasing disorder and entropy enabled the evolution of living beings up to sophisticated species with cognitive features. Our hypothesis that all twenty amino acids are necessary for the origin of life on the Earth, which entirely changes our view on evolution, confirms the evidence of organic natural amino acids from the extra-terrestrial asteroid Ryugu, which is nearly as old as our solar system.

Global Repeat Map (GRM): Advantageous Method for Discovery of Largest Higher-Order Repeats (HORs) in Neuroblastoma Breakpoint Family (NBPF) Genes, in Hornerin Exon and in Chromosome 21 Centromere.

Here we present three interesting novel human Higher-Order Repeats (HORs) discovered using the HOR-searching method with GRM algorithm: (a) The novel Neuroblastoma Breakpoint Family gene (NBPF) 3mer HOR, discovered applying GRM algorithm to human chromosome 1 (Paar et al., Mol Biol Evol 28:1877-1892, 2011). NBPF 3mer HOR is based on previously known ~1.6 kb NBPF primary repeat monomers (known as DUF1220 domain) in human chromosome 1, but the NBPF HOR was not known before its discovery by using GRM. It should be stressed that the NBPF HOR presents a unique human-specific pattern, distinguishing human from nonhuman primates. (b) The novel quartic HOR (2mer⊃2mer⊃9mer) discovered using the GRM algorithm for analysis of hornerin genes in human chromosome 1 (Paar et al., Mol Biol Evol 28:1877-1892, 2011). This quartic HOR is based on 39 bp hornerin primary repeat monomer in human chromosome 1. To our knowledge, this is the first known case of quartic HOR, with four levels of hierarchy of HOR organization. (c) The novel 33mer alpha satellite HOR in human chromosome 21, discovered using the GRM algorithm (Gluncic et al., Sci Rep 9:12629, 2019). This 33mer HOR in the smallest human chromosome is the largest alpha satellite HOR copy among all 22 somatic human chromosomes. Moreover, the same 33mer HOR is present in the hg38 human genome assembly of four human chromosomes: 21, 22, 13, and 14. We point out that the DUF1220 encoding genomic structures in NBPF genes in human chromosome 1, recently studied and related to the brain evolution and pathologies and cognitive aptitude, can be considered in the framework of the general concept of HORs, already extensively studied in genomics, especially in the centromeric region.

The novel Ideal Symmetry Genetic Code table - Common purine-pyrimidine symmetry net for all RNA and DNA species.

Ever since Nirenberg's discovery in 1961 in which codons code individual amino acids, numerous scientists searched for symmetries within the genetic code. The standard genetic code (SGC) table is an alphabetic artificial construct based on the U-C-A-G ordering of nucleotides without natural symmetries. Up to the present, complete symmetry in the genetic code has not been found, leaving doubt as to whether the symmetrical nature as the protector of order even exists. Our novel Ideal Symmetry Genetic Code (ISyGC) table reflects a unique fundamental physicochemical purine-pyrimidine symmetry net for all more than thirty known variations of nuclear and mitochondrial genetic codes. The nuclear genetic code for RNA and DNA viruses also contains the same purine-pyrimidine symmetry net. We show that the ISyGC table leads to automatic transformation into a DNA sequence akin to the 5'3 codon and 3'5 anticodon patterns. As a result of purine-pyrimidine symmetries between codons in the ISyGC table, algorithms of the first two bases as well of the third base of codons show how tRNA cognate anticodons can recognize synonymous codons during mRNA decoding. We show that the ISyGC purine-pyrimidine net with its physicochemical properties represents an evolutionary common "frozen accident" at the onset of each genetic code creation and RNA to DNA evolution. As such, during all of evolution the unique fundamental purine-pyrimidine symmetry net of all genetic codes remains unchangeable. In this way, evolution is a road paved with symmetries.

Novel look at DNA and life-Symmetry as evolutionary forcing.

After explanation of the Chargaff´s first parity rule in terms of the Watson-Crick base-pairing between the two DNA strands, the Chargaff´s second parity rule for each strand of DNA (also named strand symmetry), which cannot be explained by Watson-Crick base-pairing only, is still a challenging issue already fifty years. We show that during evolution DNA preserves its identity in the form of quadruplet A+T and C+G rich matrices based on purine-pyrimidine mirror symmetries of trinucleotides. Identical symmetries are present in our classification of trinucleotides and the genetic code table. All eukaryotes and almost all prokaryotes (bacteria and archaea) have quadruplet mirror symmetries in structural form and frequencies following the principle of Chargaff's second parity rule and Natural symmetry law of DNA creation and conservation. Some rare symbionts have mirror symmetry only in their structural form within each DNA strand. Based on our matrix analysis of closely related species, humans and Neanderthals, we find that the circular cycle of inverse proportionality between trinucleotides preserves identical relative frequencies of trinucleotides in each quadruplet and in the whole genome. According to our calculations, a change in frequencies in quadruplet matrices could lead to the creation of new species. Violation of quadruplet symmetries is practically inconsistent with life. DNA symmetries provide a key for understanding the restriction of disorder (entropy) due to mutations in the evolution of DNA.

Direct mapping of symbolic DNA sequence into frequency domain in global repeat map algorithm.

The main feature of global repeat map (GRM) algorithm (www.hazu.hr/grm/software/win/grm2012.exe) is its ability to identify a broad variety of repeats of unbounded length that can be arbitrarily distant in sequences as large as human chromosomes. The efficacy is due to the use of complete set of a K-string ensemble which enables a new method of direct mapping of symbolic DNA sequence into frequency domain, with straightforward identification of repeats as peaks in GRM diagram. In this way, we obtain very fast, efficient and highly automatized repeat finding tool. The method is robust to substitutions and insertions/deletions, as well as to various complexities of the sequence pattern. We present several case studies of GRM use, in order to illustrate its capabilities: identification of α-satellite tandem repeats and higher order repeats (HORs), identification of Alu dispersed repeats and of Alu tandems, identification of Period 3 pattern in exons, implementation of 'magnifying glass' effect, identification of complex HOR pattern, identification of inter-tandem transitional dispersed repeat sequences and identification of long segmental duplications. GRM algorithm is convenient for use, in particular, in cases of large repeat units, of highly mutated and/or complex repeats, and of global repeat maps for large genomic sequences (chromosomes and genomes).

Start/stop codon like trinucleotides extensions in primate alpha satellites.

The centromeres remain "the final frontier" in unexplored segments of genome landscape in primate genomes, characterized by 2-5 Mb arrays of evolutionary rapidly evolving alpha satellite (AS) higher order repeats (HORs). Alpha satellites as specific noncoding sequences may be also significant in light of regulatory role of noncoding sequences. Using the Global Repeat Map (GRM) algorithm we identify in NCBI assemblies of chromosome 5 the species-specific alpha satellite HORs: 13mer in human, 5mer in chimpanzee, 14mer in orangutan and 3mers in macaque. The suprachromosomal family (SF) classification of alpha satellite HORs and surrounding monomeric alpha satellites is performed and specific segmental structure was found for major alpha satellite arrays in chromosome 5 of primates. In the framework of our novel concept of start/stop Codon Like Trinucleotides (CLTs) as a "new DNA language in noncoding sequences", we find characteristics and differences of these species in CLT extensions, in particular the extensions of stop-TGA CLT. We hypothesize that these are regulators in noncoding sequences, acting at a distance, and that they can amplify or weaken the activity of start/stop codons in coding sequences in protein genesis, increasing the richness of regulatory phenomena.

The Supersymmetry Genetic Code Table and Quadruplet Symmetries of DNA Molecules Are Unchangeable and Synchronized with Codon-Free Energy Mapping during Evolution.

The Supersymmetry Genetic code (SSyGC) table is based on five physicochemical symmetries: (1) double mirror symmetry on the principle of the horizontal and vertical mirror symmetry axis between all bases (purines [A, G) and pyrimidines (U, C)] and (2) of bases in the form of codons; (3) direct-complement like codon/anticodon symmetry in the sixteen alternating boxes of the genetic code columns; (4) A + T-rich and C + G-rich alternate codons in the same row between both columns of the genetic code; (5) the same position between divided and undivided codon boxes in relation to horizontal mirror symmetry axis. The SSyGC table has a unique physicochemical purine-pyrimidine symmetry net which is as the core symmetry common for all, with more than thirty different nuclear and mitochondrial genetic codes. This net is present in the SSyGC table of all RNA and DNA living species. None of these symmetries are present in the Standard Genetic Code (SGC) table which is constructed on the alphabetic horizontal and vertical U-C-A-G order of bases. Here, we show that the free energy value of each codon incorporated as fundamentally mapping the "energy code" in the SSyGC table is compatible with mirror symmetry. On the other hand, in the SGC table, the same free energy values of codons are dispersed and a mirror symmetry between them is not recognizable. At the same time, the mirror symmetry of the SSyGC table and the DNA quadruplets together with our classification of codons/trinucleotides are perfectly imbedded in the mirror symmetry energy mapping of codons/trinucleotides and point out in favor of maintaining the integrity of the genetic code and DNA genome. We also argue that physicochemical symmetries of the SSyGC table in the manner of the purine-pyrimidine symmetry net, the quadruplet symmetry of DNA molecule, and the free energy of codons have remined unchanged during all of evolution. The unchangeable and universal symmetry properties of the genetic code, DNA molecules, and the energy code are decreasing disorder between codons/trinucleotides and shed a new light on evolution. Diversity in all living species on Earth is broad, but the symmetries of the Supersymmetry Genetic Code as the code of life and the DNA quadruplets related to the "energy code" are unique, unchangeable, and have the power of natural laws.

Tandemly repeated NBPF HOR copies (Olduvai triplets): Possible impact on human brain evolution.

Previously it was found that the neuroblastoma breakpoint family (NBPF) gene repeat units of ∼1.6 kb have an important role in human brain evolution and function. The higher order organization of these repeat units has been discovered by both methods, the higher order repeat (HOR)-searching method and the HLS searching method. Using the HOR searching method with global repeat map algorithm, here we identified the tandemly organized NBPF HORs in the human and nonhuman primate NCBI reference genomes. We identified 50 tandemly organized canonical 3mer NBPF HOR copies (Olduvai triplets), but none in nonhuman primates chimpanzee, gorilla, orangutan, and Rhesus macaque. This discontinuous jump in tandemly organized HOR copy number is in sharp contrast to the known gradual increase in the number of Olduvai domains (NBPF monomers) from nonhuman primates to human, especially from ∼138 in chimpanzee to ∼300 in human genome. Using the same global repeat map algorithm method we have also determined the 3mer tandems of canonical 3mer HOR copies in 20 randomly chosen human genomes (10 male and 10 female). In all cases, we found the same 3mer HOR copy numbers as in the case of the reference human genome, with no mutation. On the other hand, some point mutations with respect to reference genome are found for some NBPF monomers which are not tandemly organized in canonical HORs.

Tandem NBPF 3mer HORs (Olduvai triplets) in Neanderthal and two novel HOR tandem arrays in human chromosome 1 T2T-CHM13 assembly.

It is known that the ~ 1.6 kb Neuroblastoma BreakPoint Family (NBPF) repeats are human specific and contributing to cognitive capabilities, with increasing frequency in higher order repeat 3mer HORs (Olduvai triplets). From chimpanzee to modern human there is a discontinuous jump from 0 to ~ 50 tandemly organized 3mer HORs. Here we investigate the structure of NBPF 3mer HORs in the Neanderthal genome assembly of Pääbo et al., comparing it to the results obtained for human hg38.p14 chromosome 1. Our findings reveal corresponding NBPF 3mer HOR arrays in Neanderthals with slightly different monomer structures and numbers of HOR copies compared to humans. Additionally, we compute the NBPF 3mer HOR pattern for the complete telomere-to-telomere human genome assembly (T2T-CHM13) by Miga et al., identifying two novel tandem arrays of NBPF 3mer HOR repeats with 5 and 9 NBPF 3mer HOR copies. We hypothesize that these arrays correspond to novel NBPF genes (here referred to as NBPFA1 and NBPFA2). Further improving the quality of the Neanderthal genome using T2T-CHM13 as a reference would be of great interest in determining the presence of such distant novel NBPF genes in the Neanderthal genome and enhancing our understanding of human evolution.

Intragene higher order repeats in neuroblastoma breakpoint family genes distinguish humans from chimpanzees.

Much attention has been devoted to identifying genomic patterns underlying the evolution of the human brain and its emergent advanced cognitive capabilities, which lie at the heart of differences distinguishing humans from chimpanzees, our closest living relatives. Here, we identify two particular intragene repeat structures of noncoding human DNA, spanning as much as a hundred kilobases, that are present in human genome but are absent from the chimpanzee genome and other nonhuman primates. Using our novel computational method Global Repeat Map, we examine tandem repeat structure in human and chimpanzee chromosome 1. In human chromosome 1, we find three higher order repeats (HORs), two of them novel, not reported previously, whereas in chimpanzee chromosome 1, we find only one HOR, a 2mer alphoid HOR instead of human alphoid 11mer HOR. In human chromosome 1, we identify an HOR based on 39-bp primary repeat unit, with secondary, tertiary, and quartic repeat units, fully embedded in human hornerin gene, related to regenerating and psoriatric skin. Such an HOR is not found in chimpanzee chromosome 1. We find a remarkable human 3mer HOR organization based on the ~1.6-kb primary repeat unit, fully embedded within the neuroblastoma breakpoint family genes, which is related to the function of the human brain. Such HORs are not present in chimpanzees. In general, we find that human-chimpanzee differences are much larger for tandem repeats, in particularly for HORs, than for gene sequences. This may be of great significance in light of recent studies that are beginning to reveal the large-scale regulatory architecture of the human genome, in particular the role of noncoding sequences. We hypothesize about the possible importance of human accelerated HOR patterns as components in the gene expression multilayered regulatory network.

Standard Genetic Code vs. Supersymmetry Genetic Code - Alphabetical table vs. physicochemical table.

The fundamental role of symmetry in the genetic code is to decrease disorder between codons and to preserve the integrity of system. The Standard Genetic Code (SGC) table is structured alphabetically in a horizontal and vertical array of U-C-A-G bases only with aesthetic symmetry. We postulate "the symmetry theory of genetic code" which is based on the unique physicochemical purine - pyrimidine symmetry net between codons of our Supersymmetry genetic code (SSyGC) table. The common purine - pyrimidine symmetry net as "the golden rule" and a core of the SSyGC table is universal, remaining unchanged during all of evolution. It is identical for more than 30 known genetic codes including those that will be discovered in the future, as well as for all RNA and DNA species. The unique SSyGC table has five physicochemical symmetries between bases, codons, and amino acids: 1) purine - pyrimidine symmetry on the principle of the Watson - Crick pairing (A↔U, C↔G), 2) direct - complement symmetry between codons, 3) mirror symmetry between bases and codons, 4) A + T rich and C + G rich symmetry between codons, and 5) symmetry between position of amino acids. Opposite to the SGC table where the third base is inactive, in the SSyGC table the role of the third base in codons is dominant in creation of symmetries. There are also present for the first time the symmetric positions of all boxes with amino acids. Opposite of the SGC table, the SSyGC code table contains three sextets for Serine, Arginine, and Leucine, each with six codons, positioned in continuity. Multi - facet symmetries of the SSyGC table as a natural law exclude the individual random creation of amino acids even in primitive life form. Accordingly, we hypothesize that the contemporary life arose due to common activity of all natural amino acids. With discovery of the unique physicochemical Supersymmetry genetic code table, the new light is shed on the symmetry of the genetic code.

An Explanation of Exceptions from Chargaff's Second Parity Rule/Strand Symmetry of DNA Molecules.

In this article, we show that mono/oligonucleotide quadruplets, as basic structures of DNA, along with our classification of trinucleotides, disclose an organization of genomes based on purine-pyrimidine symmetry. Moreover, the structure and stability of DNA are influenced by the Watson-Crick pairing and the natural law of DNA creation and conservation, according to which the same mono- or oligonucleotide insertion must be inserted simultaneously into both strands of DNA. Taken together, they lead to quadruplets with central mirror symmetry and bidirectional DNA strand orientation and are incorporated into Chargaff's second parity rule (CSPR). Performing our quadruplet frequency analysis of all human chromosomes and of Neuroblastoma BreakPoint Family (NBPF) genes, which code Olduvai protein domains in the human genome, we show that the coding part of DNA violates CSPR. This may shed new light and give rise to a novel hypothesis on DNA creation and its evolution. In this framework, the logarithmic relationship between oligonucleotide order and minimal DNA sequence length, to establish the validity of CSPR, automatically follows from the quadruplet structure of the genomic sequence. The problem of the violation of CSPR in rare symbionts is discussed.

Large tandem, higher order repeats and regularly dispersed repeat units contribute substantially to divergence between human and chimpanzee Y chromosomes.

Comparison of human and chimpanzee genomes has received much attention, because of paramount role for understanding evolutionary step distinguishing us from our closest living relative. In order to contribute to insight into Y chromosome evolutionary history, we study and compare tandems, higher order repeats (HORs), and regularly dispersed repeats in human and chimpanzee Y chromosome contigs, using robust Global Repeat Map algorithm. We find a new type of long-range acceleration, human-accelerated HOR regions. In peripheral domains of 35mer human alphoid HORs, we find riddled features with ten additional repeat monomers. In chimpanzee, we identify 30mer alphoid HOR. We construct alphoid HOR schemes showing significant human-chimpanzee difference, revealing rapid evolution after human-chimpanzee separation. We identify and analyze over 20 large repeat units, most of them reported here for the first time as: chimpanzee and human ~1.6 kb 3mer secondary repeat unit (SRU) and ~23.5 kb tertiary repeat unit (~0.55 kb primary repeat unit, PRU); human 10848, 15775, 20309, 60910, and 72140 bp PRUs; human 3mer SRU (~2.4 kb PRU); 715mer and 1123mer SRUs (5mer PRU); chimpanzee 5096, 10762, 10853, 60523 bp PRUs; and chimpanzee 64624 bp SRU (10853 bp PRU). We show that substantial human-chimpanzee differences are concentrated in large repeat structures, at the level of as much as ~70% divergence, sizably exceeding previous numerical estimates for some selected noncoding sequences. Smeared over the whole sequenced assembly (25 Mb) this gives ~14% human-chimpanzee divergence. This is significantly higher estimate of divergence between human and chimpanzee than previous estimates.

Discovery of 33mer in chromosome 21 - the largest alpha satellite higher order repeat unit among all human somatic chromosomes.

The centromere is important for segregation of chromosomes during cell division in eukaryotes. Its destabilization results in chromosomal missegregation, aneuploidy, hallmarks of cancers and birth defects. In primate genomes centromeres contain tandem repeats of ~171 bp alpha satellite DNA, commonly organized into higher order repeats (HORs). In spite of crucial importance, satellites have been understudied because of gaps in sequencing - genomic "black holes". Bioinformatical studies of genomic sequences open possibilities to revolutionize understanding of repetitive DNA datasets. Here, using robust (Global Repeat Map) algorithm we identified in hg38 sequence of human chromosome 21 complete ensemble of alpha satellite HORs with six long repeat units (≥20 mers), five of them novel. Novel 33mer HOR has the longest HOR unit identified so far among all somatic chromosomes and novel 23mer reverse HOR is distant far from the centromere. Also, we discovered that for hg38 assembly the 33mer sequences in chromosomes 21, 13, 14, and 22 are 100% identical but nearby gaps are present; that seems to require an additional more precise sequencing. Chromosome 21 is of significant interest for deciphering the molecular base of Down syndrome and of aneuploidies in general. Since the chromosome identifier probes are largely based on the detection of higher order alpha satellite repeats, distinctions between alpha satellite HORs in chromosomes 21 and 13 here identified might lead to a unique chromosome 21 probe in molecular cytogenetics, which would find utility in diagnostics. It is expected that its complete sequence analysis will have profound implications for understanding pathogenesis of diseases and development of new therapeutic approaches.

Hierarchical structure of cascade of primary and secondary periodicities in Fourier power spectrum of alphoid higher order repeats.

BACKGROUND: Identification of approximate tandem repeats is an important task of broad significance and still remains a challenging problem of computational genomics. Often there is no single best approach to periodicity detection and a combination of different methods may improve the prediction accuracy. Discrete Fourier transform (DFT) has been extensively used to study primary periodicities in DNA sequences. Here we investigate the application of DFT method to identify and study alphoid higher order repeats. RESULTS: We used method based on DFT with mapping of symbolic into numerical sequence to identify and study alphoid higher order repeats (HOR). For HORs the power spectrum shows equidistant frequency pattern, with characteristic two-level hierarchical organization as signature of HOR. Our case study was the 16 mer HOR tandem in AC017075.8 from human chromosome 7. Very long array of equidistant peaks at multiple frequencies (more than a thousand higher harmonics) is based on fundamental frequency of 16 mer HOR. Pronounced subset of equidistant peaks is based on multiples of the fundamental HOR frequency (multiplication factor n for nmer) and higher harmonics. In general, nmer HOR-pattern contains equidistant secondary periodicity peaks, having a pronounced subset of equidistant primary periodicity peaks. This hierarchical pattern as signature for HOR detection is robust with respect to monomer insertions and deletions, random sequence insertions etc. For a monomeric alphoid sequence only primary periodicity peaks are present. The 1/fbeta- noise and periodicity three pattern are missing from power spectra in alphoid regions, in accordance with expectations. CONCLUSION: DFT provides a robust detection method for higher order periodicity. Easily recognizable HOR power spectrum is characterized by hierarchical two-level equidistant pattern: higher harmonics of the fundamental HOR-frequency (secondary periodicity) and a subset of pronounced peaks corresponding to constituent monomers (primary periodicity). The number of lower frequency peaks (secondary periodicity) below the frequency of the first primary periodicity peak reveals the size of nmer HOR, i.e., the number n of monomers contained in consensus HOR.

The role of alphoid higher order repeats (HORs) in the centromere folding.

Understanding the folding of centromere DNA in the maximally condensed methaphase chromosome remains a basic challenge in cell biology. We propose here a set of structural models with a graphical presentation of alphoid higher order repeat (HOR) distribution in the centromere folding, based on the assumption of encryption key for microtubule-centromere interaction which arises from chromosome-specific crystal-like structure of HORs. Specific HOR leads to a characteristic geometrical pattern which may be responsible for individual microtubule to recognize a specific structure of centromere in each chromosome.