I developed a mathematical method to search for DNA regions that are significantly enriched in reverse complement triplets (RCTs) and are located in sequences with strongly expressed triplet periodicity (TP). The method makes it possible to exclude the influence of TP on the number of RCTs. To search for RCTs, I used the difference between triplet frequencies and their expected number, which was determined by taking into account the TP of the analyzed region. I analyzed the genomes of 42 bacteria representing all bacterial phyla, and found that the number of DNA regions containing RCTs ranged from several hundred to several thousand per genome depending on its size. The average length of the region was about 850 DNA bases. The most common inversion symmetry (IS) pattern of the RCT-containing regions was the enrichment of the first, second, and third triplet positions with {A, G}, {A, T}, and {T, C} bases, respectively. When the sequence was rotated 180 degrees and the bases were replaced with complementary ones (IS), such enrichment of triplet positions was preserved. I suggest that the emergence of IS could be a result of evolutionary processes such as inversions, transpositions, and recombinations.

In this study, we applied the iterative procedure (IP) method to search for families of highly diverged dispersed repeats in the genome of Cyanidioschyzon merolae, which contains over 16 million bases. The algorithm included the construction of position weight matrices (PWMs) for repeat families and the identification of more dispersed repeats based on the PWMs using dynamic programming. The results showed that the C. merolae genome contained 20 repeat families comprising a total of 33,938 dispersed repeats, which is significantly more than has been previously found using other methods. The repeats varied in length from 108 to 600 bp (522.54 bp in average) and occupied more than 72% of the C. merolae genome, whereas previously identified repeats, including tandem repeats, have been shown to constitute only about 28%. The high genomic content of dispersed repeats and their location in the coding regions suggest a significant role in the regulation of the functional activity of the genome.

The exact identification of promoter sequences remains a serious problem in computational biology, as the promoter prediction algorithms under development continue to produce false-positive results. Therefore, to fully assess the validity of predicted sequences, it is necessary to perform a comprehensive test of their properties, such as the presence of downstream transcribed DNA regions behind them, or chromatin accessibility for transcription factor binding. In this paper, we examined the promoter sequences of chromosome 1 of the rice Oryza sativa genome from the Database of Potential Promoter Sequences predicted using a mathematical algorithm based on the derivation and calculation of statistically significant promoter classes. In this paper TATA motifs and cis-regulatory elements were identified in the predicted promoter sequences. We also verified the presence of potential transcription start sites near the predicted promoters by analyzing CAGE-seq data. We searched for unannotated transcripts behind the predicted sequences by de novo assembling transcripts from RNA-seq data. We also examined chromatin accessibility in the region of the predicted promoters by analyzing ATAC-seq data. As a result of this work, we identified the predicted sequences that are most likely to be promoters for further experimental validation in an in vivo or in vitro system.

We have developed a de novo method for the identification of dispersed repeats based on the use of random position-weight matrices (PWMs) and an iterative procedure (IP). The created algorithm (IP method) allows detection of dispersed repeats for which the average number of substitutions between any two repeats per nucleotide (x) is less than or equal to 1.5. We have shown that all previously developed methods and algorithms (RED, RECON, and some others) can only find dispersed repeats for x ≤ 1.0. We applied the IP method to find dispersed repeats in the genomes of E. coli and nine other bacterial species. We identify three families of approximately 1.09 × 106, 0.64 × 106, and 0.58 × 106 DNA bases, respectively, constituting almost 50% of the complete E. coli genome. The length of the repeats is in the range of 400 to 600 bp. Other analyzed bacterial genomes contain one to three families of dispersed repeats with a total number of 103 to 6 × 103 copies. The existence of such highly divergent repeats could be associated with the presence of a single-type triplet periodicity in various genes or with the packing of bacterial DNA into a nucleoid.

Abstract In this study, we modified the multiple alignment method based on the generation of random position weight matrices (RPWMs) and used it to search for tandem repeats (TRs) in the Capsicum annuum genome. The application of the modified (m)RPWM method, which considers the correlation of adjusting nucleotides, resulted in the identification of 908,072 TR regions with repeat lengths from 2 to 200 bp in the C. annuum genome, where they occupied ~29%. The most common TRs were 2 and 3 bp long followed by those of 21, 4, and 15 bp. We performed clustering analysis of TRs with repeat lengths of 2 and 21 bp and created position-weight matrices (PWMs) for each group; these templates could be used to search for TRs of a given length in any nucleotide sequence. All detected TRs can be accessed through publicly available database (http://victoria.biengi.ac.ru/capsicum_tr/). Comparison of mRPWM with other TR search methods such as Tandem Repeat Finder, T-REKS, and XSTREAM indicated that mRPWM could detect significantly more TRs at similar false discovery rates, indicating its superior performance. The developed mRPWM method can be successfully applied to the identification of highly divergent TRs, which is important for functional analysis of genomes and evolutionary studies.

We have developed a new method for promoter sequence classification based on a genetic algorithm and the MAHDS sequence alignment method. We have created four classes of human promoters, combining 17,310 sequences out of the 29,598 present in the EPD database. We searched the human genome for potential promoter sequences (PPSs) using dynamic programming and position weight matrices representing each of the promoter sequence classes. A total of 3,065,317 potential promoter sequences were found. Only 1,241,206 of them were located in unannotated parts of the human genome. Every other PPS found intersected with either true promoters, transposable elements, or interspersed repeats. We found a strong intersection between PPSs and Alu elements as well as transcript start sites. The number of false positive PPSs is estimated to be 3 × 10−8 per nucleotide, which is several orders of magnitude lower than for any other promoter prediction method. The developed method can be used to search for PPSs in various eukaryotic genomes.

In this study, we used a mathematical method for the multiple alignment of highly divergent sequences (MAHDS) to create a database of potential promoter sequences (PPSs) in the Capsicum annuum genome. To search for PPSs, 20 statistically significant classes of sequences located in the range from −499 to +100 nucleotides near the annotated genes were calculated. For each class, a position–weight matrix (PWM) was computed and then used to identify PPSs in the C. annuum genome. In total, 825,136 PPSs were detected, with a false positive rate of 0.13%. The PPSs obtained with the MAHDS method were tested using TSSFinder, which detects transcription start sites. The databank of the found PPSs provides their coordinates in chromosomes, the alignment of each PPS with the PWM, and the level of statistical significance as a normal distribution argument, and can be used in genetic engineering and biotechnology.

The aim of this work was to compare the multiple alignment methods MAHDS, T-Coffee, MUSCLE, Clustal Omega, Kalign, MAFFT, and PRANK in their ability to align highly divergent amino acid sequences. To accomplish this, we created test amino acid sequences with an average number of substitutions per amino acid (x) from 0.6 to 5.6, a total of 81 sets. Comparison of the performance of sequence alignments constructed by MAHDS and previously developed algorithms using the CS and Z score criteria and the benchmark alignment database (BAliBASE) indicated that, although the quality of the alignments built with MAHDS was somewhat lower than that of the other algorithms, it was compensated by greater statistical significance. MAHDS could construct statistically significant alignments of artificial sequences with x ≤ 4.8, whereas the other algorithms (T-Coffee, MUSCLE, Clustal Omega, Kalign, MAFFT, and PRANK) could not perform that at x > 2.4. The application of MAHDS to align 21 families of highly diverged proteins (identity < 20%) from Pfam and HOMSTRAD databases showed that it could calculate statistically significant alignments in cases when the other methods failed. Thus, MAHDS could be used to construct statistically significant multiple alignments of highly divergent protein sequences, which accumulated multiple mutations during evolution.

In this paper, we attempted to find a relation between bacteria living conditions and their genome algorithmic complexity. We developed a probabilistic mathematical method for the evaluation of k-words (6 bases length) occurrence irregularity in bacterial gene coding sequences. For this, the coding sequences from different bacterial genomes were analyzed and as an index of k-words occurrence irregularity, we used W, which has a distribution similar to normal. The research results for bacterial genomes show that they can be divided into two uneven groups. First, the smaller one has W in the interval from 170 to 475, while for the second it is from 475 to 875. Plants, metazoan and virus genomes also have W in the same interval as the first bacterial group. We suggested that second bacterial group coding sequences are much less susceptible to evolutionary changes than the first group ones. It is also discussed to use the W index as a biological stress value.

Identification of promoter sequences in the eukaryotic genome, by computer methods, is an important task of bioinformatics. However, this problem has not been solved since the best algorithms have a false positive probability of 10−3–10−4 per nucleotide. As a result of full genome analysis, there may be more false positives than annotated gene promoters. The probability of a false positive should be reduced to 10−6–10−8 to reduce the number of false positives and increase the reliability of the prediction. The method for multi alignment of the promoter sequences was developed. Then, mathematical methods were developed for calculation of the statistically important classes of the promoter sequences. Five promoter classes, from the rice genome, were created. We developed promoter classes to search for potential promoter sequences in the rice genome with a false positive number less than 10−8 per nucleotide. Five classes of promoter sequences contain 1740, 222, 199, 167 and 130 promoters, respectively. A total of 145,277 potential promoter sequences (PPSs) were identified. Of these, 18,563 are promoters of known genes, 87,233 PPSs intersect with transposable elements, and 37,390 PPSs were found in previously unannotated sequences. The number of false positives for a randomly mixed rice genome is less than 10−8 per nucleotide. The method developed for detecting PPSs was compared with some previously used approaches. The developed mathematical method can be used to search for genes, transposable elements, and transcript start sites in eukaryotic genomes.

We report a Method to Search for Highly Divergent Tandem Repeats (MSHDTR) in protein sequences which considers pairwise correlations between adjacent residues. MSHDTR was compared with some previously developed methods for searching for tandem repeats (TRs) in amino acid sequences, such as T-REKS and XSTREAM, which focus on the identification of TRs with significant sequence similarity, whereas MSHDTR detects repeats that significantly diverged during evolution, accumulating deletions, insertions, and substitutions. The application of MSHDTR to a search of the Swiss-Prot databank revealed over 15 thousand TR-containing amino acid sequences that were difficult to find using the other methods. Among the detected TRs, the most representative were those with consensus lengths of two and seven residues; these TRs were subjected to cluster analysis and the classes of patterns were identified. All TRs detected in this study have been combined into a databank accessible over the WWW.

In this study, we developed a new mathematical method for performing multiple alignment of highly divergent sequences (MAHDS), i.e., sequences that have on average more than 2.5 substitutions per position (x). We generated sets of artificial DNA sequences with x ranging from 0 to 4.4 and applied MAHDS as well as currently used multiple sequence alignment algorithms, including ClustalW, MAFFT, T-Coffee, Kalign, and Muscle to these sets. The results indicated that most of the existing methods could produce statistically significant alignments only for the sets with x < 2.5, whereas MAHDS could operate on sequences with x = 4.4. We also used MAHDS to analyze a set of promoter sequences from the Arabidopsis thaliana genome and discovered many conserved regions upstream of the transcription initiation site (from −499 to +1 bp); a part of the downstream region (from +1 to +70 bp) also significantly contributed to the obtained alignments. The possibilities of applying the newly developed method for the identification of promoter sequences in any genome are discussed. A server for multiple alignment of nucleotide sequences has been created.

In Russia and around the world, there are important questions regarding the potential threats to national and biological safety created by genetic technologies and the need to improve or introduce new, justified, and adequate measures for their control, regulation, and prevention. The article shows that a significant volume of the global market is occupied by five major transgenic crops, and producers are ready to switch to crops with an edited genome that has been approved in the United States, Argentina, and other countries. We propose a qualitatively new approach to the risk assessment of edited plants, "Safe Design," and we have also developed an extremely important, fundamentally new approach to the development of methods that combine next-generation sequencing (NGS) and Bioinformatics for the assessment of the crop import biosafety. The proposed mathematical approach provides a detailed analysis of the possible insertions of DNA fragments into the genome of edited crops and a clarification of their biological significance. The developed method can be used in the rapid screening of plants for the presence of potentially dangerous genes, viral sequences, and nonspecific promoter sequences.

Background Transposable elements (TEs) constitute a significant part of eukaryotic genomes. Short interspersed nuclear elements (SINEs) are non-autonomous TEs, which are widely represented in mammalian genomes and also found in plants. After insertion in a new position in the genome, TEs quickly accumulate mutations, which complicate their identification and annotation by modern bioinformatics methods. In this study, we searched for highly divergent SINE copies in the genome of rice ( Oryza sativa subsp. japonica ) using the Highly Divergent Repeat Search Method (HDRSM). Results The HDRSM considers correlations of neighboring symbols to construct position weight matrix (PWM) for a SINE family, which is then used to perform a search for new copies. In order to evaluate the accuracy of the method and compare it with the RepeatMasker program, we generated a set of SINE copies containing nucleotide substitutions and indels and inserted them into an artificial chromosome for analysis. The HDRSM showed better results both in terms of the number of identified inserted repeats and the accuracy of determining their boundaries. A search for the copies of 39 SINE families in the rice genome produced 14,030 hits; among them, 5704 were not detected by RepeatMasker. Conclusions The HDRSM could find divergent SINE copies, correctly determine their boundaries, and offer a high level of statistical significance. We also found that RepeatMasker is able to find relatively short copies of the SINE families with a higher level of similarity, while HDRSM is able to find more diverged copies. To obtain a comprehensive profile of SINE distribution in the genome, combined application of the HDRSM and RepeatMasker is recommended.

Currently, there is a lack of bioinformatics approaches to identify highly divergent tandem repeats (TRs) in eukaryotic genomes. Here, we developed a new mathematical method to search for TRs, which uses a novel algorithm for constructing multiple alignments based on the generation of random position weight matrices (RPWMs), and applied it to detect TRs of 2 to 50 nucleotides long in the rice genome. The RPWM method could find highly divergent TRs in the presence of insertions or deletions. Comparison of the RPWM algorithm with the other methods of TR identification showed that RPWM could detect TRs in which the average number of base substitutions per nucleotide (x) was between 1.5 and 3.2, whereas T-REKS and TRF methods could not detect divergent TRs with x > 1.5. Applied to the search of TRs in the rice genome, the RPWM method revealed that TRs occupied 5% of the genome and that most of them were 2 and 3 bases long. Using RPWM, we also revealed the correlation of TRs with dispersed repeats and transposons, suggesting that some transposons originated from TRs. Thus, the novel RPWM algorithm is an effective tool to search for highly divergent TRs in the genomes.

Using the RPWM method, we searched for tandem repeats of 2 to 50 nucleotides long in the rice genome. We compared the effectiveness of the RPWM method with Mreps, T-reks, Tandem Repeat Finder and ATR Hunter. About 70% of the tandem repeats found could not be found by other algorithms. The correlation of dispersed repeats and transposons with tandem repeats was studied in this work. We assumed that some of the dispersed repeats and transposons originated from tandem repeats

We represent here a new method for the detection of new copies of SINE elements. The method is based on the correlation of pairs of symbols. The correlation is used for the construction of a position-specific matrix as well as for the search of new repeat copies using the matrix. This allows us to enlarge the alphabet and to increase the sensitivity of the method. The method was used to study the rice genome. As a result, new copies of SINE repeats that were not included in the standard annotation were found. The number of false positives was evaluated.

In this article, we present a new method for searching for highly divergent copies of SINE elements in a genome. The method is based on the correlation of neighboring symbols both in constructing a positional weight matrix for a sequence of interest and in the genome scanning procedure. This makes possible to increase the alphabet size and, accordingly, the resolution capacity of the method. Using it, we found new copies of SINE repeats in the rice genome that have not been annotated before. The method was tested and compared with the RepeatMasker program; false positives were evaluated. SINE elements, retrotransposons, alignment-based methods, sequence similarity The work was partly supported by the RFBR Grant no. 20-016-00057.