• Development of new mathematical methods for search of multiple alignments of amino acid and nucleotide sequences;
• Development of new mathematical methods for search of pairwise alignments of amino acid and nucleotide sequences without the use of weight matrices;
• Development of mathematical methods for search of a latent periodicity in DNA or amino acid sequences with deletions and insertions;
• Study of the presence of dispersed repeats in different genomes and amino acis sequences;
• Study of the presence of latent periodicity in different nucleotide and amino acid sequences;
• Development of mathematical methods for search of change points in the genes and in the proteins;
• Development of mathematical methods for detection of phase shifts of the periodicity in genes from different organisms;
• Development of mathematical methods for biological annotations of genes of the bacteria;
• Creation of an original computer databases;
• Developing new mathematical methods for time series analysis

KEY ACHIEVEMENTS

The research team is developing new mathematical methods for studying amino acid and nucleotide sequences.  Calculations are carried out on a computer cluster of its own assembly. The results of the research activities of the group were reported at more than 50 scientific conferences both in the Russian Federation and abroad.

Currently, the group consists of 4 researchers  and 4 students. Simultaneously with the scientific activities, the group leader is engaged in teaching activities at the Department of Applied Mathematics at the National research Nuclear University (MEPhI). Lecture courses for students of mathematicians are given – “Methods of analyzing character sequences”, “Information theory” and laboratory work is conducted on the course “Methods of analyzing character sequences”. Under the guidance of the staff of the group more than 30 graduation projects were prepared. The group participated and is participating in the implementation of grants from the Russian Foundation for Basic Research, the Presidium of the Russian Academy of Sciences, Rosnauka , the Ministry of Education and Science and ISTC. As a result of the group’s work, MIR repeats are discovered in the genome of humans and other mammals and vertebrates. Prof. Korotkov EV is the author of the detection of MIR repeats in the human genome and other species. Now we found change points in genes that shows reading frame shift mutations, points of glued genes and points of inserts of DNA fragments into the genes.

A method has now been developed to search for multiple alignment of amino acid and nucleotide sequences (NP-complete task) without using pairwise comparison of sequences and without using identical k-words.   Multiple alignment is detected as a point in 4n or 20n space,   where n is the length of sequences for multiple alignment. The developed solution allows to detect such multiple alignments that are skipped by all previously developed approaches. For example, it may be sequences that have from 2.5 to 4.4 substitutions per amino acid or nucleotide. When searching for multiple alignments, random positional-weight matrices, special optimization procedures, and two-dimensional dynamic programming are used.

The method was applied primarily to search for hidden periodicity in symbolic sequences. We found a periodic structure of very many amino acid sequences and DNA sequences from different genomes. We also constructed a multiple alignment for promoter sequences from A.thaliana genome. Our method for calculation of a multi alignment is more powerful than all spectral approaches and approaches based on dynamic programming. Based on the developed methods, mathematical approaches are developed for searching for pairwise alignments of nucleotide or amino acid sequences without using predetermined weight matrices.

The main scientific achievements of the group:

• A mathematical algorithm has been developed, software has been created for search of a phase shifts of triplet periodicity in genes. The phase shift of the triplet periodicity makes it possible to identify reading frame shift mutations in the genes. It has been shown that approximately 10% of all known genes from the database (millions of genes) contain triplet periodicity phase shifts. This is about 20 times more than it is possible to register experimentally or with all previously developed mathematical methods. This allows us to conclude that mutations of the reading frame shift type have been widely used by evolution and are far from always fatal for genes . The created software is located at: http://victoria.biengi.ac.ru/fsfinder/
• A mathematical algorithm has been developed, software has been created for searching for triple- frequency fusion points in DNA. The points of disorder allow you to find potential sites of gluing together of genes and insertions of a fragment of one gene into another gene. An analysis of the genes contained in the Kegg database showed that approximately 20% of the genes contain frustration points . This shows that the processes of gene gluing and inserts occur about 10 times more often than experimental data suggest, or all the previously developed mathematical methods. This result can be used to create new genes, since fusion points are natural sites of cuts in genes that use natural processes.
• A new mathematical method has been developed, software has been created, and a Web server has been developed for annotating genes from bacteria genomes. Using the example of 104 bacterial genomes, it was shown that this method allows us to annotate at the same statistical level at ~ 19% than this can be done by all the previously developed approaches. This is a new result, as it allows to use millions of genes in biotechnology, which are currently known only as a sequence and their function is not defined. Created a site: http://genefunction.ru , where each user can annotate sequences of genes.
• A mathematical approach has been developed for finding the hidden periodicity of symbolic sequences. A large number of DNA sequences from various genomes that have latent periodicity with insertions and deletions of symbols have been identified . These are original results not currently available . The software is located on the server: http://victoria.biengi.ac.ru/splinter/login.php
• Developed a new mathematical approach to search for multiple alignment of nucleotide sequences. The method allows us to find multiple alignment of sequences for the steppe evolutionary divergen n s x <4.4 mutations per nucleotide. All known programs and algorithms allow you to do this up to x <2.5. A second approach Anna allowed to receive multiple alignment of the promoter sequences from the genome sA.thaliaha , d.melanogaster, H.sapiens
• A database of sequences from diverse genomes with different kinds of periodicity. The base is located at: http://victoria.biengi.ac.ru/cgi-bin/indelper/index.cgi
• A cds database has been developed with potential mutations of the reading frame shift type. http://victoria.biengi.ac.com/cgi-bin/frameshift/index.cgi

INNOVATIVE DEVELOPMENTS

1. Annotation (prediction of biological function) of bacterial genes
2. Search for potential mini and microsatellites in DNA sequences
3. Search for potential mutations of type pa shift reading frame in cds different genomes
4. Calculation of multiple alignment for highly diverged amino acid or nucleotide sequences (more than 2.5 mutations per amino acid or nucleotide)
5. Search for potential promoters and TSS in eukaryotic genomes.