BackgroundAlgorithms of sequence alignment are the key instruments for computer-assisted studies of biopolymers. Obviously, it is important to take into account the "quality" of the obtained alignments, i.e. how closely the algorithms manage to restore the "gold standard" alignment (GS-alignment), which superimposes positions originating from the same position in the common ancestor of the compared sequences. As an approximation of the GS-alignment, a 3D-alignment is commonly used not quite reasonably. Among the currently used algorithms of a pair-wise alignment, the best quality is achieved by using the algorithm of optimal alignment based on affine penalties for deletions (the Smith-Waterman algorithm). Nevertheless, the expedience of using local or global versions of the algorithm has not been studied.ResultsUsing model series of amino acid sequence pairs, we studied the relative "quality" of results produced by local and global alignments versus (1) the relative length of similar parts of the sequences (their "cores") and their nonhomologous parts, and (2) relative positions of the core regions in the compared sequences. We obtained numerical values of the average quality (measured as accuracy and confidence) of the global alignment method and the local alignment method for evolutionary distances between homologous sequence parts from 30 to 240 PAM and for the core length making from 10% to 70% of the total length of the sequences for all possible positions of homologous sequence parts relative to the centers of the sequences.ConclusionWe revealed criteria allowing to specify conditions of preferred applicability for the local and the global alignment algorithms depending on positions and relative lengths of the cores and nonhomologous parts of the sequences to be aligned. It was demonstrated that when the core part of one sequence was positioned above the core of the other sequence, the global algorithm was more stable at longer evolutionary distances and larger nonhomologous parts than the local algorithm. On the contrary, when the cores were positioned asymmetrically, the local algorithm was more stable at longer evolutionary distances and larger nonhomologous parts than the global algorithm. This opens a possibility for creation of a combined method allowing generation of more accurate alignments.

In many applications, the algorithmically obtained alignment ideally should restore the "golden standard" (GS) alignment, which superimposes positions originating from the same position of the common ancestor of the compared sequences. The average similarity between the algorithmically obtained and GS alignments ("the quality") is an important characteristic of an alignment algorithm. We proposed to determine the quality of an algorithm, using sequences that were artificially generated in accordance with an appropriate evolution model; the approach was applied to the global version of the Smith-Waterman algorithm (SWA). The quality of SWA is between 97% (for a PAM distance of 60) and 70% (for a PAM distance of 300). The percentage of identical aligned residues is the same for algorithmic and GS alignments. The total length of indels in algorithmic alignments is less than in the GS-mainly due to a substantial decrease in the number of indels in algorithmic alignments.

In this paper we consider properties of the difference equations (discrete mappings) obtained in the study of the population dynamics of lemmings. A bifurcation scenario is proposed for obtained equations. Certain stability zones appear under this scenario with periods varying in order of natural series and also zones with more complicated modes. The study of transitional zones (‘ordering of the chaos’) is performed with the use of analytic calculations and computational experiments. Numerical analysis of mappings uses the methods of approximation of implicitly specified sets allowing us to construct and visualize sets of ‘resonance’ parameters including the front of the so-called singularity of ‘blue sky’.

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Background The alignment of character sequences is important in bioinformatics. The quality of this procedure is determined by the substitution matrix and parameters of the insertion-deletion penalty function. These matrices are derived from sequence alignment and thus reflect the evolutionary process. Currently, in addition to evolutionary matrices, a large number of different background matrices have been obtained. To make an optimal choice of the substitution matrix and the penalty parameters, we conducted a numerical experiment using a representative sample of existing matrices of various types and origins. Results We tested both the classical evolutionary matrix series (PAM, Blosum, VTML, Pfasum); structural alignment based matrices, contact energy matrix, and matrix based on the properties of the genetic code. This study presents results for two test set types: first, we simulated sequences that reflect the divergent evolution; second, we performed tests on Balibase sequences. In both cases, we obtained the dependences of the alignment quality (Accuracy, Confidence) on the evolutionary distance between sequences and the evolutionary distance to which the substitution matrices correspond. Optimization of a combination of matrices and the penalty parameters was carried out for local and global alignment on the values of penalty function parameters. Consequently, we found that the best alignment quality is achieved with matrices corresponding to the largest evolutionary distance. These matrices prove to be universal, i.e. suitable for aligning sequences separated by both large and small evolutionary distances. We analysed the correspondence of the correlation coefficients of matrices to the alignment quality. It was found that matrices showing high quality alignment have an above average correlation value, but the converse is not true. Conclusions This study showed that the best alignment quality is achieved with evolutionary matrices designed for long distances: Gonnet, VTML250, PAM250, MIQS, and Pfasum050. The same property is inherent in matrices not only of evolutionary origin, but also of another background corresponding to a large evolutionary distance. Therefore, matrices based on structural data show alignment quality close enough to its value for evolutionary matrices. This agrees with the idea that the spatial structure is more conservative than the protein sequence.