Search for Latent Periodicity in Amino Acid Sequences with Insertions and Deletions

Abstract

The aim of this study was to show that amino acid sequences have a latent periodicity with insertions and deletions of amino acids in unknown positions of the analyzed sequence. Genetic algorithm, dynamic programming, and random weight matrices were used to develop the new mathematical algorithm for latent periodicity search. The method makes the direct optimization of the position-weight matrix for multiple sequence alignment without using pairwise alignments. The developed algorithm was applied to analyze the amino acid sequences of a small number of proteins. This study showed the presence of latent periodicity with insertions and deletions in the amino acid sequences of such proteins, for which the presence of latent periodicity was not previously known. The origin of latent periodicity with insertions and deletions is discussed.

Database of Periodic DNA Regions in Major Genomes

“…The algorithm was repeated for n from 2 to 100. The method we used to reveal DNA periodicity sequences was previously developed and applied to amino acid sequences and the details could be found in the following studies [ 4 , 5 , 39 ]. It can effectively detect periodicity in the presence of insertions, deletions, and large number of substitutions of nucleotides (on the average, more than 1 per nucleotide).…”

“…In order to avoid interference with the triplet periodicity in the genome protein-coding regions, we skipped those windows that had statistically significant triplet periodicity Z value (see [ 40 ] for details) over 3.0. In the given window we found the position weight matrix M [ 1 ], which obtained the best local alignment that maximizes similarity score F max [ 5 , 39 ] for each tested period length n (from 2 to 50). In order to account for interwindow duplicates we filtered out intersecting sequences by choosing the one having larger F max value ( mF max ).…”

“…The periods of a sequence with latent periodicity are sequences for multiple alignment that is statistically significant. The aim of this study was to apply the previously developed mathematical method [ 4 , 5 ] and to detect the DNA sequences periodicity, as well as the latent periodicity, and to create the new data bank.…”

“…But we should find the optimal weight matrix M 0 . Previously we developed a mathematical approach for detecting the matrix M 0 , as well as a method for assessing the probability P [ 4 , 5 ]. The periods multiple alignments were calculated by optimizing the PWM without using the pairwise alignments or the similarity search between periods.…”

Search for potential reading frameshifts in cds from Arabidopsis thaliana and other genomes

“…If one knows the M 0 (3, 16), then such TP periodicity shift could be found using the alignment of sequence S with the position-weight matrix (PWM) W 0 (see Equation 1). This matrix was created using M 0 (3, 16), as it was performed previously for the MT (3, 4) matrix 34 and is shown below in Equation (1). To create the W 0 (3, 16) matrix, each element of the M 0 (3, 16) matrix was transformed to the argument of the normal distribution, using the normal approximation for the binomial distribution.…”