Various algorithms, calculating distances of DNA sequences, and some computational recommendations for use such algorithms

Abstract

In recent years, various approaches have been described to determine the similarity of the DNA sequences; each of which defines a metric for the set of DNA sequences. In this paper, we propose a new approach to solving this problem; moreover, algorithms for its implementation are based on multiheuristic approach to the discrete optimization problems previously developed by us. However, the main focus of this article is to describe our original approach to compare the quality of defined metrics on the set of DNA sequences. The last approach is based on the fact, that the triples of distances between genomes should ideally form isosceles acute triangles. On the basis of this assumption, we proposed value of the norm, gives in practice acceptable results; the validity of this approach is also discussed in the article. In the course of work on the implementation of algorithms have been carried out computational experiments with 100 DNA of "distant" species, as well as with representatives of several genomes of great apes and humans. Several possible standards defined comparative quality algorithms describing metric distances on DNA sequences. Thus, the main focus of this article is to describe our original approach to compare the quality of defined metrics on the set of DNA sequences. The approach is based on the fact, that the triples of distances between genomes should ideally form isosceles acute triangles. On the basis of this assumption, we proposed value of the norm, gives in practice aссeptable results. In the course of work on the implementation of algorithms have been carried out computational experiments with 100 DNA of "distant" species, as well as with representatives of several genomes of great apes and humans.

An inverse problem for matrix processing: an improved algorithm for restoring the distance matrix for DNA chains

“…It is important to note that currently it is easy to find only a few similar algorithms on the Internet, [Needleman and Wunsch, 1970;Winkler, 1990;van der Loo, 2014] etc. (the authors' usage of Internet searches give about 10 similar algorithms only); see also the description of our algorithm in [Melnikov, Pivneva, and Trifonov, 2017] and some of our other papers cited there.…”

“…In this regard, the task of restoring such a partially filled matrix arises. We started publishing our variants of similar algorithms for restoring partially filled matrices in [Melnikov, Pivneva, and Trifonov, 2017] (the simplest algorithm was described very briefly there), after which we returned to this problem in [Melnikov and Trenina, 2018a;Melnikov and Trenina, 2018b], where a variant of the algorithm using the method of branches and boundaries was described in detail.…”

“…One of such conditions is the regularity found in the paper [Melnikov, Pivneva, and Trifonov, 2017] for distance matrices, which consists in the fact that the three elements of the matrix…”

“…Filling the table in this way, we obtain a matrix with noisy data {u δ i,j } and then we restore the u ε function by solving (1). The level of noise δ generated by this algorithm for restoring missing values can be estimated by analyzing the results of violations of the "isosceles triangle" regularity in [Melnikov, Pivneva, and Trifonov, 2017].…”

“…The sixth direction represents a new approach to comparing different heuristics for distances between DNA chains, i.e., an alternative approach to the one discussed in [Melnikov, Pivneva, and Trifonov, 2017] and some of our other papers cited there. Namely, after filling in several distance matrices with various algorithms (i.e., algorithms for obtaining distances between pairs of DNA chains), we consider all possible triangles in these matrices; note again that their number is quite large, of the order ∼ n 3 .…”