An Approach to the Exploration of Different Metrics between DNA Sequences

In practice, it often becomes necessary to calculate certain distances in a special way, not only between DNA strings, but also between any other sequences of characters. For two DNA chains, there exist several algorithms for calculating the distance; in the paper, we used five such algorithms as examples. For some algorithm under consideration and some selected set of genomes (usually several dozen examples of mitochondrial DNA, but other options are possible), a square matrix of distances between genomes is naturally formed based on the calculated distances. The main assumption made for all the problems we are considering is that in good distance determination algorithms, the triangles obtained in this matrix differ little from the isosceles triangles; this assumption is confirmed in practice. With this assumption, we determine the badness of a particular triangle, and based on it, we solve several groups of problems using heuristic algorithms. The first task is the simplest: based on the total badness of the matrix, we organize algorithms for determining the distances between genomes, from more successful to less successful. In the second group of problems, we use heuristic algorithms to restore a partially filled distance matrix. In the third group of problems, based on the calculation of the correlation coefficient between the sequences of triangle faults, we show the mutual discrepancy of some pairs of algorithms for determining the distances between DNA chains. In the fourth group of problems, based on the proximity of two distance determination algorithms, we form a table of such closeness for all pairs of algorithms, and based on it we determine the quality of the original algorithms; it is important that the obtained resulting quality of the algorithms approximately corresponds to the results of the first group of problems, despite the fact that they were calculated using completely different approaches.