Evaluation Measures of Multiple Sequence Alignments

Abstract

Multiple sequence alignments (MSAs) are frequently used in the study of families of protein sequences or DNA/RNA sequences. They are a fundamental tool for the understanding of the structure, functionality and, ultimately, the evolution of proteins. A new algorithm, the Circular Sum (CS) method, is presented for formally evaluating the quality of an MSA. It is based on the use of a solution to the Traveling Salesman Problem, which identifies a circular tour through an evolutionary tree connecting the sequences in a protein family. With this approach, the calculation of an evolutionary tree and the errors that it would introduce can be avoided altogether. The algorithm gives an upper bound, the best score that can possibly be achieved by any MSA for a given set of protein sequences. Alternatively, if presented with a specific MSA, the algorithm provides a formal score for the MSA, which serves as an absolute measure of the quality of the MSA. The CS measure yields a direct connection between an MSA and the associated evolutionary tree. The measure can be used as a tool for evaluating different methods for producing MSAs. A brief example of the last application is provided. Because it weights all evolutionary events on a tree identically, but does not require the reconstruction of a tree, the CS algorithm has advantages over the frequently used sum-of-pairs measures for scoring MSAs, which weight some evolutionary events more strongly than others. Compared to other weighted sum-of-pairs measures, it has the advantage that no evolutionary tree must be constructed, because we can find a circular tour without knowing the tree.

Assessing Activity Pattern Similarity with Multidimensional Sequence Alignment Based on a Multiobjective Optimization Evolutionary Algorithm

“…For example, the alignment in Figure 1c can be evaluated by calculating a distance score for two unidimensional alignments: L-HTH and LTWTH , and 1-232 and 14342. Formally, we calculate the sum-of-pairs alignment score (Gonnet et al 2000) of each alignment. Let S 1 and S 2 be two unidimensional sequences with length m and n , respectively.…”

A Hybrid Algorithm Using a Genetic Algorithm and Cuckoo Search Algorithm to Solve the Traveling Salesman Problem and its Application to Multiple Sequence Alignment

“…The score of the pairwise alignment can be calculated by using Needleman and Wunsch algorithm [18]. Clustalw is considered to be one of the most useful programs among the progressive multiple sequence alignment programs which provides the best quality alignments.…”

“…In order to measure the performance of a multiple sequence alignment program, a standard evaluation is used [18]. Let n be the number of sequences in the alignment, and suppose the alignment consists of m columns.…”

Multiple sequence alignment for phylogenetic purposes

“…The end result is that the patternmatching programs add fewer and / or shorter gaps to the alignment than the number of indels expected, especially for distantly related sequences Morrison and Ellis 1997;Nicholas et al 2002;Simmons and Freudenstein 2003;Löytynoja and Goldman 2005). This problem is compounded for methods based on sum-of-pairs, as these weight some evolutionary events more strongly than others (Gonnet et al 2000); and the failure of affine gap costs to deal with long gaps also violates the triangle inequality, which leads to trivial alignments (Aagesen et al 2005). There have been several empirical studies indicating the extent to which affine gap costs underestimate the probability of long indels in different types of sequences (Pascarella and Argos 1992;Benner et al 1993;Gu and Li 1995;Ophir and Graur 1997;Graham et al 2000;Qian and Goldstein 2001;Reese and Pearson 2002;Chang and Benner 2004;Keightley and Johnson 2004;Wrabl and Grishin 2004); that is, the frequency distribution of gaps in real sequences has a much longer righthand tail than the geometric distribution modelled by the affine gap cost.…”