Statistical Measures of DNA Sequence Dissimilarity under Markov Chain Models of Base Composition

Abstract

In molecular biology, the issue of quantifying the similarity between two biological sequences is very important. Past research has shown that word-based search tools are computationally efficient and can find some new functional similarities or dissimilarities invisible to other algorithms like FASTA. Recently, under the independent model of base composition, Wu, Burke, and Davison (1997, Biometrics 53, 1431 1439) characterized a family of word-based dissimilarity measures that defined distance between two sequences by simultaneously comparing the frequencies of all subsequences of n adjacent letters (i.e., n-words) in the two sequences. Specifically, they introduced the use of Mahalanobis distance and standardized Euclidean distance into the study of DNA sequence dissimilarity. They showed that both distances had better sensitivity and selectivity than the commonly used Euclidean distance. The purpose of this article is to extend Mahalanobis and standardized Euclidean distances to Markov chain models of base composition. In addition, a new dissimilarity measure based on Kullback-Leibler discrepancy between frequencies of all n-words in the two sequences is introduced. Applications to real data demonstrate that Kullback-Leibler discrepancy gives a better performance than Euclidean distance. Moreover, under a Markov chain model of order kQ for base composition, where kQ is the estimated order based on the query sequence, standardized Euclidean distance performs very well. Under such a model, it performs as well as Mahalanobis distance and better than Kullback-Leibler discrepancy and Euclidean distance. Since standardized Euclidean distance is drastically faster to compute than Mahalanobis distance, in a usual workstation/PC computing environment, the use of standardized Euclidean distance under the Markov chain model of order kQ of base composition is generally recommended. However, if the user is very concerned with computational efficiency, then the use of Kullback-Leibler discrepancy, which can be computed as fast as Euclidean distance, is recommended. This can significantly enhance the current technology in comparing large datasets of DNA sequences.

A method for assigning species into groups based on generalized Mahalanobis distance between habitat model coefficients

“…Whereas the lack of significant differences among Mahalanobisdistance-based methods can be partly attributed to the modest number of iterations used in the simulations (100) and the conservative Tukey criterion based on 18 means, we believe that only strong differences were of interest for attempting any general conclusions from these simulations. It is particularly interesting that the Euclidean distance-based methodd E (β i ,β j ) did not perform as well as our method, because in many multivariate applications a Euclidean distance is proposed as a computationally less expensive approximation to a Mahalanobis distance (e.g., Wu et al 2001).…”

rEMM: Extensible Markov Model for Data Stream Clustering inR

“…The most commonly used measures are Euclidean distance, d 2 distance (a weighted Euclidean distance), Mahalanobis distance and Kullback-Leibler discrepancy (KLD). Since Wu, Hsieh, and Li (2001) find in their experiments that KLD provides good results while it still can be computed as fast as Euclidean distance, it is also used here. Since KLD becomes −∞ for counts of zero, we add one to all counts which conceptually means that we start building the EMM with a prior that all triplets have the equal occurrence probability (see Wu et al 2001).…”

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“…Sensitivity and selectivity were computed to evaluate and compare the performance of the proposed models with other distance measures [33]. Sensitivity is expressed by the number of A. testaceum related sequences found among the first closest five library sequences.…”