Hypercomplex cross-correlation of DNA sequences

A hypercomplex representation of DNA is proposed to facilitate comparing DNA sequences with fuzzy composition. With the hypercomplex number representation, the conventional sequence analysis method, such as, dot matrix analysis, dynamic programming, and cross-correlation method have been extended and improved to align DNA sequences with fuzzy composition. The hypercomplex dot matrix analysis can provide more control over the degree of alignment desired. A new scoring system has been proposed to accommodate the hypercomplex number representation of DNA and integrated with dynamic programming alignment method. By using hypercomplex cross-correlation, the match and mismatch alignment information between two aligned DNA sequences are separately stored in the resultant real part and imaginary parts respectively. The mismatch alignment information is very useful to refine consensus sequence based motif scanning

Fast index based algorithms and software for matching position specific scoring matrices

BACKGROUND: In biological sequence analysis, position specific scoring matrices (PSSMs) are widely used to represent sequence motifs in nucleotide as well as amino acid sequences. Searching with PSSMs in complete genomes or large sequence databases is a common, but computationally expensive task. RESULTS: We present a new non-heuristic algorithm, called ESAsearch, to efficiently find matches of PSSMs in large databases. Our approach preprocesses the search space, e.g., a complete genome or a set of protein sequences, and builds an enhanced suffix array that is stored on file. This allows the searching of a database with a PSSM in sublinear expected time. Since ESAsearch benefits from small alphabets, we present a variant operating on sequences recoded according to a reduced alphabet. We also address the problem of non-comparable PSSM-scores by developing a method which allows the efficient computation of a matrix similarity threshold for a PSSM, given an E-value or a p-value. Our method is based on dynamic programming and, in contrast to other methods, it employs lazy evaluation of the dynamic programming matrix. We evaluated algorithm ESAsearch with nucleotide PSSMs and with amino acid PSSMs. Compared to the best previous methods, ESAsearch shows speedups of a factor between 17 and 275 for nucleotide PSSMs, and speedups up to factor 1.8 for amino acid PSSMs. Comparisons with the most widely used programs even show speedups by a factor of at least 3.8. Alphabet reduction yields an additional speedup factor of 2 on amino acid sequences compared to results achieved with the 20 symbol standard alphabet. The lazy evaluation method is also much faster than previous methods, with speedups of a factor between 3 and 330. CONCLUSION: Our analysis of ESAsearch reveals sublinear runtime in the expected case, and linear runtime in the worst case for sequences not shorter than | [Formula: see text] |(m )+ m - 1, where m is the length of the PSSM and [Formula: see text] a finite alphabet. In practice, ESAsearch shows superior performance over the most widely used programs, especially for DNA sequences. The new algorithm for accurate on-the-fly calculations of thresholds has the potential to replace formerly used approximation approaches. Beyond the algorithmic contributions, we provide a robust, well documented, and easy to use software package, implementing the ideas and algorithms presented in this manuscript

Using sequence compression to speedup probabilistic profile matching

none2noMatching a biological sequence against a probabilistic pattern (or profile) is a common task in computational biology. A probabilistic profile, represented as a scoring matrix, is more suitable than a deterministic pattern to retain the peculiarities of a given segment of a family of biological sequences. Brute-force algorithms take O(NP) to match a sequence of N characters against a profile of length P ≪ N. In this work, we exploit string compression techniques to speedup brute-force profile matching. We present two algorithms, based on run-length encoding (RLE) and LZ78, that reduce computational complexity by the compression factor of the encoding. While RLE provides little improvement with respect to brute-force algorithm (the number of runs is close to the number of haracters of the original sequences), LZ78 provides a sizeable advantage. The advantage is greater for DNA sequences, since the lower the number of symbols in the alphabet the higher the efficiency of LZ78. The paper shows that the proposed approach reduces the asymptotic complexity of string comparison without adding to much to the complexity of the inner loop. Moreover, the proposed techniques can be combined with existing branc and bound approaches to obtain further speed up. Experimental results refer to representative sequences taken from human genome. Results: In this work, we exploit string compression techniques to speedup brute-force profile matching. We present two algorithms, based on run-length and LZ78 encodings, that reduce computational complexity by the compression factor of the encoding.mixedV. Freschi; A. BoglioloFreschi, Valerio; Bogliolo, Alessandr