Hypercomplex cross-correlation of DNA sequences

A hypercomplex representation of DNA is proposed to facilitate comparison of DNA sequences with fuzzy composition. Using hypercomplex number representation, conventional sequence analysis method, such as, dot matrix analysis, dynamic programming, and cross-correlation method are extended and improved to align the 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, matching and mismatching alignment information between two aligned DNA sequences are stored in the resultant real part and imaginary parts, respectively. Mismatching alignment information is particularly useful for refining consensus sequence-based motif scanning.