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Open Access Highly Accessed Research article

The number of reduced alignments between two DNA sequences

Helena Andrade1, Iván Area2, Juan J Nieto13* and Ángela Torres4

Author Affiliations

1 Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain

2 Departamento de Matemática Aplicada II, E.E. Telecomunicación, Universidade de Vigo, 36310 Vigo, Spain

3 Faculty of Science, King Abdulaziz University, P.O. Box 80203, 21589 Jeddah, Saudi Arabia

4 Departamento de Psiquiatría, Radioloxía e Saúde Pública, Facultade de Medicina, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain

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BMC Bioinformatics 2014, 15:94  doi:10.1186/1471-2105-15-94

Published: 1 April 2014

Abstract

Background

In this study we consider DNA sequences as mathematical strings. Total and reduced alignments between two DNA sequences have been considered in the literature to measure their similarity. Results for explicit representations of some alignments have been already obtained.

Results

We present exact, explicit and computable formulas for the number of different possible alignments between two DNA sequences and a new formula for a class of reduced alignments.

Conclusions

A unified approach for a wide class of alignments between two DNA sequences has been provided. The formula is computable and, if complemented by software development, will provide a deeper insight into the theory of sequence alignment and give rise to new comparison methods.

AMS Subject Classification

Primary 92B05, 33C20, secondary 39A14, 65Q30

Keywords:
DNA sequence; Alignment; Difference equation