Matching and comparing sequences in molecular biology

Abstract

The primary structure of a deoxyribonucleic acid (DNA) molecule is a sequence consisting of four types of letters, A, C., G, and T, each stands for a nucleotide. The length of such a DNA sequence ranges from several thousand letters for a simple virus to three billion letters for a human. We all know that these long and mysterious sequences encode Life as well as genetic diseases, but decoding the sequences is perhaps one of the most challenging tasks in the world. The ultimate goal of molecular biology is to understand what segments of a DNA are responsible for a biological function such as the color of eyes or a genetic disease such as cancer, and how these segments are formed and work. These functionally meaningful segments of a DNA are usually called genes. To find the genes which are responsible for some biological function, a biologist often compares a set of DNA sequences that share the same function and tries to identify regions which are “conserved” in all of these sequences. On the other hand, a biologist may also infer the “closeness” of two organisms by comparing their DNA sequences and computing the degree of similarity of the sequences. Such “closeness” information is useful in the reconstruction of evolutionary histories.

In this talk, we survey various frameworks for the problem of comparing a pair or a set of sequences, including approximate string matching, string edit, (pairwise) sequence alignment, local sequence alignment, and multiple sequence alignment. For the comparison of a pair of sequences, we will describe some standard algorithms and several techniques to improve the time and space efficiency such as preprocessing and divide-and-conquer. Multiple sequence alignment has been identified as one of the most challenging problems in computational molecular biology. In the rest of the talk, we will concentrate on two important variants of multiple sequence alignment: multiple alignment with sum-of-all-pairs (SP) score and multiple alignment with tree score. Since both are NP-hard, we discuss polynomial-time approximation algorithms for these problems with a guaranteed performance bound. If time allows, we will also mention some popular heuristics for performing multiple alignment that seem to work well in practice but do not have a guaranteed performance.

Computational molecular biology is emerging as a fast growing interdisciplinary field involving biology, computer science, statistics, applied mathematics, etc. and is providing a lot of interesting algorithmic questions for theoretical computer scientists to solve. We hope that this brief survey will serve as an introduction to one (important) aspect of the field. Most of the results mentioned above or a pointer to them can be found in the following literature.

Research supported in part by NSERC Research Grant OGP0046613 and MRC/NSERC CGAT Grant GO-12278.