Introduction

Abstract

This chapter is intended to provide an introduction to mutations and sequence alignment. First, we introduce background related to biological sequence alignment and give an easy-to-follow review of the progress made in alignment methods. The mathematical problems driven by alignment analysis are then discussed. We then give the basic concepts involved in alignment models. The biological mutations are classified into four types. The mathematical notion of biological sequence and alignment is introduced for further discussion. After that, the dynamic programming algorithm, which is the most popular algorithm of pairwise alignment is reviewed here. This algorithm includes the Needle-Wunsch algorithm for global alignment and the Smith-Waterman algorithm for local alignment. Finally, we introduce correlation functions of local sequence pairwise alignment matrices among multiple sequences, which is applied in the super pairwise alignment (SPA) and the super multiple sequences alignment (SMA).