DNA Sequencing - Tabu and Scatter Search Combined

1. Biochemical Preliminaries and Problem Formulation DNA sequencing is one of the most important problems in computational molecular biology. The goal is to determine a sequence of nucleotides of a DNA fragment. Such a fragment is usually written as a sequence of the letters A, C, G, and T, representing four nucleotides composing the fragment, i.e., adenine, cytosine, guanine, and thymine, respectively. A short sequence of nucleotides is called an oligonucleotide. The sequencing process uses as input data a set of oligonucleotides of equal length, which are subsequences of one strand of the examined DNA fragment, and are derived from a hybridization experiment. Next, an original sequence of a known length is reconstructed, taking advantage of the fact that the oligonucleotides overlap one another. In the hybridization experiment (Bains and Smith 1988, Lysov et al. 1988, Southern 1988, Drmanac et al. 1989), a complete oligonucleotide library is compared with many copies of one strand of the examined DNA fragment. The library consists of all 4 short onestrand DNA fragments of length l. In order to use the library, fragments are constructed in a special way on a DNA chip (Southern 1988, Fodor et al. 1991, Pease et al. 1994), where each element of the library has unique coordinates of the chip. During the hybridization reaction, copies of the longer DNA fragment join to oligonucleotides from the library in their complementary locations. Then, as a result of reading a fluorescent image of the chip, one obtains a set of oligonucleotides that are subfragments of the examined DNA fragment. This set is named the spectrum. If the hybridization experiment were executed without errors, then the spectrum would be ideal, i.e., it would contain only all subsequences of length l of the original sequence of the known length n. In this case, the spectrum consists of n− l+ 1 elements and to reconstruct the original sequence one must find an order of spectrum elements such that neighboring elements always overlap on l− 1 nucleotides (see Example 1). There are several exact methods for solving the DNA sequencing problem with the ideal spectrum, described for example in Bains and Smith (1988), Lysov et al. (1988), or in Drmanac et al. (1989), but only the one proposed in Pevzner (1989) works in polynomial time. Example 1. Suppose the original sequence to be found is ACTCTGG, n = 7. In the hybridization experiment one can use, for example, the complete library of oligonucleotides of length l = 3, composed of the following 43 = 64 oligonucleotides: {AAA, AAC, AAG, AAT, ACA, TTG, TTT}. As a result of the experiment performed without errors one obtains the ideal spectrum for this sequence, containing all