Brief Communication Rearrangements of Dna Sequences and Sbh*

Despite recent advances in DNA sequencing by hybridization it is still a random shotgun method. Even if one manages to routinely sequence short DNA fragments by SBH these fragments have to be assembled into the final genomic sequence. Recently different additional biochemical experiments were suggested which potentially may drastically increase the resolving power of SBH. However biologists frequently cannot estimate the computer science limitations of the proposed additional experiments and no computational studies of additional experiments for SBH were provided yet. The paper discusses a combinatorial technique which might help a biologist to analyze different additional biochemical experiments and to combine these data with SBH data to increase the resolving power of SBH. DNA sequencing by hybridization (SBH) is a challenging al.ternative to the classical DNA sequencing methods. The basic approach is to build an array (Sequencing Chip) of short oligonucleotides, to use hybridization for finding oligonucleotide (q-gram) composition of an unknown DNA fragment and to reconstruct the fragment by a combinatorial algorithm [see Pevzner & Lipshutz (1994) for a recent review]. A number of major breakthroughs in SBH were reported recently; Fodor et al. (1991) developed photolithographic technique for building chips, Southern et al. (1992) built the first sequencing chip, Drmanac er al. (1993) read the first DNA fragment by SBH. However, the original SBH chip containing all 4* = 65536 octanucleotides in insufficient for sequencing long DNA fragments. In particular, Pevzner (1989) demonstrated that even in the case of an i&al (errorless) SBH experiment one can hope to reconstruct a 200 nucleotide long sequence only in 94 out of 100 cases. To increase the resolving power of SBH chips Bains (1991), Pevzner et al. (1991) and Pevzner & Lipshutz (1994) developed different optimized chips; in particular binary chips allow one to sequence a 1800 bp fragment using a 64 kb chip. However, despite recent advances, SBH is still a random shotgun method. Even if one manages to routinely sequence 200-300 bp fragments with 64 kb SBH chips (1500-1800 bp with binary chips) these fragments have to be assembled into the final genomic sequence. Recently different additional *Some toaics included in this work have been discussed during* the Third International Workshop on Open Prob kens of Computational Molecular Biology, Telluride, Cola., 11-25 July 1993. biochemical experiments were suggested which potentially may make SBH a true genomic sequencing method (Drmanac et d., 1989; Khrapko et al., 1989; Drmanac & Crkvenjakov, 1992; Chetverin & Kramer, 1993). However biologists frequently cannot estimate the computer science limitations of the proposed additional experiments and, to our knowledge, almost no computational studies of additional experiments for SBH were provided yet. Hence biologists are unable to make even a preliminary judgement on how the proposed additional experiments increase the resolving power of SBH. To analyze different additional biochemical experiments one needs a characterization theorem providing a description of all DNA sequences with the given SBH spectrum. The paper studies a compact description of all DNA sequences with the same SBH spectrum (i.e. with the same q-gram composition where q is the length of oligonucleotides on the chip) in terms of equivalent transformations. This problem is related to a fingerprint technique in combinatorial pattern matching recently analyzed by Ukkonen (1992). Studying q-gram distance between texts Ukkonen (1992) raised a problem of word transformations preserving q-gram distance and conjectured that all words with the same q-gram composition can be transformed into each other by means of natural transformations (transpositions and rotations). The proposed characterization of sequences with the same SBH spectrum is based on a combinatorial technique (alternating cycles in colored graphs) which allows one to analyze different additional data about the sequence in the framework of the same theoretical model. This technique has already led us to the