A recent idea for determining the three-dimensional structure of a protein uses antibody recognition of surface structure and random peptide libraries to map antibody epitope combining sites. Antibodies that bind to the surface of the protein of interest can be used as "witnesses" to report the structure of the protein as follows: Proteins are composed of linear polypeptide chains that come together in complex spatial folding patterns to create the native protein structures and these folded

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... ctures form the binding sites for the antibodies. Short amino acid probe sequences, which bind to the active region of each antibody, can be selected from random sequence peptide libraries. These probe sequences can often be aligned to discontinuous regions of the one-dimensional target sequence of a protein. Such alignments indicate how pieces of the protein sequence must be folded together in space and thus provide valuable long-range constraints for solving the overall 3-D structure. This new approach is applicable to the very large number of proteins that are refractory to current approaches to structure determination and has the advantage of requiring very small amounts of the target protein. The binding site of an antibody is a surface, not just a linear sequence, so the epitope mapping alignment problem is outside the scope of classical string alignment algorithms, such as Smith-Waterman. We formalize the alignment problem that is at the heart of this new approach, prove that the epitope mapping alignment problem is NP-complete, and give some initial results using a branch-and-bound algorithm to map two real-life cases.