A Bayes-optimal sequence-structure theory that unifies protein sequence-structure recognition and alignment

A rigorous Bayesian analysis is presented that unifies protein sequence-str ucture alignment and recognition. Given a sequence, explicit formulae are d erived to select (1) its globally most probable core structure from a struc ture library; (2) its globally most probable alignment to a given core stru cture; (3) its most probable joint core structure and alignment chosen glob ally across the entire library; and (4) its most probable individual segmen ts, secondary structure, and super-secondary structures across the entire l ibrary. The computations involved are NP-hard in the general case (3D-3D). Fast exact recursions for the restricted sequence singleton-only (1D-3D) ca se are given. Conclusions include: (a) the most probable joint core structu re and alignment is not necessarily the most probable alignment of the most probable core structure, but rather maximizes the product of core and alig nment probabilities; (b) use of a sequence-independent linear or affine gap penalty may result in the highest-probability threading not having the low est score; (c) selecting the most probable core structure from the library (core structure selection or fold recognition only) involves comparing prob abilities summed over all possible alignments of the sequence to the core, and not comparing individual optimal (or near-optimal) sequence-structure a lignments; and (d) assuming uninformative priors, core structure selection is equivalent to comparing the ratio of two global means. (C) 1998 Society for Mathematical Biology.