Global optimum protein threading with gapped alignment and empirical pair score functions.

We describe a branch-and-bound search algorithm for finding the exact global optimum gapped sequence-structure alignment ("threading") between a protein sequence and a protein core or structural model, using an arbitrary amino acid pair score function (e.g. contact potentials, knowledge-based potentials, potentials of mean force, etc.). The search method imposes minimal conditions on how structural environments are defined or the form of the score function, and allows arbitrary sequence-specific functions for scoring loops and active site residues. Consequently the search method can be used with many different score functions and threading methodologies; this paper illustrates five from the literature. On a desktop workstation running LISP, we have found the global optimum protein sequence-structure alignment in NP-hard search spaces as large as 9.6 x 10(31), at rates ranging as high as 6.8 x 10(28) equivalent threadings per second (most of which are pruned before they ever are examined explicitly). Continuing the procedure past the global optimum enumerates successive candidate threadings in monotonically increasing score order. We give efficient algorithms for search space size, uniform random sampling, segment placement probabilities, mean, standard deviation and partition function. The method should prove useful for structure prediction, as well as for critical evaluation of new pair score functions.