Efficient computation of root mean square deviations under rigid transformations.

The computation of root mean square deviations (RMSD) is an important step in many bioinformatics applications. If approached naively, each RMSD computation takes time linear in the number of atoms. In addition, a careful implementation is required to achieve numerical stability, which further increases runtimes. In practice, the structural variations under consideration are often induced by rigid transformations of the protein, or are at least dominated by a rigid component. In this work, we show how RMSD values resulting from rigid transformations can be computed in constant time from the protein's covariance matrix, which can be precomputed in linear time. As a typical application scenario is protein clustering, we will also show how the Ward-distance which is popular in this field can be reduced to RMSD evaluations, yielding a constant time approach for their computation.

Computing H/D-exchange rates of single residues from data of proteolytic fragments.

BACKGROUND: Protein conformation and protein/protein interaction can be elucidated by solution-phase Hydrogen/Deuterium exchange (sHDX) coupled to high-resolution mass analysis of the digested protein or protein complex. In sHDX experiments mutant proteins are compared to wild-type proteins or a ligand is added to the protein and compared to the wild-type protein (or mutant). The number of deuteriums incorporated into the polypeptides generated from the protease digest of the protein is related to the solvent accessibility of amide protons within the original protein construct. RESULTS: In this work, sHDX data was collected on a 14.5 T FT-ICR MS. An algorithm was developed based on combinatorial optimization that predicts deuterium exchange with high spatial resolution based on the sHDX data of overlapping proteolytic fragments. Often the algorithm assigns deuterium exchange with single residue resolution. CONCLUSIONS: With our new method it is possible to automatically determine deuterium exchange with higher spatial resolution than the level of digested fragments.

Multiple sequence alignment with arbitrary gap costs: computing an optimal solution using polyhedral combinatorics.

Multiple sequence alignment is one of the dominant problems in computational molecular biology. Numerous scoring functions and methods have been proposed, most of which result in NP-hard problems. In this paper we propose for the first time a general formulation for multiple alignment with arbitrary gap-costs based on an integer linear program (ILP). In addition we describe a branch-and-cut algorithm to effectively solve the ILP to optimality. We evaluate the performances of our approach in terms of running time and quality of the alignments using the BAliBase database of reference alignments. The results show that our implementation ranks amongst the best programs developed so far.

A combinatorial approach to protein docking with flexible side chains.

Rigid-body docking approaches are not sufficient to predict the structure of a protein complex from the unbound (native) structures of the two proteins. Accounting for side chain flexibility is an important step towards fully flexible protein docking. This work describes an approach that allows conformational flexibility for the side chains while keeping the protein backbone rigid. Starting from candidates created by a rigid-docking algorithm, we demangle the side chains of the docking site, thus creating reasonable approximations of the true complex structure. These structures are ranked with respect to the binding free energy. We present two new techniques for side chain demangling. Both approaches are based on a discrete representation of the side chain conformational space by the use of a rotamer library. This leads to a combinatorial optimization problem. For the solution of this problem, we propose a fast heuristic approach and an exact, albeit slower, method that uses branch-and-cut techniques. As a test set, we use the unbound structures of three proteases and the corresponding protein inhibitors. For each of the examples, the highest-ranking conformation produced was a good approximation of the true complex structure.