Optimal simultaneous superpositioning of multiple structures with missing data

TL;DR: This work uses the expectation–maximization algorithm, a classic statistical technique for dealing with incomplete data, to find both maximum-likelihood solutions and the optimal least-squares solution as a special case for superposition when some of the data are missing.

Abstract: Motivation: Superpositioning is an essential technique in structural biology that facilitates the comparison and analysis of conformational differences among topologically similar structures Performing a superposition requires a one-to-one correspondence, or alignment, of the point sets in the different structures However, in practice, some points are usually ‘missing’ from several structures, for example, when the alignment contains gaps Current superposition methods deal with missing data simply by superpositioning a subset of points that are shared among all the structures This practice is inefficient, as it ignores important data, and it fails to satisfy the common least-squares criterion In the extreme, disregarding missing positions prohibits the calculation of a superposition altogether Results: Here, we present a general solution for determining an optimal superposition when some of the data are missing We use the expectation–maximization algorithm, a classic statistical technique for dealing with incomplete data, to find both maximum-likelihood solutions and the optimal least-squares solution as a special case Availability and implementation: The methods presented here are implemented in THESEUS 20, a program for superpositioning macromolecular structures ANSI C source code and selected compiled binaries for various computing platforms are freely available under the GNU open source license from http://wwwtheseus3dorg Contact: dtheobald@brandeisedu Supplementary information:Supplementary data are available at Bioinformatics online