The computational complexity of orientation search in cryo-electron microscopy

Abstract

In this paper we study the problem of determining three-dimensional orientations for noisy projections of randomly oriented identical particles. The problem is of central importance in the tomographic reconstruction of the density map of macromolecular complexes from electron microscope images and it has been studied intensively for more than 30 years. We analyze the computational complexity of the problem and show that while several variants of the problem are NP-hard and inapproximable, some restrictions are polynomial-time approximable within a constant factor or even solvable in logarithmic space. The negative complexity results give a partial justification for the heuristic methods used in the orientation search, and the positive complexity results have some positive implications also to a different problem of finding functionally analogous genes. © Springer-Verlag 2004.