Estimation of variance in single-particle reconstruction using the bootstrap technique

Density maps of a molecule obtained by single-particle reconstruction from thousands of molecule projections exhibit strong changes in local definition and reproducibility, as a consequence of conformational variability of the molecule and non-stoichiometry of ligand binding. These changes complicate the interpretation of density maps in terms of molecular structure. A three-dimensional (3-D) variance map provides an effective tool to assess the structural definition in each volume element. In this work, the different contributions to the 3-D variance in a single-particle reconstruction are discussed, and an effective method for the estimation of the 3-D variance map is proposed, using a bootstrap technique of sampling. Computations with test data confirm the viability, computational efficiency, and accuracy of the method under conditions encountered in practical circumstances. (c) 2006 Elsevier Inc. All rights reserved.