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.