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The real-space 3D covariance estimation we published recently constitutes a very significant advance in methodology (Liao et al., 2015). In a heterogeneous dataset of a molecular machine such as the ribosome one would wish to identify and locate interdependencies between movements of different domains and the binding of functional ligands. These interdependencies can be expressed by the variance/covariance matrix, a matrix with N x N entries if N is the total number of voxels. Diagonal elements are those of the 3D variance components. The normal inquiry would be confined to the contents of a single row or a single column of that matrix; i.e., by focusing on one voxel and asking for its correlation with all N-1 other voxels of the volume. We call such a subset of the complete covariance matrix a “covariance map with reference to the selected voxel.” Hstau Liao found a fast way to estimate the 3D covariance map within a selected region of interest directly from the original particle data. For instance, we might want to know if binding of the factor DHX29 has an effect on the position of the 40S subunit head in the pre-initiation complex. In that case, we would select for reference a voxel lying within DHX29 in the DHX29-40S map, and use a region confined to the 40S subunit head for a mask that defines the region where the covariance map should be estimated.