In cryo-electron microscopy (EM), thanks to rapid freezing of the specimen, macromolecular assemblies and machines can be captured in their native, aqueous environment, and their native structure is preserved. In addition to the expected conformational heterogeneity of the assemblies that is due to fluctuations of the structure around the ground state, one can expect to capture molecules in different functional states, especially if the binding of a ligand induces a conformational change in the macromolecular assembly. Therefore, data set of images from an EM experiment must be interpreted as a mixture of projections from similar but not identical structures.
In order to separate images of molecules that are ligand-bound from those that are unbound and to reveal the conformational variability of the complex, we have developed a real-space analysis of 3-D variance/covariance in macromolecules reconstructed from a set of their projections using a statistical bootstrap resampling technique. In this method, a new set of projections is selected with replacements from the available whole set of projections; thus, in the resampled set some of the original projections will appear more than once, while others will be omitted. This selection process is repeated a number of times and for each new set of projections the corresponding 3-D volume is calculated. Next, the voxel-by-voxel variance of the resulting set of bootstrap volumes is calculated. The target variance is obtained using a relationship between the variance of arithmetic means for sampling with replacements and the sample variance. Similar relation holds for the correlations between voxels of bootstrap volumes and correlations between voxels of the original, although unknown structures. Thus, it is possible to apply eigenanalysis to the bootstrap volumes and obtain information about conformational variability of the molecule.
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The power of the technique is illustrated using data from a 70S Thermus thermophilus ribosome complexed with G protein EF-G in the presence of the non-hydrolyzable GTP analogue GMPPNP. We demonstrate that we can reveal the rachet-like rearrangement of the subunits of the ribosome. Using factorial coordinates of the 2D projection data obtained by comparing them with projections of eigenvolumes, we can classify projections into nearly homogeneous groups corresponding to well-defined states of the ribosome. We also demonstrate that eigenvolumes can be interpreted in terms of plausible movements of the subunits of the complex revealing, directly from the data, its conformational modes.