Protein synthesis by the ribosome involves large-scale rearrangements of the "small" subunit (SSU; ~ 1 MDa), which include inter- and intra-subunit rotational motions. With more than 1000 structures of ribosomes and ribosomal subunits now publicly available, it is becoming increasingly difficult to design precise experiments that are based on a comprehensive analysis of all known rotation states. To overcome this limitation, we present the Ribosome Angle Decomposition (RAD) method, where the

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... entation of each small subunit head and body is described in terms of three angular coordinates (rotation, tilt and tilt direction) and a single translation. To demonstrate the utility of the accompanying software (RADtool) we applied it to all published ribosome and mitoribosome structures. This identified and analyzed 1077 fully-assembled ribosome complexes, as well as 280 isolated small subunits from 48 organisms. The RAD approach quantitatively distinguishes between previously described qualitative rotational features, determines when rotation-only descriptions are insufficient, and shows that tilt-like rearrangements of the SSU head and body are pervasive in both prokaryotic and eukaryotic ribosomes. Together, the presented database and technique provide a robust platform for systematically analyzing, visualizing, and comparing subunit orientations of ribosomes from all kingdoms of life. Accordingly, the RAD resource establishes a common foundation with which structural, simulation, single-molecule and biochemical efforts can precisely interrogate the dynamics of this prototypical molecular machine.