Defining the limits and reliability of rigid-body fitting in cryo-EM maps using multi-scale image pyramids

Cryo-electron microscopy provides fascinating structural insight into large macromolecular machines at increasing detail. Despite significant advances in the field, the resolution of the resulting three-dimensional images is still typically insufficient for de novo model building. To bridge the resolution gap and give an atomic interpretation to the data, high-resolution models are typically placed into the density as rigid bodies. Unfortunately, this is often done manually using graphics software, a subjective method that can lead to over-interpretation of the data. A more objective approach is to perform an exhaustive cross-correlation-based search to fit subunits into the density. Here we show, using five experimental ribosome maps ranging in resolution from 5.5 to 6.9 Å, that cross-correlation-based fitting is capable of successfully fitting subunits correctly in the density for over 90% of the cases. Importantly, we provide indicators for the reliability and ambiguity of a fit, using the Fisher z-transformation and its associated confidence intervals, giving a formal approach to identify over-interpreted regions in the density. In addition, we quantify the resolution requirement for a successful fit as a function of the subunit size. For larger subunits the resolution of the data can be down-filtered to 20 Å while still retaining an unambiguous fit. We leverage this information through the use of multi-scale image pyramids to accelerate the search up to 30-fold on CPUs and 40-fold on GPUs at a negligible loss in success rate. We implemented this approach in our rigid-body fitting software PowerFit, which can be freely downloaded from https://github.com/haddocking/powerfit.