Non-uniform refinement: Adaptive regularization improves single particle cryo-EM reconstruction

Ali Punjani; Haowei Zhang; David J. Fleet

Local resolution estimates [8, 2] or local statistical tests [23] can also be used to adaptively filter a 3D map. This technique is used extensively for visualization, for assessing map quality in different regions of a particle, and during molecular model building. The family of filters and local filter band-limits are typically selected to maximize subjective visual quality and are therefore not optimized against the estimator used to determine local resolution. Considerations are also not made in this technique to control the number of degrees of freedom or model complexity of the local filter parameters. Furthermore, information from opposite half-set reconstructions is typically shared, breaking independence. While local resolution estimation followed by local filtering is generally satisfactory as a one-time post-processing 15 . CC-BY-NC-ND 4.0 International license author/funder. It is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2019.12.15.877092 doi: bioRxiv preprint Non-uniform refinement: cross-validation optimal filtering Iterative local resolution estimation + local filtering A B step for visualization, in our experience it can lead to severe over-fitting when used iteratively in a refinement as a substitute for the regularization step in Alg. 1. Figure 8 gives an example of the over-fitting that often occurs. During iterative refinement, small mis-estimations of local resolution at a few locations (due to high estimator variance [2] ) cause subtle over-or under-fitting, leaving slight density variations. Over multiple iterations of refinement, these errors can produce strong erroneous density that contaminate particle alignments and the local estimation of resolution itself, creating a vicious cycle. A related technique using iterative local resolution and filtering was described briefly in EMAN2.2 documentation [1] and may suffer the same problem. The resulting artefacts (e.g., streaking and spikey density radiating from the structure) are particularly prevalent in datasets with junk particles, structured outliers, or small particles that are already difficult to align. To mitigate these problems, the approach we advocate couples an implicit resolution measure to a particular choice of local regularizer, with optimization explicitly designed to control model capacity and avoid over-fitting of regularizer parameters. Another related technique, used in cisTEM [11] and its predecessor Frealign [12] , entails the manual creation of a mask to directly label a region of a structure that one expects to be disordered (eg., a detergent micelle), followed by low-pass filtering in that region to a single pre-set resolution at each iteration of refinement. This technique, one of the first to acknowledge and address the issue of simultaneous under-and over-fitting, shares the same intuitions behind non-uniform refinement. Nevertheless, it relies on manual decisions about how to regularize a map during refinement. Refinement is sensitive to regularization, and manual choices necessitate a trial and error process that can be tedious and difficult to replicate across datasets or by others.