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

Ali Punjani; Haowei Zhang; David J. Fleet

Iterative refinement methods (Algorithm 1), which provide state of the art results (e.g., [1, 11, 22, 35] ), can be interpreted as variants of block-coordinate descent or the expectation-maximization algorithm [7] , performing maximum-likelihood or maximum-a-posteriori estimation of model parameters from obser- Figure 1 : A 3D map from uniform iterative refinement (in cryoSPARC) reveals spatial variations in structure properties in a prototypical membrane protein (TRPA1 ion channel, EMPIAR-10024 [21] ). The density map is shown with a low threshold, where color depicts local resolution [2] as a proxy for local structure properties. The core inner region (red) is more rigid and resolved to higher resolution. The solvent facing region (yellow) is less well ordered. The detergent micelle (light blue) is largely disordered. A flexible tail at the bottom (blue) is blurred due to motion. In uniform refinement, a shift-invariant regularizer smooths all regions equally. This uniformity leaves high frequency noise to accumulate in disordered regions (under-regularization), while discarding resolvable signal in rigid regions (over-regularization). Non-uniform refinement is designed to alleviate these problems.