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

Ali Punjani; Haowei Zhang; David J. Fleet

Single particle cryogenic electron microscopy (cryo-EM) is a rapidly advancing technique for determining high resolution 3D structures of proteins and protein complexes. There are several reasons that cryo-EM has become a tool of choice for recent structural biology projects [5] , but key among them is the fact that cryo-EM can be used to study classes of proteins for which other techniques (e.g., X-ray crystallography and nuclear magnetic resonance) are not effective. These include membrane proteins, proteins larger than ∼30kDa with multiple conformational states, or with flexible or disordered domains. In all of these cases, the proteins are composed of regions with varying structural properties. Membrane proteins in particular are often encapsulated in detergent micelles or lipid nanodiscs, creating a large disordered region of density around the hydrophobic region of the protein. Despite the common occurrence of such spatial variability, most state-of-the-art 3D refinement algorithms are based on the mathematical assumption of uniformity (rigidity) of the particle. This paper formulates a cross-validation regularization framework for single particle cryo-EM refinement, one that explicitly provides for the spatial inhomogeneity generated by various physical phenomena (disorder, motion, occupancy, etc) found in a typical molecular complex. Our proposed framework incorporates general domain knowledge about proteins, without specific knowledge of any particular molecule. Within this framework we derive a novel refinement algorithm, called non-uniform refinement, that accounts for structural variability, while taking care to ensure that the algorithm retains favourable statistical properties for validation and that it does not introduce avenues for over-fitting during 3D reconstruction.