Cross-validation in cryo-EM-based structural modeling

Single-particle cryo-electron microscopy (cryo-EM) is a powerful approach to determine the structure of large macromolecules and assemblies thereof in many cases at subnanometer resolution. It has become popular to refine or flexibly fit atomic models into density maps derived from cryo-EM experiments. These density maps are typically significantly lower in resolution than electron density maps obtained from X-ray diffraction experiments, such that the number of parameters that need to be determined is much larger than the number of experimental observables. Overfitting and misinterpretation of the density, thus, becomes a serious problem. For diffraction data a cross-validation approach has been introduced almost twenty years ago, however, no such approach has been described yet for structure refinement against cryo-EM density maps, even though the overfitting problem is, due to the lower resolution, significantly larger. We present a cross-validation approach for real-space refinement against cryo-EM density maps in analogy to cross-validation typically used in crystallography. Our approach is able to detect overfitting and allows for optimizing the choice of restraints used in the refinement. The approach is demonstrated on three protein structures with simulated data and on experimental data of the rotavirus double-layer particle. Since cross-validation requires splitting the data set into at least two independent sets, we further present an approach to quantify correlations between the structure factor sets. This analysis is also helpful for other cross-validation applications, such as refinements against diffraction data or 3D reconstructions of cryo-EM density maps