Voronoi diagram-based compensation of preferred particle orientations in cryo-EM 3D reconstructions

To reveal functional properties of biological complexes using single-particle cryo electron microscopy (cryo-EM), it is important to obtain maps without distortions. 3D reconstructions can be obtained from back-projection of the individual 2D projections of the particles, a concept that assumes equally distributed orientations. However, most biological samples exhibit preferential views due to preferred particle orientations, e.g., at the air–water interface or on a carbon surface of a cryo-EM grid. Here, we present a method based on Voronoi diagrams that takes into account the Euler angle distribution of particles through individual image weighting, thus reducing 3D reconstruction artefacts emanating from preferential particle orientations. Voronoi diagrams are built from the Euler angle values plotted on a sphere in order to graphically display particle orientations, and the assignment of the projection weights is then calculated, being proportional to the individual Voronoi polygon areas. We implemented this real-space approach into a 3D reconstruction routine that allows performing automated weighting. The method was validated using a back-projection algorithm on synthetic model data and on real experimental data with different point group symmetries and in the presence or absence of preferential views, revealing a particular benefit for asymmetric objects.