Molecule Mechanics from Cryo-EM Images and Multiple Reconstructed Densities

Abstract

After the resolution revolution, cryo-EM moves from sets of individual structures, to understanding properties of biological samples as a whole, like pathways between resolved structures and binding affinities. Extracting these molecule mechanics as probability distribution of arbitrary observables, like open and close configuation, or small molecule binding probabilities however, is still challenging despite increasing resolution and numbers of resolved structures of a single complex, due to the non-trivial connection three dimensional structures and all the possible molecule conformations they represent. Here, we present how to resolve all molecule conformations that are represented by three dimensional structures and pathways between multiple reconstructed densities. The opening and closing dynamics of adenylate kinase are used to verify our the method, using ensemble-averaged density maps of open and closed state. In the ribosome-selB complex, our method further refines structural transitions for GTPase activation. In our work, the free energy for each molecule conformation under a cryo-EM experiment is derived from a probabilistic formulation of the complete cryo-EM measurement process. It is shown why a set of reconstructed densities is a good approximation to the rigorous but computationally challenging calculation of conformation weights from all cryo-EM images. It is found that morphing densities and refining structures into cryo-EM maps is tightly coupled through the measure of goodness-of-fit. With these insights, we asess how much of all underlying configurations are represented by single densities and sample pathways between densities, that represent physical intermediate states of the ribosome-selB complex upon GTPase activation.