A Computational Modeling of Macromolecular Ensemble Conformation and Blurring in Cryo EM

It is well known that Cryo EM results in 3D construction in which subnuits of a macromolecular complex may appear to be blurred and bloated. This issue affects the accuracy of positional and orientational information about the subnits extracted from such reconstructions. The blurring can be due to classification or averaging steps in the analysis or due to mobility of the quaternary macromolecular structure. Such effects cannot be captured by traditional models of EM. In this paper we propose a mathematical framework and algorithm to model this phenomenon. We use clustering methods such as the K-means algorithm to roughly resolve the different rigid subunits in the 3D density obtained from a macromolecular complex. Then we model the blurring effect in each (resolved) submit as an ensemble of rigid body motions (i.e., orientations and translations), specifically we use the Gaussian probability density (with unknown covariance and mean) on the group of rigid body motions in 3D. We relate the shape of each resolved (blurred) subunit to the unknown parameters of the Gaussian using the known structure of the subnit (from PDB). This gives a system of equations with unknowns being the parameters of the Gaussian. The system, in general, is underdetermined, however, we impose physically meaningful regularization constraints to obtain unique solutions. Thereby we are able to obtain more accurate orientation and positional information. We show the performance of the algorithm on simulated data. We also discuss prospect of this method in combination (or fusion) with SAXS data in order to reinforce information from both modalities.