Abstract
Structural biology has evolved greatly due to the advances introduced in fields like electron microscopy. This image-capturing technique, combined with improved algorithms and current data processing software, allows the recovery of different conformational states of a macromolecule, opening new possibilities for the study of its flexibility and dynamic events. However, the ensemble analysis of these different conformations, and in particular their placement into a common variable space in which the differences and similarities can be easily recognized, is not an easy matter. To simplify the analysis of continuous heterogeneity data, this work proposes a new automatic algorithm that relies on a mathematical basis defined over the sphere to estimate the deformation fields describing conformational transitions among different structures. Thanks to the approximation of these deformation fields, it is possible to describe the forces acting on the molecules due to the presence of different motions. It is also possible to represent and compare several structures in a low-dimensional mapping, which summarizes the structural characteristics of different states. All these analyses are integrated into a common framework, providing the user with the ability to combine them seamlessly. In addition, this new approach is a significant step forward compared with principal component analysis and normal mode analysis of cryo-electron microscopy maps, avoiding the need to select components or modes and producing localized analysis.
Highlights
The application in electron microscopy of techniques such as cryo-electron microscopy, single-particle analysis (SPA) (Carroni & Saibil, 2016) or electron cryo-tomography (Schur, 2019) has proven to be a versatile tool to trace highresolution structures
Full details are provided in Appendices A and B, here it suffices to say that we use a generalized form of Zernike polynomials to expand functions on a ball
We conclude that the new approach is capable of reproducing the results of previous supervised methods that perform similar analyses and accurately groups the seven cryo-electron microscopy (cryo-EM) structures [indicated by their EMDB (Electron Microscopy Data Bank, https://www.ebi.ac.uk/emdb/) identification numbers] into two groups of conformers, each representative of a different functional state
Summary
The application in electron microscopy of techniques such as cryo-electron microscopy (cryo-EM), single-particle analysis (SPA) (Carroni & Saibil, 2016) or electron cryo-tomography (Schur, 2019) has proven to be a versatile tool to trace highresolution structures. Cryo-EM SPA has proven to be especially good at providing one structure, but a series of them, with most methods aiming to resolve stable states that are referred to as classes. In this way, we get a first approximation to the conformational landscape of the macromolecule, albeit restricted to these stable states. The complete characterization of a conformational landscape can only be achieved through the analysis of multiple transient and stable states needed to describe the molecular flexibility in a more accurate manner The knowledge of these transient and stable states leads to a better description of how structural
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