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.

Centro Nacional de Biotecnologia CSIC C Darwin 3 Cantoblanco Madrid 28049 Spain

Department of Computational and Systems Biology University of Pittsburgh Pennsylvania USA

Department of Statistics and Data Science Yale University New Haven Connecticut USA

Faculty of Informatics Masaryk University Botanická 68a 60200 Brno Czech Republic

Institute of Computer Science Masaryk University Botanická 68a 60200 Brno Czech Republic

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Estimating conformational landscapes from Cryo-EM particles by 3D Zernike polynomials