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The final publication is available at Springer via http://dx.doi.org/10.1007/s10479-006-0078-8 ; Electron Microscopy is a valuable tool for the elucidation of the three-dimensional structure of macromolecular complexes. Knowledge about the macromolecular structure provides important information about its function and how it is carried out. This work addresses the issue of three-dimensional reconstruction of biological macromolecules from electron microscopy images. In particular, it focuses on a methodology known as "single-particles" and makes a thorough review of all those steps that can be expressed as an optimization problem. In spite of important advances in recent years, there are still unresolved challenges in the field that offer an excellent testbed for new and more powerful optimization techniques. ; We acknowledge partial support from the "Comunidad Autónoma de Madrid" through grants CAM-07B-0032-2002, GR/SAL/0653/2004 and GR/SAL/0342/2004, the "Comisión Interministerial de Ciencia yTecnologia" of Spain through grants BIO2001-1237, BIO2001-4253-E, BIO2001-4339-E, BIO2002- 10855-E, BFU2004-00217/BMC, the Spanish FIS grant (G03/185), the European Union through grants QLK2- 2000-00634, QLRI-2000-31237, QLRT-2000-0136, QLRI-2001-00015, FP6-502828 and the NIH through grant HL70472. Alberto Pascual and Roberto Marabini acknowledge support by the Spanish Ramon y Cajal Program.

The source code (LocalDeblur) can be found at https://github.com/I2PC/xmipp and can be run using Scipion (http://scipion.cnb.csic.es) (release numbers greater than or equal 1.2.1) ; Recent technological advances and computational developments have allowed the reconstruction of Cryo-Electron Microscopy (cryo-EM) maps at near-atomic resolution. On a typical workflow and once the cryo-EM map has been calculated, a sharpening process is usually performed to enhance map visualization, a step that has proven very important in the key task of structural modeling. However, sharpening approaches, in general, neglects the local quality of the map, which is clearly suboptimal. Results Here, a new method for local sharpening of cryo-EM density maps is proposed. The algorithm, named LocalDeblur, is based on a local resolution-guided Wiener restoration approach of the original map. The method is fully automatic and, from the user point of view, virtually parameter-free, without requiring either a starting model or introducing any additional structure factor correction or boosting. Results clearly show a significant impact on map interpretability, greatly helping modeling. In particular, this local sharpening approach is especially suitable for maps that present a broad resolution range, as is often the case for membrane proteins or macromolecules with high flexibility, all of them otherwise very suitable and interesting specimens for cryo-EM. To our knowledge, and leaving out the use of local filters, it represents the first application of local resolution in cryo-EM sharpening ; The authors would like to acknowledge economical support from: the Comunidad de Madrid through grant CAM (S2017/BMD-3817), the Spanish Ministry of Economy and Competitiveness (BIO2016-76400-R) and the European Union and Horizon 2020 through grants INSTRUCT-ULTRA (INFRADEV-03-2016-2017, Proposal: 731005) and iNEXT (INFRAIA-1-2014-2015, Proposal: 653706)

We have developed a new data collection method and processing framework in full field cryo soft X-ray tomography to computationally extend the depth of field (DOF) of a Fresnel zone plate lens. Structural features of 3D-reconstructed eukaryotic cells that are affected by DOF artifacts in standard reconstruction are now recovered. This approach, based on focal series projections, is easily applicable with closed expressions to select specific data acquisition parameters. ; This work was partially supported by MINECO grants BFU2014-54181 to JLC and AIC-A-2011-0638, BIO2013-44647-R and BIO2016-76400-R to JMC, Madrid. Regional government grants S2013/MIT-2850 to JLC and S2010/BMD-2305 to JMC, National Science Foundation grant DMS-1114901 to GTH, the European Union through BioStruct-X Project 283570 and Horizon 2020 through grant iNEXT (INFRAIA-1-2014-2015, Proposal: 653706). ; Sí

Using a new consensus-based image-processing approach together with principal component analysis, the flexibility and conformational dynamics of the SARS-CoV-2 spike in the prefusion state have been analysed. These studies revealed concerted motions involving the receptor-binding domain (RBD), N-terminal domain, and subdomains 1 and 2 around the previously characterized 1-RBD-up state, which have been modeled as elastic deformations. It is shown that in this data set there are not well defined, stable spike conformations, but virtually a continuum of states. An ensemble map was obtained with minimum bias, from which the extremes of the change along the direction of maximal variance were modeled by flexible fitting. The results provide a warning of the potential image-processing classification instability of these complicated data sets, which has a direct impact on the interpretability of the results. ; The authors would like to acknowledge financial support from CSIC (PIE/COVID-19 No. 202020E079), the Comunidad de Madrid through grant CAM (S2017/BMD-3817), the Spanish Ministry of Science and Innovation through projects SEV 2017-0712, FPU-2015/264 and PID2019-104757RB-I00/AEI/ FEDER, the Instituto de Salud Carlos III [PT17/0009/0010 (ISCIII-SGEFI/ERDF)], and the European Union and Horizon 2020 through grants INSTRUCT–ULTRA (INFRADEV-03-2016-2017, Proposal 731005), EOSC Life (INFRAEOSC-04-2018, Proposal 824087), HighResCells (ERC-2018-SyG, Proposal 810057), IMpaCT (WIDESPREAD- 03-2018, Proposal 857203), CORBEL (INFRADEV-1-2014-1, Proposal 654248) and EOSC–Synergy (EINFRA-EOSC-5, Proposal 857647). HDT and BF were supported by NIH grant GM125769 and JSM was supported by NIH grant R01-AI127521