Flexible helical protein polymers exemplified by actin filaments, microtubules and bacterial flagella areubiquitous in biology. Due to their size and intrinsic irregularities, the structure of these polymers cannot be solved by Xraycrystallography. Since half a century, three-dimensional (3D) reconstruction from two-dimensional (2D) ElectronMicroscopy (EM) images appears as a method of choice to solve the structure of large helical polymers. However,depending on the degree of flexibility of the analyzed helices, the 3D reconstruction process can still be a daunting task.For the most regular helices, the classical reciprocal space-based Fourier-Bessel approach can allow both to determinethe helical symmetry and to calculate 3D structures. For more flexible structures, recent “single-particle” approachesconsist in segmentation of long irregular helices into short (i.e. locally more regular) segments and their processing asasymmetrical objects with defined symmetry-imposed constraints (Egelman, 2000; Sachse et al., 2007). However, twomajor difficulties remain: the heterogeneous data must be sorted into homogeneous populations and the helical symmetryfor each population has to be determined. In the presented work, we explored various single-particle approaches,developed new analysis methods, and implemented most of them into a user-friendly processing pipeline. The targetbiological objects were helical nucleocapsids of two negative strand RNA viruses, Measles (MeV) and VesicularStomatitis Virus (VSV ; the prototype for Rabies), the latter being particularly flexible in terms of helical parameters(diameter, number of subunits per turn). Nucleocapsids are formed by the viral genomic RNA coated by thenucleoprotein and serve as a template for viral replication and transcription. To overcome the heterogeneity problem, weused 2D classification, described general processing protocols and applications for helical segments, and introduced anew classification method based on the power spectra of the images. The determination of helical symmetry(ies) wasaddressed by a novel approach relying on ab initio exhaustive search of helical parameters whereby we start from asingle 2D image, reconstruct as many 3D structures as parameters to test by cropping the image and assigning views tothe obtained segments, and calculate the cross-correlation (CC) of the reprojection of the 3D model with the initialimage. Applied to artificial data sets, the method was effectively able to detect a maximum of CC for the true symmetryparameters, but also showed intrinsic ambiguities of helical symmetry determination on which we extensively comment.Altogether, the result of this method-oriented work allowed us to address several biological questions. First, the 3Dreconstruction by negative stain EM of two forms of nucleocapsids of MeV coupled to a docking of a homologouscrystal structure enabled us to determine the orientation of the nucleoprotein and of the RNA in the nucleocapsids.Secondly, we assessed the structure of in vitro formed nucleocapsids of VSV and showed that assemblies close to thenative viral nucleocapsids can be formed in the absence of any other viral proteins, thus providing new insights into theassembly of this virus. As a perspective of this work, our pipeline of flexible helical analysis is being extended andsuccessfully used for other projects.
