Virus-like particles (VLPs) are noninfectious nanocapsules that can be used for drug delivery or vaccine applications. VLPs can be assembled from virus capsid proteins around a condensing agent, such as RNA, DNA, or a charged polymer. Electrostatic interactions play an important role in the assembly reaction. VLPs assemble from many copies of capsid protein, with a combinatorial number of intermediates. Hence, the mechanism of the reaction is poorly understood. In this paper, we combined solution small-angle X-ray scattering (SAXS), cryo-transmission electron microscopy (TEM), and computational modeling to determine the effect of ionic strength on the assembly of Simian Vacuolating Virus 40 (SV40)-like particles. We mixed poly(styrene sulfonate) with SV40 capsid protein pentamers at different ionic strengths. We then characterized the assembly product by SAXS and cryo-TEM. To analyze the data, we performed Langevin dynamics simulations using a coarse-grained model that revealed incomplete, asymmetric VLP structures consistent with the experimental data. We found that close to physiological ionic strength, $$T=1$$VLPs coexisted with VP1 pentamers. At lower or higher ionic strengths, incomplete particles coexisted with pentamers and $$T=1$$particles. Including the simulated structures was essential to explain the SAXS data in a manner that is consistent with the cryo-TEM images.

The current challenges of structural biophysics include determining the structure of large self-assembled complexes, resolving the structure of ensembles of complex structures and their mass fraction, and unraveling the dynamic pathways and mechanisms leading to the formation of complex structures from their subunits. Modern synchrotron solution X-ray scattering data enable simultaneous high-spatial and high-temporal structural data required to address the current challenges of structural biophysics. These data are complementary to crystallography, NMR, and cryo-TEM data. However, the analysis of solution scattering data is challenging; hence many different analysis tools, listed in the SAS Portal (http://smallangle.org/), were developed. In this review, we start by briefly summarizing classical X-ray scattering analyses providing insight into fundamental structural and interaction parameters. We then describe recent developments, integrating simulations, theory, and advanced X-ray scattering modeling, providing unique insights into the structure, energetics, and dynamics of self-assembled complexes. The structural information is essential for understanding the underlying physical chemistry principles leading to self-assembled supramolecular architectures and computational structural refinement.

This article presents an upgrade of the ıt D}+ software [Ginsburg ıt et al.} (2019). ıt J. Appl. Cryst.} \bf 52, 219–242], expanding its hierarchical solution X-ray scattering modeling capabilities for fiber diffraction and single crystallographic orientations. This upgrade was carried out using the reciprocal grid algorithm [Ginsburg ıt et al.} (2016). ıt J. Chem. Inf. Model.} \bf 56, 1518–1527], providing ıt D}+ its computational strength. Furthermore, the extensive modifications made to the Python API of ıt D}+ are described, broadening the X-ray analysis performed with ıt D}+ to account for the effects of the instrument-resolution function and polydispersity. In addition, structure-factor and radial-distribution-function modules were added, taking into account the effects of thermal fluctuations and intermolecular interactions. Finally, numerical examples demonstrate the usage and potential of the added features.

{Virus-like particles (VLPs) are noninfectious nanocapsules that can be used for drug delivery or vaccine applications. VLPs can be assembled from virus capsid proteins around a condensing agent like RNA, DNA, or a charged polymer. Electrostatic interactions play an important role in the assembly reaction. VLPs assemble from many copies of capsid protein, with combinatorial intermediates, and therefore the mechanism of the reaction is poorly understood. In this paper, we determined the effect of ionic strength on the assembly of Simian Vacuolating Virus 40 (SV40)-like particles. We mixed poly(styrene sulfonate) with SV40 capsid protein pentamers at different ionic strengths. We then characterized the assembly product by solution small-angle X-ray scattering (SAXS) and cryo-TEM. To analyze the data, we performed Brownian dynamics simulations using a coarse-grained model that revealed incomplete, asymmetric VLP structures that were consistent with the experimental data. We found that close to physiological ionic strength