Remarkably, uniform virus-like particles self-assemble in a process that appears to follow a rapid kinetic mechanism. The mechanisms by which spherical viruses assemble from hundreds of capsid proteins around nucleic acid, however, are yet unresolved. Using Time-Resolved Small-Angle X-ray Scattering (TR-SAXS) we have been able to directly visualize SV40 VP1 pentamers encapsidating short RNA molecules (500 mers). This assembly process yields T = 1 icosahedral particles comprised of 12 pentamers and one RNA molecule. The reaction is nearly 1/3 complete within 35 milliseconds, following a two–state kinetic process with no detectable intermediates. Theoretical analysis of kinetics, using a master equation, shows that the assembly process nucleates at the RNA and continues by a cascade of elongation reactions in which one VP1 pentamer is added at a time, with a rate of approximately 109 M−1 s−1. The reaction is highly robust and faster than the predicted diffusion limit. The emerging molecular mechanism, which appears to be general to viruses that assemble around nucleic acids, implicates long-ranged electrostatic interactions. The model proposes that the growing nucleo-protein complex acts as an electrostatic antenna that attracts other capsid subunits for the encapsidation process.

X+ is a user‐friendly multi‐core accelerated program that fully analyses solution X‐ray scattering radially integrated images. This software is particularly useful for analysing supramolecular self‐assemblies, often found in biology, and for reconstructing the scattering signal in its entirety. The program enables various ways of subtracting background noise. The user selects a geometric model and defines as many layers of that shape as needed. The thickness and electron density of each layer are the fitting parameters. An initial guess is input by the user and the program calculates the form‐factor parameters that best fit the data. The polydispersity of one size parameter at a time can be taken into account. The program can then address the assembly of those shapes into different lattice symmetries. This is accounted for by fitting the parameters of the structure factor, using various peak line shapes. The models of the program and selected features are presented. Among them are the model‐fitting procedure, which includes both absolute and relative constraints, data smoothing, signal decomposition for separation of form and structure factors, goodness‐of‐fit verification procedures, error estimation, and automatic feature recognition in the data, such as correlation peaks and baseline. The program's intuitive graphical user interface runs on Windows PCs. Using X+, the exact structure of a microtubule in a crowded environment, and the structure, domain size, and elastic and interaction parameters of lipid bilayers, were obtained.

In this paper, the analysis of several involved models, relevant for evaluating solution X-ray scattering form factors of supramolecular self-assembled structures, is presented. Different geometrical models are discussed, and the scattering form factors of several layers of those shapes are evaluated. The thickness and the electron density of each layer are parameters in those models. The models include Gaussian electron density profiles and/or uniform electron density profiles at each layer. Various forms of cuboid, layered, spherical, cylindrical, and helical structures are carefully treated. The orientation-averaged scattering intensities of those form factors are calculated. Similar classes of form factors are examined and compared, and their fit to scattering data of lipid bilayers, capsids of the Simian virus 40 virus-like particle and microtubule is discussed. A more detailed model of discrete helices composed of uniform spheres was derived and compared to solution X-ray scattering data of microtubules. Our analyses show that when high-resolution data are available the more detailed models with Gaussian electron density profiles or helical structures composed of spheres should be used to better capture all the elements in the scattering curves. The models presented in this paper may also be applied, with minor corrections, for the analysis of solution neutron scattering data.

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In many biochemical processes large biomolecular assemblies play important roles. X-ray scattering is a label-free bulk method that can probe the structure of large self-assembled complexes in solution. As we demonstrate in this paper, solution X-ray scattering can measure complex supramolecular assemblies at high sensitivity and resolution. At high resolution, however, data analysis of larger complexes is computationally demanding. We present an efficient method to compute the scattering curves from complex structures over a wide range of scattering angles. In our computational method, structures are defined as hierarchical trees in which repeating subunits are docked into their assembly symmetries, describing the manner subunits repeat in the structure (in other words, the locations and orientations of the repeating subunits). The amplitude of the assembly is calculated by computing the amplitudes of the basic subunits on 3D reciprocal-space grids, moving up in the hierarchy, calculating the grids of larger structures, and repeating this process for all the leaves and nodes of the tree. For very large structures, we developed a hybrid method that sums grids of smaller subunits in order to avoid numerical artifacts. We developed protocols for obtaining high-resolution solution X-ray scattering data from taxol-free microtubules at a wide range of scattering angles. We then validated our method by adequately modeling these high-resolution data. The higher speed and accuracy of our method, over existing methods, is demonstrated for smaller structures: short microtubule and tobacco mosaic virus. Our algorithm may be integrated into various structure prediction computational tools, simulations, and theoretical models, and provide means for testing their predicted structural model, by calculating the expected X-ray scattering curve and comparing with experimental data.