SCT: a suite of programs for comparing atomistic models with small-angle scattering data

Abstract

Small-angle X-ray and neutron scattering techniques characterize proteins in solution and complement high-resolution structural studies. They are of particular utility when large proteins cannot be crystallized or when the structure is altered by solution conditions. Atomistic models of the averaged structure can be generated through constrained modelling, a technique in which known domain or subunit structures are combined with linker models to produce candidate global conformations. By randomizing the configuration adopted by the different elements of the model, thousands of candidate structures are produced. Next, theoretical scattering curves are generated for each model for trial-and-error fits to the experimental data. From these, a small family of best-fit models is identified. In order to facilitate both the computation of theoretical scattering curves from atomistic models and their comparison with experiment, the SCT suite of tools was developed. SCT also includes programs that provide sequence-based estimates of protein volume (either incorporating hydration or not) and add a hydration layer to models for X-ray scattering modelling. The original SCT software, written in Fortran, resulted in the first atomistic scattering structures to be deposited in the Protein Data Bank, and 77 structures for antibodies, complement proteins and anionic oligosaccharides were determined between 1998 and 2014. For the first time, this software is publicly available, alongside an easier-to-use reimplementation of the same algorithms in Python. Both versions of SCT have been released as open-source software under the Apache 2 license and are available for download from https://github.com/dww100/sct.

Keywords: X-ray scattering; analytical ultracentrifugation; constrained modelling; hydration shells; neutron scattering.

Figure 1

Schematic representation of a scattering experiment. (a) An incident beam is shown scattering from two point scatterers (represented by the black dots) within a globular macromolecule. The diffracted rays are in phase with each other but out of step by λ at the scattering angle shown, causing constructive interference. The accumulation of these events at low angles gives rise to the scattering pattern of the macromolecule. (b) In a typical small-angle scattering experiment, diffraction from high-scattering-density macromolecules in a low-scattering-density solution gives rise to a scattering pattern on an area detector. q is the scattering vector . The radial average of the scattering pattern about the position of the direct main beam gives rise to the scattering curve in reciprocal space.

Figure 2

Constrained modelling algorithm in SCT. First, candidate full atomistic structures of the target macromolecule are generated. That illustrated is for human IgA1, taken from Boehm et al. (1999 ▶). A grid transformation is performed on each structure to produce a lower-resolution (coarse-grained) sphere model, which is used to calculate a theoretical scattering curve via the Debye equation. The R factor determines if the theoretical curve reproduces the experimental curve in the same Q range. Models with low R factors are inferred to represent the average solution structure.

Figure 3

Grid transformation algorithms in SCT. (a) A two-dimensional schematic of the grid conversion shows how coarse-grained sphere models are derived from atomistic structures. A grid of equal divisions is created that contains all atoms within the input structure. If more than a specified cutoff number of atoms is found within a division, a ‘sphere’ is added to the final model with a radius of half the grid box width. This algorithm is applied in three dimensions to create sphere models from atomistic structures. (b) This schematic shows how up to 26 hydration spheres as required are added to each existing sphere in the ‘dry’ model to produce a hydrated sphere model. Hydration spheres are located on the corners and mid-points of the sides of a cube, with a dimension of four times the sphere radius (r). The original sphere is shown in green, with the hydration locations in black. (c) A hydration layer is required when modelling X-ray scattering data. The hydration layer of water molecules at the surface is added by surrounding each green sphere in the coarse-grained sphere model of the dry protein (top view) with blue hydration spheres of the same radius as shown (middle view). Overlapping and excess blue hydration spheres are subsequently filtered out to match the hydrated volume calculated from the macromolecular sequence, as shown at the bottom.

Figure 4

Comparison of neutron and X-ray scattering data with models of human immunoglobulin IgG4 composed of Fab and Fc regions (Rayner et al., 2014 ▶). (a) Atomistic structures of an extended asymmetric (left) and a compact asymmetric (right) IgG4 model. In these, the Fc region is viewed in a similar orientation. (b), (c) Comparisons of the calculated scattering curves for sphere models generated by SCT from the atomistic models with neutron and X-ray experimental data, respectively. The Q range is depicted from 0.2 to 1.6 nm⁻¹. In both cases, the compact asymmetric model (blue curve: PDB code 4pto) gives good fits to the experimental data, whereas the extended model (red curve) does not.