2.5. Analysis of SAXS Data

The raw two-dimensional scattering data were processed through a number of steps. First, the raw SAXS data frames were reduced by intensity normalization (using scattering by water to place data on an absolute scale), background subtraction, and scattering vector calibration using SCATTERBRAIN 2.82 program (http://archive.synchrotron.org.au/aussyncbeamlines/saxswaxs/software-saxswaxs). A SAXS profile plot was then derived by plotting the normalized integrated intensity of the scattering signal against the frame number using CHROMIX (ATSAS 2.8.3 suite [66]) (see Scheme 2). If the profile indicated that the sample eluted as a homogeneous single species off the SEC column, then the scattering data were processed into a 1D-scattering curve. However, if the sample contained partially unresolved multiple species, then its scattering data was first deconvoluted before proceeding with further analysis. Simple deconvolution involved using SVD/EFA BioXTAS RAW [67], where the singular value decomposition (SVD) function defined the number of components in the sample (referred to as eigenvalues). Then the evolving factor analysis (EFA) method was utilized to define the boundaries and extract the scattering curves of each component.

The frames of interest were first averaged and subtracted from the buffer frames using CHROMIX. Then the processed scattering data were transformed into a 1D-scattering curve using the PRIMUSQT program from ATSAS 2.8.3 suite [66], where log of scattering intensity (log(I)) was plotted against the scattering vector q = 4πλ⁻¹sinθ, in which 2θ represents the scattering angle, and λ defines the x-ray wavelength of 1.0332 Å) (Scheme 2).

Characteristic parameters can be retrieved from the scattering pattern of the samples that describe the homogeneity, fold, size, and overall shape of the sample (Scheme 3). Analysis was conducted using programs within the PRIMUSQT ATSAS 2.8.3 suite [66]. Initially, the 1D-scattering curve is converted into a double logarithmic plot to highlight that the low-q data has an artefact free profile, a plateau, consistent with a monodisperse protein sample. Plotting low q data using the Guinier distribution analysis (log(I) vs q²) through the AUTORG method allows estimation of the radius of gyration (Rg) and the extrapolated intensity at zero scattering angle I(0), describing the overall size of the molecule. The assumption of a globular shape for the Guinier plot is valid when qRg ≤ 1.3 (denoted q·Rg max) and the Guinier analysis is linear, which is also consistent with a profile of a monodisperse protein sample. Next, the data are converted into a Kratky plot (I·q² vs q) to assess the shape and fold of the molecule. In addition, the Kratky plot provides information regarding the oligomeric state of the molecule [68]. An indirect inverse Fourier transformation of the scattering data performed using AUTOGNOM results in the pairwise distribution function P(r) curve, which represents the distribution of interatomic distances (r) within the molecule. The molecule’s maximum diameter (D_max) can be determined from the P(r) curve as P(r) approaches zero at r >> 0 (Scheme 3).

Furthermore, the Rg and I(0) can be accurately calculated from the P(r) curve using all the experimental data, unlike the Guinier analysis, which uses only a small subset at low q. The excluded particle volume (also termed Porod volume, V) is calculated through the DATPOROD program using I(0) values attained from the P(r) plot (Scheme 3). The Porod volume (V) can then be used to directly estimate the molecular weight (MW in Daltons) of the solute (MW ≈ V (in ų)·(average protein density ~1.1 g·cm⁻³)·N_A(in mol⁻¹)·1 × 10⁻²⁴ ų/cm³) ≈ V·0.6) [69] providing valuable information about the oligomeric state of the molecule (Scheme 3). Furthermore, the MW can also be calculated from I(0) if the concentration is accurately known using a previously described method [70].

Low-resolution 3D-models can then be computed through ab initio shape restoration using the DAMMIF program by applying restraints of biophysical parameters attained from the 1D scattering curve. The assumption that scattering by the oligonucleotide can with negligible error be treated as scattering by the protein is justified as follows. The 9-mer oligonucleotide (formula; C₈₉H₁₂₅N₂₄O₆₃P₉) used has intrinsic scattering of X-rays, F₀₀₀, of 1450 e^-; the protein (formula C₁₁₀₂H₁₆₃₂N₃₀₂O₃₀₅S₁₃Zn) has F₀₀₀ of 13,036 e^- (give or take a few electrons of water tightly associated with the protein, and to a lesser extent with the partly buried oligonucleotide). Now, assuming equal volumes per non-hydrogen atom and reconfiguring the oligonucleotide to have the protein composition of the A3B_CTD, gives then a difference in scattering of just 256 e^- more for the oligonucleotide than if it had been protein. This difference is insignificant in comparison to the total scattering of 14,486 e-. However, it is important to note that the total scattering of the oligonucleotide is highly significant at just over 1/10th that of the protein and thus is potentially observable. Thus, for calculation of molecular envelopes protein-only was assumed. The DAMMIF program first generates several models, which are then averaged (DAMAVER) and are further filtered by cut-off volume constraints based on derived SAXS analysis parameters (DAMFILT) to produce the dummy filled models. The normalized spatial discrepancy (NSD) score quantitatively measures the similarities between the generated set of 3D envelope models, where NSD ≤ 0.9 is an acceptable variance [71,72]. These envelope models can be superimposed with atomic models to assemble a high-resolution model. Lastly, rigid body modelling is conducted using FoXS [73,74] and CRYSOL [66] (corrected for standard error) by comparing the experimental scattering data to the back-calculated 1D-scattering profiles of atomic structures or model structures, to validate the model. From these programs a fitting parameter termed the Chi² value (also called χ²) can be obtained. Chi² gives a measure of the discrepancies between the experimental scattering data and the back-calculated 1D-scattering profiles of atomic structures; a Chi² equal to one would indicate a perfect fit.