Anomalous Small Angle X-Ray Scattering Simulations: Proof of Concept for Distance Measurements for Nanoparticle-Labelled Biomacromolecules in Solution

Abstract

Anomalous small angle X-ray scattering can in principle be used to determine distances between metal label species on biological molecules. Previous experimental studies in the past were unable to distinguish the label-label scattering contribution from that of the molecule, because of the use of atomic labels; these labels contribute only a small proportion of the total scattering signal. However, with the development of nanocrystal labels (of 50–100 atoms) there is the possibility for a renewed attempt at applying anomalous small angle X-ray scattering for distance measurement. This is because the contribution to the scattered signal is necessarily considerably stronger than for atomic labels. Here we demonstrate through simulations, the feasibility of the technique to determine the end-to-end distances of labelled nucleic acid molecules as well as other internal distances mimicking a labelled DNA binding protein if the labels are dissimilar metal nanocrystals. Of crucial importance is the ratio of mass of the nanocrystals to that of the labelled macromolecule, as well as the level of statistical errors in the scattering intensity measurements. The mathematics behind the distance determination process is presented, along with a fitting routine than incorporates maximum entropy regularisation.

Quantitative evaluation of statistical errors in small-angle X-ray scattering measurements

“…A number of increasingly powerful analysis techniques have been and are being developed to analyse SAXS data (see x1). Not only do these techniques require a precise treatment of experimental errors, but very often they rely on simulated SAXS data for testing and performance evaluation (Schindler et al, 2016;Bernadó et al, 2007;Pinfield & Scott, 2014;Zettl et al, 2016). There are several programs to compute SAXS profiles from high-resolution structures (Svergun et al, 1995;Schneidman-Duhovny et al, 2010;Poitevin et al, 2011;Ravikumar et al, 2013;Chen & Hub, 2015).…”

“…In particular, in the context of simulating SAXS profiles, different models for the error on scattering profiles have been put forward. A popular choice of model for the error on SAXS profiles is to add Gaussian noise to the scattering intensity in every q bin with zero mean and a constant standard deviation (Bernadó et al, 2007;Schindler et al, 2016;Fö rster et al, 2008;Pinfield & Scott, 2014), which is often expressed as a percentage of the forward scattering intensity I(0) or the scattering intensity at the highest scattering angle I(q max ). This choice of a constant Gaussian error corresponds to setting the variance 2 (q) = a 2 , where a is a constant.…”

“…This choice of a constant Gaussian error corresponds to setting the variance 2 (q) = a 2 , where a is a constant. Values for a described in the literature (Fö rster et al, 2008;Pinfield & Scott, 2014;Zettl et al, 2016) range from 0.3I(q max ) to 10 À4 I(0). Given that the scattering intensity for biological macromolecules tends to decrease with increasing q, the choice of a constant standard deviation for all q values corresponds to a (often much) larger relative error at higher q.…”

Emerging applications of small angle solution scattering in structural biology

“…Although small anomalous contribution due to the cross‐term between the label and the protein segment is usable, scattering contribution due to the interference within the anomalous scattering metal component itself is negligible . Theoretical calculations predict that the use of metal clusters, such as a gold nanocrystal, may alleviate this problem for ASAXS studies . With further explorations of dissimilar anomalous scattering atomic clusters as labels to measure specific distances, and concomitant development of theories, applications of ASAXS‐based molecular rulers to probe intricate conformational changes and molecular recognition processes may become routine.…”

“…Theoretical calculations predict that the use of metal clusters, such as a gold nanocrystal, may alleviate this problem for ASAXS studies . With further explorations of dissimilar anomalous scattering atomic clusters as labels to measure specific distances, and concomitant development of theories, applications of ASAXS‐based molecular rulers to probe intricate conformational changes and molecular recognition processes may become routine.…”