Refining conformational ensembles of flexible proteins against small-angle X-ray scattering data

Abstract

Intrinsically disordered proteins and flexible regions in multi-domain proteins display substantial conformational heterogeneity. Characterizing the conformational ensembles of these proteins in solution typically requires combining one or more biophysical techniques with computational modelling or simulations. Experimental data can either be used to assess the accuracy of a computational model or to refine the computational model to get a better agreement with the experimental data. In both cases, one generally needs a so-called forward model, i.e. an algorithm to calculate experimental observables from individual conformations or ensembles. In many cases, this involve one or more parameters that need to be set, and it is not always trivial to determine the optimal values or to understand the impact on the choice of parameters. For example, in the case of small-angle X-ray scattering (SAXS) experiments, many forward models include parameters that describe the contribution of the hydration layer to the background-subtracted experimental data. Often, one also needs to fit a scale and an offset for the SAXS data, but across the entire ensemble. Here, we present a protocol to dissect the effect of free-parameters on the calculated SAXS intensities, and to identify a reliable set of values. We have implemented this procedure in our Bayesian/Maximum Entropy framework for ensemble refinement, and demonstrate the results on three intrinsically disordered proteins and a three-domain protein connected by flexible linkers. Our results show that the resulting ensembles can depend substantially on the parameters used for hydration effects, and suggests that these should be chosen carefully. We also find a set of parameters that work robustly across all proteins.

Improving Martini 3 for disordered and multidomain proteins

“…After each trajectory had been backmapped to all-atom resolution, we extracted 15000 frames (evenly distributed in the time-series) to calculate SAXS profiles using Pepsi-SAXS ( Grudinin et al, 2017 ). To avoid potential problems of overfitting the parameters for the contrast of the hydration layer ( δρ ) and the displaced solvent ( r 0 ) (if these are fitted individually to each structure) we used values that have previously been shown to provide good agreement with experiment for flexible proteins ( Pesce and Lindorff-Larsen, 2021 ). Values for the intensity of the forward scattering ( I (0)) and the constant background ( cst ) were fitted globally with least-squares regression weighted by the experimental errors using the Scikit-learn python library ( Pedregosa et al, 2011 ).…”

Conformational ensembles of intrinsically disordered proteins and flexible multidomain proteins

“…When studying IDPs, it is a general problem that empirically-derived forward models are often trained on folded proteins, and may not capture e.g. solvation properties of IDPs (Piana et al, 2015;Henriques et al, 2018;Pesce and Lindorff-Larsen, 2021). However, it is challenging to obtain training sets of accurate IDP ensembles with experimental data available that are independent of the forward model one wishes to optimize (Lindorff-Larsen and Kragelund, 2021).…”

On the potential of machine learning to examine the relationship between sequence, structure, dynamics and function of intrinsically disordered proteins

“…A number of such forward models exist for SAXS experiments, that differ in how they treat solvent effects, as well as in accuracy and computational efficiency (Hub, 2018). Impor-tantly, different forward models may give different views of a conformational ensemble (Cordeiro et al, 2017;Henriques et al, 2018), because-depending on the relationship between structure and measurement-different ensembles will be needed to agree with the experiments (Pesce and Lindorff-Larsen, 2021).…”

“…While this may be true, this is very difficult to validate. One approach towards this goal may be to use more refined forward models to derive the ensembles (Hub, 2018;Hermann and Hub, 2019), to reparameterize simplified models using such more refined methods (Henriques et al, 2018), or to refine ensembles and forward models in a self-consistent manner (Rieping et al, 2005;Brookes and Head-Gordon, 2016;Pesce and Lindorff-Larsen, 2021).…”