Bayesian inference of protein ensembles from SAXS data

Abstract

The inherent flexibility of intrinsically disordered proteins (IDPs) and multi-domain proteins with intrinsically disordered regions (IDRs) presents challenges to structural analysis. These macromolecules need to be represented by an ensemble of conformations, rather than a single structure. Small-angle X-ray scattering (SAXS) experiments capture ensemble-averaged data for the set of conformations. We present a Bayesian approach to ensemble inference from SAXS data, called Bayesian ensemble SAXS (BE-SAXS). We address two issues with existing methods: the use of a finite ensemble of structures to represent the underlying distribution, and the selection of that ensemble as a subset of an initial pool of structures. This is achieved through the formulation of a Bayesian posterior of the conformational space. BE-SAXS modifies a structural prior distribution in accordance with the experimental data. It uses multi-step expectation maximization, with alternating rounds of Markov-chain Monte Carlo simulation and empirical Bayes optimization. We demonstrate the method by employing it to obtain a conformational ensemble of the antitoxin PaaA2 and comparing the results to a published ensemble.

Combining molecular dynamics simulations with small-angle X-ray and neutron scattering data to study multi-domain proteins in solution

“…As mentioned in the introduction, there are several ways to combine MD simulations with SAS data (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20), but we here used the Bayesian/Maximum Entropy (BME) method (3) and the above-calculated SAXS and SANS intensities to reweight the trajectories. For details of BME see (3) as well as code and examples online https://github.com/KULL-Centre/BME.…”

“…In that case, however, simulations and experiments may be used synergistically to generate and refine the description of flexible molecules. Thus, as described by us and others, SAXS and molecular simulations can be combined to determine a structural ensemble that represents the system, and is compatible with the information in the force field and the experimental constraints from SAXS (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20).…”

Revisiting the earliest signatures of amyloidogenesis: Roadmaps emerging from computational modeling and experiment

“…The SAXS-based EOM technique has been upgraded to EOM 2.0 with flexible ensemble size, optimized conformational weights and, crucially for studying aggregation of monomers, support for low molecular weight oligomers and complexes (Tria, Mertens, Kachala, & Svergun, 2015). A novel approach named Bayesian Ensemble SAXS (BE-SAXS) (Antonov, Olsson, Boomsma, & Hamelryck, 2016) implements a probabilistic Bayesian model to generate SAXS-based ensembles and can be used with a broad range of experimental constraints. BE-SAXS puts no restriction on the ensemble size, an improvement over earlier BSS-SAXS and SES.…”

SAS profile correlations reveal SAS hierarchical nature and information content

“…More than 60% of all articles on the topic of SAXS ensembles have been published in the last five years, following the development of a number of methods for ensemble modelling (EOM [14], MES [15], BSS-SAXS [16], EROS [17], SES [18] and BE-SAXS [19]. In these methods, the SAS profile is almost always modelled as a weighted average of the profiles of the individual conformations.…”

“…Yet, the number of parameters, which in essence is three times the number of atoms times the number of structures, still becomes very large for such systems, and the risk of overfitting is not negligible. The most promising approach in that respect is the recently proposed BE-SAXS [19]. It proposes a generative model for the protein ensemble fitted on experimental SAXS data.…”