Experimental noise in small-angle scattering can be assessed using the Bayesian indirect Fourier transformation

Benchmarking predictive methods for small-angle X-ray scattering from atomic coordinates of proteins using maximum likelihood consensus data

Stimulated by informal conversations at the XVII International Small Angle Scattering (SAS) conference (Traverse City, 2017), an international team of experts undertook a round-robin exercise to produce a large dataset from proteins under standard solution conditions. These data were used to generate consensus SAS profiles for xylose isomerase, urate oxidase, xylanase, lysozyme and ribonuclease A. Here, we apply a new protocol using maximum likelihood with a larger number of the contributed datasets to generate improved consensus profiles. We investigate the fits of these profiles to predicted profiles from atomic coordinates that incorporate different models to account for the contribution to the scattering of water molecules of hydration surrounding proteins in solution. Programs using an implicit, shell-type hydration layer generally optimize fits to experimental data with the aid of two parameters that adjust the volume of the bulk solvent excluded by the protein and the contrast of the hydration layer. For these models, we found the error-weighted residual differences between the model and the experiment generally reflected the subsidiary maxima and minima in the consensus profiles that are determined by the size of the protein plus the hydration layer. By comparison, all-atom solute and solvent molecular dynamics (MD) simulations are without the benefit of adjustable parameters and, nonetheless, they yielded at least equally good fits with residual differences that are less reflective of the structure in the consensus profile. Further, where MD simulations accounted for the precise solvent composition of the experiment, specifically the inclusion of ions, the modelled radius of gyration values were significantly closer to the experiment. The power of adjustable parameters to mask real differences between a model and the structure present in solution is demonstrated by the results for the conformationally dynamic ribonuclease A and calculations with pseudo-experimental data. This study shows that, while methods invoking an implicit hydration layer have the unequivocal advantage of speed, care is needed to understand the influence of the adjustable parameters. All-atom solute and solvent MD simulations are slower but are less susceptible to false positives, and can account for thermal fluctuations in atomic positions, and more accurately represent the water molecules of hydration that contribute to the scattering profile.

Design of intrinsically disordered protein variants with diverse structural properties

Intrinsically disordered proteins (IDPs) perform a broad range of functions in biology, suggesting that the ability to design IDPs could help expand the repertoire of proteins with novel functions. Computational design of IDPs with specific conformational properties has, however, been difficult because of their substantial dynamics and structural complexity. We describe a general algorithm for designing IDPs with specific structural properties. We demonstrate the power of the algorithm by generating variants of naturally occurring IDPs that differ in compaction, long-range contacts, and propensity to phase separate. We experimentally tested and validated our designs and analyzed the sequence features that determine conformations. We show how our results are captured by a machine learning model, enabling us to speed up the algorithm. Our work expands the toolbox for computational protein design and will facilitate the design of proteins whose functions exploit the many properties afforded by protein disorder.

Rescaling protein-protein interactions improves Martini 3 for flexible proteins in solution

Multidomain proteins with flexible linkers and disordered regions play important roles in many cellular processes, but characterizing their conformational ensembles is difficult. We have previously shown that the coarse-grained model, Martini 3, produces too compact ensembles in solution, that may in part be remedied by strengthening protein-water interactions. Here, we show that decreasing the strength of protein-protein interactions leads to improved agreement with experimental data on a wide set of systems. We show that the 'symmetry' between rescaling protein-water and protein-protein interactions breaks down when studying interactions with or within membranes; rescaling protein-protein interactions better preserves the binding specificity of proteins with lipid membranes, whereas rescaling protein-water interactions preserves oligomerization of transmembrane helices. We conclude that decreasing the strength of protein-protein interactions improves the accuracy of Martini 3 for IDPs and multidomain proteins, both in solution and in the presence of a lipid membrane.

Recovery from desensitization in GluA2 AMPA receptors is affected by a single mutation in the N-terminal domain interface

AMPA-type ionotropic glutamate receptors (AMPARs) are central to various neurological processes, including memory and learning. They assemble as homo- or heterotetramers of GluA1, GluA2, GluA3, and GluA4 subunits, each consisting of an N-terminal domain (NTD), a ligand-binding domain, a transmembrane domain, and a C-terminal domain. While AMPAR gating is primarily controlled by reconfiguration in the ligand-binding domain layer, our study focuses on the NTDs, which also influence gating, yet the underlying mechanism remains enigmatic. In this investigation, we employ molecular dynamics simulations to evaluate the NTD interface strength in GluA1, GluA2, and NTD mutants GluA2-H229N and GluA1-N222H. Our findings reveal that GluA1 has a significantly weaker NTD interface than GluA2. The NTD interface of GluA2 can be weakened by a single point mutation in the NTD dimer-of-dimer interface, namely H229N, which renders GluA2 more GluA1-like. Electrophysiology recordings demonstrate that this mutation also leads to slower recovery from desensitization. Moreover, we observe that lowering the pH induces more splayed NTD states and enhances desensitization in GluA2. We hypothesized that H229 was responsible for this pH sensitivity; however, GluA2-H229N was also affected by pH, meaning that H229 is not solely responsible and that protons exert their effect across multiple domains of the AMPAR. In summary, our work unveils an allosteric connection between the NTD interface strength and AMPAR desensitization.

AlphaFold-predicted protein structures and small-angle X-ray scattering: insights from an extended examination of selected data in the Small-Angle Scattering Biological Data Bank

By providing predicted protein structures from nearly all known protein sequences, the artificial intelligence program AlphaFold (AF) is having a major impact on structural biology. While a stunning accuracy has been achieved for many folding units, predicted unstructured regions and the arrangement of potentially flexible linkers connecting structured domains present challenges. Focusing on single-chain structures without prosthetic groups, an earlier comparison of features derived from small-angle X-ray scattering (SAXS) data taken from the Small-Angle Scattering Biological Data Bank (SASBDB) is extended to those calculated using the corresponding AF-predicted structures. Selected SASBDB entries were carefully examined to ensure that they represented data from monodisperse protein solutions and had sufficient statistical precision and q resolution for reliable structural evaluation. Three examples were identified where there is clear evidence that the single AF-predicted structure cannot account for the experimental SAXS data. Instead, excellent agreement is found with ensemble models generated by allowing for flexible linkers between high-confidence predicted structured domains. A pool of representative structures was generated using a Monte Carlo method that adjusts backbone dihedral allowed angles along potentially flexible regions. A fast ensemble modelling method was employed that optimizes the fit of pair distance distribution functions [P(r) versus r] and intensity profiles [I(q) versus q] computed from the pool to their experimental counterparts. These results highlight the complementarity between AF prediction, solution SAXS and molecular dynamics/conformational sampling for structural modelling of proteins having both structured and flexible regions.

Combining Experiments and Simulations to Examine the Temperature-Dependent Behavior of a Disordered Protein

Intrinsically disordered proteins are a class of proteins that lack stable folded conformations and instead adopt a range of conformations that determine their biochemical functions. The temperature-dependent behavior of such disordered proteins is complex and can vary depending on the specific protein and environment. Here, we have used molecular dynamics simulations and previously published experimental data to investigate the temperature-dependent behavior of histatin 5, a 24-residue-long polypeptide. We examined the hypothesis that histatin 5 undergoes a loss of polyproline II (PPII) structure with increasing temperature, leading to more compact conformations. We found that the conformational ensembles generated by the simulations generally agree with small-angle X-ray scattering data for histatin 5, but show some discrepancies with the hydrodynamic radius as probed by pulsed-field gradient NMR spectroscopy, and with the secondary structure information derived from circular dichroism. We attempted to reconcile these differences by reweighting the conformational ensembles against the scattering and NMR data. By doing so, we were in part able to capture the temperature-dependent behavior of histatin 5 and to link the observed decrease in hydrodynamic radius with increasing temperature to a loss of PPII structure. We were, however, unable to achieve agreement with both the scattering and NMR data within experimental errors. We discuss different possible reasons for this including inaccuracies in the force field, differences in conditions of the NMR and scattering experiments, and issues related to the calculation of the hydrodynamic radius from conformational ensembles. Our study highlights the importance of integrating multiple types of experimental data when modeling conformational ensembles of disordered proteins and how environmental factors such as the temperature influence them.

Effect of Cholesterol on the Structure and Composition of Glyco-DIBMA Lipid Particles

Different amphiphilic co-polymers have been introduced to produce polymer-lipid particles with nanodisc structure composed of an inner lipid bilayer and polymer chains self-assembled as an outer belt. These particles can be used to stabilize membrane proteins in solution and enable their characterization by means of biophysical methods, including small-angle X-ray scattering (SAXS). Some of these co-polymers have also been used to directly extract membrane proteins together with their associated lipids from native membranes. Styrene/maleic acid and diisobutylene/maleic acid are among the most commonly used co-polymers for producing polymer-lipid particles, named SMALPs and DIBMALPs, respectively. Recently, a new co-polymer, named Glyco-DIBMA, was produced by partial amidation of DIBMA with the amino sugar N-methyl-d-glucosamine. Polymer-lipid particles produced with Glyco-DIBMA, named Glyco-DIBMALPs, exhibit improved structural properties and stability compared to those of SMALPs and DIBMALPs while retaining the capability of directly extracting membrane proteins from native membranes. Here, we characterize the structure and lipid composition of Glyco-DIBMALPs produced with either 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) or 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). Glyco-DIBMALPs were also prepared with mixtures of either POPC or DMPC and cholesterol at different mole fractions. We estimated the lipid content in the Glyco-DIBMALPs and determined the particle structure and morphology by SAXS. We show that the Glyco-DIBMALPs are nanodisc-like particles whose size and shape depend on the polymer/lipid ratio. This is relevant for designing nanodisc particles with a tunable diameter according to the size of the membrane protein to be incorporated. We also report that the addition of >20 mol % cholesterol strongly perturbed the formation of Glyco-DIBMALPs. Altogether, we describe a detailed characterization of the Glyco-DIBMALPs, which provides relevant inputs for future application of these particles in the biophysical investigation of membrane proteins.

Assessment of models for calculating the hydrodynamic radius of intrinsically disordered proteins

Diffusion measurements by pulsed-field gradient NMR and fluorescence correlation spectroscopy can be used to probe the hydrodynamic radius of proteins, which contains information about the overall dimension of a protein in solution. The comparison of this value with structural models of intrinsically disordered proteins is nonetheless impaired by the uncertainty of the accuracy of the methods for computing the hydrodynamic radius from atomic coordinates. To tackle this issue, we here build conformational ensembles of 11 intrinsically disordered proteins that we ensure are in agreement with measurements of compaction by small-angle x-ray scattering. We then use these ensembles to identify the forward model that more closely fits the radii derived from pulsed-field gradient NMR diffusion experiments. Of the models we examined, we find that the Kirkwood-Riseman equation provides the best description of the hydrodynamic radius probed by pulsed-field gradient NMR experiments. While some minor discrepancies remain, our results enable better use of measurements of the hydrodynamic radius in integrative modeling and for force field benchmarking and parameterization.

Small-angle x-ray and neutron scattering of MexR and its complex with DNA supports a conformational selection binding model

In this work, we used small-angle x-ray and neutron scattering to reveal the shape of the protein-DNA complex of the Pseudomonas aeruginosa transcriptional regulator MexR, a member of the multiple antibiotics resistance regulator (MarR) family, when bound to one of its native DNA binding sites. Several MarR-like proteins, including MexR, repress the expression of efflux pump proteins by binding to DNA on regulatory sites overlapping with promoter regions. When expressed, efflux proteins self-assemble to form multiprotein complexes and actively expel highly toxic compounds out of the host organism. The mutational pressure on efflux-regulating MarR family proteins is high since deficient DNA binding leads to constitutive expression of efflux pumps and thereby supports acquired multidrug resistance. Understanding the functional outcome of such mutations and their effects on DNA binding has been hampered by the scarcity of structural and dynamic characterization of both free and DNA-bound MarR proteins. Here, we show how combined neutron and x-ray small-angle scattering of both states in solution support a conformational selection model that enhances MexR asymmetry in binding to one of its promoter-overlapping DNA binding sites.

Deciphering the Alphabet of Disorder-Glu and Asp Act Differently on Local but Not Global Properties

Compared to folded proteins, the sequences of intrinsically disordered proteins (IDPs) are enriched in polar and charged amino acids. Glutamate is one of the most enriched amino acids in IDPs, while the chemically similar amino acid aspartate is less enriched. So far, the underlying functional differences between glutamates and aspartates in IDPs remain poorly understood. In this study, we examine the differential effects of aspartate and glutamates in IDPs by comparing the function and conformational ensemble of glutamate and aspartate variants of the disordered protein Dss1, using a range of assays, including interaction studies, nuclear magnetic resonance spectroscopy, small-angle X-ray scattering and molecular dynamics simulation. First, we analyze the sequences of the rapidly growing database of experimentally verified IDPs (DisProt) and show that glutamate enrichment is not caused by a taxonomy bias in IDPs. From analyses of local and global structural properties as well as cell growth and protein-protein interactions using a model acidic IDP from yeast and three Glu/Asp variants, we find that while the Glu/Asp variants support similar function and global dimensions, the variants differ in their binding affinities and population of local transient structural elements. We speculate that these local structural differences may play roles in functional diversity, where glutamates can support increased helicity, important for folding and binding, while aspartates support extended structures and form helical caps, as well as playing more relevant roles in, e.g., transactivation domains and ion-binding.

Improving Martini 3 for Disordered and Multidomain Proteins

Coarse-grained molecular dynamics simulations are a useful tool to determine conformational ensembles of proteins. Here, we show that the coarse-grained force field Martini 3 underestimates the global dimensions of intrinsically disordered proteins (IDPs) and multidomain proteins when compared with small-angle X-ray scattering (SAXS) data and that increasing the strength of protein-water interactions favors more expanded conformations. We find that increasing the strength of interactions between protein and water by ca. 10% results in improved agreement with the SAXS data for IDPs and multidomain proteins. We also show that this correction results in a more accurate description of self-association of IDPs and folded proteins and better agreement with paramagnetic relaxation enhancement data for most IDPs. While simulations with this revised force field still show deviations to experiments for some systems, our results suggest that it is overall a substantial improvement for coarse-grained simulations of soluble proteins.

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

Intrinsically disordered proteins and flexible regions in multidomain proteins display substantial conformational heterogeneity. Characterizing the conformational ensembles of these proteins in solution typically requires combining one or more biophysical techniques with computational modeling 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 involves 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 and displaced solvent to the background-subtracted experimental data. Often, one also needs to fit a scale factor and a constant background for the SAXS data but across the entire ensemble. Here, we present a protocol to dissect the effect of the 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 four intrinsically disordered proteins and a protein with three domains connected by flexible linkers. Our results show that the resulting ensembles can depend on the parameters used for solvent effects and suggest that these should be chosen carefully. We also find a set of parameters that work robustly across all proteins.