New opportunities for tensor-free calculations of residual dipolar couplings for the study of protein dynamics

Residual dipolar couplings (RDCs) can provide exquisitely detailed information about the structure and dynamics of proteins. It is challenging, however, to extract such information from RDC measurements in conformationally heterogeneous states of proteins because of the complex relationship between RDCs and protein structures. To obtain new insights into this problem, we discuss methods of calculating the RDCs that do not require the definition of an alignment tensor. These methods can help in particular in the search of effective ways to use RDCs to characterise disordered or partially disordered states of proteins.     

Incorporation of evolutionary information into Rosetta comparative modeling

Prediction of protein structures from sequences is a fundamental problem in computational biology. Algorithms that attempt to predict a structure from sequence primarily use two sources of information. The first source is physical in nature: proteins fold into their lowest energy state. Given an energy function that describes the interactions governing folding, a method for constructing models of protein structures, and the amino acid sequence of a protein of interest, the structure prediction problem becomes a search for the lowest energy structure. Evolution provides an orthogonal source of information: proteins of similar sequences have similar structure, and therefore proteins of known structure can guide modeling. The relatively successful Rosetta approach takes advantage of the first, but not the second source of information during model optimization. Following the classic work by Andrej Sali and colleagues, we develop a probabilistic approach to derive spatial restraints from proteins of known structure using advances in alignment technology and the growth in the number of structures in the Protein Data Bank. These restraints define a region of conformational space that is high-probability, given the template information, and we incorporate them into Rosetta's comparative modeling protocol. The combined approach performs considerably better on a benchmark based on previous CASP experiments. Incorporating evolutionary information into Rosetta is analogous to incorporating sparse experimental data: in both cases, the additional information eliminates large regions of conformational space and increases the probability that energy-based refinement will hone in on the deep energy minimum at the native state.     

Use of residual dipolar couplings as restraints in ab initio protein structure prediction

NMR residual dipolar couplings (RDCs), in the form of the projection angles between the respective internuclear bond vectors, are used as structural restraints in the ab initio structure prediction of a test set of six proteins. The restraints are applied using a recently developed SICHO (SIde-CHain-Only) lattice protein model that employs a replica exchange Monte Carlo (MC) algorithm to search conformational space. Using a small number of RDC restraints, the quality of the predicted structures is improved as reflected by lower RMSD/dRMSD (root mean square deviation/distance root mean square deviation) values from the corresponding native structures and by the higher correlation of the most cooperative mode of motion of each predicted structure with that of the native structure. The latter, in particular, has possible implications for the structure-based functional analysis of predicted structures.     

Determination of the Individual Roles of the Linker Residues in the Interdomain Motions of Calmodulin Using NMR Chemical Shifts

Many protein molecules are formed by two or more domains whose structures and dynamics are closely related to their biological functions. It is thus important to develop methods to determine the structural properties of these multidomain proteins. Here, we characterize the interdomain motions in the calcium-bound state of calmodulin (Ca^2 +-CaM) using NMR chemical shifts as replica-averaged structural restraints in molecular dynamics simulations. We find that the conformational fluctuations of the interdomain linker, which are largely responsible for the overall interdomain motions of CaM, can be well described by exploiting the information provided by chemical shifts. We thus identify 10 residues in the interdomain linker region that change their conformations upon substrate binding. Five of these residues (Met76, Lys77, Thr79, Asp80 and Ser81) are highly flexible and cover the range of conformations observed in the substrate-bound state, while the remaining five (Arg74, Lys75, Asp78, Glu82 and Glu83) are much more rigid and do not populate conformations typical of the substrate-bound form. The ensemble of conformations representing the Ca^2 +-CaM state obtained in this study is in good agreement with residual dipolar coupling, paramagnetic resonance enhancement, small-angle X-ray scattering and fluorescence resonance energy transfer measurements, which were not used as restraints in the calculations. These results provide initial evidence that chemical shifts can be used to characterize the conformational fluctuations of multidomain proteins.     

Measuring membrane protein bond orientations in nanodiscs via residual dipolar couplings

Membrane proteins are involved in numerous vital biological processes. To understand membrane protein functionality, accurate structural information is required. Usually, structure determination and dynamics of membrane proteins are studied in micelles using either solution state NMR or X‐ray crystallography. Even though invaluable information has been obtained by this approach, micelles are known to be far from ideal mimics of biological membranes often causing the loss or decrease of membrane protein activity. Recently, nanodiscs, which are composed of a lipid bilayer surrounded by apolipoproteins, have been introduced as a more physiological alternative than micelles for NMR investigations on membrane proteins. Here, we show that membrane protein bond orientations in nanodiscs can be obtained by measuring residual dipolar couplings (RDCs) with the outer membrane protein OmpX embedded in nanodiscs using Pf1 phage as an alignment medium. The presented collection of membrane protein RDCs in nanodiscs represents an important step toward more comprehensive structural and dynamical NMR‐based investigations of membrane proteins in a natural bilayer environment.     

A structure refinement protocol combining NMR residual dipolar couplings and small angle scattering restraints

We present the implementation of a target function based on Small Angle Scattering data (Gabel et al. Eur Biophys J 35(4):313-327, 2006) into the Crystallography and NMR Systems (CNS) and demonstrate its utility in NMR structure calculations by simultaneous application of small angle scattering (SAS) and residual dipolar coupling (RDC) restraints. The efficiency and stability of the approach are demonstrated by reconstructing the structure of a two domain region of the 31 kDa nuclear export factor TAP (TIP-associated protein). Starting with the high resolution X-ray structures of the two individual TAP domains, the translational and orientational domain arrangement is refined simultaneously. We tested the stability of the protocol against variations of the SAS target parameters and the number of RDCs and their uncertainties. The activation of SAS restraints results in an improved translational clustering of the domain positions and lifts part of the fourfold degeneracy of their orientations (associated with a single alignment tensor). The resulting ensemble of structures reflects the conformational space that is consistent with the experimental SAS and RDC data. The SAS target function is computationally very efficient. SAS restraints can be activated at different levels of precision and only a limited SAS angular range is required. When combined with additional data from chemical shift perturbation, paramagnetic relaxation enhancement or mutational analysis the SAS refinement is an efficient approach for defining the topology of multi-domain and/or multimeric biomolecular complexes in solution based on available high resolution structures (NMR or X-ray) of the individual domains.     

Rapid measurement of residual dipolar couplings for fast fold elucidation of proteins

It has been demonstrated that protein folds can be determined using appropriate computational protocols with NMR chemical shifts as the sole source of experimental restraints. While such approaches are very promising they still suffer from low convergence resulting in long computation times to achieve accurate results. Here we present a suite of time- and sensitivity optimized NMR experiments for rapid measurement of up to six RDCs per residue. Including such an RDC data set, measured in less than 24 h on a single aligned protein sample, greatly improves convergence of the Rosetta-NMR protocol, allowing for overnight fold calculation of small proteins. We demonstrate the performance of our fast fold calculation approach for ubiquitin as a test case, and for two RNA-binding domains of the plant protein HYL1. Structure calculations based on simulated RDC data highlight the importance of an accurate and precise set of several complementary RDCs as additional input restraints for high-quality de novo structure determination.     

Capturing Conformational States in Proteins Using Sparse Paramagnetic NMR Data

Capturing conformational changes in proteins or protein-protein complexes is a challenge for both experimentalists and computational biologists. Solution nuclear magnetic resonance (NMR) is unique in that it permits structural studies of proteins under greatly varying conditions, and thus allows us to monitor induced structural changes. Paramagnetic effects are increasingly used to study protein structures as they give ready access to rich structural information of orientation and long-range distance restraints from the NMR signals of backbone amides, and reliable methods have become available to tag proteins with paramagnetic metal ions site-specifically and at multiple sites. In this study, we show how sparse pseudocontact shift (PCS) data can be used to computationally model conformational states in a protein system, by first identifying core structural elements that are not affected by the environmental change, and then computationally completing the remaining structure based on experimental restraints from PCS. The approach is demonstrated on a 27 kDa two-domain NS2B-NS3 protease system of the dengue virus serotype 2, for which distinct closed and open conformational states have been observed in crystal structures. By changing the input PCS data, the observed conformational states in the dengue virus protease are reproduced without modifying the computational procedure. This data driven Rosetta protocol enables identification of conformational states of a protein system, which are otherwise difficult to obtain either experimentally or computationally.     

A geometric arrangement algorithm for structure determination of symmetric protein homo-oligomers from NOEs and RDCs

Nuclear magnetic resonance (NMR) spectroscopy is a primary tool to perform structural studies of proteins in physiologically-relevant solution conditions. Restraints on distances between pairs of nuclei in the protein, derived from the nuclear Overhauser effect (NOE), provide information about the structure of the protein in its folded state. NMR studies of symmetric protein homo-oligomers present a unique challenge. Using X-filtered NOESY experiments, it is possible to determine whether an NOE restrains a pair of protons across different subunits or within a single subunit, but current experimental techniques are unable to determine in which subunits the restrained protons lie. Consequently, it is difficult to assign NOEs to particular pairs of subunits with certainty, thus hindering the structural analysis of the oligomeric state. Computational approaches are needed to address this subunit ambiguity, but traditional solutions often rely on stochastic search coupled with simulated annealing and simulations of simplified molecular dynamics, which have many tunable parameters that must be chosen carefully and can also fail to report structures consistent with the experimental restraints. In addition, these traditional approaches rarely provide guarantees on running time or solution quality. We reduce the structure determination of homo-oligomers with cyclic symmetry to computing geometric arrangements of unions of annuli in a plane. Our algorithm, disco, runs in expected O(n2) time, where n is the number of distance restraints, potentially assigned ambiguously. disco is guaranteed to report the exact set of oligomer structures consistent with the distance restraints and also with orientational restraints from residual dipolar couplings (RDCs). We demonstrate our method using two symmetric protein complexes: the trimeric E. coli diacylglycerol kinase (DAGK) and a dimeric mutant of the immunoglobulin-binding domain B1 of streptococcal protein G (GB1). In both cases, disco computes oligomer structures with high precision and also finds distance restraints that are either mutually inconsistent or inconsistent with the RDCs. The entire protocol DISCO has been completely automated in a software package that is freely available and open-source at www.cs.duke.edu/donaldlab/software.php.     

Requirements on paramagnetic relaxation enhancement data for membrane protein structure determination by NMR

Nuclear magnetic resonance (NMR) structure calculations of the α-helical integral membrane proteins DsbB, GlpG, and halorhodopsin show that distance restraints from paramagnetic relaxation enhancement (PRE) can provide sufficient structural information to determine their structure with an accuracy of about 1.5?? in the absence of other long-range conformational restraints. Our systematic study with simulated NMR data shows that about one spin label per transmembrane helix is necessary for obtaining enough PRE distance restraints to exclude wrong topologies, such as pseudo mirror images, if only limited other NMR restraints are available. Consequently, an experimentally realistic amount of PRE data enables α-helical membrane protein structure determinations that would not be feasible with the very limited amount of conventional NOESY data normally available for these systems. These findings are in line with our recent first de novo NMR structure determination of a heptahelical integral membrane protein, proteorhodopsin, that relied extensively on PRE data.     

Assessment of molecular structure using frame-independent orientational restraints derived from residual dipolar couplings

Residual dipolar couplings measured in weakly aligning liquid-crystalline solvent contain valuable information on the structure of biomolecules in solution. Here we demonstrate that dipolar couplings (DCs) can be used to derive a comprehensive set of pairwise angular restraints that do not depend on the orientation of the alignment tensor principal axes. These restraints can be used to assess the agreement between a trial protein structure and a set of experimental dipolar couplings by means of a graphic representation termed a `DC consistency map'. Importantly, these maps can be used to recognize structural elements consistent with the experimental DC data and to identify structural parameters that require further refinement, which could prove important for the success of DC-based structure calculations. This approach is illustrated for the 42 kDa maltodextrin-binding protein.     

De novo determination of internuclear vector orientations from residual dipolar couplings measured in three independent alignment media

The straightforward interpretation of solution state residual dipolar couplings (RDCs) in terms of internuclear vector orientations generally requires prior knowledge of the alignment tensor, which in turn is normally estimated using a structural model. We have developed a protocol which allows the requirement for prior structural knowledge to be dispensed with as long as RDC measurements can be made in three independent alignment media. This approach, called Rigid Structure from Dipolar Couplings (RSDC), allows vector orientations and alignment tensors to be determined de novo from just three independent sets of RDCs. It is shown that complications arising from the existence of multiple solutions can be overcome by careful consideration of alignment tensor magnitudes in addition to the agreement between measured and calculated RDCs. Extensive simulations as well applications to the proteins ubiquitin and Staphylococcal protein GB1 demonstrate that this method can provide robust determinations of alignment tensors and amide N-H bond orientations often with better than 10 degrees accuracy, even in the presence of modest levels of internal dynamics.     

How reliable are pseudocontact shifts induced in proteins and ligands by mobile paramagnetic metal tags? A modelling study

The anisotropic component of the magnetic susceptibility tensor (Δχ tensor) associated with various paramagnetic metal ions can induce pseudocontact shifts (PCSs) and residual dipolar couplings (RDCs) in proteins, yielding valuable restraints in structural studies. In particular, PCSs have successfully been used to study ligands that bind to proteins tagged with a paramagnetic metal ion, which is of great interest in fragment-based drug design. To create easy-to-interpret PCSs, the metal ion must be attached to the protein in a rigid manner. Most of the existing methods for site-specific attachment of a metal tag, however, result in tethers with residual flexibility. Here we present model calculations to quantify the extent, to which mobility of the metal-binding tag can compromise the quality of the Δχ tensor that can be determined from the PCSs observed in the protein. Assuming that the protein can be approximated by a sphere and the tag is attached by a single tether, the results show that a single effective ?χ tensor can describe the PCSs and RDCs of the protein spins very well even in the presence of substantial tag mobility, implying that PCSs of ligands in binding pockets of the protein can be predicted with similar accuracy. In contrast, the quality of the PCS prediction for nuclear spins positioned above the surface of the protein is significantly poorer, with implications for studies of protein–protein complexes. The simulations probed the sensitivity of the effective Δχ tensor to different parameters, including length of the tether between protein and metal ion, protein size, type and amplitude of tag motion, tensor orientation relative to the protein and direction of tag motion. Tether length and amplitude of motion were identified as two key parameters. It is shown that the amplitude of tag motions cannot be quantified by simple comparisons of the effective Δχ tensor with the alignment tensor determined from RDCs.     

Analysis of conformational variation in macromolecular structural models

Experimental conditions or the presence of interacting components can lead to variations in the structural models of macromolecules. However, the role of these factors in conformational selection is often omitted by in silico methods to extract dynamic information from protein structural models. Structures of small peptides, considered building blocks for larger macromolecular structural models, can substantially differ in the context of a larger protein. This limitation is more evident in the case of modeling large multi-subunit macromolecular complexes using structures of the individual protein components. Here we report an analysis of variations in structural models of proteins with high sequence similarity. These models were analyzed for sequence features of the protein, the role of scaffolding segments including interacting proteins or affinity tags and the chemical components in the experimental conditions. Conformational features in these structural models could be rationalized by conformational selection events, perhaps induced by experimental conditions. This analysis was performed on a non-redundant dataset of protein structures from different SCOP classes. The sequence-conformation correlations that we note here suggest additional features that could be incorporated by in silico methods to extract dynamic information from protein structural models.     

Wiggle—Predicting Functionally Flexible Regions from Primary Sequence

The Wiggle series are support vector machine–based predictors that identify regions of functional flexibility using only protein sequence information. Functionally flexible regions are defined as regions that can adopt different conformational states and are assumed to be necessary for bioactivity. Many advances have been made in understanding the relationship between protein sequence and structure. This work contributes to those efforts by making strides to understand the relationship between protein sequence and flexibility. A coarse-grained protein dynamic modeling approach was used to generate the dataset required for support vector machine training. We define our regions of interest based on the participation of residues in correlated large-scale fluctuations. Even with this structure-based approach to computationally define regions of functional flexibility, predictors successfully extract sequence-flexibility relationships that have been experimentally confirmed to be functionally important. Thus, a sequence-based tool to identify flexible regions important for protein function has been created. The ability to identify functional flexibility using a sequence based approach complements structure-based definitions and will be especially useful for the large majority of proteins with unknown structures. The methodology offers promise to identify structural genomics targets amenable to crystallization and the possibility to engineer more flexible or rigid regions within proteins to modify their bioactivity.     

Wiggle-predicting functionally flexible regions from primary sequence

The Wiggle series are support vector machine-based predictors that identify regions of functional flexibility using only protein sequence information. Functionally flexible regions are defined as regions that can adopt different conformational states and are assumed to be necessary for bioactivity. Many advances have been made in understanding the relationship between protein sequence and structure. This work contributes to those efforts by making strides to understand the relationship between protein sequence and flexibility. A coarse-grained protein dynamic modeling approach was used to generate the dataset required for support vector machine training. We define our regions of interest based on the participation of residues in correlated large-scale fluctuations. Even with this structure-based approach to computationally define regions of functional flexibility, predictors successfully extract sequence-flexibility relationships that have been experimentally confirmed to be functionally important. Thus, a sequence-based tool to identify flexible regions important for protein function has been created. The ability to identify functional flexibility using a sequence based approach complements structure-based definitions and will be especially useful for the large majority of proteins with unknown structures. The methodology offers promise to identify structural genomics targets amenable to crystallization and the possibility to engineer more flexible or rigid regions within proteins to modify their bioactivity.     

SPEACH_AF: Sampling protein ensembles and conformational heterogeneity with Alphafold2

The unprecedented performance of Deepmind’s Alphafold2 in predicting protein structure in CASP XIV and the creation of a database of structures for multiple proteomes and protein sequence repositories is reshaping structural biology. However, because this database returns a single structure, it brought into question Alphafold’s ability to capture the intrinsic conformational flexibility of proteins. Here we present a general approach to drive Alphafold2 to model alternate protein conformations through simple manipulation of the multiple sequence alignment via in silico mutagenesis. The approach is grounded in the hypothesis that the multiple sequence alignment must also encode for protein structural heterogeneity, thus its rational manipulation will enable Alphafold2 to sample alternate conformations. A systematic modeling pipeline is benchmarked against canonical examples of protein conformational flexibility and applied to interrogate the conformational landscape of membrane proteins. This work broadens the applicability of Alphafold2 by generating multiple protein conformations to be tested biologically, biochemically, biophysically, and for use in structure-based drug design.