Restraints In Molecular Dynamics Simulations Research Articles

Combined Small-Angle X-ray and Neutron Scattering Restraints in Molecular Dynamics Simulations.

Small-angle X-ray and small-angle neutron scattering (SAXS/SANS) provide unique structural information on biomolecules and their complexes in solution. SANS may provide multiple independent data sets by means of contrast variation experiments, that is, by measuring at different D2O concentrations and different perdeuteration conditions of the biomolecular complex. However, even the combined data from multiple SAXS/SANS sets is by far insufficient to define all degrees of freedom of a complex, leading to a significant risk of overfitting when refining biomolecular structures against SAXS/SANS data. Hence, to control against overfitting, the low-information SAXS/SANS data must be complemented by accurate physical models, and, if possible, refined models should be cross-validated against independent data not used during the refinement. We present a method for refining atomic biomolecular structures against multiple sets of SAXS and SANS data using all-atom molecular dynamics simulations. Using the protein citrate synthase and the protein/RNA complex Sxl-Unr-msl2 mRNA as test cases, we demonstrate how multiple SAXS and SANS sets may be used for refinement and cross-validation, thereby excluding overfitting during refinement. For the Sxl-Unr-msl2 complex, we find that perdeuteration of the Unr domain leads to a unique, slightly compacted conformation, whereas other perdeuteration conditions lead to similar solution conformations compared to the nondeuterated state. In line with our previous method for predicting SAXS curves, SANS curves were predicted with explicit-solvent calculations, taking atomic models for both the hydration layer and the excluded solvent into account, thereby avoiding the use of solvent-related fitting parameters and solvent-reduced neutron scattering lengths. We expect the method to be useful for deriving and validating solution structures of biomolecules and soft-matter complexes, and for critically assessing whether multiple SAXS and SANS sets are mutually compatible.

Multiple helical conformations of the helix-turn-helix region revealed by NOE-restrained MD simulations of tryptophan aporepressor, TrpR.

The nature of flexibility in the helix-turn-helix region of E. coli trp aporepressor has been unexplained for many years. The original ensemble of nuclear magnetic resonance (NMR structures showed apparent disorder, but chemical shift and relaxation measurements indicated a helical region. Nuclear Overhauser effect (NOE) data for a temperature-sensitive mutant showed more helical character in its helix-turn-helix region, but nevertheless also led to an apparently disordered ensemble. However, conventional NMR structure determination methods require all structures in the ensemble to be consistent with every NOE simultaneously. This work uses an alternative approach in which some structures of the ensemble are allowed to violate some NOEs to permit modeling of multiple conformational states that are in dynamic equilibrium. Newly measured NOE data for wild-type aporepressor are used as time-averaged distance restraints in molecular dynamics simulations to generate an ensemble of helical conformations that is more consistent with the observed NMR data than the apparent disorder in the previously reported NMR structures. The results indicate the presence of alternating helical conformations that provide a better explanation for the flexibility of the helix-turn-helix region of trp aporepressor. Structures representing these conformations have been deposited with PDB ID: 5TM0. Proteins 2017; 85:731-740. © 2016 Wiley Periodicals, Inc.

Assessment of the utility of contact-based restraints in accelerating the prediction of protein structure using molecular dynamics simulations.

Molecular dynamics (MD) simulation is a well-established tool for the computational study of protein structure and dynamics, but its application to the important problem of protein structure prediction remains challenging, in part because extremely long timescales can be required to reach the native structure. Here, we examine the extent to which the use of low-resolution information in the form of residue-residue contacts, which can often be inferred from bioinformatics or experimental studies, can accelerate the determination of protein structure in simulation. We incorporated sets of 62, 31, or 15 contact-based restraints in MD simulations of ubiquitin, a benchmark system known to fold to the native state on the millisecond timescale in unrestrained simulations. One-third of the restrained simulations folded to the native state within a few tens of microseconds-a speedup of over an order of magnitude compared with unrestrained simulations and a demonstration of the potential for limited amounts of structural information to accelerate structure determination. Almost all of the remaining ubiquitin simulations reached near-native conformations within a few tens of microseconds, but remained trapped there, apparently due to the restraints. We discuss potential methodological improvements that would facilitate escape from these near-native traps and allow more simulations to quickly reach the native state. Finally, using a target from the Critical Assessment of protein Structure Prediction (CASP) experiment, we show that distance restraints can improve simulation accuracy: In our simulations, restraints stabilized the native state of the protein, enabling a reasonable structural model to be inferred.

Characterization of the Conformational Fluctuations in the Josephin Domain of Ataxin-3

As for a variety of other molecular recognition processes, conformational fluctuations play an important role in the cleavage of polyubiquitin chains by the Josephin domain of ataxin-3. The interaction between Josephin and ubiquitin appears to be mediated by the motions of α-helical hairpin that is unusual among deubiquitinating enzymes. Here, we characterized the conformational fluctuations of the helical hairpin by incorporating NMR measurements as replica-averaged restraints in molecular dynamics simulations, and by validating the results by small-angle x-ray scattering measurements. This approach allowed us to define the extent of the helical hairpin motions and suggest a role of such motions in the recognition of ubiquitin.

The Importance of Intrinsic Order in a Disordered Protein Ligand

The Importance of Intrinsic Order in a Disordered Protein Ligand

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 (Ca2+-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 Ca2+-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.

Determination of the Individual Roles of the Linker Residues in the Inter-Domain 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 challenging, however, to determine the structural properties of these multidomain proteins because of their conformational heterogeneity. Here, we characterize the interdomain motions in the calcium-bound state of calmodulin (Ca2+-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 interdomain motions of CaM, can be well described by exploiting the information provided by chemical shifts, as these parameters are particularly sensitive to the local geometry of polypeptide chains. We thus identify ten residues in the interdomain linker region that change their conformation upon substrate binding. Five of these residues (Met76, Lys 77, 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 Ca2+-CaM state obtained in this study is in agreement with residual dipolar coupling, paramagnetic resonance enhancement and small-angle X-ray scattering measurements, which were not used as restraints in the calculations. These results thus illustrate how CaM binds to its substrates by interdigitated residues in the interdomain linker that follow either the conformational selection or the induced fit mechanisms.

Replica-Averaged Metadynamics.

A statistical mechanics description of complex molecular systems involves the determination of ensembles of conformations that represent their Boltzmann distributions. The observable properties of these systems can be then predicted by calculating averages over such ensembles. In principle, given accurate energy functions and efficient sampling methods, these ensembles can be generated by molecular dynamics simulations. In practice, however, often the energy functions are known only approximately and the sampling can be carried out only in a limited manner. We describe here a method that enables to increase simultaneously both the quality of the energy functions and of the extent of the sampling in a system-dependent manner. The method is based on the incorporation of experimental data as replica-averaged structural restraints in molecular dynamics simulations and exploits the metadynamics framework to enhance the sampling. The application to the case of α-conotoxin SI, a 13-residue peptide that has been characterized extensively by experimental measurements, shows that the approach that we describe enables accurate free energy landscapes to be generated. The analysis of these landscapes indicates the presence of a low population state in equilibrium with the native state in which the only aromatic residue of α-conotoxin SI is exposed to the solvent, which is a feature that may predispose the peptide to interact with its partners.

Structures of the Excited States of Phospholamban and Shifts in Their Populations upon Phosphorylation

Phospholamban is an integral membrane protein that controls the calcium balance in cardiac muscle cells. As the function and regulation of this protein require the active involvement of low populated states in equilibrium with the native state, it is of great interest to acquire structural information about them. In this work, we calculate the conformations and populations of the ground state and the three main excited states of phospholamban by incorporating nuclear magnetic resonance residual dipolar couplings as replica-averaged structural restraints in molecular dynamics simulations. We then provide a description of the manner in which phosphorylation at Ser16 modulates the activity of the protein by increasing the sizes of the populations of its excited states. These results demonstrate that the approach that we describe provides a detailed characterization of the different states of phospholamban that determine the function and regulation of this membrane protein. We anticipate that the knowledge of conformational ensembles enable the design of new dominant negative mutants of phospholamban by modulating the relative populations of its conformational substates.

Characterization of the Interdomain Motions in Hen Lysozyme Using Residual Dipolar Couplings as Replica-Averaged Structural Restraints in Molecular Dynamics Simulations

Hen lysozyme is an enzyme characterized by the presence of two domains whose relative motions are involved in the mechanism of binding and release of the substrates. By using residual dipolar couplings as replica-averaged structural restraints in molecular dynamics simulations, we characterize the breathing motions describing the interdomain fluctuations of this protein. We found that the ensemble of conformations that we determined spans the entire range of structures of hen lysozyme deposited in the Protein Data Bank, including both the free and bound states, suggesting that the thermal motions in the free state provide access to the structures populated upon binding. The approach that we present illustrates how the use of residual dipolar couplings as replica-averaged structural restraints in molecular dynamics simulations makes it possible to explore conformational fluctuations of a relatively large amplitude in proteins.

A method of determining RNA conformational ensembles using structure-based calculations of residual dipolar couplings

We describe a method of determining the conformational fluctuations of RNA based on the incorporation of nuclear magnetic resonance (NMR) residual dipolar couplings (RDCs) as replica-averaged structural restraints in molecular dynamics simulations. In this approach, the alignment tensor required to calculate the RDCs corresponding to a given conformation is estimated from its shape, and multiple replicas of the RNA molecule are simulated simultaneously to reproduce in silico the ensemble-averaging procedure performed in the NMR measurements. We provide initial evidence that with this approach it is possible to determine accurately structural ensembles representing the conformational fluctuations of RNA by applying the reference ensemble test to the trans-activation response element of the human immunodeficiency virus type 1.

Molecular dynamics simulations with replica-averaged structural restraints generate structural ensembles according to the maximum entropy principle

In order to characterise the dynamics of proteins, a well-established method is to incorporate experimental parameters as replica-averaged structural restraints into molecular dynamics simulations. Here, we justify this approach in the case of interproton distance information provided by nuclear Overhauser effects by showing that it generates ensembles of conformations according to the maximum entropy principle. These results indicate that the use of replica-averaged structural restraints in molecular dynamics simulations, given a force field and a set of experimental data, can provide an accurate approximation of the unknown Boltzmann distribution of a system.

Assessment of the Use of NMR Chemical Shifts as Replica-Averaged Structural Restraints in Molecular Dynamics Simulations to Characterize the Dynamics of Proteins

It has been recently proposed that NMR chemical shifts can be used as replica-averaged structural restraints in molecular dynamics simulations to determine the conformational fluctuations of proteins. In this work, we assess the accuracy of this approach by considering its application to the case of ribonuclease A. We found that the agreement between experimental and calculated chemical shifts improves on average when the chemical shifts are used as replica-averaged restraints with respect to the cases in which X-ray structures or ensembles of structures obtained by standard molecular dynamics simulations are considered. These results indicate that the use of chemical shifts as structural restraints enables a bias of the conformational sampling to be introduced in a system-specific manner to reproduce accurately the conformational fluctuations of proteins.

Determination of structural fluctuations of proteins from structure-based calculations of residual dipolar couplings

Residual dipolar couplings (RDCs) have the potential of providing detailed information about the conformational fluctuations of proteins. It is very challenging, however, to extract such information because of the complex relationship between RDCs and protein structures. A promising approach to decode this relationship involves structure-based calculations of the alignment tensors of protein conformations. By implementing this strategy to generate structural restraints in molecular dynamics simulations we show that it is possible to extract effectively the information provided by RDCs about the conformational fluctuations in the native states of proteins. The approach that we present can be used in a wide range of alignment media, including Pf1, charged bicelles and gels. The accuracy of the method is demonstrated by the analysis of the Q factors for RDCs not used as restraints in the calculations, which are significantly lower than those corresponding to existing high-resolution structures and structural ensembles, hence showing that we capture effectively the contributions to RDCs from conformational fluctuations.

Characterization of the Conformational Equilibrium between the Two Major Substates of RNase A Using NMR Chemical Shifts

Following the recognition that NMR chemical shifts can be used for protein structure determination, rapid advances have recently been made in methods for extending this strategy for proteins and protein complexes of increasing size and complexity. A remaining major challenge is to develop approaches to exploit the information contained in the chemical shifts about conformational fluctuations in native states of proteins. In this work we show that it is possible to determine an ensemble of conformations representing the free energy surface of RNase A using chemical shifts as replica-averaged restraints in molecular dynamics simulations. Analysis of this surface indicates that chemical shifts can be used to characterize the conformational equilibrium between the two major substates of this protein.

Determination of Conformational Equilibria in Proteins Using Residual Dipolar Couplings

In order to carry out their functions, proteins often undergo significant conformational fluctuations that enable them to interact with their partners. The accurate characterization of these motions is key in order to understand the mechanisms by which macromolecular recognition events take place. Nuclear magnetic resonance spectroscopy offers a variety of powerful methods to achieve this result. We discuss a method of using residual dipolar couplings as replica-averaged restraints in molecular dynamics simulations to determine large amplitude motions of proteins, including those involved in the conformational equilibria that are established through interconversions between different states. By applying this method to ribonuclease A, we show that it enables one to characterize the ample fluctuations in interdomain orientations expected to play an important functional role.

Using NMR Chemical Shifts as Structural Restraints in Molecular Dynamics Simulations of Proteins

We introduce a procedure to determine the structures of proteins by incorporating NMR chemical shifts as structural restraints in molecular dynamics simulations. In this approach, the chemical shifts are expressed as differentiable functions of the atomic coordinates and used to compute forces to generate trajectories that lead to the reduction of the differences between experimental and calculated chemical shifts. We show that this strategy enables the folding of a set of proteins with representative topologies starting from partially denatured initial conformations without the use of additional experimental information. This method also enables the straightforward combination of chemical shifts with other standard NMR restraints, including those derived from NOE, J-coupling, and residual dipolar coupling measurements. We illustrate this aspect by calculating the structure of a transiently populated excited state conformation from chemical shift and residual dipolar coupling data measured by relaxation dispersion NMR experiments.

Determination of the Free Energy Landscape of α-Synuclein Using Spin Label Nuclear Magnetic Resonance Measurements

Natively unfolded proteins present a challenge for structure determination because they populate highly heterogeneous ensembles of conformations. A useful source of structural information about these states is provided by paramagnetic relaxation enhancement measurements by nuclear magnetic resonance spectroscopy, from which long-range interatomic distances can be estimated. Here we describe a method for using such distances as restraints in molecular dynamics simulations to obtain a mapping of the free energy landscapes of natively unfolded proteins. We demonstrate the method in the case of alpha-synuclein and validate the results by a comparison with electron transfer measurements. Our findings indicate that our procedure provides an accurate estimate of the relative statistical weights of the different conformations populated by alpha-synuclein in its natively unfolded state.

Residual dipolar coupling investigation of a heparin tetrasaccharide confirms the limited effect of flexibility of the iduronic acid on the molecular shape of heparin

The solution conformation of a fully sulfated heparin-derived tetrasaccharide, I, was studied in the presence of a 4-fold excess of Ca2+. Proton–proton and proton–carbon residual dipolar couplings (RDCs) were measured in a neutral aligning medium. The order parameters of two rigid hexosamine rings of I were determined separately using singular value decomposition and ab initio structures of disaccharide fragments of I. The order parameters were very similar implying that a common order tensor can be used to analyze the structure of I. Using one order tensor, RDCs of both hexosamine rings were used as restraints in molecular dynamics simulations. RDCs of the inner iduronic acid were calculated for every point of the molecular dynamics trajectory. The fitting of the calculated RDCs of the two forms of the iduronic acid to the experimental values yielded a population of 1C4 and 2So conformers of iduronic acid that agreed well with the analysis based on proton–proton scalar coupling constants. The glycosidic linkage torsion angles in RDC-restrained molecular dynamics (MD) structures of I are consistent with the interglycosidic three-bond proton–carbon coupling constants. These structures also show that the shape of heparin is not affected dramatically by the conformational flexibility of the iduronic acid ring. This is in line with conclusions of previous studies based on MD simulations and the analysis of 1H-1H NOEs. Our work therefore demonstrates the effectiveness of RDCs in the conformational analysis of glycosaminoglycans.

Mapping of Two Networks of Residues That Exhibit Structural and Dynamical Changes upon Binding in a PDZ Domain Protein

We describe the changes in structure and dynamics that occur in the second PDZ domain of human tyrosine phosphatase 1E upon binding the small peptide RA-GEF2 by an analysis of NMR data based on their use as ensemble-averaged restraints in molecular dynamics simulations. This approach reveals the presence of two interconnected networks of residues, the first exhibiting structural changes and the second dynamical changes upon binding, and it provides a detailed mapping of the regions of increased and decreased mobility upon binding. Analysis of the dynamical properties of the residues in these networks reveals that conformational changes are transmitted through pathways of coupled side-chain reorientations. These results illustrate how the strategy we described, in which NMR data are used in combination with molecular dynamics simulations, can be used to characterize in detail the complex organization of the changes in structure and dynamics that take place in proteins upon binding.