Characterization of the interdomain motions in hen lysozyme using residual dipolar couplings as replica-averaged structural restraints in molecular dynamics simulations

Mapping protein dynamics at high spatial resolution with temperature-jump X-ray crystallography

Understanding and controlling protein motion at atomic resolution is a hallmark challenge for structural biologists and protein engineers because conformational dynamics are essential for complex functions such as enzyme catalysis and allosteric regulation. Time-resolved crystallography offers a window into protein motions, yet without a universal perturbation to initiate conformational changes the method has been limited in scope. Here we couple a solvent-based temperature jump with time-resolved crystallography to visualize structural motions in lysozyme, a dynamic enzyme. We observed widespread atomic vibrations on the nanosecond timescale, which evolve on the submillisecond timescale into localized structural fluctuations that are coupled to the active site. An orthogonal perturbation to the enzyme, inhibitor binding, altered these dynamics by blocking key motions that allow energy to dissipate from vibrations into functional movements linked to the catalytic cycle. Because temperature jump is a universal method for perturbing molecular motion, the method demonstrated here is broadly applicable for studying protein dynamics.

MDexciteR: Enhanced Sampling Molecular Dynamics by Excited Normal Modes or Principal Components Obtained from Experiments

Molecular dynamics with excited normal modes (MDeNM) is an enhanced sampling method for exploring conformational changes in proteins with minimal biases. The excitation corresponds to injecting kinetic energy along normal modes describing intrinsic collective motions. Herein, we developed a new automated open-source implementation, MDexciteR (https://github.com/mcosta27/MDexciteR), enabling the integration of MDeNM with two commonly used simulation programs with GPU support. Second, we generalized the method to include the excitation of principal components calculated from experimental ensembles. Finally, we evaluated whether the use of coarse-grained normal modes calculated with elastic network representations preserved the performance and accuracy of the method. The advantages and limitations of these new approaches are discussed based on results obtained for three different protein test cases: two globular and a protein/membrane system.

Structures Controlled by Entropy: The Flexibility of Strychnine as Example

To study the flexibility of strychnine, we performed molecular dynamics simulations with orientational tensorial constraints (MDOC). Tensorial constraints are derived from nuclear magnetic resonance (NMR) interaction tensors, for instance, from residual dipolar couplings (RDCs). Used as orientational constraints, they rotate the whole molecule and molecular parts with low rotational barriers. Since the NMR parameters are measured at ambient temperatures, orientational constraints generate conformers that populate the whole landscape of Gibbs free energy. In MDOC, structures are populated that are not only controlled by energy but by the entropy term TΔS of the Gibbs free energy. In the case of strychnine, it is shown that ring conformers are populated, which has not been discussed in former investigations. These conformer populations are not only in accordance with RDCs but fulfill nuclear Overhauser effect (NOE)-derived distance constraints and ³J_HH couplings as well.

The role of structural dynamics in the thermal adaptation of hyperthermophilic enzymes

Proteins from hyperthermophilic organisms are evolutionary optimised to adopt functional structures and dynamics under conditions in which their mesophilic homologues are generally inactive or unfolded. Understanding the nature of such adaptation is of crucial interest to clarify the underlying mechanisms of biological activity in proteins. Here we measured NMR residual dipolar couplings of a hyperthermophilic acylphosphatase enzyme at 80°C and used these data to generate an accurate structural ensemble representative of its native state. The resulting energy landscape was compared to that obtained for a human homologue at 37°C, and additional NMR experiments were carried out to probe fast (¹⁵N relaxation) and slow (H/D exchange) backbone dynamics, collectively sampling fluctuations of the two proteins ranging from the nanosecond to the millisecond timescale. The results identified key differences in the strategies for protein-protein and protein-ligand interactions of the two enzymes at the respective physiological temperatures. These include the dynamical behaviour of a β-strand involved in the protection against aberrant protein aggregation and concerted motions of loops involved in substrate binding and catalysis. Taken together these results elucidate the structure-dynamics-function relationship associated with the strategies of thermal adaptation of protein molecules.

REDCRAFT: A computational platform using residual dipolar coupling NMR data for determining structures of perdeuterated proteins in solution

Nuclear Magnetic Resonance (NMR) spectroscopy is one of the three primary experimental means of characterizing macromolecular structures, including protein structures. Structure determination by solution NMR spectroscopy has traditionally relied heavily on distance restraints derived from nuclear Overhauser effect (NOE) measurements. While structure determination of proteins from NOE-based restraints is well understood and broadly used, structure determination from Residual Dipolar Couplings (RDCs) is relatively less well developed. Here, we describe the new features of the protein structure modeling program REDCRAFT and focus on the new Adaptive Decimation (AD) feature. The AD plays a critical role in improving the robustness of REDCRAFT to missing or noisy data, while allowing structure determination of larger proteins from less data. In this report we demonstrate the successful application of REDCRAFT in structure determination of proteins ranging in size from 50 to 145 residues using experimentally collected data, and of larger proteins (145 to 573 residues) using simulated RDC data. In both cases, REDCRAFT uses only RDC data that can be collected from perdeuterated proteins. Finally, we compare the accuracy of structure determination from RDCs alone with traditional NOE-based methods for the structurally novel PF.2048.1 protein. The RDC-based structure of PF.2048.1 exhibited 1.0 Å BB-RMSD with respect to a high-quality NOE-based structure. Although optimal strategies would include using RDC data together with chemical shift, NOE, and other NMR data, these studies provide proof-of-principle for robust structure determination of largely-perdeuterated proteins from RDC data alone using REDCRAFT.

Residual Dipolar Couplings have the potential to improve the accuracy and reduce the time needed to characterize protein structures. In addition, RDC data have been demonstrated to concurrently elucidate structure of proteins, provide assignment of resonances, and characterize the internal dynamics of proteins. Given all the advantages associated with the study of proteins from RDC data, based on the statistics provided by the Protein Databank (PDB), surprisingly only 124 proteins (out of nearly 150,000 proteins) have utilized RDCs as part of their structure determination. Even a smaller subset of these proteins (approximately 7) have utilized RDCs as the primary source of data for structure determination. One key factor in the use of RDCs is the challenging computational and analytical aspects of this source of data. In this report, we demonstrate the success of the REDCRAFT software package in structure determination of proteins using RDC data that can be collected from small and large proteins in a routine fashion. REDCRAFT accomplishes the challenging task of structure determination from RDCs by introducing a unique search and optimization technique that is both robust and computationally tractable. Structure determination from routinely collectable RDC data using REDCRAFT can complement existing methods to provide faster and more accurate studies of larger and more complex protein structures by NMR spectroscopy in solution state.

A quantum biochemistry investigation of the protein-protein interactions for the description of allosteric modulation on biomass-degrading chimera

The worldwide dependence of population on fossil fuels continues to have several harmful implications for the environment. Bioethanol is an excellent option for renewable fuel to replace the current greenhouse gas emitters. In addition, its production by enzymatic route has gained space among the industrial processes because it replaces the traditional acid treatment. Due to its high versatility, the xylanase family is used in this process as an accessory enzyme for degrading the lignocellulosic substrate of biomass. A chimera built by a xylanolytic domain (Xyl) and a xylose-binding protein (XBP) showed an experimentally improved catalytic efficiency and interdomain allosteric modulation after xylose binding. In this context, we performed a quantum biochemistry characterization of the interactions between these domains and dynamic cross-correlation (DCC) analysis after performing molecular dynamics (DM) simulations of the systems in the presence and absence of xylose in the XBP active site. We used the density functional theory (DFT) within the molecular fractionation with the conjugated caps (MFCC) approach to describe the pair energies, and the corresponding energy difference between the chimera domains responsible for the allosteric effect and amino acid DCC to evaluate the interdomain coupling differences between the energy states. The detailed energetic investigation together with the related structural and dynamics counterparts revealed the molecular mechanisms of chimeric improvement of the xylanase activity observed experimentally. This mechanism was correlated with greater stability and high connectivity at the interdomain interface in the xylose bound relative to the free chimera. We identify the contributions of hydrogen bonds, hydrophobic interactions and water-mediated interactions in the interdomain region responsible for stability together with the structural and dynamical elements related to the allosteric effect. Taken together, these observations led to a comprehensive understanding of the chimera's modulatory action that occurs through the formation of a highly connected interface that makes the essential movements related to xylanolytic activity in xylanase correlated to those of the xylose-binding protein.

A Hierarchical Approach to Predict Conformation-Dependent Histidine Protonation States in Stable and Flexible Proteins

Solution acidity measured by pH is an important environmental factor that affects protein structure. It influences the protonation state of protein residues, which in turn may be coupled to protein conformational changes, unfolding, and ligand binding. It remains difficult to compute and measure the p K_a of individual residues, as well as to relate them to pH-dependent protein transitions. This paper presents a hierarchical approach to compute the p K_a of individual protonatable residues, specifically histidines, coupled with underlying structural changes of a protein. A fast and efficient free energy perturbation (FEP) algorithm has also been developed utilizing a fast implementation of standard molecular dynamics (MD) algorithms. Specifically, a CUDA version of the AMBER MD engine is used in this paper. Eight histidine p K_a's are computed in a diverse set of pH stable proteins to demonstrate the proposed approach's utility and assess the predictive quality of the AMBER FF99SB force field. A reference molecule is carefully selected and tested for convergence. A hierarchical approach is used to model p K_a's of the six histidine residues of the diphtheria toxin translocation domain (DTT), which exhibits a diverse ensemble of individual conformations and pH-dependent unfolding. The hierarchical approach consists of first sampling equilibrium conformational ensembles of a protein with protonated and neutral histidine residues via long equilibrium MD simulations (Flores-Canales, J. C.; et al. bioRxiv, 2019, 572040). A clustering method is then used to identify sampled protein conformations, and p K_a's of histidines in each protein conformation are computed. Finally, an ensemble averaging formalism is developed to compute weighted average histidine p K_a's. These can be compared with an apparent experimentally measured p K_a of the DTT protein and thus allows us to propose a mechanism of pH-dependent unfolding of the DTT protein.

Determination of the conformational states of strychnine in solution using NMR residual dipolar couplings in a tensor-free approach

Small molecules with rotatable bonds can occupy different conformational states in solution as a consequence of their thermal fluctuations. The accurate determination of the structures of such states, as well as of their statistical weights, has been challenging because of the technical difficulties in extracting information from experimental measurements, which are normally averaged over the conformational space available. Here, to achieve this objective, we present an approach based on a recently proposed tensor-free method for incorporating NMR residual dipolar couplings as structural restraints in replica-averaged molecular dynamics simulations. This approach enables the information provided by the experimental data to be used in the spirit of the maximum entropy principle to determine the structural ensembles of small molecules. Furthermore, in order to enhance the sampling of the conformational space we incorporated the metadynamics method in the simulations. We illustrate the method in the case of strychnine, determining the three major conformational states of this small molecule and their associated occupation probabilities.

Atomistic structural ensemble refinement reveals non-native structure stabilizes a sub-millisecond folding intermediate of CheY

The dynamics of globular proteins can be described in terms of transitions between a folded native state and less-populated intermediates, or excited states, which can play critical roles in both protein folding and function. Excited states are by definition transient species, and therefore are difficult to characterize using current experimental techniques. Here, we report an atomistic model of the excited state ensemble of a stabilized mutant of an extensively studied flavodoxin fold protein CheY. We employed a hybrid simulation and experimental approach in which an aggregate 42 milliseconds of all-atom molecular dynamics were used as an informative prior for the structure of the excited state ensemble. This prior was then refined against small-angle X-ray scattering (SAXS) data employing an established method (EROS). The most striking feature of the resulting excited state ensemble was an unstructured N-terminus stabilized by non-native contacts in a conformation that is topologically simpler than the native state. Using these results, we then predict incisive single molecule FRET experiments as a means of model validation. This study demonstrates the paradigm of uniting simulation and experiment in a statistical model to study the structure of protein excited states and rationally design validating experiments.

Exploring free energy landscapes of large conformational changes: molecular dynamics with excited normal modes

Proteins are found in solution as ensembles of conformations in dynamic equilibrium. Exploration of functional motions occurring on micro- to millisecond time scales by molecular dynamics (MD) simulations still remains computationally challenging. Alternatively, normal mode (NM) analysis is a well-suited method to characterize intrinsic slow collective motions, often associated with protein function, but the absence of anharmonic effects preclude a proper characterization of conformational distributions in a multidimensional NM space. Using both methods jointly appears to be an attractive approach that allows an extended sampling of the conformational space. In line with this view, the MDeNM (molecular dynamics with excited normal modes) method presented here consists of multiple-replica short MD simulations in which motions described by a given subset of low-frequency NMs are kinetically excited. This is achieved by adding additional atomic velocities along several randomly determined linear combinations of NM vectors, thus allowing an efficient coupling between slow and fast motions. The relatively high-energy conformations generated with MDeNM are further relaxed with standard MD simulations, enabling free energy landscapes to be determined. Two widely studied proteins were selected as examples: hen egg lysozyme and HIV-1 protease. In both cases, MDeNM provides a larger extent of sampling in a few nanoseconds, outperforming long standard MD simulations. A high degree of correlation with motions inferred from experimental sources (X-ray, EPR, and NMR) and with free energy estimations obtained by metadynamics was observed. Finally, the large sets of conformations obtained with MDeNM can be used to better characterize relevant dynamical populations, allowing for a better interpretation of experimental data such as SAXS curves and NMR spectra.

Role of Conformational Motions in Enzyme Function: Selected Methodologies and Case Studies

It is now common knowledge that enzymes are mobile entities relying on complex atomic-scale dynamics and coordinated conformational events for proper ligand recognition and catalysis. However, the exact role of protein dynamics in enzyme function remains either poorly understood or difficult to interpret. This mini-review intends to reconcile biophysical observations and biological significance by first describing a number of common experimental and computational methodologies employed to characterize atomic-scale residue motions on various timescales in enzymes, and second by illustrating how the knowledge of these motions can be used to describe the functional behavior of enzymes and even act upon it. Two biologically relevant examples will be highlighted, namely the HIV-1 protease and DNA polymerase β enzyme systems.

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.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Controlling Allosteric Networks in Proteins

Allosteric transition, defined as conformational changes induced by ligand binding, is one of the fundamental properties of proteins. Allostery has been observed and characterized in many proteins, and has been recently utilized to control protein function via regulation of protein activity. Here, we review the physical and evolutionary origin of protein allostery, as well as its importance to protein regulation, drug discovery, and biological processes in living systems. We describe recently developed approaches to identify allosteric pathways, connected sets of pairwise interactions that are responsible for propagation of conformational change from the ligand-binding site to a distal functional site. We then present experimental and computational protein engineering approaches for control of protein function by modulation of allosteric sites. As an example of application of these approaches, we describe a synergistic computational and experimental approach to rescue the cystic-fibrosis-associated protein cystic fibrosis transmembrane conductance regulator, which upon deletion of a single residue misfolds and causes disease. This example demonstrates the power of allosteric manipulation in proteins to both elucidate mechanisms of molecular function and to develop therapeutic strategies that rescue those functions. Allosteric control of proteins provides a tool to shine a light on the complex cascades of cellular processes and facilitate unprecedented interrogation of biological systems.

Investigating protein conformational energy landscapes and atomic resolution dynamics from NMR dipolar couplings: a review

Nuclear magnetic resonance spectroscopy is exquisitely sensitive to protein dynamics. In particular inter-nuclear dipolar couplings, that become measurable in solution when the protein is dissolved in a dilute liquid crystalline solution, report on all conformations sampled up to millisecond timescales. As such they provide the opportunity to describe the Boltzmann distribution present in solution at atomic resolution, and thereby to map the conformational energy landscape in unprecedented detail. The development of analytical methods and approaches based on numerical simulation and their application to numerous biologically important systems is presented.

KCTD5 is endowed with large, functionally relevant, interdomain motions

The KCTD family is an emerging class of proteins that are involved in important biological processes whose biochemical and structural properties are rather poorly characterized or even completely undefined. We here used KCTD5, the only member of the family with a known three-dimensional structure, to gain insights into the intrinsic structural stability of the C-terminal domain (CTD) and into the mutual dynamic interplay between the two domains of the protein. Molecular dynamics (MD) simulations indicate that in the simulation timescale (120 ns), the pentameric assembly of the CTD is endowed with a significant intrinsic stability. Moreover, MD analyses also led to the identification of exposed β-strand residues. Being these regions intrinsically sticky, they could be involved in the substrate recognition. More importantly, simulations conducted on the full-length protein provide interesting information of the relative motions between the BTB domain and the CTD of the protein. Indeed, the dissection of the overall motion of the protein is indicative of a large interdomain twisting associated with limited bending movements. Notably, MD data indicate that the entire interdomain motion is pivoted by a single residue (Ser150) of the hinge region that connects the domains. The functional relevance of these motions was evaluated in the context of the functional macromolecular machinery in which KCTD5 is involved. This analysis indicates that the interdomain twisting motion here characterized may be important for the correct positioning of the substrate to be ubiquitinated with respect to the other factors of the ubiquitination machinery.

Pressure-induced structural transition of mature HIV-1 protease from a combined NMR/MD simulation approach

We investigate the pressure-induced structural changes in the mature human immunodeficiency virus type 1 protease dimer, using residual dipolar coupling (RDC) measurements in a weakly oriented solution. (1)DNH RDCs were measured under high-pressure conditions for an inhibitor-free PR and an inhibitor-bound complex, as well as for an inhibitor-free multidrug resistant protease bearing 20 mutations (PR20). While PR20 and the inhibitor-bound PR were little affected by pressure, inhibitor-free PR showed significant differences in the RDCs measured at 600 bar compared with 1 bar. The structural basis of such changes was investigated by MD simulations using the experimental RDC restraints, revealing substantial conformational perturbations, specifically a partial opening of the flaps and the penetration of water molecules into the hydrophobic core of the subunits at high pressure. This study highlights the exquisite sensitivity of RDCs to pressure-induced conformational changes and illustrates how RDCs combined with MD simulations can be used to determine the structural properties of metastable intermediate states on the folding energy landscape.

Molecular Dynamics of Biomolecules through Direct Analysis of Dipolar Couplings

Residual dipolar couplings (RDCs) are important probes in structural biology, but their analysis is often complicated by the determination of an alignment tensor or its associated assumptions. We here apply the maximum entropy principle to derive a tensor-free formalism which allows for direct, dynamic analysis of RDCs and holds the classic tensor formalism as a special case. Specifically, the framework enables us to robustly analyze data regardless of whether a clear separation of internal and overall dynamics is possible. Such a separation is often difficult in the core subjects of current structural biology, which include multidomain and intrinsically disordered proteins as well as nucleic acids. We demonstrate the method is tractable and self-consistent and generalizes to data sets comprised of observations from multiple different alignment conditions.

Integrative, dynamic structural biology at atomic resolution--it's about time

Biomolecules adopt a dynamic ensemble of conformations, each with the potential to interact with binding partners or perform the chemical reactions required for a multitude of cellular functions. Recent advances in X-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy and other techniques are helping us realize the dream of seeing--in atomic detail--how different parts of biomolecules shift between functional substates using concerted motions. Integrative structural biology has advanced our understanding of the formation of large macromolecular complexes and how their components interact in assemblies by leveraging data from many low-resolution methods. Here, we review the growing opportunities for integrative, dynamic structural biology at the atomic scale, contending there is increasing synergistic potential between X-ray crystallography, NMR and computer simulations to reveal a structural basis for protein conformational dynamics at high resolution.

Structure of a low-population intermediate state in the release of an enzyme product

Enzymes can increase the rate of biomolecular reactions by several orders of magnitude. Although the steps of substrate capture and product release are essential in the enzymatic process, complete atomic-level descriptions of these steps are difficult to obtain because of the transient nature of the intermediate conformations, which makes them largely inaccessible to standard structure determination methods. We describe here the determination of the structure of a low-population intermediate in the product release process by human lysozyme through a combination of NMR spectroscopy and molecular dynamics simulations. We validate this structure by rationally designing two mutations, the first engineered to destabilise the intermediate and the second to stabilise it, thus slowing down or speeding up, respectively, product release. These results illustrate how product release by an enzyme can be facilitated by the presence of a metastable intermediate with transient weak interactions between the enzyme and product.

Recent advances in the understanding of two-step nucleation of protein crystals

The two-step mechanism of nucleation of crystals in solutions posits that the formation of crystal nuclei occurs within structures of extended lifetimes, in which the nucleating solute is at high concentration. The validity of this mechanism has been demonstrated for proteins, small-molecule organic and inorganic materials, colloids, and polymers. Due to large molecule sizes, proteins are an ideal system to study the details of this nucleation pathway, in particular the formation mechanisms of the nucleation precursors and the associated physico-chemical rules. The precursors of protein crystal nuclei are protein-rich clusters of sizes ∼100 nm that contain 10 000–100 000 molecules and occupy less than 10⁻³of the total solution volume. Here we demonstrate, using oblique illumination microscopy, the liquid nature of the clusters of the protein lysozyme and reveal their inhomogeneous structure. We test a hypothesis put forth by theory that clusters primarily consist of transient protein oligomers. For this, we explore how varying the strength of the Coulomb interaction affects the cluster characteristics. We find that the cluster’s size is insensitive to variations of pH and ionic strength. In contrast, the addition of urea, a chaotropic agent that leads to protein unfolding, strongly decreases the cluster size. Shear stress, a known protein denaturant, induced by bubbling of the solutions with an inert gas, elicits a similar response. These observations support partial protein unfolding, followed by dimerization, as the mechanism of cluster formation. The amide hydrogen–deuterium exchange, monitored by nuclear magnetic resonance, highlights that lysozyme conformational flexibility is a condition for the formation of the protein-rich clusters and facilitates the nucleation of protein crystals.

Conformational recognition of an intrinsically disordered protein

There is a growing interest in understanding the properties of intrinsically disordered proteins (IDPs); however, the characterization of these states remains an open challenge. IDPs appear to have functional roles that diverge from those of folded proteins and revolve around their ability to act as hubs for protein-protein interactions. To gain a better understanding of the modes of binding of IDPs, we combined statistical mechanics, calorimetry, and NMR spectroscopy to investigate the recognition and binding of a fragment from the disordered protein Gab2 by the growth factor receptor-bound protein 2 (Grb2), a key interaction for normal cell signaling and cancer development. Structural ensemble refinement by NMR chemical shifts, thermodynamics measurements, and analysis of point mutations indicated that the population of preexisting bound conformations in the free-state ensemble of Gab2 is an essential determinant for recognition and binding by Grb2. A key role was found for transient polyproline II (PPII) structures and extended conformations. Our findings are likely to have very general implications for the biological behavior of IDPs in light of the evidence that a large fraction of these proteins possess a specific propensity to form PPII and to adopt conformations that are more extended than the typical random-coil states.

A simple and fast approach for predicting (1)H and (13)C chemical shifts: toward chemical shift-guided simulations of RNA

We introduce a simple and fast approach for predicting RNA chemical shifts from interatomic distances that performs with an accuracy similar to existing predictors and enables the first chemical shift-restrained simulations of RNA to be carried out. Our analysis demonstrates that the applied restraints can effectively guide conformational sampling toward regions of space that are more consistent with chemical shifts than the initial coordinates used for the simulations. As such, our approach should be widely applicable in mapping the conformational landscape of RNAs via chemical shift-guided molecular dynamics simulations. The simplicity and demonstrated sensitivity to three-dimensional structure should also allow our method to be used in chemical shift-based RNA structure prediction, validation, and refinement.

Efficient and Minimal Method to Bias Molecular Simulations with Experimental Data

A primary goal in molecular simulations is to modify the potential energy of a system so that properties of the simulation match experimental data. This is traditionally done through iterative cycles of simulation and reparameterization. An alternative approach is to bias the potential energy so that the system matches experimental data. This can be done while minimally changing the underlying free energy of the molecular simulation. Current minimal biasing methods require replicas, which can lead to unphysical dynamics and introduces new complexity: the choice of replica number and their properties. Here, we describe a new method, called experiment directed simulation that does not require replicas, converges rapidly, can match many data simultaneously, and minimally modifies the potential. The experiment directed simulation method is demonstrated on model systems and a three-component electrolyte simulation. The theory used to derive the method also provides insight into how changing a molecular force-field impacts the expected value of observables in simulation.

A tensor-free method for the structural and dynamical refinement of proteins using residual dipolar couplings

Residual dipolar couplings (RDCs) are parameters measured in nuclear magnetic resonance spectroscopy that can provide exquisitely detailed information about the structure and dynamics of biological macromolecules. We describe here a method of using RDCs for the structural and dynamical refinement of proteins that is based on the observation that the RDC between two atomic nuclei depends directly on the angle ϑ between the internuclear vector and the external magnetic field. For every pair of nuclei for which an RDC is available experimentally, we introduce a structural restraint to minimize the deviation from the value of the angle ϑ derived from the measured RDC and that calculated in the refinement protocol. As each restraint involves only the calculation of the angle ϑ of the corresponding internuclear vector, the method does not require the definition of an overall alignment tensor to describe the preferred orientation of the protein with respect to the alignment medium. Application to the case of ubiquitin demonstrates that this method enables an accurate refinement of the structure and dynamics of this protein to be obtained.

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.

Chemical exchange in biomacromolecules: past, present, and future

The perspective reviews quantitative investigations of chemical exchange phenomena in proteins and other biological macromolecules using NMR spectroscopy, particularly relaxation dispersion methods. The emphasis is on techniques and applications that quantify the populations, interconversion kinetics, and structural features of sparsely populated conformational states in equilibrium with a highly populated ground state. Applications to folding, molecular recognition, catalysis, and allostery by proteins and nucleic acids are highlighted.