Comparison of Different Reweighting Approaches for the Calculation of Conformational Variability of Macromolecules from Molecular Simulations

Implementation of Time-Averaged Restraints with UNRES Coarse-Grained Model of Polypeptide Chains

Time-averaged restraints from nuclear magnetic resonance (NMR) measurements have been implemented in the UNRES coarse-grained model of polypeptide chains in order to develop a tool for data-assisted modeling of the conformational ensembles of multistate proteins, intrinsically disordered proteins (IDPs) and proteins with intrinsically disordered regions (IDRs), many of which are essential in cell biology. A numerically stable variant of molecular dynamics with time-averaged restraints has been introduced, in which the total energy is conserved in sections of a trajectory in microcanonical runs, the bath temperature is maintained in canonical runs, and the time-average-restraint-force components are scaled up with the length of the memory window so that the restraints affect the simulated structures. The new approach restores the conformational ensembles used to generate ensemble-averaged distances, as demonstrated with synthetic restraints. The approach results in a better fitting of the ensemble-averaged interproton distances to those determined experimentally for multistate proteins and proteins with intrinsically disordered regions, which puts it at an advantage over all-atom approaches with regard to the determination of the conformational ensembles of proteins with diffuse structures, owing to a faster and more robust conformational search.

Are Protein Conformational Ensembles in Agreement with Experimental Data? A Geometrical Interpretation of the Problem

The conformational variability of biological macromolecules can play an important role in their biological function. Therefore, understanding conformational variability is expected to be key for predicting the behavior of a particular molecule in the context of organism-wide studies. Several experimental methods have been developed and deployed for accessing this information, and computational methods are continuously updated for the profitable integration of different experimental sources. The outcome of this endeavor is conformational ensembles, which may vary significantly in properties and composition when different ensemble reconstruction methods are used, and this raises the issue of comparing the predicted ensembles against experimental data. In this article, we discuss a geometrical formulation to provide a framework for understanding the agreement of an ensemble prediction to the experimental observations.

Boosting Ensemble Refinement with Transferable Force-Field Corrections: Synergistic Optimization for Molecular Simulations

A novel method combining the force-field fitting approach and ensemble refinement by the maximum entropy principle is presented. Its formulation allows us to continuously interpolate between these two methods, which can thus be interpreted as two limiting cases. A cross-validation procedure enables us to correctly assess the relative weight of both of them, distinguishing scenarios in which the combined approach is meaningful from those in which either ensemble refinement or force-field fitting separately prevails. The efficacy of their combination is examined for a realistic case study of RNA oligomers. Within the new scheme, molecular dynamics simulations are integrated with experimental data provided by nuclear magnetic resonance measures. We show that force-field corrections are in general superior when applied to the appropriate force-field terms but are automatically discarded by the method when applied to inappropriate force-field terms.

Exploring the impact of alignment media on RDC analysis of phosphorus-containing compounds: a molecular docking approach

Residual dipolar couplings (RDCs) are employed in NMR analysis when conventional methods, such as J-couplings and nuclear Overhauser effects (NOEs) fail. Low-energy (optimized) conformers are often used as input structures in RDC analysis programs. However, these low-energy structures do not necessarily resemble conformations found in anisotropic environments due to interactions with the alignment medium, especially if the analyte molecules are flexible. Considering interactions with alignment media in RDC analysis, we developed and evaluated a molecular docking-based approach to generate more accurate conformer ensembles for compounds in the presence of the poly-γ-benzyl-L-glutamate alignment medium. We designed chiral phosphorus-containing compounds that enabled us to utilize 31P NMR parameters for the stereochemical analysis. Using P3D/PALES software to evaluate diastereomer discrimination, we found that our conformer ensembles outperform moderately the standard, low-energy conformers in RDC analysis. To further improve our results, we (i) averaged the experimental values of the molecular docking-based conformers by applying the Boltzmann distribution and (ii) optimized the structures through normal mode relaxation, thereby enhancing the Pearson correlation factor R and even diastereomer discrimination in some cases. Nevertheless, we presume that significant differences between J-couplings in isotropic and in anisotropic environments may preclude RDC measurements for flexible molecules. Therefore, generating conformer ensembles based on molecular docking enhances RDC analysis for mildly flexible systems while flexible molecules may require applying more advanced approaches, in particular approaches including dynamical effects.

Computational modeling multiple conformational states of proteins with residual dipolar coupling data

Solution nuclear magnetic resonance spectroscopy provides unique opportunities to study the structure and dynamics of biomolecules in aqueous environments. While spin relaxation methods are well recognized for their ability to probe timescales of motion, residual dipolar couplings (RDCs) provide access to amplitudes and directions of motion, characteristics that are important to the function of these molecules. Although observed in the 1960s, the acquisition and computational analysis of RDCs has gained significant momentum in recent years, and particularly applications to motion in proteins have become more numerous. This trend may well continue as RDCs can easily leverage structures produced by new computational methods (e.g., AlphaFold) to produce functional descriptions. In this report, we provide examples and a summary of the ways that RDCs have been used to confirm the existence of internal dynamics, characterize the type of dynamics, and recover atomic-scale structural ensembles that define the full range of conformational sampling.

Paramagnetic NMR restraints for the characterization of protein structural rearrangements

Mobility is a common feature of biomacromolecules, often fundamental for their function. Thus, in many cases, biomacromolecules cannot be described by a single conformation, but rather by a conformational ensemble. NMR paramagnetic data demonstrated quite informative to monitor this conformational variability, especially when used in conjunction with data from different sources. Due to their long-range nature, paramagnetic data can, for instance, i) clearly demonstrate the occurrence of conformational rearrangements, ii) reveal the presence of minor conformational states, sampled only for a short time, iii) indicate the most representative conformations within the conformational ensemble sampled by the molecule, iv) provide an upper limit to the weight of each conformation.

Integrating experimental data with molecular simulations to investigate RNA structural dynamics

Conformational dynamics is crucial for ribonucleic acid (RNA) function. Techniques such as nuclear magnetic resonance, cryo-electron microscopy, small- and wide-angle X-ray scattering, chemical probing, single-molecule Förster resonance energy transfer, or even thermal or mechanical denaturation experiments probe RNA dynamics at different time and space resolutions. Their combination with accurate atomistic molecular dynamics (MD) simulations paves the way for quantitative and detailed studies of RNA dynamics. First, experiments provide a quantitative validation tool for MD simulations. Second, available data can be used to refine simulated structural ensembles to match experiments. Finally, comparison with experiments allows for improving MD force fields that are transferable to new systems for which data is not available. Here we review the recent literature and provide our perspective on this field.

The evolution of paramagnetic NMR as a tool in structural biology

Paramagnetic NMR data contain extremely accurate long-range information on metalloprotein structures and, when used in the frame of integrative structural biology approaches, they allow for the retrieval of structural details to a resolution that is not achievable using other techniques. Paramagnetic data thus represent an extremely powerful tool to refine protein models in solution, especially when coupled to X-ray or cryoelectron microscopy data, to monitor the formation of complexes and determine the relative arrangements of their components, and to highlight the presence of conformational heterogeneity. More recently, theoretical and computational advancements in quantum chemical calculations of paramagnetic NMR observables are progressively opening new routes in structural biology, because they allow for the determination of the structure within the coordination sphere of the metal center, thus acting as a loupe on sites that are difficult to observe but very important for protein function.

Characterizing conformational ensembles of multi-domain proteins using anisotropic paramagnetic NMR restraints

It has been over two decades since paramagnetic NMR started to form part of the essential techniques for structural analysis of proteins under physiological conditions. Paramagnetic NMR has significantly expanded our understanding of the inherent flexibility of proteins, in particular, those that are formed by combinations of two or more domains. Here, we present a brief overview of techniques to characterize conformational ensembles of such multi-domain proteins using paramagnetic NMR restraints produced through anisotropic metals, with a focus on the basics of anisotropic paramagnetic effects, the general procedures of conformational ensemble reconstruction, and some representative reweighting approaches.

Conformational Space Sampled by Domain Reorientation of Linear Diubiquitin Reflected in Its Binding Mode for Target Proteins

Linear polyubiquitin chains regulate diverse signaling proteins, in which the chains adopt various conformations to recognize different target proteins. Thus, the structural plasticity of the chains plays an important role in controlling the binding events. Herein, paramagnetic NMR spectroscopy is employed to explore the conformational space sampled by linear diubiquitin, a minimal unit of linear polyubiquitin, in its free state. Rigorous analysis of the data suggests that, regarding the relative positions of the ubiquitin units, particular regions of conformational space are preferentially sampled by the molecule. By combining these results with further data collected for charge-reversal derivatives of linear diubiquitin, structural insights into the factors underlying the binding events of linear diubiquitin are obtained.

Characterization of lanthanoid-binding proteins using NMR spectroscopy

The variety of magnetic properties exhibited by paramagnetic lanthanoids provides outstanding information in NMR-based structural biology and therefore can be a very useful tool for characterizing lanthanoid-binding proteins. Because of their dependence on the relative positions of the protein nuclei and of the lanthanoid ion, the paramagnetic restraints (PCS, PRDC and PRE) provide information on structure and dynamics of proteins. In this Chapter, we cover the use of lanthanoids in structural biology including protein sample preparation, NMR experiments and data interpretation.