Nuclear Magnetic Resonance Ensemble Research Articles

Importance of the Force Field Choice in Capturing Functionally Relevant Dynamics in the von Willebrand Factor.

Whether recent updates and new releases of atomistic force fields can model the structural and dynamical properties of proteins containing both folded and partially disordered domains is still unclear. To address this fundamental question, we tested eight recently released force fields against our set of nuclear magnetic resonance (NMR) observables for a complex and medically relevant system, the major factor VIII binding region on the von Willebrand factor. This biomedically important region comprises both a folded and a partially structured domain. By using an enhanced sampling technique (temperature replica-exchange molecular dynamics simulations), we find that some force fields indeed rise to the challenge and capture the structural and dynamical features of the NMR ensemble and, therefore, are the appropriate choice for simulations of proteins with partially structured domains. What is more, we show that only such force fields can qualitatively capture the effects of a pathogenic mutation on the structural ensemble.

PDB2CD visualises dynamics within protein structures

Proteins tend to have defined conformations, a key factor in enabling their function. Atomic resolution structures of proteins are predominantly obtained by either solution nuclear magnetic resonance (NMR) or crystal structure methods. However, when considering a protein whose structure has been determined by both these approaches, on many occasions, the resultant conformations are subtly different, as illustrated by the examples in this study. The solution NMR approach invariably results in a cluster of structures whose conformations satisfy the distance boundaries imposed by the data collected; it might be argued that this is evidence of the dynamics of proteins when in solution. In crystal structures, the proteins are often in an energy minimum state which can result in an increase in the extent of regular secondary structure present relative to the solution state depicted by NMR, because the more dynamic ends of alpha helices and beta strands can become ordered at the lower temperatures. This study examines a novel way to display the differences in conformations within an NMR ensemble and between these and a crystal structure of a protein. Circular dichroism (CD) spectroscopy can be used to characterise protein structures in solution. Using the new bioinformatics tool, PDB2CD, which generates CD spectra from atomic resolution protein structures, the differences between, and possible dynamic range of, conformations adopted by a protein can be visualised.

Evidence of conformational selection driving the formation of ligand binding sites in protein-protein interfaces.

Many protein-protein interactions (PPIs) are compelling targets for drug discovery, and in a number of cases can be disrupted by small molecules. The main goal of this study is to examine the mechanism of binding site formation in the interface region of proteins that are PPI targets by comparing ligand-free and ligand-bound structures. To avoid any potential bias, we focus on ensembles of ligand-free protein conformations obtained by nuclear magnetic resonance (NMR) techniques and deposited in the Protein Data Bank, rather than on ensembles specifically generated for this study. The measures used for structure comparison are based on detecting binding hot spots, i.e., protein regions that are major contributors to the binding free energy. The main tool of the analysis is computational solvent mapping, which explores the surface of proteins by docking a large number of small “probe” molecules. Although we consider conformational ensembles obtained by NMR techniques, the analysis is independent of the method used for generating the structures. Finding the energetically most important regions, mapping can identify binding site residues using ligand-free models based on NMR data. In addition, the method selects conformations that are similar to some peptide-bound or ligand-bound structure in terms of the properties of the binding site. This agrees with the conformational selection model of molecular recognition, which assumes such pre-existing conformations. The analysis also shows the maximum level of similarity between unbound and bound states that is achieved without any influence from a ligand. Further shift toward the bound structure assumes protein-peptide or protein-ligand interactions, either selecting higher energy conformations that are not part of the NMR ensemble, or leading to induced fit. Thus, forming the sites in protein-protein interfaces that bind peptides and can be targeted by small ligands always includes conformational selection, although other recognition mechanisms may also be involved.

Predicting the Predictive Power of IDP Ensembles

The function of intrinsically disordered proteins may be interpreted in terms of their structural ensembles. The article by Schwalbe and colleagues in this issue of Structure combines NMR and SAXS constraints to generate structural ensembles that unveil important functional and pathological features.

All-Atom Ensemble Modeling to Analyze Small-Angle X-Ray Scattering of Glycosylated Proteins

The flexible and heterogeneous nature of carbohydrate chains often renders glycoproteins refractory to traditional structure determination methods. Small-angle X-ray scattering (SAXS) can be a useful tool for obtaining structural information of these systems. All-atom modeling of glycoproteins with flexible glycan chains was applied to interpret the solution SAXS data for a set of glycoproteins. For simpler systems (single glycan, with a well-defined protein structure), all-atom modeling generates models in excellent agreement with the scattering pattern and reveals the approximate spatial occupancy of the glycan chain in solution. For more complex systems (several glycan chains, or unknown protein substructure), the approach can still provideinsightful models, though the orientations of glycans become poorly determined. Ab initio shape reconstructions appear to capture the global morphology of glycoproteins but in most cases offer littleinformation about glycan spatial occupancy. The all-atom modeling methodology is available as a web server at http://salilab.org/allosmod-foxs.

Investigation of the Leggett-Garg Inequality for Precessing Nuclear Spins

We report experimental implementation of a protocol for testing the Leggett-Garg inequality (LGI) for nuclear spins precessing in an external magnetic field. The implementation involves certain controlled operations, performed in parallel on pairs of spin-1/2 nuclei (target and probe) from molecules of a nuclear magnetic resonance ensemble, which enable evaluation of temporal correlations from an LG string. Our experiment demonstrates violation of the LGI for time intervals between successive measurements, over which the effects of relaxation on the quantum state of target spin are negligible. Further, it is observed that the temporal correlations decay, and the same target spin appears to display macrorealistic behavior consistent with LGI.

Quantum demonstration of a bio-molecular solution of the satisfiability problem on spin-based ensemble

DNA computation (DNAC) has been proposed to solve the satisfiability (SAT) problem due to operations in parallel on extremely large numbers of strands. This paper attempts to treat the DNA-based bio-molecular solution for the SAT problem from the quantum mechanical perspective with a purpose to explore the relationship between DNAC and quantum computation (QC). To achieve this goal, it first builds up the correspondence of operations between QC and DNAC. Then it gives an example for the case of two variables and three clauses for details of this theory. It also demonstrates a three-qubit experiment for solving the simplest SAT problem with a single variable on a liquid-state nuclear magnetic resonance ensemble to verify this theory. Some discussions are made for the potential application and for further exploration of the present work.

Computational identification of slow conformational fluctuations in proteins.

Conformational flexibility of proteins has been linked to their designated functions. Slow conformational fluctuations occurring at the microsecond to millisecond time scale, in particular, have recently attracted considerable interest in connection to the mechanism of enzyme catalysis. Computational methods are providing valuable insights into the connection between protein structure, flexibility, and function. In this report, we present studies on identification and characterization of microsecond flexibility of ubiquitin, based on quasi-harmonic analysis (QHA) and normal-mode analysis (NMA). The results indicate that the slowest 10 QHA modes, computed from the 0.5 mus molecular dynamics ensemble, contribute over 78% of all motions. The identified slow movements show over 75% similarity with the conformational fluctuations observed in nuclear magnetic resonance ensemble and also agree with displacements in the set of X-ray structures. The slowest modes show high flexibility in the beta1-beta2, alpha1-beta3, and beta3-beta4 loop regions, with functional implications in the mechanism of binding other proteins. NMA of ubiquitin structures was not able to reproduce the long time scale fluctuations, as they were found to strongly depend on the reference structures. Further, conformational fluctuations coupled to the cis/trans isomerization reaction catalyzed by the enzyme cyclophilin A (CypA), occurring at the microsecond to millisecond time scale, have also been identified and characterized on the basis of QHA of conformations sampled along the reaction pathway. The results indicate that QHA covers the same conformational landscape as the experimentally observed CypA flexibility. Overall, the identified slow conformational fluctuations in ubiquitin and CypA indicate that the intrinsic flexibility of these proteins is closely linked to their designated functions.

X‐ray vs. NMR structures as templates for computational protein design

Certain protein-design calculations involve using an experimentally determined high-resolution structure as a template to identify new sequences that can adopt the same fold. This approach has led to the successful design of many novel, well-folded, native-like proteins. Although any atomic-resolution structure can serve as a template in such calculations, most successful designs have used high-resolution crystal structures. Because there are many proteins for which crystal structures are not available, it is of interest whether nuclear magnetic resonance (NMR) templates are also appropriate. We have analyzed differences between using X-ray and NMR templates in side-chain repacking and design calculations. We assembled a database of 29 proteins for which both a high-resolution X-ray structure and an ensemble of NMR structures are available. Using these pairs, we compared the rotamericity, chi(1)-angle recovery, and native-sequence recovery of X-ray and NMR templates. We carried out design using RosettaDesign on both types of templates, and compared the energies and packing qualities of the resulting structures. Overall, the X-ray structures were better templates for use with Rosetta. However, for approximately 20% of proteins, a member of the reported NMR ensemble gave rise to designs with similar properties. Re-evaluating RosettaDesign structures with other energy functions indicated much smaller differences between the two types of templates. Ultimately, experiments are required to confirm the utility of particular X-ray and NMR templates. But our data suggest that the lack of a high-resolution X-ray structure should not preclude attempts at computational design if an NMR ensemble is available.

Simulation of general three-body interactions in a nuclear magnetic resonance ensemble quantum computer

Three-body interaction plays an important role in many-body physics, and quantum computer is efficient in simulating many-body interactions. We have experimentally demonstrated the general three-body interactions in a three-qubit nuclear magnetic resonance ensemble quantum computer. Using a nuclear magnetic resonance computer we implemented general forms of three-body interactions including σ 1 x σ 2 z σ 3 x and σ 1 x σ 2 z σ 3 y The results show good agreement between theory and experiment. We have also given a concise and practical formula for a general n-body interaction in terms of one-and two-body interactions.

Conformer Selection and Induced Fit in Flexible Backbone Protein–Protein Docking Using Computational and NMR Ensembles

Accommodating backbone flexibility continues to be the most difficult challenge in computational docking of protein–protein complexes. Towards that end, we simulate four distinct biophysical models of protein binding in RosettaDock, a multiscale Monte-Carlo-based algorithm that uses a quasi-kinetic search process to emulate the diffusional encounter of two proteins and to identify low-energy complexes. The four binding models are as follows: (1) key-lock (KL) model, using rigid-backbone docking; (2) conformer selection (CS) model, using a novel ensemble docking algorithm; (3) induced fit (IF) model, using energy-gradient-based backbone minimization; and (4) combined conformer selection/induced fit (CS/IF) model. Backbone flexibility was limited to the smaller partner of the complex, structural ensembles were generated using Rosetta refinement methods, and docking consisted of local perturbations around the complexed conformation using unbound component crystal structures for a set of 21 target complexes. The lowest-energy structure contained > 30% of the native residue–residue contacts for 9, 13, 13, and 14 targets for KL, CS, IF, and CS/IF docking, respectively. When applied to 15 targets using nuclear magnetic resonance ensembles of the smaller protein, the lowest-energy structure recovered at least 30% native residue contacts in 3, 8, 4, and 8 targets for KL, CS, IF, and CS/IF docking, respectively. CS/IF docking of the nuclear magnetic resonance ensemble performed equally well or better than KL docking with the unbound crystal structure in 10 of 15 cases. The marked success of CS and CS/IF docking shows that ensemble docking can be a versatile and effective method for accommodating conformational plasticity in docking and serves as a demonstration for the CS theory—that binding-competent conformers exist in the unbound ensemble and can be selected based on their favorable binding energies.

Structural study of Ac‐Phe‐[Orn‐Pro‐dCha‐Trp‐Arg], a potent C5a receptor antagonist, by NMR

The cyclic hexapeptide Ac(0)-Phe(1)-[Orn(2)-Pro(3)-dCha(4)-Trp(5)-Arg(6)] (the square brackets denote cyclization) is a potent antagonist against C5a (the a-fragment of complement protein C5) binding to C5a receptor (C5aR) and an excellent candidate to become a therapeutic agent against diseases that involve unregulated activation of the complement system. We present the solution structure determination of this cyclic C5aR peptide antagonist (cC5aR-pa), using nuclear magnetic resonance (NMR) data and restrained molecular dynamics-based simulated annealing in torsion angle space with NMR-derived distance and torsion angle restraints. The calculated NMR ensemble of structures demonstrates the presence of a predominant conformation of a distorted type II' beta-turn in the segment Pro(3)-dCha(4)-Trp(5)-Arg(6). We critically examine the calculated structure with measured NMR parameters, such as nuclear Overhauser enhancement (NOE) connectivity patterns and intensities characteristic of specific structures, (3)J(H(N)-H(alpha)) scalar coupling constants, temperature coefficients for NH groups, and differences between observed chemical shifts and their random coil values. The raw NMR data are consistent with the presence of the type II' beta-turn, but also indicate the presence of conformational inter-conversion. The calculated three-dimensional coordinates for cC5aR-pa will form the basis for further computational studies and for the development of pharmacophore models.

A large data set comparison of protein structures determined by crystallography and NMR: Statistical test for structural differences and the effect of crystal packing

The existence of a large number of proteins for which both nuclear magnetic resonance (NMR) and X-ray crystallographic coordinates have been deposited into the Protein Data Bank (PDB) makes the statistical comparison of the corresponding crystal and NMR structural models over a large data set possible, and facilitates the study of the effect of the crystal environment and other factors on structure. We present an approach for detecting statistically significant structural differences between crystal and NMR structural models which is based on structural superposition and the analysis of the distributions of atomic positions relative to a mean structure. We apply this to a set of 148 protein structure pairs (crystal vs NMR), and analyze the results in terms of methodological and physical sources of structural difference. For every one of the 148 structure pairs, the backbone root-mean-square distance (RMSD) over core atoms of the crystal structure to the mean NMR structure is larger than the average RMSD of the members of the NMR ensemble to the mean, with 76% of the structure pairs having an RMSD of the crystal structure to the mean more than a factor of two larger than the average RMSD of the NMR ensemble. On average, the backbone RMSD over core atoms of crystal structure to the mean NMR is approximately 1 A. If non-core atoms are included, this increases to 1.4 A due to the presence of variability in loops and similar regions of the protein. The observed structural differences are only weakly correlated with the age and quality of the structural model and differences in conditions under which the models were determined. We examine steric clashes when a putative crystalline lattice is constructed using a representative NMR structure, and find that repulsive crystal packing plays a minor role in the observed differences between crystal and NMR structures. The observed structural differences likely have a combination of physical and methodological causes. Stabilizing attractive interactions arising from intermolecular crystal contacts which shift the equilibrium of the crystal structure relative to the NMR structure is a likely physical source which can account for some of the observed differences. Methodological sources of apparent structural difference include insufficient sampling or other issues which could give rise to errors in the estimates of the precision and/or accuracy.

Realization of the new summing algorithm on an NMR ensemble quantum computer

A summing algorithm is to evaluate and sum up a set of function samples. The paper [J. Phys. A. 35, L597(2001)] presented a new summing algorithm using ensemble computing which results in an exponential speedup. Here, we experimentally implemented the new algorithm on a four-qubit liquid state nuclear magnetic resonance ensemble system.

An interferometric complementarity experiment in a bulk nuclear magnetic resonance ensemble

We have experimentally demonstrated the interferometric complementarity, which relates the distinguishability $D$ quantifying the amount of which-way (WW) information to the fringe visibility $V$ characterizing the wave feature of a quantum entity, in a bulk ensemble by Nuclear Magnetic Resonance (NMR) techniques. We primarily concern on the intermediate cases: partial fringe visibility and incomplete WW information. We propose a quantitative measure of $D$ by an alternative geometric strategy and investigate the relation between $D$ and entanglement. By measuring $D$ and $V$ independently, it turns out that the duality relation $D^{2}+V^{2}=1$ holds for pure quantum states of the markers.

Experimental realization of the Brüschweiler’s algorithm in a homonuclear system

Compared with classical search algorithms, Grover quantum algorithm [L. K. Grover, Phys. Rev. Lett. 79, 325 (1997)] achieves quadratic speedup and Brüschweiler hybrid quantum algorithm [R. Brüschweiler, Phys. Rev. Lett. 85, 4815 (2000)] achieves an exponential speedup. In this paper, we report the experimental realization of the Brüschweiler algorithm in a three-qubit nuclear magnetic resonance ensemble system. The pulse sequences are used for the algorithms and the measurement method used here is improved on that used by Brüschweiler, namely, instead of quantitatively measuring the spin projection of the ancilla bit, we utilize the shape of the ancilla bit spectrum. By simply judging the downwardness or upwardness of the corresponding peaks in an ancilla bit spectrum, the bit value of the marked state can be read out, especially the geometric nature of this read-out can make the results more robust against errors.

Approximate Quantum Counting on an NMR Ensemble Quantum Computer

We demonstrate the implementation of a quantum algorithm for estimating the number of matching items in a search operation using a two qubit nuclear magnetic resonance (NMR) quantum computer.

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Accommodating backbone flexibility continues to be the most difficult challenge in computational docking of protein–protein complexes. Towards that end, we simulate four distinct biophysical models of protein binding in RosettaDock, a multiscale Monte-Carlo-based algorithm that uses a quasi-kinetic search process to emulate the diffusional encounter of two proteins and to identify low-energy complexes. The four binding models are as follows: (1) key-lock (KL) model, using rigid-backbone docking; (2) conformer selection (CS) model, using a novel ensemble docking algorithm; (3) induced fit (IF) model, using energy-gradient-based backbone minimization; and (4) combined conformer selection/induced fit (CS/IF) model. Backbone flexibility was limited to the smaller partner of the complex, structural ensembles were generated using Rosetta refinement methods, and docking consisted of local perturbations around the complexed conformation using unbound component crystal structures for a set of 21 target complexes. The lowest-energy structure contained > 30% of the native residue–residue contacts for 9, 13, 13, and 14 targets for KL, CS, IF, and CS/IF docking, respectively. When applied to 15 targets using nuclear magnetic resonance ensembles of the smaller protein, the lowest-energy structure recovered at least 30% native residue contacts in 3, 8, 4, and 8 targets for KL, CS, IF, and CS/IF docking, respectively. CS/IF docking of the nuclear magnetic resonance ensemble performed equally well or better than KL docking with the unbound crystal structure in 10 of 15 cases. The marked success of CS and CS/IF docking shows that ensemble docking can be a versatile and effective method for accommodating conformational plasticity in docking and serves as a demonstration for the CS theory—that binding-competent conformers exist in the unbound ensemble and can be selected based on their favorable binding energies.