Conformational entropy changes upon lactose binding to the carbohydrate recognition domain of galectin-3

The conformational entropy of proteins can make significant contributions to the free energy of ligand binding. NMR spin relaxation enables site-specific investigation of conformational entropy, via order parameters that parameterize local reorientational fluctuations of rank-2 tensors. Here we have probed the conformational entropy of lactose binding to the carbohydrate recognition domain of galectin-3 (Gal3), a protein that plays an important role in cell growth, cell differentiation, cell cycle regulation, and apoptosis, making it a potential target for therapeutic intervention in inflammation and cancer. We used ¹⁵N spin relaxation experiments and molecular dynamics simulations to monitor the backbone amides and secondary amines of the tryptophan and arginine side chains in the ligand-free and lactose-bound states of Gal3. Overall, we observe good agreement between the experimental and computed order parameters of the ligand-free and lactose-bound states. Thus, the ¹⁵N spin relaxation data indicate that the molecular dynamics simulations provide reliable information on the conformational entropy of the binding process. The molecular dynamics simulations reveal a correlation between the simulated order parameters and residue-specific backbone entropy, re-emphasizing that order parameters provide useful estimates of local conformational entropy. The present results show that the protein backbone exhibits an increase in conformational entropy upon binding lactose, without any accompanying structural changes.     

How does it really move? Recent progress in the investigation of protein nanosecond dynamics by NMR and simulation

Nuclear magnetic resonance (NMR) spin relaxation experiments currently probe molecular motions on timescales from picoseconds to nanoseconds. The detailed interpretation of these motions in atomic detail benefits from complementarity with the results from molecular dynamics (MD) simulations. In this mini-review, we describe the recent developments in experimental techniques to study the backbone dynamics from ¹⁵N relaxation and side-chain dynamics from ¹³C relaxation, discuss the different analysis approaches from model-free to dynamics detectors, and highlight the many ways that NMR relaxation experiments and MD simulations can be used together to improve the interpretation and gain insights into protein dynamics.     

Quadrupole Relaxation of the 7Li+ Ion in Dilute Aqueous Solution Determined by Experimental and Theoretical Methods

A combination of molecular dynamics simulations (MD), ab initio selfconsistent field (SCF) calculations and nuclear magnetic resonance relaxation time experiments (NMR) is a powerful battery of techniques to investigate the molecular origins of the nuclear quadrupole relaxation mechanism for ⁷Li⁺ ions in dilute aqueous solution.     

Validating Solution Ensembles from Molecular Dynamics Simulation by Wide-Angle X-ray Scattering Data

Wide-angle x-ray scattering (WAXS) experiments of biomolecules in solution have become increasingly popular because of technical advances in light sources and detectors. However, the structural interpretation of WAXS profiles is problematic, partly because accurate calculations of WAXS profiles from structural models have remained challenging. In this work, we present the calculation of WAXS profiles from explicit-solvent molecular dynamics (MD) simulations of five different proteins. Using only a single fitting parameter that accounts for experimental uncertainties because of the buffer subtraction and dark currents, we find excellent agreement to experimental profiles both at small and wide angles. Because explicit solvation eliminates free parameters associated with the solvation layer or the excluded solvent, which would require fitting to experimental data, we minimize the risk of overfitting. We further find that the influence from water models and protein force fields on calculated profiles are insignificant up to q ≈ 15 nm^?1. Using a series of simulations that allow increasing flexibility of the proteins, we show that incorporating thermal fluctuations into the calculations significantly improves agreement with experimental data, demonstrating the importance of protein dynamics in the interpretation of WAXS profiles. In addition, free MD simulations up to one microsecond suggest that the calculated profiles are highly sensitive with respect to minor conformational rearrangements of proteins, such as an increased flexibility of a loop or an increase of the radius of gyration by  <  1%. The present study suggests that quantitative comparison between MD simulations and experimental WAXS profiles emerges as an accurate tool to validate solution ensembles of biomolecules.     

Spectral densities of nitrogen nuclei in Escherichia coli ribonuclease HI obtained by 15N NMR relaxation and molecular dynamics

Summary Spectral densities of the ¹⁵N amide in Escherichia coli ribonuclease HI, obtained from NMR relaxation experiments, were compared with those calculated using a molecular dynamics (MD) simulation. All calculations and comparisons assumed that the auto-correlation function describing the internal motions of the molecule was independent of the auto-correlation function associated with overall rotational diffusion. Comparisons were limited to those residues for which the auto-correlation function of internal motions rapidly relaxed and reached a steady state within 205 ps. The results show the importance of frequency components as well as amplitudes of internal motions in order to obtain a meaningful comparison of MD simulations with NMR data.     

Tilt and Azimuthal Angles of a Transmembrane Peptide: A Comparison between Molecular Dynamics Calculations and Solid-State NMR Data of Sarcolipin in Lipid Membranes

We report molecular dynamics simulations in the explicit membrane environment of a small membrane-embedded protein, sarcolipin, which regulates the sarcoplasmic reticulum Ca-ATPase activity in both cardiac and skeletal muscle. In its monomeric form, we found that sarcolipin adopts a helical conformation, with a computed average tilt angle of 28 ± 6° and azymuthal angles of 66 ± 22°, in reasonable accord with angles determined experimentally (23 ± 2° and 50 ± 4°, respectively) using solid-state NMR with separated-local-field experiments. The effects of time and spatial averaging on both ¹⁵N chemical shift anisotropy and ¹H/¹⁵N dipolar couplings have been analyzed using short-time averages of fast amide out-of-plane motions and following principal component dynamic trajectories. We found that it is possible to reproduce the regular oscillatory patterns observed for the anisotropic NMR parameters (i.e., PISA wheels) employing average amide vectors. This work highlights the role of molecular dynamics simulations as a tool for the analysis and interpretation of solid-state NMR data.     

Accuracy and precision of NMR relaxation experiments and MD simulations for characterizing protein dynamics

Model-free parameters obtained from nuclear magnetic resonance (NMR) relaxation experiments and molecular dynamics (MD) simulations commonly are used to describe the intramolecular dynamical properties of proteins. To assess the relative accuracy and precision of experimental and simulated model-free parameters, three independent data sets derived from backbone ¹⁵N NMR relaxation experiments and two independent data sets derived from MD simulations of Escherichia coli ribonuclease HI are compared. The widths of the distributions of the differences between the order parameters for pairs of NMR data sets are congruent with the uncertainties derived from statistical analyses of individual data sets; thus, current protocols for analyzing NMR data encapsulate random uncertainties appropriately. Large differences in order parameters for certain residues are attributed to systematic differences between samples for intralaboratory comparisons and unknown, possibly magnetic field-dependent, experimental effects for interlaboratory comparisons. The widths of distributions of the differences between the order parameters for two NMR sets are similar to widths of distributions for an NMR and an MD set or for two MD sets. The linear correlations between the order parameters for an MD set and an NMR set are within the range of correlations observed between pairs of NMR sets. These comparisons suggest that the NMR and MD generalized order parameters for the backbone amide N—H bond vectors are of comparable accuracy for residues exhibiting motions on a fast time scale (<100 ps). Large discrepancies between NMR and MD order parameters for certain residues are attributed to the occurrence of “rare” motional events over the simulation trajectories, the disruption of an element of secondary structure in one of the simulations, and lack of consensus among the experimental data sets. Consequently, (easily detectable) severe distortions of local protein structure and infrequent motional events in MD simulations appear to be the most serious artifacts affecting the accuracy and precision, respectively, of MD order parameters relative to NMR values. In addition, MD order parameters for motions on a fast (<100 ps) timescale are more precisely determined than their NMR counterparts, thereby permitting more detailed dynamic characterization of biologically important residues by MD simulation than is sometimes possible by experimental methods. Proteins 28:481–493, 1997. © 1997 Wiley-Liss, Inc.     

Interpretation of H-NMR Experiments on the Orientation of the Transmembrane Helix WALP23 by Computer Simulations

Orientation, dynamics, and packing of transmembrane helical peptides are important determinants of membrane protein structure, dynamics, and function. Because it is difficult to investigate these aspects by studying real membrane proteins, model transmembrane helical peptides are widely used. NMR experiments provide information on both orientation and dynamics of peptides, but they require that motional models be interpreted. Different motional models yield different interpretations of quadrupolar splittings (QS) in terms of helix orientation and dynamics. Here, we use coarse-grained (CG) molecular dynamics (MD) simulations to investigate the behavior of a well-known model transmembrane peptide, WALP23, under different hydrophobic matching/mismatching conditions. We compare experimental ²H-NMR QS (directly measured in experiments), as well as helix tilt angle and azimuthal rotation (not directly measured), with CG MD simulation results. For QS, the agreement is significantly better than previously obtained with atomistic simulations, indicating that equilibrium sampling is more important than atomistic details for reproducing experimental QS. Calculations of helix orientation confirm that the interpretation of QS depends on the motional model used. Our simulations suggest that WALP23 can form dimers, which are more stable in an antiparallel arrangement. The origin of the preference for the antiparallel orientation lies not only in electrostatic interactions but also in better surface complementarity. In most cases, a mixture of monomers and antiparallel dimers provides better agreement with NMR data compared to the monomer and the parallel dimer. CG MD simulations allow predictions of helix orientation and dynamics and interpretation of QS data without requiring any assumption about the motional model.     

Off-resonance rotating-frame relaxation dispersion experiment for 13C in aromatic side chains using L-optimized TROSY-selection

Protein dynamics on the microsecond–millisecond time scales often play a critical role in biological function. NMR relaxation dispersion experiments are powerful approaches for investigating biologically relevant dynamics with site-specific resolution, as shown by a growing number of publications on enzyme catalysis, protein folding, ligand binding, and allostery. To date, the majority of studies has probed the backbone amides or side-chain methyl groups, while experiments targeting other sites have been used more sparingly. Aromatic side chains are useful probes of protein dynamics, because they are over-represented in protein binding interfaces, have important catalytic roles in enzymes, and form a sizable part of the protein interior. Here we present an off-resonance R _1ρ experiment for measuring microsecond to millisecond conformational exchange of aromatic side chains in selectively ¹³C labeled proteins by means of longitudinal- and transverse-relaxation optimization. Using selective excitation and inversion of the narrow component of the ¹³C doublet, the experiment achieves significant sensitivity enhancement in terms of both signal intensity and the fractional contribution from exchange to transverse relaxation; additional signal enhancement is achieved by optimizing the longitudinal relaxation recovery of the covalently attached ¹H spins. We validated the L-TROSY-selected R _1ρ experiment by measuring exchange parameters for Y23 in bovine pancreatic trypsin inhibitor at a temperature of 328 K, where the ring flip is in the fast exchange regime with a mean waiting time between flips of 320 μs. The determined chemical shift difference matches perfectly with that measured from the NMR spectrum at lower temperatures, where separate peaks are observed for the two sites. We further show that potentially complicating effects of strong scalar coupling between protons (Weininger et al. in J Phys Chem B 117: 9241–9247, 2013b) can be accounted for using a simple expression, and provide recommendations for data acquisition when the studied system exhibits this behavior. The present method extends the repertoire of relaxation methods tailored for aromatic side chains by enabling studies of faster processes and improved control over artifacts due to strong coupling.     

Relating side-chain mobility in proteins to rotameric transitions: Insights from molecular dynamics simulations and NMR

The dynamic aspect of proteins is fundamental to understanding protein stability and function. One of the goals of NMR studies of side-chain dynamics in proteins is to relate spin relaxation rates to discrete conformational states and the timescales of interconversion between those states. Reported here is a physical analysis of side-chain dynamics that occur on a timescale commensurate with monitoring by ²H spin relaxation within methyl groups. Motivated by observations made from tens-of-nanoseconds long MD simulations on the small protein eglin c in explicit solvent, we propose a simple molecular mechanics-based model for the motions of side-chain methyl groups. By using a Boltzmann distribution within rotamers, and by considering the transitions between different rotamer states, the model semi-quantitatively correlates the population of rotamer states with ‘model-free’ order parameters typically fitted from NMR relaxation experiments. Two easy-to-use, analytical expressions are given for converting S²_axis’ values (order parameter for C–CH₃ bond) into side-chain rotamer populations. These predict that S²_axis’ values below 0.8 result from population of more than one rotameric state. The relations are shown to predict rotameric sampling with reasonable accuracy on the ps–ns timescale for eglin c and are validated for longer timescales on ubiquitin, for which side-chain residual dipolar coupling (RDC) data have been collected.     

On the similarity of properties in solution or in the crystalline state: A molecular dynamics study of hen lysozyme

As protein crystals generally possess a high water content, it is assumed that the behaviour of a protein in solution and in crystal environment is very similar. This assumption can be investigated by molecular dynamics (MD) simulation of proteins in the different environments. Two 2ns simulations of hen egg white lysozyme (HEWL) in crystal and solution environment are compared to one another and to experimental data derived from both X-ray and NMR experiments, such as crystallographic B-factors, NOE atom–atom distance bounds, ³J_{H N}-coupling constants, and ¹H-¹⁵N bond vector order parameters. Both MD simulations give very similar results. The crystal simulation reproduces X-ray and NMR data slightly better than the solution simulation.     

Choice of Force Field for Proteins Containing Structured and Intrinsically Disordered Regions

Biomolecular force fields optimized for globular proteins fail to properly reproduce properties of intrinsically disordered proteins. In particular, parameters of the water model need to be modified to improve applicability of the force fields to both ordered and disordered proteins. Here, we compared performance of force fields recommended for intrinsically disordered proteins in molecular dynamics simulations of three proteins differing in the content of ordered and disordered regions (two proteins consisting of a well-structured domain and of a disordered region with and without a transient helical motif and one disordered protein containing a region of increased helical propensity). The obtained molecular dynamics trajectories were used to predict measurable parameters, including radii of gyration of the proteins and chemical shifts, residual dipolar couplings, paramagnetic relaxation enhancement, and NMR relaxation data of their individual residues. The predicted quantities were compared with experimental data obtained within this study or published previously. The results showed that the NMR relaxation parameters, rarely used for benchmarking, are particularly sensitive to the choice of force-field parameters, especially those defining the water model. Interestingly, the TIP3P water model, leading to an artificial structural collapse, also resulted in unrealistic relaxation properties. The TIP4P-D water model, combined with three biomolecular force-field parameters for the protein part, significantly improved reliability of the simulations. Additional analysis revealed only one particular force field capable of retaining the transient helical motif observed in NMR experiments. The benchmarking protocol used in our study, being more sensitive to imperfections than the commonly used tests, is well suited to evaluate the performance of newly developed force fields.     

Acyl chain order parameter profiles in phospholipid bilayers: computation from molecular dynamics simulations and comparison with <Superscript>2</Superscript>H NMR experiments

Order parameters from deuterium NMR are often used to validate or calibrate molecular dynamics simulations. This paper gives a short overview of the literature in which experimental order parameters from ²H NMR are compared to those calculated from MD simulations. The different ways in which order parameters from experiment are used to calibrate and validate simulations are reviewed. In the second part of this review, a case study of cholesterol in a DMPC bilayer is presented. It is concluded that the agreement between experimental data and simulation is favorable in the hydrophobic region of the membrane, for both the phospholipids and cholesterol. In the interfacial region the agreement is less satisfactory, probably because of the high polarity of this region which makes the correct computation of the electrostatics more complex. Presented at the joint biannual meeting of the SFB-GEIMM-GRIP, Anglet France, 14–19 October, 2006.     

Solution conformation and dynamics of a tetrasaccharide related to the LewisX antigen deduced by NMR relaxation measurements

¹H-NMR cross-relaxation rates and nonselectivelongitudinal relaxation times have been obtained at two magnetic fields (7.0and 11.8 T) and at a variety of temperatures for the branchedtetrasaccharide methyl3-O--N-acetyl-galactosaminyl--galactopyranosyl-(14)[3-O--fucosyl]-glucopyranoside (1), an inhibitor of astrocyte growth. Inaddition, ¹³C-NMR relaxation data have also been recorded atboth fields. The ¹H-NMR relaxation data have been interpretedusing different motional models to obtain proton–proton correlationtimes. The results indicate that the GalNAc and Fuc rings display moreextensive local motion than the two inner Glc and Gal moieties, since thosepresent significantly shorter local correlation times. The¹³C-NMR relaxation parameters have been interpreted in termsof the Lipari–Szabo model-free approach. Thus, order parameters andinternal motion correlation times have been deduced. As obtained for the¹H-NMR relaxation data, the two outer residues possess smallerorder parameters than the two inner rings. Internal correlation times are inthe order of 100 ps. The hydroxymethyl groups have also different behaviour,with the exocyclic carbon on the glucopyranoside unit showing the highestS². Molecular dynamics simulations using a solvated systemhave also been performed and internal motion correlation functions have beendeduced from these calculations. Order parameters and interproton distanceshave been compared to those inferred from the NMR measurements. The obtainedresults are in fair agreement with the experimental data.     

Acceptable protein and solvent behavior in primary hydration shell simulations of hen lysozyme

The "primary hydration shell" method in molecular dynamics simulations uses a two- to three-layer thick shell of explicitly represented water molecules as the solvent around the protein of interest. We show that despite its simplicity, this computationally cheap model is capable of predicting acceptable water and protein behavior using the CHARMM22/CMAP potential function. For protein dynamics, comparisons are made with Lipari-Szabo order parameters. These have been derived from NMR relaxation parameters for pico-nano second motions of the NH groups in the main-chain and NH(2) groups in Asn/Gln side chains in hen lysozyme. It is also shown that an even simpler, and therefore faster, water-shell model leads to results in similarly good agreement with experiments, and also compared with simulations using a full box of water with periodic boundary conditions or with an implicit solvation model. Thus, the primary hydration shell method should be useful in making larger systems accessible to extensive simulations.     

High-Resolution NMR Reveals Secondary Structure and Folding of Amino Acid Transporter from Outer Chloroplast Membrane

Solving high-resolution structures for membrane proteins continues to be a daunting challenge in the structural biology community. In this study we report our high-resolution NMR results for a transmembrane protein, outer envelope protein of molar mass 16 kDa (OEP16), an amino acid transporter from the outer membrane of chloroplasts. Three-dimensional, high-resolution NMR experiments on the ¹³C, ¹⁵N, ²H-triply-labeled protein were used to assign protein backbone resonances and to obtain secondary structure information. The results yield over 95% assignment of N, H_N, CO, C_α, and C_β chemical shifts, which is essential for obtaining a high resolution structure from NMR data. Chemical shift analysis from the assignment data reveals experimental evidence for the first time on the location of the secondary structure elements on a per residue basis. In addition T _1Z and T₂ relaxation experiments were performed in order to better understand the protein dynamics. Arginine titration experiments yield an insight into the amino acid residues responsible for protein transporter function. The results provide the necessary basis for high-resolution structural determination of this important plant membrane protein.