Insights into the mobility of methyl-bearing side chains in proteins from (3)J(CC) and (3)J(CN) couplings

Insights into Ligand-Mediated Activation of an Oligomeric Ring-Shaped Gene-Regulatory Protein from Solution- and Solid-State NMR

The 91 kDa oligomeric ring-shaped ligand binding protein TRAP (trp RNA binding attenuation protein) regulates the expression of a series of genes involved in tryptophan (Trp) biosynthesis in bacilli. When cellular Trp levels rise, the free amino acid binds to sites buried in the interfaces between each of the 11 (or 12, depending on the species) protomers in the ring. Crystal structures of Trp-bound TRAP show the Trp ligands are sequestered from solvent by a pair of loops from adjacent protomers that bury the bound ligand via polar contacts to several threonine residues. Binding of the Trp ligands occurs cooperatively, such that successive binding events occur with higher apparent affinity but the structural basis for this cooperativity is poorly understood. We used solution methyl-TROSY NMR relaxation experiments focused on threonine and isoleucine sidechains, as well as magic angle spinning solid-state NMR 13C-13C and 15N-13C chemical shift correlation spectra on uniformly labeled samples recorded at 800 and 1200 MHz, to characterize the structure and dynamics of the protein. Methyl 13C relaxation dispersion experiments on ligand-free apo TRAP revealed concerted exchange dynamics on the µs-ms time scale, consistent with transient sampling of conformations that could allow ligand binding. Cross-correlated relaxation experiments revealed widespread disorder on fast timescales. Chemical shifts for methyl-bearing side chains in apo- and Trp-bound TRAP revealed subtle changes in the distribution of sampled sidechain rotameric states. These observations reveal a pathway and mechanism for induced conformational changes to generate homotropic Trp-Trp binding cooperativity.

Machine-learned molecular mechanics force fields from large-scale quantum chemical data

The development of reliable and extensible molecular mechanics (MM) force fields-fast, empirical models characterizing the potential energy surface of molecular systems-is indispensable for biomolecular simulation and computer-aided drug design. Here, we introduce a generalized and extensible machine-learned MM force field, espaloma-0.3, and an end-to-end differentiable framework using graph neural networks to overcome the limitations of traditional rule-based methods. Trained in a single GPU-day to fit a large and diverse quantum chemical dataset of over 1.1 M energy and force calculations, espaloma-0.3 reproduces quantum chemical energetic properties of chemical domains highly relevant to drug discovery, including small molecules, peptides, and nucleic acids. Moreover, this force field maintains the quantum chemical energy-minimized geometries of small molecules and preserves the condensed phase properties of peptides and folded proteins, self-consistently parametrizing proteins and ligands to produce stable simulations leading to highly accurate predictions of binding free energies. This methodology demonstrates significant promise as a path forward for systematically building more accurate force fields that are easily extensible to new chemical domains of interest.

Parsing Dynamics of Protein Backbone NH and Side-Chain Methyl Groups using Molecular Dynamics Simulations

Experimental NMR spectroscopy and theoretical molecular dynamics (MD) simulations provide complementary insights into protein conformational dynamics and hence into biological function. The present work describes an extensive set of backbone NH and side-chain methyl group generalized order parameters for the Escherichia coli ribonuclease HI (RNH) enzyme derived from 2-μs microsecond MD simulations using the OPLS4 and AMBER-FF19SB force fields. The simulated generalized order parameters are compared with values derived from NMR 15N and 13CH2D spin relaxation measurements. The squares of the generalized order parameters, S2 for the N-H bond vector and Saxis2 for the methyl group symmetry axis, characterize the equilibrium distribution of vector orientations in a molecular frame of reference. Optimal agreement between simulated and experimental results was obtained by averaging S2 or Saxis2 calculated by dividing the simulated trajectories into 50 ns blocks (∼five times the rotational diffusion correlation time for RNH). With this procedure, the median absolute deviations (MAD) between experimental and simulated values of S2 and Saxis2 are 0.030 (NH) and 0.061 (CH3) for OPLS4 and 0.041 (NH) and 0.078 (CH3) for AMBER-FF19SB. The MAD between OPLS4 and AMBER-FF19SB are 0.021 (NH) and 0.072 (CH3). The generalized order parameters for the methyl group symmetry axis can be decomposed into contributions from backbone fluctuations, between-rotamer dihedral angle transitions, and within-rotamer dihedral angle fluctuations. Analysis of the simulation trajectories shows that (i) backbone and side chain conformational fluctuations exhibit little correlation and that (ii) fluctuations within rotamers are limited and highly uniform with values that depend on the number of dihedral angles considered. Low values of Saxis2, indicative of enhanced side-chain flexibility, result from between-rotamer transitions that can be enhanced by increased local backbone flexibility.

Unraveling motion in proteins by combining NMR relaxometry and molecular dynamics simulations: A case study on ubiquitin

Nuclear magnetic resonance (NMR) relaxation experiments shine light onto the dynamics of molecular systems in the picosecond to millisecond timescales. As these methods cannot provide an atomically resolved view of the motion of atoms, functional groups, or domains giving rise to such signals, relaxation techniques have been combined with molecular dynamics (MD) simulations to obtain mechanistic descriptions and gain insights into the functional role of side chain or domain motion. In this work, we present a comparison of five computational methods that permit the joint analysis of MD simulations and NMR relaxation experiments. We discuss their relative strengths and areas of applicability and demonstrate how they may be utilized to interpret the dynamics in MD simulations with the small protein ubiquitin as a test system. We focus on the aliphatic side chains given the rigidity of the backbone of this protein. We find encouraging agreement between experiment, Markov state models built in the χ1/χ2 rotamer space of isoleucine residues, explicit rotamer jump models, and a decomposition of the motion using ROMANCE. These methods allow us to ascribe the dynamics to specific rotamer jumps. Simulations with eight different combinations of force field and water model highlight how the different metrics may be employed to pinpoint force field deficiencies. Furthermore, the presented comparison offers a perspective on the utility of NMR relaxation to serve as validation data for the prediction of kinetics by state-of-the-art biomolecular force fields.

Understanding Cysteine Reactivity in Protein Environments with Electric Fields

The role cysteine residues play in proteins is mediated by their protonation state, whereby the thiolate form of the side chain is highly reactive while the thiol form is more inert. However, the pKa of cysteine residues is hard to predict as it can differ widely from its reference value in solution, an effect that is accentuated by local effects in the heterogeneous protein environment. Here, we present a new approach to the prediction of cysteine reactivity based on electric field calculations at the thiol/thiolate group. We validated our approach by predicting the protonation state of cysteine residues in different protein environments (in the active site, at the protein surface, and buried within the protein interior), including Cys-25 in papaya protease omega, which was proven problematic for the more traditional constant pH molecular dynamics (MD) technique. We predict pKa shifts consistent with experimental observations, and the decomposition of the electric fields into contributions from molecular fragments provides a direct handle to rationalize local pH and pKa effects in proteins without introducing parameters other than those of the force field used for MD simulations.

Mixed, nonclassical behavior in a classic allosteric protein

Allostery is a major driver of biological processes requiring coordination. Thus, it is one of the most fundamental and remarkable phenomena in nature, and there is motivation to understand and manipulate it to a multitude of ends. Today, it is often described in terms of two phenomenological models proposed more than a half-century ago involving only T(tense) or R(relaxed) conformations. Here, methyl-based NMR provides extensive detail on a dynamic T to R switch in the classical dimeric allosteric protein, yeast chorismate mutase (CM), that occurs in the absence of substrate, but only with the activator bound. Switching of individual subunits is uncoupled based on direct observation of mixed TR states in the dimer. This unique finding excludes both classic models and solves the paradox of a coexisting hyperbolic binding curve and highly skewed substrate-free T-R equilibrium. Surprisingly, structures of the activator-bound and effector-free forms of CM appear the same by NMR, providing another example of the need to account for dynamic ensembles. The apo enzyme, which has a sigmoidal activity profile, is shown to switch, not to R, but to a related high-energy state. Thus, the conformational repertoire of CM does not just change as a matter of degree depending on the allosteric input, be it effector and/or substrate. Rather, the allosteric model appears to completely change in different contexts, which is only consistent with modern ensemble-based frameworks.

Fitting Force Field Parameters to NMR Relaxation Data

We present an approach to optimize force field parameters using time-dependent data from NMR relaxation experiments. To do so, we scan parameters in the dihedral angle potential energy terms describing the rotation of the methyl groups in proteins and compare NMR relaxation rates calculated from molecular dynamics simulations with the modified force fields to deuterium relaxation measurements of T4 lysozyme. We find that a small modification of C^γ methyl groups improves the agreement with experiments both for the protein used to optimize the force field and when validating using simulations of CI2 and ubiquitin. We also show that these improvements enable a more effective a posteriori reweighting of the MD trajectories. The resulting force field thus enables more direct comparison between simulations and side-chain NMR relaxation data and makes it possible to construct ensembles that better represent the dynamics of proteins in solution.

Probing Methyl Group Dynamics in Proteins by NMR Cross-Correlated Dipolar Relaxation and Molecular Dynamics Simulations

Nuclear magnetic resonance (NMR) spin relaxation is the most informative approach to experimentally probe the internal dynamics of proteins on the picosecond to nanosecond time scale. At the same time, molecular dynamics (MD) simulations of biological macromolecules are steadily improving through better physical models, enhanced sampling methods, and increased computational power, and they provide exquisite information about flexibility and its role in protein stability and molecular interactions. Many examples have shown that MD is now adept in probing protein backbone motion, but improvements are still required toward a quantitative description of the dynamics of side chains, for example, probed by the dynamics of methyl groups. Thus far, the comparison of computation with experiment for side chain dynamics has primarily focused on the relaxation of ¹³C and ²H nuclei induced by autocorrelated variation of spin interactions. However, the cross-correlation of ¹³C-¹H dipolar interactions in methyl groups offers an attractive alternative. Here, we establish a computational framework to extract cross-correlation relaxation parameters of methyl groups in proteins from all-atom MD simulations. To demonstrate the utility of the approach, cross-correlation relaxation rates of ubiquitin are computed from MD simulations performed with the AMBER99SB*-ILDN and CHARMM36 force fields. Simulation results were found to agree well with those obtained by experiment. Moreover, the data obtained with the two force fields are highly consistent.

Explicit Models of Motion to Understand Protein Side-Chain Dynamics

Nuclear magnetic relaxation is widely used to probe protein dynamics. For decades, most analyses of relaxation in proteins have relied successfully on the model-free approach, forgoing mechanistic descriptions of motion. Model-free types of correlation functions cannot describe a large carbon-13 relaxation dataset in protein side chains. Here, we use molecular dynamics simulations to design explicit models of motion and solve Fokker-Planck diffusion equations. These models of motion provide better agreement with relaxation data, mechanistic insight, and a direct link to configuration entropy.

Proton TOCSY NMR relaxation rates quantitate protein side chain mobility in the Pin1 WW domain

Protein side chain dynamics play a vital role in many biological processes, but differentiating mobile from rigid side chains remains a technical challenge in structural biology. Solution NMR spectroscopy is ideally suited for this but suffers from limited signal-to-noise, signal overlap, and a need for fractional ¹³C or ²H labeling. Here we introduce a simple strategy measuring initial ¹H relaxation rates during a ¹H TOCSY sequence like DIPSI-2, which can be appended to the beginning of any multi-dimensional NMR sequence that begins on ¹H. The TOCSY RF field compels all ¹H atoms to behave similarly under the influence of strong coupling and rotating frame cross-relaxation, so that differences in relaxation rates are due primarily to side chain mobility. We apply the scheme to a thermostable mutant Pin1 WW domain and demonstrate that the observed ¹H relaxation rates correlate well with two independent NMR measures of side-chain dynamics, cross-correlated ¹³C relaxation rates in ¹³C^βH₂ methylene groups and maximum observable ³J couplings sensitive to the χ₁ side chain dihedral angle (³J_Hα,Hβ, ³J_N,Hβ, and ³J_CO,Hβ). The most restricted side chains belong to Trp26 and Asn40, which are closely packed to constitute the folding center of the WW domain. None of the other conserved aromatic residues is as immobile as the first tryptophan side chain of the WW domain. The proposed ¹H relaxation methodology should make it relatively easy to measure side chain dynamics on uniformly ¹⁵N- or ¹³C-labeled proteins, so long as chemical shift assignments are obtainable.

Explicit models of motions to analyze NMR relaxation data in proteins

Nuclear Magnetic Resonance (NMR) is a tool of choice to characterize molecular motions. In biological macromolecules, pico- to nano-second motions, in particular, can be probed by nuclear spin relaxation rates which depend on the time fluctuations of the orientations of spin interaction frames. For the past 40 years, relaxation rates have been successfully analyzed using the Model Free (MF) approach which makes no assumption on the nature of motions and reports on the effective amplitude and time-scale of the motions. However, obtaining a mechanistic picture of motions from this type of analysis is difficult at best, unless complemented with molecular dynamics (MD) simulations. In spite of their limited accuracy, such simulations can be used to obtain the information necessary to build explicit models of motions designed to analyze NMR relaxation data. Here, we present how to build such models, suited in particular to describe motions of methyl-bearing protein side-chains and compare them with the MF approach. We show on synthetic data that explicit models of motions are more robust in the presence of rotamer jumps which dominate the relaxation in methyl groups of protein side-chains. We expect this work to motivate the use of explicit models of motion to analyze MD and NMR data.

Tuning the Catalytic Activity of Synthetic Enzyme KE15 with DNA

Efficiency improvement of synthetic enzymes through scaffold modifications suffers from limitations in terms of effectiveness, cost, and potential devastating consequences for protein structural stability. Here, we propose an alternative to scaffold modification, within electrostatic preorganization theory, where the enzyme's greater environment is designed to support the evolution of the reaction in the active site. We demonstrate the feasibility of such an approach by placing a (polar) DNA fragment in the surroundings of the Kemp eliminase enzyme KE15 (structure from Houk's group) and computing the resulting change in catalytic activity. We find that the introduction of a DNA fragment magnifies the contribution of protein residues to the stabilization of the transition state, estimated from electric field calculations with polarizable molecular dynamics. Our randomly generated test systems reveal a 2.0 kcal/mol reduction in activation energy, suggesting that even more significant catalytic improvements could be made by optimizing DNA size, sequence, and orientation with respect to the enzyme, validating our approach.

How Much Entropy Is Contained in NMR Relaxation Parameters?

Solution-state NMR relaxation experiments are the cornerstone to study internal protein dynamics at an atomic resolution on time scales that are faster than the overall rotational tumbling time τ_R. Since the motions described by NMR relaxation parameters are connected to thermodynamic quantities like conformational entropies, the question arises how much of the total entropy is contained within this tumbling time. Using all-atom molecular dynamics simulations of the T4 lysozyme, we found that entropy buildup is rather fast for the backbone, such that the majority of the entropy is indeed contained in the short-time dynamics. In contrast, the contribution of the slow dynamics of side chains on time scales beyond τ_R on the side-chain conformational entropy is significant and should be taken into account for the extraction of accurate thermodynamic properties.

Observation of Sub-Microsecond Protein Methyl-Side Chain Dynamics by Nanoparticle-Assisted NMR Spin Relaxation

Amino-acid side-chain properties in proteins are key determinants of protein function. NMR spin relaxation of side chains is an important source of information about local protein dynamics and flexibility. However, traditional solution NMR relaxation methods are most sensitive to sub-nanosecond dynamics lacking information on slower ns-μs time-scale motions. Nanoparticle-assisted NMR spin relaxation (NASR) of methyl-side chains is introduced here as a window into these ns-μs dynamics. NASR utilizes the transient and nonspecific interactions between folded proteins and slowly tumbling spherical nanoparticles (NPs), whereby the increase of the relaxation rates reflects motions on time scales from ps all the way to the overall tumbling correlation time of the NPs ranging from hundreds of ns to μs. The observed motional amplitude of each methyl group can then be expressed by a model-free NASR S² order parameter. The method is demonstrated for ²H-relaxation of CH₂D methyl moieties and cross-correlated relaxation of CH₃ groups for proteins Im7 and ubiquitin in the presence of anionic silica-nanoparticles. Both types of relaxation experiments, dominated by either quadrupolar or dipolar interactions, yield highly consistent results. Im7 shows additional dynamics on the intermediate time scales taking place in a functionally important loop, whereas ubiquitin visits the majority of its conformational substates on the sub-ns time scale. These experimental observations are in good agreement with 4-10 μs all-atom molecular dynamics trajectories. NASR probes side-chain dynamics on a much wider range of motional time scales than previously possible, thereby providing new insights into the interplay between protein structure, dynamics, and molecular interactions that govern protein function.

A twist in the road less traveled: The AMBER ff15ipq-m force field for protein mimetics

We present a new force field, AMBER ff15ipq-m, for simulations of protein mimetics in applications from therapeutics to biomaterials. This force field is an expansion of the AMBER ff15ipq force field that was developed for canonical proteins and enables the modeling of four classes of artificial backbone units that are commonly used alongside natural α residues in blended or "heterogeneous" backbones: chirality-reversed D-α-residues, the Cα-methylated α-residue Aib, homologated β-residues (β3) bearing proteinogenic side chains, and two cyclic β residues (βcyc; APC and ACPC). The ff15ipq-m force field includes 472 unique atomic charges and 148 unique torsion terms. Consistent with the AMBER IPolQ lineage of force fields, the charges were derived using the Implicitly Polarized Charge (IPolQ) scheme in the presence of explicit solvent. To our knowledge, no general force field reported to date models the combination of artificial building blocks examined here. In addition, we have derived Karplus coefficients for the calculation of backbone amide J-coupling constants for β3Ala and ACPC β residues. The AMBER ff15ipq-m force field reproduces experimentally observed J-coupling constants in simple tetrapeptides and maintains the expected conformational propensities in reported structures of proteins/peptides containing the artificial building blocks of interest-all on the μs timescale. These encouraging results demonstrate the power and robustness of the IPolQ lineage of force fields in modeling the structure and dynamics of natural proteins as well as mimetics with protein-inspired artificial backbones in atomic detail.

Determining methyl sidechain conformations in a CS-ROSETTA model using methyl 1H-13C residual dipolar couplings

Modelling of protein structures based on backbone chemical shifts, using programs such as CS-ROSETTA, is becoming increasingly popular, especially for systems where few restraints are available or where homologous structures are already known. While the reliability of CS-ROSETTA calculations can be improved by incorporation of some additional backbone NMR data such as those afforded by residual dipolar couplings or minimal NOE data sets involving backbone amide protons, the sidechain conformations are largely modelled by statistical energy terms. Here, we present a simple method based on methyl residual dipolar couplings that can be used to determine the rotameric state of the threefold symmetry axis of methyl groups that occupy a single rotamer, determine rotameric distributions, and identify regions of high flexibility. The method is demonstrated for methyl side chains of a deletion variant of the human chaperone DNAJB6b.

Determining isoleucine side-chain rotamer-sampling in proteins from 13C chemical shift

A framework is presented to derive the conformational sampling of isoleucine side chains from nuclear magnetic resonance ¹³C chemical shifts.

Chemical shifts are often the only nuclear magnetic resonance parameter that can be obtained for challenging macromolecular systems. Here we present a framework to derive the conformational sampling of isoleucine side chains from ¹³C chemical shifts and demonstrate that side-chain conformations in a low-populated folding intermediate can be determined.

Computational Analysis of Energy Landscapes Reveals Dynamic Features That Contribute to Binding of Inhibitors to CFTR-Associated Ligand

The CFTR-associated ligand PDZ domain (CALP) binds to the cystic fibrosis transmembrane conductance regulator (CFTR) and mediates lysosomal degradation of mature CFTR. Inhibition of this interaction has been explored as a therapeutic avenue for cystic fibrosis. Previously, we reported the ensemble-based computational design of a novel peptide inhibitor of CALP, which resulted in the most binding-efficient inhibitor to date. This inhibitor, kCAL01, was designed using osprey and evinced significant biological activity in in vitro cell-based assays. Here, we report a crystal structure of kCAL01 bound to CALP and compare structural features against iCAL36, a previously developed inhibitor of CALP. We compute side-chain energy landscapes for each structure to not only enable approximation of binding thermodynamics but also reveal ensemble features that contribute to the comparatively efficient binding of kCAL01. Finally, we compare the previously reported design ensemble for kCAL01 vs the new crystal structure and show that, despite small differences between the design model and crystal structure, significant biophysical features that enhance inhibitor binding are captured in the design ensemble. This suggests not only that ensemble-based design captured thermodynamically significant features observed in vitro, but also that a design eschewing ensembles would miss the kCAL01 sequence entirely.

NMR Methods for Characterizing the Basic Side Chains of Proteins: Electrostatic Interactions, Hydrogen Bonds, and Conformational Dynamics

NMR spectroscopy is a powerful tool for studying protein dynamics. Conventionally, NMR studies on protein dynamics have probed motions of protein backbone NH, side-chain aromatic, and CH₃ groups. Recently, there has been remarkable progress in NMR methodologies that can characterize motions of cationic groups in protein side chains. These NMR methods allow investigations of the dynamics of positively charged lysine (Lys) and arginine (Arg) side chains and their hydrogen bonds as well as their electrostatic interactions important for protein function. Here, describing various practical aspects, we provide an overview of the NMR methods for dynamics studies of Lys and Arg side chains. Some example data on protein-DNA complexes are shown. We will also explain how molecular dynamics (MD) simulations can facilitate the interpretation of the NMR data on these basic side chains. Studies combining NMR and MD have revealed the highly dynamic nature of short-range electrostatic interactions via ion pairs, especially those involving Lys side chains.

Chemical shift-based methods in NMR structure determination

Chemical shifts are highly sensitive probes harnessed by NMR spectroscopists and structural biologists as conformational parameters to characterize a range of biological molecules. Traditionally, assignment of chemical shifts has been a labor-intensive process requiring numerous samples and a suite of multidimensional experiments. Over the past two decades, the development of complementary computational approaches has bolstered the analysis, interpretation and utilization of chemical shifts for elucidation of high resolution protein and nucleic acid structures. Here, we review the development and application of chemical shift-based methods for structure determination with a focus on ab initio fragment assembly, comparative modeling, oligomeric systems, and automated assignment methods. Throughout our discussion, we point out practical uses, as well as advantages and caveats, of using chemical shifts in structure modeling. We additionally highlight (i) hybrid methods that employ chemical shifts with other types of NMR restraints (residual dipolar couplings, paramagnetic relaxation enhancements and pseudocontact shifts) that allow for improved accuracy and resolution of generated 3D structures, (ii) the utilization of chemical shifts to model the structures of sparsely populated excited states, and (iii) modeling of sidechain conformations. Finally, we briefly discuss the advantages of contemporary methods that employ sparse NMR data recorded using site-specific isotope labeling schemes for chemical shift-driven structure determination of larger molecules. With this review, we aim to emphasize the accessibility and versatility of chemical shifts for structure determination of challenging biological systems, and to point out emerging areas of development that lead us towards the next generation of tools.

Developing a molecular dynamics force field for both folded and disordered protein states

Many proteins that perform important biological functions are completely or partially disordered under physiological conditions. Molecular dynamics simulations could be a powerful tool for the structural characterization of such proteins, but it has been unclear whether the physical models (force fields) used in simulations are sufficiently accurate. Here, we systematically compare the accuracy of a number of different force fields in simulations of both ordered and disordered proteins, finding that each force field has strengths and limitations. We then describe a force field that substantially improves on the state-of-the-art accuracy for simulations of disordered proteins without sacrificing accuracy for folded proteins, thus broadening the range of biological systems amenable to molecular dynamics simulations.

Molecular dynamics (MD) simulation is a valuable tool for characterizing the structural dynamics of folded proteins and should be similarly applicable to disordered proteins and proteins with both folded and disordered regions. It has been unclear, however, whether any physical model (force field) used in MD simulations accurately describes both folded and disordered proteins. Here, we select a benchmark set of 21 systems, including folded and disordered proteins, simulate these systems with six state-of-the-art force fields, and compare the results to over 9,000 available experimental data points. We find that none of the tested force fields simultaneously provided accurate descriptions of folded proteins, of the dimensions of disordered proteins, and of the secondary structure propensities of disordered proteins. Guided by simulation results on a subset of our benchmark, however, we modified parameters of one force field, achieving excellent agreement with experiment for disordered proteins, while maintaining state-of-the-art accuracy for folded proteins. The resulting force field, a99SB-disp, should thus greatly expand the range of biological systems amenable to MD simulation. A similar approach could be taken to improve other force fields.

Narrowing the gap between experimental and computational determination of methyl group dynamics in proteins

A synergistic analysis of methyl NMR relaxation data and MD simulations identifies ways to improve studies of protein dynamics.

Perspectives on paramagnetic NMR from a life sciences infrastructure

The effects arising in NMR spectroscopy because of the presence of unpaired electrons, collectively referred to as "paramagnetic NMR" have attracted increasing attention over the last decades. From the standpoint of the structural and mechanistic biology, paramagnetic NMR provides long range restraints that can be used to assess the accuracy of crystal structures in solution and to improve them by simultaneous refinements through NMR and X-ray data. These restraints also provide information on structure rearrangements and conformational variability in biomolecular systems. Theoretical improvements in quantum chemistry calculations can nowadays allow for accurate calculations of the paramagnetic data from a molecular structural model, thus providing a tool to refine the metal coordination environment by matching the paramagnetic effects observed far away from the metal. Furthermore, the availability of an improved technology (higher fields and faster magic angle spinning) has promoted paramagnetic NMR applications in the fast-growing area of biomolecular solid-state NMR. Major improvements in dynamic nuclear polarization have been recently achieved, especially through the exploitation of the Overhauser effect occurring through the contact-driven relaxation mechanism: the very large enhancement of the ¹³C signal observed in a variety of liquid organic compounds at high fields is expected to open up new perspectives for applications of solution NMR.

Recent advances in measuring the kinetics of biomolecules by NMR relaxation dispersion spectroscopy

Protein function can be modulated or dictated by the amplitude and timescale of biomolecular motion, therefore it is imperative to study protein dynamics. Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful technique capable of studying timescales of motion that range from those faster than molecular reorientation on the picosecond timescale to those that occur in real-time. Across this entire regime, NMR observables can report on the amplitude of atomic motion, and the kinetics of atomic motion can be ascertained with a wide variety of experimental techniques from real-time to milliseconds and several nanoseconds to picoseconds. Still a four orders of magnitude window between several nanoseconds and tens of microseconds has remained elusive. Here, we highlight new relaxation dispersion NMR techniques that serve to cover this "hidden-time" window up to hundreds of nanoseconds that achieve atomic resolution while studying the molecule under physiological conditions.

Structure restraints from heteronuclear pseudocontact shifts generated by lanthanide tags at two different sites

Pseudocontact shifts (PCS) encode long-range information on 3D structures of protein backbones and side-chains. The level of structural detail that can be obtained increases with the number of different sites tagged with a paramagnetic metal ion to generate PCSs. Here we show that PCSs from two different sites can suffice to determine the structure of polypeptide chains and their location and orientation relative to the magnetic susceptibility tensor χ, provided that PCSs are available for ¹H as well as heteronuclear spins. In addition, PCSs from two different sites are shown to provide detailed structural information on the conformation of methyl group-bearing amino-acid side-chains. A previously published ensemble structure of ubiquitin is shown to explain the magnetic susceptibility and alignment tensors slightly better than structures that try to explain the experimental data by a single conformation, illustrating the potential of PCSs as a tool to investigate small conformational changes.

The Exact NOE as an Alternative in Ensemble Structure Determination

The structure-function paradigm is increasingly replaced by the structure-dynamics-function paradigm. All protein activity is steered by the interplay between enthalpy and entropy. Conformational dynamics serves as a proxy of conformational entropy. Therefore, it is essential to study not only the average conformation but also the spatial sampling of a protein on all timescales. To this purpose, we have established a protocol for determining multiple-state ensembles of proteins based on exact nuclear Overhauser effects (eNOEs). We have recently extended our previously reported eNOE data set for the protein GB3 by a very large set of backbone and side-chain residual dipolar couplings and three-bond J couplings. Here, we demonstrate that at least four structural states are required to represent the complete data set by dissecting the contributions to the CYANA target function, which quantifies restraint violations in structure calculation. We present a four-state ensemble of GB3, which largely preserves the characteristics obtained from eNOEs only. Due to the abundance of the input data, the ensemble and χ(1) angles in particular are well suited for cross-validation of the input data and comparison to x-ray structures. Principal component analysis is used to automatically identify and validate relevant states of the ensembles. Overall, our findings suggest that eNOEs are a valuable alternative to traditional NMR probes in spatial elucidation of proteins.

FF12MC: A revised AMBER forcefield and new protein simulation protocol

Specialized to simulate proteins in molecular dynamics (MD) simulations with explicit solvation, FF12MC is a combination of a new protein simulation protocol employing uniformly reduced atomic masses by tenfold and a revised AMBER forcefield FF99 with (i) shortened CH bonds, (ii) removal of torsions involving a nonperipheral sp(3) atom, and (iii) reduced 1-4 interaction scaling factors of torsions ϕ and ψ. This article reports that in multiple, distinct, independent, unrestricted, unbiased, isobaric-isothermal, and classical MD simulations FF12MC can (i) simulate the experimentally observed flipping between left- and right-handed configurations for C14-C38 of BPTI in solution, (ii) autonomously fold chignolin, CLN025, and Trp-cage with folding times that agree with the experimental values, (iii) simulate subsequent unfolding and refolding of these miniproteins, and (iv) achieve a robust Z score of 1.33 for refining protein models TMR01, TMR04, and TMR07. By comparison, the latest general-purpose AMBER forcefield FF14SB locks the C14-C38 bond to the right-handed configuration in solution under the same protein simulation conditions. Statistical survival analysis shows that FF12MC folds chignolin and CLN025 in isobaric-isothermal MD simulations 2-4 times faster than FF14SB under the same protein simulation conditions. These results suggest that FF12MC may be used for protein simulations to study kinetics and thermodynamics of miniprotein folding as well as protein structure and dynamics. Proteins 2016; 84:1490-1516. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

Studying Dynamics by Magic-Angle Spinning Solid-State NMR Spectroscopy: Principles and Applications to Biomolecules

Magic-angle spinning solid-state NMR spectroscopy is an important technique to study molecular structure, dynamics and interactions, and is rapidly gaining importance in biomolecular sciences. Here we provide an overview of experimental approaches to study molecular dynamics by MAS solid-state NMR, with an emphasis on the underlying theoretical concepts and differences of MAS solid-state NMR compared to solution-state NMR. The theoretical foundations of nuclear spin relaxation are revisited, focusing on the particularities of spin relaxation in solid samples under magic-angle spinning. We discuss the range of validity of Redfield theory, as well as the inherent multi-exponential behavior of relaxation in solids. Experimental challenges for measuring relaxation parameters in MAS solid-state NMR and a few recently proposed relaxation approaches are discussed, which provide information about time scales and amplitudes of motions ranging from picoseconds to milliseconds. We also discuss the theoretical basis and experimental measurements of anisotropic interactions (chemical-shift anisotropies, dipolar and quadrupolar couplings), which give direct information about the amplitude of motions. The potential of combining relaxation data with such measurements of dynamically-averaged anisotropic interactions is discussed. Although the focus of this review is on the theoretical foundations of dynamics studies rather than their application, we close by discussing a small number of recent dynamics studies, where the dynamic properties of proteins in crystals are compared to those in solution.

How to tackle protein structural data from solution and solid state: An integrated approach

Long-range NMR restraints, such as diamagnetic residual dipolar couplings and paramagnetic data, can be used to determine 3D structures of macromolecules. They are also used to monitor, and potentially to improve, the accuracy of a macromolecular structure in solution by validating or "correcting" a crystal model. Since crystal structures suffer from crystal packing forces they may not be accurate models for the macromolecular structures in solution. However, the presence of real differences should be tested for by simultaneous refinement of the structure using both crystal and solution NMR data. To achieve this, the program REFMAC5 from CCP4 was modified to allow the simultaneous use of X-ray crystallographic and paramagnetic NMR data and/or diamagnetic residual dipolar couplings. Inconsistencies between crystal structures and solution NMR data, if any, may be due either to structural rearrangements occurring on passing from the solution to solid state, or to a greater degree of conformational heterogeneity in solution with respect to the crystal. In the case of multidomain proteins, paramagnetic restraints can provide the correct mutual orientations and positions of domains in solution, as well as information on the conformational variability experienced by the macromolecule.

Physicochemical Properties of Ion Pairs of Biological Macromolecules

Ion pairs (also known as salt bridges) of electrostatically interacting cationic and anionic moieties are important for proteins and nucleic acids to perform their function. Although numerous three-dimensional structures show ion pairs at functionally important sites of biological macromolecules and their complexes, the physicochemical properties of the ion pairs are not well understood. Crystal structures typically show a single state for each ion pair. However, recent studies have revealed the dynamic nature of the ion pairs of the biological macromolecules. Biomolecular ion pairs undergo dynamic transitions between distinct states in which the charged moieties are either in direct contact or separated by water. This dynamic behavior is reasonable in light of the fundamental concepts that were established for small ions over the last century. In this review, we introduce the physicochemical concepts relevant to the ion pairs and provide an overview of the recent advancement in biophysical research on the ion pairs of biological macromolecules.

Compiled data set of exact NOE distance limits, residual dipolar couplings and scalar couplings for the protein GB3

We compiled an NMR data set consisting of exact nuclear Overhauser enhancement (eNOE) distance limits, residual dipolar couplings (RDCs) and scalar (J) couplings for GB3, which forms one of the largest and most diverse data set for structural characterization of a protein to date. All data have small experimental errors, which are carefully estimated. We use the data in the research article Vogeli et al., 2015, Complementarity and congruence between exact NOEs and traditional NMR probes for spatial decoding of protein dynamics, J. Struct. Biol., 191, 3, 306–317, doi:10.1016/j.jsb.2015.07.008 [1] for cross-validation in multiple-state structural ensemble calculation. We advocate this set to be an ideal test case for molecular dynamics simulations and structure calculations.

ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from ff99SB

Molecular mechanics is powerful for its speed in atomistic simulations, but an accurate force field is required. The Amber ff99SB force field improved protein secondary structure balance and dynamics from earlier force fields like ff99, but weaknesses in side chain rotamer and backbone secondary structure preferences have been identified. Here, we performed a complete refit of all amino acid side chain dihedral parameters, which had been carried over from ff94. The training set of conformations included multidimensional dihedral scans designed to improve transferability of the parameters. Improvement in all amino acids was obtained as compared to ff99SB. Parameters were also generated for alternate protonation states of ionizable side chains. Average errors in relative energies of pairs of conformations were under 1.0 kcal/mol as compared to QM, reduced 35% from ff99SB. We also took the opportunity to make empirical adjustments to the protein backbone dihedral parameters as compared to ff99SB. Multiple small adjustments of φ and ψ parameters were tested against NMR scalar coupling data and secondary structure content for short peptides. The best results were obtained from a physically motivated adjustment to the φ rotational profile that compensates for lack of ff99SB QM training data in the β-ppII transition region. Together, these backbone and side chain modifications (hereafter called ff14SB) not only better reproduced their benchmarks, but also improved secondary structure content in small peptides and reproduction of NMR χ1 scalar coupling measurements for proteins in solution. We also discuss the Amber ff12SB parameter set, a preliminary version of ff14SB that includes most of its improvements.

Improved Peptide and Protein Torsional Energetics with the OPLSAA Force Field

The development and validation of new peptide dihedral parameters are reported for the OPLS-AA force field. High accuracy quantum chemical methods were used to scan φ, ψ, χ1, and χ2 potential energy surfaces for blocked dipeptides. New Fourier coefficients for the dihedral angle terms of the OPLS-AA force field were fit to these surfaces, utilizing a Boltzmann-weighted error function and systematically examining the effects of weighting temperature. To prevent overfitting to the available data, a minimal number of new residue-specific and peptide-specific torsion terms were developed. Extensive experimental solution-phase and quantum chemical gas-phase benchmarks were used to assess the quality of the new parameters, named OPLS-AA/M, demonstrating significant improvement over previous OPLS-AA force fields. A Boltzmann weighting temperature of 2000 K was determined to be optimal for fitting the new Fourier coefficients for dihedral angle parameters. Conclusions are drawn from the results for best practices for developing new torsion parameters for protein force fields.

Equilibrium transitions between side-chain conformations in leucine and isoleucine

Despite recent improvements in computational methods for protein design, we still lack a quantitative, predictive understanding of the intrinsic probabilities for amino acids to adopt particular side-chain conformations. Surprisingly, this question has remained unsettled for many years, in part because of inconsistent results from different experimental approaches. To explicitly determine the relative populations of different side-chain dihedral angles, we performed all-atom hard-sphere Langevin Dynamics simulations of leucine (Leu) and isoleucine (Ile) dipeptide mimetics with stereo-chemical constraints and repulsive-only steric interactions between non-bonded atoms. We determine the relative populations of the different χ(1) and χ(2) dihedral angle combinations as a function of the backbone dihedral angles ϕ and ψ. We also propose, and test, a mechanism for inter-conversion between the different side-chain conformations. Specifically, we discover that some of the transitions between side-chain dihedral angle combinations are very frequent, whereas others are orders of magnitude less frequent, because they require rare coordinated motions to avoid steric clashes. For example, to transition between different values of χ(2), the Leu side-chain bond angles κ(1) and κ(2) must increase, whereas to transition in χ(1), the Ile bond angles λ(1) and λ(2) must increase. These results emphasize the importance of computational approaches in stimulating further experimental studies of the conformations of side-chains in proteins. Moreover, our studies emphasize the power of simple steric models to inform our understanding of protein structure, dynamics, and design.

Visualizing transient dark states by NMR spectroscopy

Myriad biological processes proceed through states that defy characterization by conventional atomic-resolution structural biological methods. The invisibility of these 'dark' states can arise from their transient nature, low equilibrium population, large molecular weight, and/or heterogeneity. Although they are invisible, these dark states underlie a range of processes, acting as encounter complexes between proteins and as intermediates in protein folding and aggregation. New methods have made these states accessible to high-resolution analysis by nuclear magnetic resonance (NMR) spectroscopy, as long as the dark state is in dynamic equilibrium with an NMR-visible species. These methods - paramagnetic NMR, relaxation dispersion, saturation transfer, lifetime line broadening, and hydrogen exchange - allow the exploration of otherwise invisible states in exchange with a visible species over a range of timescales, each taking advantage of some unique property of the dark state to amplify its effect on a particular NMR observable. In this review, we introduce these methods and explore two specific techniques - paramagnetic relaxation enhancement and dark state exchange saturation transfer - in greater detail.

Banding of NMR-derived methyl order parameters: implications for protein dynamics

Our understanding of protein folding, stability, and function has begun to more explicitly incorporate dynamical aspects. Nuclear magnetic resonance has emerged as a powerful experimental method for obtaining comprehensive site-resolved insight into protein motion. It has been observed that methyl-group motion tends to cluster into three "classes" when expressed in terms of the popular Lipari-Szabo model-free squared generalized order parameter. Here the origins of the three classes or bands in the distribution of order parameters are examined. As a first step, a Bayesian based approach, which makes no a priori assumption about the existence or number of bands, is developed to detect the banding of Oaxis2 values derived either from NMR experiments or molecular dynamics simulations. The analysis is applied to seven proteins with extensive molecular dynamics simulations of these proteins in explicit water to examine the relationship between O2 and fine details of the motion of methyl bearing side chains. All of the proteins studied display banding, with some subtle differences. We propose a very simple yet plausible physical mechanism for banding. Finally, our Bayesian method is used to analyze the measured distributions of methyl group motions in the catabolite activating protein and several of its mutants in various liganded states and discuss the functional implications of the observed banding to protein dynamics and function.

Extensive conformational heterogeneity within protein cores

Basic principles of statistical mechanics require that proteins sample an ensemble of conformations at any nonzero temperature. However, it is still common to treat the crystallographic structure of a protein as the structure of its native state, largely because high-resolution structural characterization of protein flexibility remains a profound challenge. To assess the typical degree of conformational heterogeneity within folded proteins, we construct Markov state models describing the thermodynamics and kinetics of proteins ranging from 72 to 263 residues in length. Each of these models is built from hundreds of microseconds of atomically detailed molecular dynamics simulations. Examination of the side-chain degrees of freedom reveals that almost every residue visits at least two rotameric states over this time frame, with rotamer transition rates spanning a wide range of time scales (from nanoseconds to tens of microseconds). We also report substantial backbone dynamics on time scales longer than are typically addressed by experimental measures of protein flexibility, such as NMR order parameters. Finally, we demonstrate that these extensive rearrangements are consistent with NMR and crystallographic data, which supports the validity of our models. Altogether, these results depict the interior of proteins not as well-ordered solids, as is often imagined, but instead as dense fluids, which undergo substantial structural fluctuations despite their high packing fraction.

Side chain conformational averaging in human dihydrofolate reductase

The three-dimensional structures of the dihydrofolate reductase enzymes from Escherichia coli (ecDHFR or ecE) and Homo sapiens (hDHFR or hE) are very similar, despite a rather low level of sequence identity. Whereas the active site loops of ecDHFR undergo major conformational rearrangements during progression through the reaction cycle, hDHFR remains fixed in a closed loop conformation in all of its catalytic intermediates. To elucidate the structural and dynamic differences between the human and E. coli enzymes, we conducted a comprehensive analysis of side chain flexibility and dynamics in complexes of hDHFR that represent intermediates in the major catalytic cycle. Nuclear magnetic resonance relaxation dispersion experiments show that, in marked contrast to the functionally important motions that feature prominently in the catalytic intermediates of ecDHFR, millisecond time scale fluctuations cannot be detected for hDHFR side chains. Ligand flux in hDHFR is thought to be mediated by conformational changes between a hinge-open state when the substrate/product-binding pocket is vacant and a hinge-closed state when this pocket is occupied. Comparison of X-ray structures of hinge-open and hinge-closed states shows that helix αF changes position by sliding between the two states. Analysis of χ₁ rotamer populations derived from measurements of ³J_CγCO and ³J_CγN couplings indicates that many of the side chains that contact helix αF exhibit rotamer averaging that may facilitate the conformational change. The χ₁ rotamer adopted by the Phe31 side chain depends upon whether the active site contains the substrate or product. In the holoenzyme (the binary complex of hDHFR with reduced nicotinamide adenine dinucleotide phosphate), a combination of hinge opening and a change in the Phe31 χ₁ rotamer opens the active site to facilitate entry of the substrate. Overall, the data suggest that, unlike ecDHFR, hDHFR requires minimal backbone conformational rearrangement as it proceeds through its enzymatic cycle, but that ligand flux is brokered by more subtle conformational changes that depend on the side chain motions of critical residues.

Microscopic insights into the NMR relaxation-based protein conformational entropy meter

Conformational entropy is a potentially important thermodynamic parameter contributing to protein function. Quantitative measures of conformational entropy are necessary for an understanding of its role but have been difficult to obtain. An empirical method that utilizes changes in conformational dynamics as a proxy for changes in conformational entropy has recently been introduced. Here we probe the microscopic origins of the link between conformational dynamics and conformational entropy using molecular dynamics simulations. Simulation of seven proteins gave an excellent correlation with measures of side-chain motion derived from NMR relaxation. The simulations show that the motion of methyl-bearing side chains are sufficiently coupled to that of other side chains to serve as excellent reporters of the overall side-chain conformational entropy. These results tend to validate the use of experimentally accessible measures of methyl motion--the NMR-derived generalized order parameters--as a proxy from which to derive changes in protein conformational entropy.

Quantum Mechanical Study of Vicinal J Spin-Spin Coupling Constants for the Protein Backbone

We have performed densisty functional theory (DFT) calculations of vicinal J coupling constants involving the backbone torsional angle for the protein GB3 using our recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach (Xiao He et al. J. Phys. Chem. B 2009, 113, 10380-10388). Interestingly, the calculated values based on an NMR structure are more accurate than those based on a high-resolution X-ray strucure because the NMR structure was refined using a large number of residual dipolar couplings (RDCs) whereas the hydrogen atoms were added into the X-ray structure in idealized positions, confirming that the postioning of the hydrogen atoms relative to the backbone atoms is important to the accuracy of J coupling constant prediction. By comparing three Karplus equations, our results have demonstrated that hydrogen bonding, substituent and electrostatic effects could have significant impacts on vicinal J couplings even though they depend mostly on the intervening dihedral angles. The root-mean-square deviations (RMSDs) of the calculated (3)J(H(N),H(α)), (3)J(H(N),C(β)), (3)J(H(N),C') values based on the NMR structure are 0.52, 0.25, and 0.35 Hz, respectively, after taking the dynamic effect into consideration. The excellent accuracy demonstrates that our AF-QM/MM approach is a useful tool to study the relationship between J coupling constants and the structure and dynamics of proteins.

PTRAJ and CPPTRAJ: Software for Processing and Analysis of Molecular Dynamics Trajectory Data

We describe PTRAJ and its successor CPPTRAJ, two complementary, portable, and freely available computer programs for the analysis and processing of time series of three-dimensional atomic positions (i.e., coordinate trajectories) and the data therein derived. Common tools include the ability to manipulate the data to convert among trajectory formats, process groups of trajectories generated with ensemble methods (e.g., replica exchange molecular dynamics), image with periodic boundary conditions, create average structures, strip subsets of the system, and perform calculations such as RMS fitting, measuring distances, B-factors, radii of gyration, radial distribution functions, and time correlations, among other actions and analyses. Both the PTRAJ and CPPTRAJ programs and source code are freely available under the GNU General Public License version 3 and are currently distributed within the AmberTools 12 suite of support programs that make up part of the Amber package of computer programs (see http://ambermd.org ). This overview describes the general design, features, and history of these two programs, as well as algorithmic improvements and new features available in CPPTRAJ.