Ensemble MD simulations restrained via crystallographic data: accurate structure leads to accurate dynamics

Functional protein dynamics in a crystal

Proteins are molecular machines and to understand how they work, we need to understand how they move. New pump-probe time-resolved X-ray diffraction methods open up ways to initiate and observe protein motions with atomistic detail in crystals on biologically relevant timescales. However, practical limitations of these experiments demands parallel development of effective molecular dynamics approaches to accelerate progress and extract meaning. Here, we establish robust and accurate methods for simulating dynamics in protein crystals, a nontrivial process requiring careful attention to equilibration, environmental composition, and choice of force fields. With more than seven milliseconds of sampling of a single chain, we identify critical factors controlling agreement between simulation and experiments and show that simulated motions recapitulate ligand-induced conformational changes. This work enables a virtuous cycle between simulation and experiments for visualizing and understanding the basic functional motions of proteins.

Functional Protein Dynamics in a Crystal

Proteins are molecular machines and to understand how they work, we need to understand how they move. New pump-probe time-resolved X-ray diffraction methods open up ways to initiate and observe protein motions with atomistic detail in crystals on biologically relevant timescales. However, practical limitations of these experiments demands parallel development of effective molecular dynamics approaches to accelerate progress and extract meaning. Here, we establish robust and accurate methods for simulating dynamics in protein crystals, a nontrivial process requiring careful attention to equilibration, environmental composition, and choice of force fields. With more than seven milliseconds of sampling of a single chain, we identify critical factors controlling agreement between simulation and experiments and show that simulated motions recapitulate ligand-induced conformational changes. This work enables a virtuous cycle between simulation and experiments for visualizing and understanding the basic functional motions of proteins.

X-ray Crystallography Module in MD Simulation Program Amber 2023. Refining the Models of Protein Crystals

The MD simulation package Amber offers an attractive platform to refine crystallographic structures of proteins: (i) state-of-the-art force fields help to regularize protein coordinates and reconstruct the poorly diffracting elements of the structure, such as flexible loops; (ii) MD simulations restrained by the experimental diffraction data provide an effective strategy to optimize structural models of protein crystals, including explicitly modeled interstitial solvent as well as crystal contacts. Here, we present the new crystallography module xray, released as a part of the Amber 2023 package. This module contains functions to calculate and scale structure factors (including the contributions from bulk solvent), evaluate the maximum-likelihood-type crystallographic potential, and compute its derivative forces. The X-ray functionality of Amber no longer relies on external dependencies so that the full advantage of GPU acceleration can be taken. This makes it possible to refine in a short time hundreds of crystal models, including supercell models comprised of multiple unit cells. The new automated Amber-based refinement procedure leads to an appreciable improvement in Rfree (in some cases, by as much as 0.067) as well as MolProbity scores.

Molecular-dynamics simulations of macromolecular diffraction, part I: Preparation of protein crystal simulations

Molecular-dynamics (MD) simulations of protein crystals enable the prediction of structural and dynamical features of both the protein and the solvent components of macromolecular crystals, which can be validated against diffraction data from X-ray crystallographic experiments. The simulations have been useful for studying and predicting both Bragg and diffuse scattering in protein crystallography; however, the preparation is not yet automated and includes choices and tradeoffs that can impact the results. Here we examine some of the intricacies and consequences of the choices involved in setting up MD simulations of protein crystals for the study of diffraction data, and provide a recipe for preparing the simulations, packaged in an accompanying Jupyter notebook. This article and the accompanying notebook are intended to serve as practical resources for researchers wishing to put these models to work.

MD simulations of macromolecular crystals: Implications for the analysis of Bragg and diffuse scattering

Some of our most detailed information about structure and dynamics of macromolecules comes from X-ray-diffraction studies in crystalline environments. More than 170,000 atomic models have been deposited in the Protein Data Bank, and the number of observations (typically of intensities of Bragg diffraction peaks) is generally quite large, when compared to other experimental methods. Nevertheless, the general agreement between calculated and observed intensities is far outside the experimental precision, and the majority of scattered photons fall between the sharp Bragg peaks, and are rarely taken into account. This chapter considers how molecular dynamics simulations can be used to explore the connections between microscopic behavior in a crystalline lattice and observed scattering intensities, and point the way to new atomic models that could more faithfully recapitulate Bragg intensities and extract useful information from the diffuse scattering that lies between those peaks.

Modeling a unit cell: crystallographic refinement procedure using the biomolecular MD simulation platform Amber

A procedure has been developed for the refinement of crystallographic protein structures based on the biomolecular simulation program Amber. The procedure constructs a model representing a crystal unit cell, which generally contains multiple protein molecules and is fully hydrated with TIP3P water. Periodic boundary conditions are applied to the cell in order to emulate the crystal lattice. The refinement is conducted in the form of a specially designed short molecular-dynamics run controlled by the Amber ff14SB force field and the maximum-likelihood potential that encodes the structure-factor-based restraints. The new Amber-based refinement procedure has been tested on a set of 84 protein structures. In most cases, the new procedure led to appreciably lower R free values compared with those reported in the original PDB depositions or obtained by means of the industry-standard phenix.refine program. In particular, the new method has the edge in refining low-accuracy scrambled models. It has also been successful in refining a number of molecular-replacement models, including one with an r.m.s.d. of 2.15 Å. In addition, Amber-refined structures consistently show superior MolProbity scores. The new approach offers a highly realistic representation of protein-protein interactions in the crystal, as well as of protein-water interactions. It also offers a realistic representation of protein crystal dynamics (akin to ensemble-refinement schemes). Importantly, the method fully utilizes the information from the available diffraction data, while relying on state-of-the-art molecular-dynamics modeling to assist with those elements of the structure that do not diffract well (for example mobile loops or side chains). Finally, it should be noted that the protocol employs no tunable parameters, and the calculations can be conducted in a matter of several hours on desktop computers equipped with graphical processing units or using a designated web service.

Unveiling the "invisible" druggable conformations of GDP-bound inactive Ras

The prevalent view on whether Ras is druggable has gradually changed in the recent decade with the discovery of effective inhibitors binding to cryptic sites unseen in the native structures. Despite the promising advances, therapeutics development toward higher potency and specificity is challenged by the elusive nature of these binding pockets. Here we derive a conformational ensemble of guanosine diphosphate (GDP)-bound inactive Ras by integrating spin relaxation-validated atomistic simulation with NMR chemical shifts and residual dipolar couplings, which provides a quantitative delineation of the intrinsic dynamics up to the microsecond timescale. The experimentally informed ensemble unequivocally demonstrates the preformation of both surface-exposed and buried cryptic sites in Ras•GDP, advocating design of inhibition by targeting the transient druggable conformers that are invisible to conventional experimental methods. The viability of the ensemble-based rational design has been established by retrospective testing of the ability of the Ras•GDP ensemble to identify known ligands from decoys in virtual screening.

Molecular dynamics simulation of the heart type fatty acid binding protein in a crystal environment

Crystallographic data comes from a space-time average over all the unit cells within the crystal, so dynamic phenomena do not contribute significantly to the diffraction data. Many efforts have been made to reconstitute the movement of the macromolecules and explore the microstates that the confined proteins can adopt in the crystalline network. We explored different strategies to simulate a heart fatty acid binding protein (H-FABP) crystal by means of Molecular Dynamics (MD) simulations. We evaluate the effect of introducing restraints according to experimental isotropic B-factors and we analyzed the H-FABP motions in the crystal using Principal Component Analysis (PCA), isotropic and anisotropic B-factors. We compared the behavior of the protein simulated in the crystal confinement versus in solution, and we observed the effect of that confinement in the mobility of the protein residues. Restraining one-third of Cα atoms based on experimental B-factors produce lower B-factors than simulations without restraints, showing that the position restraint of the atoms with the lowest experimental B-factor is a good strategy to maintain the geometry of the crystal with an obvious decrease in the degrees of motion of the protein. PCA shows that, as position restraint reduces the conformational space explored by the system, the motion of the crystal is better recovered, for an essential subspace of the same size, in the simulations without restraints. Restraining only one Cα seems to be a good balance between giving flexibility to the system and preserving its structure. Communicated by Ramaswamy H. Sarma.

On Restraints in End-Point Protein-Ligand Binding Free Energy Calculations

The impact of harmonic restraints on protein heavy atoms and ligand atoms on end-point free energy calculations is systematically characterized for 54 protein-ligand complexes. We observe that stronger restraints reduce the equilibration time and statistical inefficiency, suppress conformational sampling, influence correlation with experiment, and monotonically decrease the estimated loss of entropy upon binding, leading to stronger estimated binding free energies in most systems. A statistical estimator that reweights for the biasing potential and includes data prior to the estimated equilibration time has the highest correlation with experiment. A spring constant of 20 cal mol^-1 Å^-2 maintains a near-native energy landscape and suppresses artifactual energy minima while minimally limiting thermal fluctuations about the crystal structure. © 2019 Wiley Periodicals, Inc.

Biomolecular Solvation Structure Revealed by Molecular Dynamics Simulations

To compare ordered water positions from experiment with those from molecular dynamics (MD) simulations, a number of MD models of water structure in crystalline endoglucanase were calculated. The starting MD model was derived from a joint X-ray and neutron diffraction crystal structure, enabling the use of experimentally assigned protonation states. Simulations were performed in the crystalline state, using a periodic 2 × 2 × 2 supercell with explicit solvent. Water X-ray and neutron scattering density maps were computed from MD trajectories using standard macromolecular crystallography methods. In one set of simulations, harmonic restraints were applied to bias the protein structure toward the crystal structure. For these simulations, the recall of crystallographic waters using strong peaks in the MD water electron density was very good, and there also was substantial visual agreement between the boomerang-like wings of the neutron scattering density and the crystalline water hydrogen positions. An unrestrained simulation also was performed. For this simulation, the recall of crystallographic waters was much lower. For both restrained and unrestrained simulations, the strongest water density peaks were associated with crystallographic waters. The results demonstrate that it is now possible to recover crystallographic water structure using restrained MD simulations but that it is not yet reasonable to expect unrestrained MD simulations to do the same. Further development and generalization of MD water models for force-field development, macromolecular crystallography, and medicinal chemistry applications is now warranted. In particular, the combination of room-temperature crystallography, neutron diffraction, and crystalline MD simulations promises to substantially advance modeling of biomolecular solvation.

Molecular Dynamics Simulations of Macromolecular Crystals

The structures of biological macromolecules would not be known to their present extent without X-ray crystallography. Most simulations of globular proteins in solution begin by surrounding the crystal structure of the monomer in a bath of water molecules, but the standard simulation employing periodic boundary conditions is already close to a crystal lattice environment. With simple protocols, the same software and molecular models can perform simulations of the crystal lattice, including all asymmetric units and solvent to fill the box. Throughout the history of molecular dynamics, studies of crystal lattices have served to investigate the quality of the underlying force fields, correlate the simulated ensembles to experimental structure factors, and extrapolate the behavior in lattices to behavior in solution. Powerful new computers are enabling molecular simulations with greater realism and statistical convergence. Meanwhile, the advent of exciting new methods in crystallography, including femtosecond free-electron lasers and image reconstruction for time-resolved crystallography on slurries of small crystals, is expanding the range of structures accessible to X-ray diffraction. We review past fusions of simulations and crystallography, then look ahead to the ways that simulations of crystal structures will enhance structural biology in the future.

Slow conformational exchange and overall rocking motion in ubiquitin protein crystals

Proteins perform their functions in solution but their structures are most frequently studied inside crystals. Here we probe how the crystal packing alters microsecond dynamics, using solid-state NMR measurements and multi-microsecond MD simulations of different crystal forms of ubiquitin. In particular, near-rotary-resonance relaxation dispersion (NERRD) experiments probe angular backbone motion, while Bloch–McConnell relaxation dispersion data report on fluctuations of the local electronic environment. These experiments and simulations reveal that the packing of the protein can significantly alter the thermodynamics and kinetics of local conformational exchange. Moreover, we report small-amplitude reorientational motion of protein molecules in the crystal lattice with an ~3–5° amplitude on a tens-of-microseconds time scale in one of the crystals, but not in others. An intriguing possibility arises that overall motion is to some extent coupled to local dynamics. Our study highlights the importance of considering the packing when analyzing dynamics of crystalline proteins.

X-ray crystallography is the main method for protein structure determination. Here the authors combine solid-state NMR measurements and molecular dynamics simulations and show that crystal packing alters the thermodynamics and kinetics of local conformational exchange as well as overall rocking motion of protein molecules in the crystal lattice.

Identifying and Visualizing Macromolecular Flexibility in Structural Biology

Structural biology comprises a variety of tools to obtain atomic resolution data for the investigation of macromolecules. Conventional structural methodologies including crystallography, NMR and electron microscopy often do not provide sufficient details concerning flexibility and dynamics, even though these aspects are critical for the physiological functions of the systems under investigation. However, the increasing complexity of the molecules studied by structural biology (including large macromolecular assemblies, integral membrane proteins, intrinsically disordered systems, and folding intermediates) continuously demands in-depth analyses of the roles of flexibility and conformational specificity involved in interactions with ligands and inhibitors. The intrinsic difficulties in capturing often subtle but critical molecular motions in biological systems have restrained the investigation of flexible molecules into a small niche of structural biology. Introduction of massive technological developments over the recent years, which include time-resolved studies, solution X-ray scattering, and new detectors for cryo-electron microscopy, have pushed the limits of structural investigation of flexible systems far beyond traditional approaches of NMR analysis. By integrating these modern methods with powerful biophysical and computational approaches such as generation of ensembles of molecular models and selective particle picking in electron microscopy, more feasible investigations of dynamic systems are now possible. Using some prominent examples from recent literature, we review how current structural biology methods can contribute useful data to accurately visualize flexibility in macromolecular structures and understand its important roles in regulation of biological processes.

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.

Characterization of fibril dynamics on three timescales by solid-state NMR

A multi-timescale analysis of the backbone dynamics of HET-s (218-289) fibrils is described based on multiple site-specific R 1 and R 1ρ data sets and S (2) measurements via REDOR for most backbone (15)N and (13)Cα nuclei. (15)N and (13)Cα data are fitted with motions at three timescales. Slow motion is found, indicating a global fibril motion. We further investigate the effect of (13)C-(13)C transfer in measurement of (13)Cα R 1. Finally, we show that it is necessary to go beyond the Redfield approximation for slow motions in order to obtain accurate numerical values for R 1ρ.

Computational Methodologies for Real-Space Structural Refinement of Large Macromolecular Complexes

The rise of the computer as a powerful tool for model building and refinement has revolutionized the field of structure determination for large biomolecular systems. Despite the wide availability of robust experimental methods capable of resolving structural details across a range of spatiotemporal resolutions, computational hybrid methods have the unique ability to integrate the diverse data from multimodal techniques such as X-ray crystallography and electron microscopy into consistent, fully atomistic structures. Here, commonly employed strategies for computational real-space structural refinement are reviewed, and their specific applications are illustrated for several large macromolecular complexes: ribosome, virus capsids, chemosensory array, and photosynthetic chromatophore. The increasingly important role of computational methods in large-scale structural refinement, along with current and future challenges, is discussed.

Protein stabilizer, NDSB-195, enhances the dynamics of the β4 -α2 loop of ubiquitin

Non-detergent sulfobetaines (NDSBs) are a new group of small, synthetic protein stabilizers, which have advantages over classical compatible osmolytes, such as polyol, amines, and amino acids: they do not increase solution viscosity, unlike polyols, and they are zwitterionic at all pH ranges, unlike amines and amino acids. NDSBs also facilitate the crystallization and refolding of proteins. The mechanism whereby NDSBs exhibit such activities, however, remains elusive. To gain insight into this mechanism, we studied, using nuclear magnetic resonance (NMR), the effects of dimethylethylammonium propane sulfonate (NDSB-195) on the dynamics of ubiquitin, on which a wealth of information has been accumulated. By analyzing the line width of amide proton resonances and the transverse relaxation rates of nitrogen atoms, we found that NDSB-195 enhances the microsecond-millisecond dynamics of a β4 -α2 loop of ubiquitin. Although those compounds that enhance protein dynamics are generally considered to destabilize protein molecules, NDSB-195 enhanced the stability of ubiquitin against guanidium chloride denaturation. Thus, the simultaneous enhancement of stability and flexibility by a single compound can be attained.

Observing the overall rocking motion of a protein in a crystal

The large majority of three-dimensional structures of biological macromolecules have been determined by X-ray diffraction of crystalline samples. High-resolution structure determination crucially depends on the homogeneity of the protein crystal. Overall ‘rocking' motion of molecules in the crystal is expected to influence diffraction quality, and such motion may therefore affect the process of solving crystal structures. Yet, so far overall molecular motion has not directly been observed in protein crystals, and the timescale of such dynamics remains unclear. Here we use solid-state NMR, X-ray diffraction methods and μs-long molecular dynamics simulations to directly characterize the rigid-body motion of a protein in different crystal forms. For ubiquitin crystals investigated in this study we determine the range of possible correlation times of rocking motion, 0.1–100 μs. The amplitude of rocking varies from one crystal form to another and is correlated with the resolution obtainable in X-ray diffraction experiments.

Small-amplitude overall motion of molecules in crystals limits the achievable resolution in X-ray diffraction, yet little is known about its exact nature. Here, the authors obtain NMR, XRD and MD data from three different crystal forms of a protein (ubiquitin) to gain insight into amplitude and timescale of such motions.

Molecular dynamics simulation of triclinic lysozyme in a crystal lattice

Molecular dynamics simulations of crystals can enlighten interpretation of experimental X-ray crystallography data and elucidate structural dynamics and heterogeneity in biomolecular crystals. Furthermore, because of the direct comparison against experimental data, they can inform assessment of molecular dynamics methods and force fields. We present microsecond scale results for triclinic hen egg-white lysozyme in a supercell consisting of 12 independent unit cells using four contemporary force fields (Amber ff99SB, ff14ipq, ff14SB, and CHARMM 36) in crystalline and solvated states (for ff14SB only). We find the crystal simulations consistent across multiple runs of the same force field and robust to various solvent equilibration schemes. However, convergence is slow compared with solvent simulations. All the tested force fields reproduce experimental structural and dynamic properties well, but Amber ff14SB maintains structure and reproduces fluctuations closest to the experimental model: its average backbone structure differs from the deposited structure by 0.37Å; by contrast, the average backbone structure in solution differs from the deposited by 0.65Å. All the simulations are affected by a small progressive deterioration of the crystal lattice, presumably due to imperfect modeling of hydrogen bonding and other crystal contact interactions; this artifact is smallest in ff14SB, with average lattice positions deviating by 0.20Å from ideal. Side-chain disorder is surprisingly low with fewer than 30% of the nonglycine or alanine residues exhibiting significantly populated alternate rotamers. Our results provide helpful insight into the methodology of biomolecular crystal simulations and indicate directions for future work to obtain more accurate energy models for molecular dynamics.

Access to Cα backbone dynamics of biological solids by 13C T1 relaxation and molecular dynamics simulation

We introduce a labeling scheme for magic angle spinning (MAS) solid-state NMR that is based on deuteration in combination with dilution of the carbon spin system. The labeling strategy achieves spectral editing by simplification of the HαCα and aliphatic side chain spectral region. A reduction in both proton and carbon spin density in combination with fast spinning (≥50 kHz) is essential to retrieve artifact-free (13)C-R1 relaxation data for aliphatic carbons. We obtain good agreement between the NMR experimental data and order parameters extracted from a molecular dynamics (MD) trajectory, which indicates that carbon based relaxation parameters can yield complementary information on protein backbone as well as side chain dynamics.

All-atom crystal simulations of DNA and RNA duplexes

BACKGROUND

Molecular dynamics simulations can complement experimental measures of structure and dynamics of biomolecules. The quality of such simulations can be tested by comparisons to models refined against experimental crystallographic data.

METHODS

We report simulations of DNA and RNA duplexes in their crystalline environment. The calculations mimic the conditions for PDB entries 1D23 [d(CGATCGATCG)2] and 1RNA [(UUAUAUAUAUAUAA)2], and contain 8 unit cells, each with 4 copies of the Watson-Crick duplex; this yields in aggregate 64μs of duplex sampling for DNA and 16μs for RNA.

RESULTS

The duplex structures conform much more closely to the average structure seen in the crystal than do structures extracted from a solution simulation with the same force field. Sequence-dependent variations in helical parameters, and in groove widths, are largely maintained in the crystal structure, but are smoothed out in solution. However, the integrity of the crystal lattice is slowly degraded in both simulations, with the result that the interfaces between chains become heterogeneous. This problem is more severe for the DNA crystal, which has fewer inter-chain hydrogen bond contacts than does the RNA crystal.

CONCLUSIONS

Crystal simulations using current force fields reproduce many features of observed crystal structures, but suffer from a gradual degradation of the integrity of the crystal lattice.

GENERAL SIGNIFICANCE

The results offer insights into force-field simulations that test their ability to preserve weak interactions between chains, which will be of importance also in non-crystalline applications that involve binding and recognition. This article is part of a Special Issue entitled Recent developments of molecular dynamics.