Glass transition in SPC/E water and in a protein solution: A molecular dynamics simulation study

Single-particle Cryo-EM and molecular dynamics simulations: A perfect match

Knowledge of the structure and dynamics of biomolecules is key to understanding the mechanisms underlying their biological functions. Single-particle cryo-electron microscopy (cryo-EM) is a powerful structural biology technique to characterize complex biomolecular systems. Here, we review recent advances of how Molecular Dynamics (MD) simulations are being used to increase and enhance the information extracted from cryo-EM experiments. We will particularly focus on the physics underlying these experiments, how MD facilitates structure refinement, in particular for heterogeneous and non-isotropic resolution, and how thermodynamic and kinetic information can be extracted from cryo-EM data.

Effects of cryo-EM cooling on structural ensembles

Structure determination by cryo electron microscopy (cryo-EM) provides information on structural heterogeneity and ensembles at atomic resolution. To obtain cryo-EM images of macromolecules, the samples are first rapidly cooled down to cryogenic temperatures. To what extent the structural ensemble is perturbed during cooling is currently unknown. Here, to quantify the effects of cooling, we combined continuum model calculations of the temperature drop, molecular dynamics simulations of a ribosome complex before and during cooling with kinetic models. Our results suggest that three effects markedly contribute to the narrowing of the structural ensembles: thermal contraction, reduced thermal motion within local potential wells, and the equilibration into lower free-energy conformations by overcoming separating free-energy barriers. During cooling, barrier heights below 10 kJ/mol were found to be overcome, which is expected to reduce B-factors in ensembles imaged by cryo-EM. Our approach now enables the quantification of the heterogeneity of room-temperature ensembles from cryo-EM structures.

The rapid temperature drop during plunge-freezing affects the structural ensembles obtained by cryo-EM. To quantify the extent of perturbation, Bock and Grubmüller combined continuum calculations, MD simulations, and kinetic models.

Heterogeneous Solvation in Distinctive Protein-Protein Interfaces Revealed by Molecular Dynamics Simulations

Water, despite being a driving force in biochemical processes, has an elusively complex microscopic behavior. While water can increase its local density near amphiphilic protein surfaces, water is also thought to evaporate from hydrophobic surfaces and cavities, an effect known as "dewetting". The existence and extent of dewetting effects remains elusive due to the difficulty in observing clear "drying" transitions in experiments or simulations. Here, we use explicit solvent molecular dynamics (MD) simulations to study the molecular solvation at the binding interfaces of two distinctive molecular complexes: the highly hydrophilic barnase-barstar and the highly hydrophobic MDM2-p53. Our simulations, in conjunction with simple volumetric analyses, reveal a strikingly different water behavior at the binding interfaces of these two molecular complexes. In both complexes, we observe significant changes in the water local density as the two proteins approach, supporting the existence of a clear dewetting transition in the case of MDM2-p53, with an onset distance of 5.6-7.6 Å. Furthermore, the solvation analysis reported herein is a valuable tool to capture and quantify persistent or transient dewetting events in future explicit solvent MD simulations.

Hydrogen-bond dynamics at the bio-water interface in hydrated proteins: a molecular-dynamics study

Water is fundamental to the biochemistry of enzymes. It is well known that without a minimum amount of water, enzymes are not biologically active. Bare minimal solvation for biological function corresponds to about a single layer of water covering enzymes' surfaces. Many contradictory studies on protein-hydration-water-coupled dynamics have been published in recent decades. Following prevailing wisdom, a dynamical crossover in hydration water (at around 220 K for hydrated lysozymes) can trigger larger-amplitude motions of the protein, activating, in turn, biological functions. Here, we present a molecular-dynamics-simulation study on a solvated model protein (hen egg-white lysozyme), in which we determine, inter alia, the relaxation dynamics of the hydrogen-bond network between the protein and its hydration water molecules on a residue-per-residue basis. Hydrogen-bond breakage/formation kinetics is rather heterogeneous in temperature dependence (due to the heterogeneity of the free-energy surface), and is driven by the magnitude of thermal motions of various different protein residues which provide enough thermal energy to overcome energy barriers to rupture their respective hydrogen bonds with water. In particular, arginine residues exhibit the highest number of such hydrogen bonds at low temperatures, losing almost completely such bonding above 230 K. This suggests that hydration water's dynamical crossover, observed experimentally for hydrated lysozymes at ∼220 K, lies not at the origin of the protein residues' larger-amplitude motions, but rather arises as a consequence thereof. This highlights the need for new experimental investigations, and new interpretations to link protein dynamics to functions, in the context of key interrelationships with the solvation layer.

Role of Hydration Layer in Dynamical Transition in Proteins: Insights from Translational Self-Diffusivity

Elucidation of the role of hydration water underpinning dynamical crossover in proteins has proven challenging. Indeed, many contradictory findings in the literature seek to establish either causal or correlative links between water and protein behavior. Here, via molecular dynamics, we compute the temperature dependence of mean-square displacement and translational self-diffusivities for both hen egg white lysozyme and its hydration layer from 190 to 300 K. We find that the protein's mobility increases sharply at ∼230 K, indicating dynamical onset; concerted motion with hydration-water molecules is evident up to ∼285 K, confirming dynamical correlation between them. Exploring underlying mechanisms of such concerted motion, we scrutinize the water-protein hydrogen-bonding network as a function of temperature, noting sharp deviation from linearity of the hydrogen bond number's profile with temperature originating near the protein dynamical transition. Our studies reveal a common temperature profile/dependence of self-diffusivity values of the protein, hydration water, and the bulk solvent, originating from a common dependence on the bulk solvent viscosity, η_S. The key mechanistic role adopted by the protein-water hydrogen bond network in relation to the onset of proteins' dynamical transition is also discussed.

Derivation of mean-square displacements for protein dynamics from elastic incoherent neutron scattering

The derivation of mean-square displacements from elastic incoherent neutron scattering (EINS) of proteins is examined, with the aid of experiments on camphor-bound cytochrome P450cam and complementary molecular dynamics simulations. It is shown that a q(4) correction to the elastic incoherent structure factor (where q is the scattering vector) can be simply used to reliably estimate from the experiment both the average mean-square atomic displacement, <Δr(2)> of the nonexchanged hydrogen atoms in the protein and its variance, σ(2). The molecular dynamics simulation results are in broad agreement with the experimentally derived <Δr(2)> and σ(2) derived from EINS on instruments at two different energy resolutions, corresponding to dynamics on the ∼100 ps and ∼1 ns time scales. Significant dynamical heterogeneity is found to arise from methyl-group rotations. The easy-to-apply q(4) correction extends the information extracted from elastic incoherent neutron scattering experiments and should be of wide applicability.

Resilience of the iron environment in heme proteins

Conformational flexibility is essential to the functional behavior of proteins. We use an effective force constant introduced by Zaccai, the resilience, to quantify this flexibility. Site-selective experimental and computational methods allow us to determine the resilience of heme protein active sites. The vibrational density of states of the heme Fe determined using nuclear resonance vibrational spectroscopy provides a direct experimental measure of the resilience of the Fe environment, which we compare quantitatively with values derived from the temperature dependence of atomic mean-squared displacements in molecular dynamics simulations. Vibrational normal modes in the THz frequency range dominate the resilience. Both experimental and computational methods find a higher resilience for cytochrome c than for myoglobin, which we attribute to the increased number of covalent links to the peptide in the former protein. For myoglobin, the resilience of the iron environment is larger than the average resilience previously determined for hydrogen sites using neutron scattering. Experimental results suggest a slightly reduced resilience for cytochrome c upon oxidation, although the change is smaller than reported in previous Mössbauer investigations on a bacterial cytochrome c, and is not reproduced by the simulations. Oxidation state also has no significant influence on the compressibility calculated for cyt c, although a slightly larger compressibility is predicted for myoglobin.

Role of protein-water hydrogen bond dynamics in the protein dynamical transition

The role of water in protein dynamics has been investigated using molecular dynamics simulations of crystals and a dehydrated powder. On the 100 ps time scale, the anharmonic and diffusive motions involved in the protein structural relaxation are correlated with the protein-water hydrogen bond dynamics. The complete structural relaxation of the protein requires relaxation of the hydrogen bond network via solvent translational displacement. Inhibiting the solvent translational mobility, and therefore the protein-water hydrogen bond dynamics, has an effect on the protein relaxation similar to dehydration.

Structure and dynamics of calmodulin in solution

To characterize the dynamic behavior of calmodulin in solution, we have carried out molecular dynamics (MD) simulations of the Ca2+-loaded structure. The crystal structure of calmodulin was placed in a solvent sphere of radius 44 A, and 6 Cl- and 22 Na+ ions were included to neutralize the system and to model a 150 mM salt concentration. The total number of atoms was 32,867. During the 3-ns simulation, the structure exhibits large conformational changes on the nanosecond time scale. The central alpha-helix, which has been shown to unwind locally upon binding of calmodulin to target proteins, bends and unwinds near residue Arg74. We interpret this result as a preparative step in the more extensive structural transition observed in the "flexible linker" region 74-82 of the central helix upon complex formation. The major structural change is a reorientation of the two Ca2+-binding domains with respect to each other and a rearrangement of alpha-helices in the N-terminus domain that makes the hydrophobic target peptide binding site more accessible. This structural rearrangement brings the domains to a more favorable position for target binding, poised to achieve the orientation observed in the complex of calmodulin with myosin light-chain kinase. Analysis of solvent structure reveals an inhomogeneity in the mobility of water in the vicinity of the protein, which is attributable to the hydrophobic effect exerted by calmodulin's binding sites for target peptides.

Two Calorimetrically Distinct States of Liquid Water Below 150 Kelvin

Vapor-deposited amorphous solid and hyperquenched glassy water were found to irreversibly transform, on compression at 77 kelvin, to a high-density amorphous solid. On heating at atmospheric pressure, this solid became viscous water (water B), with a reversible glass-liquid transition onset at 129 +/- 2 kelvin. A different form of viscous water (water A) was formed by heating the uncompressed vapor-deposited amorphous solid and hyperquenched liquid water. On thermal cycling up to 148 kelvin, water B remained kinetically and thermodynamically distinct from water A. The occurrence of these two states, which do not interconvert, helps explain both the configurational relaxation of water and stress-induced amorphization.

Temperature dependence of dynamics of hydrated myoglobin. Comparison of force field calculations with neutron scattering data

Molecular dynamics is used to probe the atomic motions of the carboxy-myoglobin protein as a function of temperature. Simulations of 150 picoseconds in length are carried out on the protein at 20, 60, 100, 180, 220, 240, 260, 280, 300, 320 and 340 K. The simulations attempt to mimic neutron scattering experiments very closely by including a partial hydration shell around the protein. Theoretical elastic, quasielastic and inelastic neutron scattering data are derived from the trajectories and directly compared with experiment. Compared to experiment, the simulation-derived elastic scattering curves show a decrease in intensity as a function of the scattering wavevector, q2. The inelastic and quasielastic spectra show that the inelastic peak is shifted to lower frequency than the experimental value, while quasielastic behavior is in good agreement with experiment. This suggests that the theoretical model is too flexible in the harmonic limit (low temperature), but accurately reproduces high-temperature behavior. Time correlation functions of the intermediate scattering function are determined. At low temperature there is one fast decay process, and at high temperatures there is an additional slow relaxation process that is due to quasielastic scattering. The average atomic fluctuations show that the protein behaves harmonically at low temperatures. At approximately 210 K, a glass-like transition in atomic fluctuations is seen. Above the transition temperature, the atomic fluctuations exhibit both harmonic and anharmonic behavior. Comparison of protein mobility behavior with experiment indicate the fluctuations derived from simulations are larger in the harmonic region. However, the anharmonic region agrees very well with experiment. The anharmonicity is large at all temperatures, with a gradual monotonic increase from 0.5 at 20 K to greater than 0.7 at 340 K without a noticeable change at the glass transition temperature. Heavy-atom dihedral transitions are monitored as a function of temperature. Trends in the type of dihedral transitions that occur with temperature are clearly visible. Dihedral transitions involving backbone atoms occur only above the glass transition temperature. The overall protein behavior results suggest that at low temperatures there is purely vibrational motion with one fast decay process, and above the glass transition temperature there is more anharmonic motion with a fast and a slower relaxation process occurring simultaneously.(ABSTRACT TRUNCATED AT 400 WORDS)