Hydrated myoglobin's anharmonic fluctuations are not primarily due to dihedral transitions

Modulation of free energy landscapes as a strategy for the design of antimicrobial peptides

Computational design of antimicrobial peptides (AMPs) is a promising area of research for developing novel agents against drug-resistant bacteria. AMPs are present naturally in many organisms, from bacteria to humans, a time-tested mechanism that makes them attractive as effective antibiotics. Depending on the environment, AMPs can exhibit α-helical or β-sheet conformations, a mix of both, or lack secondary structure; they can be linear or cyclic. Prediction of their structures is challenging but critical for rational design. Promising AMP leads can be developed using essentially two approaches: traditional modeling of the physicochemical mechanisms that determine peptide behavior in aqueous and membrane environments and knowledge-based, e.g., machine learning (ML) techniques, that exploit ever-growing AMP databases. Here, we explore the conformational landscapes of two recently ML-designed AMPs, characterize the dependence of these landscapes on the medium conditions, and identify features in peptide and membrane landscapes that mediate protein-membrane association. For both peptides, we observe greater conformational diversity in an aqueous solvent than in a less polar solvent, and one peptide is seen to alter its conformation more dramatically than the other upon the change of solvent. Our results support the view that structural rearrangement in response to environmental changes is central to the mechanism of membrane-structure disruption by linear peptides. We expect that the design of AMPs by ML will benefit from the incorporation of peptide conformational substates as quantified here with molecular simulations.

Bifurcated hydrogen bonding and asymmetric fluctuations in a carbohydrate crystal studied via X-ray crystallography and computational analysis

The structure of the O-methyl glycoside of the naturally occurring 6-O-[(R)-1-carboxyethyl]-α-D-galactopyranose, C10H18O8, has been determined by X-ray crystallography at 100 K, supplementing the previously determined structure obtained at 293 K (Acta Crystallogr.1996, C52, 2285-2287). Molecular dynamics simulations of this glycoside were performed in the crystal environment with different numbers of units cells included in the primary simulation system at both 100 and 293 K. The calculated unit cell parameters and the intramolecular geometries (bonds, angles, and dihedrals) agree well with experimental results. Atomic fluctuations, including B-factors and anisotropies, are in good agreement with respect to the relative values on an atom-by-atom basis. In addition, the fluctuations increase with increasing simulation system size, with the simulated values converging to values lower than those observed experimentally indicating that the simulation model is not accounting for all possible contributions to the experimentally observed B-factors, which may be related to either the simulation time scale or size. In the simulations, the hydroxyl group of O7 is found to form bifurcated hydrogen bonds with O6 and O8 of an adjacent molecule, with the interactions dominated by the HO7-O6 interaction. Quantum mechanical calculations support this observation.

A direct coupling between global and internal motions in a single domain protein? MD investigation of extreme scenarios

Proteins are not rigid molecules, but exhibit internal motions on timescales ranging from femto- to milliseconds and beyond. In solution, proteins also experience global translational and rotational motions, sometimes on timescales comparable to those of the internal fluctuations. The possibility that internal and global motions may be directly coupled has intriguing implications, given that enzymes and cell signaling proteins typically associate with binding partners and cellular scaffolds. Such processes alter their global motion and may affect protein function. Here, we present molecular dynamics simulations of extreme case scenarios to examine whether a possible relationship exists. In our model protein, a ubiquitin-like RhoGTPase binding domain of plexin-B1, we removed either internal or global motions. Comparisons with unrestrained simulations show that internal and global motions are not appreciably coupled in this single-domain protein. This lack of coupling is consistent with the observation that the dynamics of water around the protein, which is thought to permit, if not stimulate, internal dynamics, is also largely independent of global motion. We discuss implications of these results for the structure and function of proteins.

Refinement of the primary hydration shell model for molecular dynamics simulations of large proteins

A realistic representation of water molecules is important in molecular dynamics simulation of proteins. However, the standard method of solvating biomolecules, that is, immersing them in a box of water with periodic boundary conditions, is computationally expensive. The primary hydration shell (PHS) method, developed more than a decade ago and implemented in CHARMM, uses only a thin shell of water around the system of interest, and so greatly reduces the computational cost of simulations. Applying the PHS method, especially to larger proteins, revealed that further optimization and a partial reworking was required and here we present several improvements to its performance. The model is applied to systems with different sizes, and both water and protein behaviors are compared with those observed in standard simulations with periodic boundary conditions and, in some cases, with experimental data. The advantages of the modified PHS method over its original implementation are clearly apparent when it is applied to simulating the 82 kDa protein Malate Synthase G.

Toward quantitative simulations of carbon monoxide escape pathways in myoglobin

Straightforward molecular dynamics trajectories have been computed to explore the diffusion of carbon monoxide through myoglobin. The classical equations of motion were integrated for 2 ns and the resulting pathways analyzed. Two types of runs were examined. Type i: Myoglobin and a ligand embedded in a periodic box with 9996 water molecules; the water molecules are rigid but the bonds of the protein are flexible. Type ii: Myoglobin with a solvation shell (153 water molecules) in which all bond lengths are fixed. In trajectories of type i, the diffusing ligand visits a significant part of the protein matrix and was not constrained to the proximity of the heme pocket before escaping. The maximum time of the trajectories was 2 ns. It was shorter if the ligand escaped earlier. Two ligands (from a total of 88) escape to the solvent from nonclassical gates (non-E-helix gates). In trajectories of type ii, the overall fluctuations of the protein are smaller and the ligand explores significantly smaller internal space. The escape rate from type ii trajectories (11 of 400) is comparable to type i and is not dramatically different from experiment (1 of 100). Interestingly, the two simulations with comparable rates sampled different pathways. In trajectories of type ii, we observe escapes from the classical gate (His 64) and from the Xe4 cavity. Further studies (that are underway) are required to define the escape pathways and the overall rate.

Origin of the dynamic transition upon pressurization of crystalline proteins

We study the role of hydration water in the dynamic transition of low-hydrated proteins upon pressurization found recently (Meinhold, L.; Smith, J. C. Phys. Rev. E 2005, 72, 061908). Clustering and percolation of water in the hydration shells of protein molecules in crystalline Staphylococcal nuclease are analyzed at various pressures. The number of water molecules in the hydration shell increases and the hydrogen-bonded network of hydration water spans with increasing pressure. The dynamic transition of protein occurs when the spanning water network exists with the probability of about 50% and hydration water shows large density fluctuations. Formation of a spanning water network upon pressurization promotes protein dynamics as in the case of the dynamic transition with increasing hydration. Properties of hydration water in various thermodynamic states and their influence on biological function are discussed.

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

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

The role of calcium in the conformational dynamics and thermal stability of the D-galactose/D-glucose-binding protein from Escherichia coli

We have characterized stability and conformational dynamics of the calcium depleted D-galactose/D-glucose-binding protein (GGBP) from Escherichia coli. The structural stability of the protein was investigated by steady state and time resolved fluorescence, and far-UV circular dichroism in the temperature range from 20 degrees C to 70 degrees C. We have found that the absence of the Ca(2+) ion results in a significant destabilization of the C-terminal domain of the protein. In particular, the melting temperature decreases by about 10 degrees C with the simultaneous loss of the melting cooperativity. Time resolved fluorescence quenching revealed significant loosening of the protein when highly shielded Trp residue(s) became accessible to acrylamide at higher temperatures. We have documented a significant stabilizing effect of glucose that mostly reverts the effect of calcium, that is, the thermal stability of the protein increases by about 10 degrees C and the melting cooperativity is restored. Moreover, the protein structure remains compact with low amplitude of the segmental mobility up to high temperatures. We have used molecular dynamics to identify the structural feature responsible for changes in the temperature stability. Disintegration of the Ca(2+)-binding loop seems to be responsible for the loss of the stability in the absence of calcium. The new insights on the structural properties and temperature stability of the calcium depleted GGBP contribute to better understanding of the protein function and constitute important information for the development of new biotechnological applications of this class of proteins.

Librational motion of spin-labeled lipids in high-cholesterol containing membranes from echo-detected EPR spectra

Two-pulse, echo-detected (ED) electron paramagnetic resonance (EPR) spectroscopy was used to study the librational motions of spin-labeled lipids in membranes of dipalmitoylphosphatidylcholine + 50 mol % cholesterol. The temperature dependence, over the range 77-240 K, and the dependence on position of spin-labeling in the sn-2 chain (n=5, 7, 10, 12, and 14) of the phospholipid, were characterized in detail. The experimental ED-spectra were corrected for instantaneous spin diffusion arising from static spin-spin interactions, by using spectra recorded at 77 K, where motional contributions are negligible. Simulations according to a model of rapid, small-amplitude librations about an axis whose direction is randomly distributed are able to describe the experimental spectra. Calibrations, in terms of the amplitude-correlation time product, alpha2tauc, were constructed for diagnostic spectral line-height ratios at different echo delay times, and for relaxation spectra obtained from the ratio of ED-spectra recorded at two different echo delays. The librational amplitude, alpha2, was determined for a spin label at the 14-C position of the lipid chain from the partially motionally averaged hyperfine splitting in the conventional EPR spectra. The librational correlation time, tauc, which is deduced from combination of the conventional and ED-EPR results, lies in the subnanosecond regime and depends only weakly on temperature. The temperature dependence of the ED-EPR spectra arises mainly from an increase in librational amplitude with increasing temperature, and position down the lipid chain. A gradual transition takes place at higher temperatures, from a situation in which segmental torsional librations are cumulative, i.e., the contributions of the individual segments add up progressively upon going down the chain, to one of concerted motion only weakly dependent on chain position. Such librational motions are important for glass-like states and are generally relevant to high lipid packing densities, e.g., in cholesterol-containing raft domains and condensed complexes.

Structure, dynamics and reactions of protein hydration water

The apparent simplicity of the water molecule belies the wide range of fascinating protein phenomena in which it participates. We review recent computer simulation work on buried, internal water molecules, discussing the thermodynamics of water molecule binding and the participation of water in proton transfer reactions. Surface water molecules are also considered, with emphasis on the modification of average solvent structure on a protein surface, the role of water in the protein dynamical 'glass' transition and a simplified description of the protein motions thereby activated.

The 'glass transition' in protein dynamics: what it is, why it occurs, and how to exploit it

All proteins undergo a dramatic change in their dynamical properties at approximately 200 K. Above this temperature, their dynamic behavior is dominated by large-scale collective motions of bonded and nonbonded groups of atoms. At lower temperatures, simple harmonic vibrations predominate. The transition has been described as a 'glass transition' to emphasize certain similarities between the change in dynamic behavior of individual protein molecules and the changes in viscosity and other properties of liquids when they form a glass. The glass transition may reflect the intrinsic temperature dependence of the motions of atoms in the protein itself, in the bound solvent on the surface of the protein, or it may reflect contributions from both. Protein function is significantly altered below this transition temperature; a fact that can be exploited to trap normally unstable intermediates in enzyme-catalyzed reactions and stabilize them for periods long enough to permit their characterization by high-resolution protein crystallography.

Adhesive-cohesive model for protein compressibility: an alternative perspective on stability

As a dynamic property of folded proteins, protein compressibility provides important information about the forces that govern structural stability. We relate intrinsic compressibility to stability by using molecular dynamics to identify a molecular basis for the variation in compressibility among globular proteins. We find that excess surface charge accounts for this variation not only for the proteins simulated by molecular dynamics but also for a larger set of globular proteins. This dependence on charge distribution forms the basis for an adhesive-cohesive model of protein compressibility in which attractive forces from solvent compete with tertiary interactions that favor folding. Further, a newly recognized correlation between compressibility and the heat capacity of unfolding infers a link between compressibility and the enthalpy of unfolding. This linkage, together with the adhesive-cohesive model for compressibility, leads to the conclusion that folded proteins can gain enthalpic stability from a uniform distribution of charged atoms, as opposed to partitioning charge to the protein surface. Whether buried charged groups can be energetically stabilizing is a fundamental, yet controversial, question regarding protein structure. The analysis reported here implies that one mechanism to gain enthalpic stability involves positioning charge inside the protein in an optimal structural arrangement.

MD simulation of a plastocyanin mutant adsorbed onto a gold surface

MD simulation of plastocyanin, an electron transfer protein, adsorbed onto a gold surface, has been performed for 10 ns. Starting from the crystallographic structure of a poplar plastocyanin mutant engineered with the insertion of a disulfide bridge, the protein has been anchored to a gold substrate modeled by a cluster of three layers in the Au<111> configuration. A number of significant structural and dynamical properties of the protein molecule, covalently bound through either one or two sulfur atoms to the gold surface, has been extracted and compared with those of the free protein. Attention has been paid to investigate the dynamical aspects putatively related to the electron transfer process. In particular, the cross-correlation function between specific active site vibrations and all the other protein atom motions and the principal component analysis have been calculated in order to put into evidence dynamical correlation of some functional relevance. The results are discussed also in connection with related experiments.

Translational hydration water dynamics drives the protein glass transition

Experimental and computer simulation studies have revealed the presence of a glass-like transition in the internal dynamics of hydrated proteins at approximately 200 K involving an increase of the amplitude of anharmonic dynamics. This increase in flexibility has been correlated with the onset of protein activity. Here, we determine the driving force behind the protein transition by performing molecular dynamics simulations of myoglobin surrounded by a shell of water. A dual heat bath method is used with which, in any given simulation, the protein and solvent are held at different temperatures, and sets of simulations are performed varying the temperature of the components. The results show that the protein transition is driven by a dynamical transition in the hydration water that induces increased fluctuations primarily in side chains in the external regions of the protein. The water transition involves activation of translational diffusion and occurs even in simulations where the protein atoms are held fixed.

Radially softening diffusive motions in a globular protein

Molecular dynamics simulation, quasielastic neutron scattering and analytical theory are combined to characterize diffusive motions in a hydrated protein, C-phycocyanin. The simulation-derived scattering function is in approximate agreement with experiment and is decomposed to determine the essential contributions. It is found that the geometry of the atomic motions can be modeled as diffusion in spheres with a distribution of radii. The time dependence of the dynamics follows stretched exponential behavior, reflecting a distribution of relaxation times. The average side chain and backbone dynamics are quantified and compared. The dynamical parameters are shown to present a smooth variation with distance from the core of the protein. Moving outward from the center of the protein there is a progressive increase of the mean sphere size, accompanied by a narrowing and shifting to shorter times of the relaxation time distribution. This smooth, "radially softening" dynamics may have important consequences for protein function. It also raises the possibility that the dynamical or "glass" transition with temperature observed experimentally in proteins might be depth dependent, involving, as the temperature decreases, progressive freezing out of the anharmonic dynamics with increasing distance from the center of the protein.

Simulated and NMR-derived backbone dynamics of a protein with significant flexibility: a comparison of spectral densities for the betaARK1 PH domain

A 7.6 ns molecular dynamics trajectory of the betaARK1 PH domain in explicit water with appropriate ions was calculated at 300 K. Spectral densities at omega = 0, omega(N), and 0.87omega(H) and the model-free parameters were evaluated from the experimental as well as the simulated data, taking the anisotropic overall motion of the protein into account. Experimental and simulated spectral densities are in reasonable general agreement for NH bond vectors, where the corresponding motions have converged within the simulation time. A sufficient sampling of the motions for NH bonds within flexible parts of the protein requires a longer simulation time. The simulated spectral densities J(0) and J(omega(N)) are, on average, 4.5% and 16% lower than the experimental data; the corresponding numbers for the core residues are about 6%; the high-frequency spectral densities J(0.87omega(H)) are lower by, on average, 16% (21% for the core). The simulated order parameters, S(2), are also lower, although the overall disagreement between the simulation and experiment is less pronounced: 1% for all residues and 6% for the core. The observed systematic decrease of simulated spectral density and the order parameters compared to the experimental data can be partially attributed to the ultrafast librational motion of the NH bonds with respect to their peptide plane, which was analyzed in detail. This systematic difference is most pronounced for J(0.87omega(H)), which appears to be most sensitive to the slow, subnanosecond time scale of internal motion, whereas J(0) and J(omega(N)) are dominated by the overall rotational tumbling of the protein. Similar discrepancies are observed between the experimentally measured (15)N relaxation parameters (R(1), R(2), NOE) and their values calculated from the simulated spectral densities. The analysis of spectral densities provides additional information regarding the comparison of the simulated and experimental data, not available from the model-free analysis.

Backbone motions in a crystalline protein from field-dependent 2H-NMR relaxation and line-shape analysis

We have used 2H-nmr to study backbone dynamics of the 2H-labeled, slowly exchanging amide sites of fully hydrated, crystalline hen egg white lysozyme. Order parameters are determined from the residual quadrupole coupling and values increase from S2 = 0.85 at 290 K to S2 = 0.94 at 200 K. Dynamical rates are determined from spin-lattice relaxation at three nmr frequencies (38.8, 61.5, and 76.7 MHz). The approach used here is thus distinct from solution nmr studies where dynamical amplitudes and rates are both determined from relaxation measurements. At temperatures below 250 K, relaxation is independent of the nmr frequency indicating that backbone motions are fast compared to the nmr frequencies. However, as the temperature is increased above 250 K, relaxation is significantly more efficient at the lowest frequency, which shows, in addition, the presence of motions that are slow compared to the nmr frequencies. Using the values of S2 determined from the residual quadrupole coupling and a model-free relaxation formalism that allows for fast and slow internal motions, we conclude that these slow motions have correlation times in the range of 0.1 to 1.0 microsecond and are effectively frozen out at 250 K where fast motions of the amide planes with approximately 15 ps effective correlation times and 9 degrees rms amplitudes dominate relaxation. The fast internal motions increase slightly in amplitude as the temperature rises toward 290 K, but the correlation time, as is also observed in solution nmr studies of RNase H, is approximately constant. These findings are consistent with hypotheses of dynamic glass transitions in hydrated proteins arising from temperature-dependent damping of harmonic modes of motion above the transition point.

Effective energy function for proteins in solution

A Gaussian solvent-exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self-energy contribution is accounted for primarily by the exclusion model. Ionic side-chains are neutralized, and a distance-dependent dielectric constant is used to approximate the charge-charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high-temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins.

The temperature dependence of internal molecular motions in hydrated and dry alpha-amylase: the role of hydration water in the dynamical transition of proteins

Internal molecular motions of proteins are strongly affected by environmental conditions, like temperature and hydration. As known from numerous studies, the dynamical behavior of hydrated proteins on the picosecond time scale is characterized by vibrational motions in the low-temperature regime and by an onset of stochastic large-amplitude fluctuations at a transition temperature of 180-230 K. The present study reports on the temperature dependence of internal molecular motions as measured with incoherent neutron scattering from the globular water-soluble protein alpha-amylase and from a protein-lipid complex of rhodopsin in disk membranes. Samples of alpha-amylase have been measured in a hydrated and dehydrated state. In contrast to the hydrated sample, which exhibits a pronounced dynamical transition near 200 K, the dehydrated alpha-amylase does not show an appreciable proportion of stochastic large-amplitude fluctuations and no dynamical transition in the measured temperature range of 140-300 K. The obtained results, which are compared to the dynamical behavior of protein-lipid complexes, are discussed with respect to the influence of hydration on the dynamical transition and in the framework of the glass transition.

Water-coupled low-frequency modes of myoglobin and lysozyme observed by inelastic neutron scattering

Conformational changes of proteins often involve the relative motion of rigid structural domains. Normal mode analysis and molecular dynamics simulations of small globular proteins predict delocalized vibrations with frequencies below 20 cm(-1), which may be overdamped in solution due to solvent friction. In search of these modes, we have studied deuterium-exchanged myoglobin and lysozyme using inelastic neutron scattering in the low-frequency range at full and low hydration to modify the degree of damping. At room temperature, the hydrated samples exhibit a more pronounced quasielastic spectrum due to diffusive motions than the dehydrated samples. The analysis of the corresponding lineshapes suggests that water modifies mainly the amplitude, but not the characteristic time of fast protein motions. At low temperatures, in contrast, the dehydrated samples exhibit larger motional amplitudes than the hydrated ones. The excess scattering, culminating at 16 cm(-1), is suggested to reflect water-coupled librations of polar side chains that are depressed in the hydrated system by strong intermolecular hydrogen bonding. Both myoglobin and lysozyme exhibit ultra-low-frequency modes below 10 cm(-1) in the dry state, possibly related to the breathing modes predicted by harmonic analysis.

NMR evidence for slow collective motions in cyanometmyoglobin

Residual dipolar couplings observed in NMR spectra at very high magnetic fields have been measured to a high degree of accuracy for the paramagnetic protein cyanometmyoglobin. Deviations of these measurements from predictions based on available crystallographic and solution structures are largely systematic and well correlated within a given helix of this highly alpha-helical protein. These observations can be explained by invoking collective motion and small displacements of representative helices from their reported average positions in the solid state. Thus, the measurements appear to be capable of providing important insights into slower, collective protein motions, which are likely to be important for function, and which have been difficult to study using established experimental techniques.