Solvent effects in the slow dynamics of proteins

Anisotropic Network Analysis of Open/Closed HCN4 Channel Advocates Asymmetric Subunit Cooperativity in cAMP Modulation of Gating

Hyperpolarization-activated cyclic nucleotide-modulated (HCN) channels are opened in an allosteric manner by membrane hyperpolarization and cyclic nucleotides such as cAMP. Because of conflicting reports from experimental studies on whether cAMP binding to the four available binding sites in the channel tetramer operates cooperatively in gating, we employ here a computational approach as a promising route to examine ligand-induced conformational changes after binding to individual sites. By combining an elastic network model (ENM) with linear response theory (LRT) for modeling the apo-holo transition of the cyclic nucleotide-binding domain (CNBD) in HCN channels, we observe a distinct pattern of cooperativity matching the "positive-negative-positive" cooperativity reported from functional studies. This cooperativity pattern is highly conserved among HCN subtypes (HCN4, HCN1), but only to a lesser extent visible in structurally related channels, which are only gated by voltage (KAT1) or cyclic nucleotides (TAX4). This suggests an inherent cooperativity between subunits in HCN channels as part of a ligand-triggered gating mechanism in these channels.

Energy condensation and dipole alignment in protein dynamics

The possibility that distant biomolecules in a cell interact via electromagnetic (e.m.) radiation was proposed many years ago to explain the high rate of encounters of partners in some enzymatic reactions. The results of two recent experiments designed to test the propensity of protein bovine serum albumin (BSA) to interact via e.m. radiation with other proteins were interpreted in a theoretical framework based on three main assumptions: (i) in order to experience this kind of interaction the protein must be in an out-of-equilibrium state; (ii) in this state there is a condensation of energy in low-frequency vibrational modes; and (iii) the hydration layers of water around the protein sustain the energy condensation. In the present paper we present the results of molecular dynamics simulations of BSA in four states: at equilibrium and out-of-equilibrium in water, and at room and high temperature in vacuum. By comparing physical properties of the system in the four states, our simulations provide a qualitative and quantitative assessment of the three assumptions on which the theoretical framework is based. Our results confirm the assumptions of the theoretical model showing energy condensation at low frequency and electretlike alignment between the protein's and the water's dipoles; they also allow a quantitative estimate of the contribution of the out-of-equilibrium state and of the water to the observed behavior of the protein. In particular, it has been found that in the out-of-equilibrium state the amplitude of the oscillation of the protein's dipole moment greatly increases, thereby enhancing a possible absorption or emission of e.m. radiation. The analysis of BSA's dynamics outlined in the present paper provides a procedure for checking the propensity of a biomolecule to interact via e.m. radiation with its biochemical partners.

Computing the Structural Dynamics of RVFV L Protein Domain in Aqueous Glycerol Solutions

Many biological and biotechnological processes are controlled by protein–protein and protein–solvent interactions. In order to understand, predict, and optimize such processes, it is important to understand how solvents affect protein structure during protein–solvent interactions. In this study, all-atom molecular dynamics are used to investigate the structural dynamics and energetic properties of a C-terminal domain of the Rift Valley Fever Virus L protein solvated in glycerol and aqueous glycerol solutions in different concentrations by molecular weight. The Generalized Amber Force Field is modified by including restrained electrostatic potential atomic charges for the glycerol molecules. The peptide is considered in detail by monitoring properties like the root-mean-squared deviation, root-mean-squared fluctuation, radius of gyration, hydrodynamic radius, end-to-end distance, solvent-accessible surface area, intra-potential energy, and solvent–peptide interaction energies for hundreds of nanoseconds. Secondary structure analysis is also performed to examine the extent of conformational drift for the individual helices and sheets. We predict that the peptide helices and sheets are maintained only when the modeling strategy considers the solvent with lower glycerol concentration. We also find that the solvent-peptide becomes more cohesive with decreasing glycerol concentrations. The density and radial distribution function of glycerol solvent calculated when modeled with the modified atomic charges show a very good agreement with experimental results and other simulations at 298.15K.

Conformational dynamics of a multidomain protein by neutron scattering and computational analysis

The flexible conformations of a multidomain protein are responsible for its biological functions. Although MurD, a 47-kDa protein that consists of three domains, sequentially changes its domain conformation from an open form to a closed form through a semiclosed form in its enzymatic reaction, the domain dynamics in each conformation remains unclear. In this study, we verify the conformational dynamics of MurD in the corresponding three states (apo and ATP- and inhibitor-bound states) with a combination of small-angle x-ray and neutron scattering (SAXS and SANS), dynamic light scattering (DLS), neutron backscattering (NBS), neutron spin echo (NSE) spectroscopy, and molecular dynamics (MD) simulations. Applying principal component analysis of the MD trajectories, twisting and open-closed domain modes are identified as the major collective coordinates. The deviations of the experimental SAXS profiles from the theoretical calculations based on the known crystal structures become smaller in the ATP-bound state than in the apo state, and a further decrease is evident upon inhibitor binding. These results suggest that domain motions of the protein are suppressed step by step of each ligand binding. The DLS and NBS data yield collective and self-translational diffusion constants, respectively, and we used them to extract collective domain motions in nanometer and nanosecond scales from the NSE data. In the apo state, MurD shows both twisting and open-closed domain modes, whereas an ATP binding suppresses twisting domain motions, and a further reduction of open-closed mode is seen in the inhibitor-binding state. These observations are consistent with the structure modifications measured by the small-angle scattering as well as the MD simulations. Such changes in the domain dynamics associated with the sequential enzymatic reactions should be related to the affinity and reaction efficiency with a ligand that binds specifically to each reaction state.

Terahertz Frequency Spectroscopy to Determine Cold Shock Protein Stability upon Solvation and Evaporation - A Molecular Dynamics Study

Infrared (IR) and Terahertz (THz) spectroscopy simulations were carried out using CHARMM35b2 to determine protein stability. The stabilities of three bacterial cold shock proteins (Csps) originating from mesophiles, thermophiles and hyper- thermophiles respectively were investigated in this study. The three different Csps were investigated by Normal-Mode analysis and Molecular Dynamics simulation of THz spectra using the Hessian matrix for solvated systems, interpreted in the harmonic approximation at optimum near-melting temperatures of each homologue, by incorporating differences in the hydrous and anhydrous states of the Csps. The results show slight variations in the large scale protein motion. However, the IR spectra of Csps observed at the low frequency saddle surface region, clearly distinguishes the thermophilic and mesophilic proteins based on their stability. Further studies on protein stability employing low-frequency collective modes have the potential to reveal functionally important conformational changes that are biologically significant.

Calculation of the infrared spectra of proteins

The CHARMM22 force field with associated partial charges is used to calculate the infrared spectra of a number of small proteins and some larger biothreat proteins. The calculated high-frequency region, from about 2,500 to 3,500 cm(-1), is dominated by stretching modes of hydrogen bonded to other atoms, and is very similar in all proteins. There is a peak at 3,430 cm(-1) whose intensity is predicted by these calculations to be a direct measure of arginine content. The calculated low-frequency THz region, up to 300 cm(-1), is also very similar in all the proteins and just reflects the vibrational density of states in agreement with experimental results. Calculations show that the intermediate-frequency region between 500 and 1,200 cm(-1) shows the greatest difference between individual proteins and is also the least affected by water absorption. However, to match experimental measurements in the amide region, it was necessary to reduce the hydrogen partial charges.

Comparing the intrinsic dynamics of multiple protein structures using elastic network models

BACKGROUND

Elastic network models (ENMs) are based on the simple idea that a protein can be described as a set of particles connected by springs, which can then be used to describe its intrinsic flexibility using, for example, normal mode analysis. Since the introduction of the first ENM by Monique Tirion in 1996, several variants using coarser protein models have been proposed and their reliability for the description of protein intrinsic dynamics has been widely demonstrated. Lately an increasing number of studies have focused on the meaning of slow dynamics for protein function and its potential conservation through evolution. This leads naturally to comparisons of the intrinsic dynamics of multiple protein structures with varying levels of similarity.

SCOPE OF REVIEW

We describe computational strategies for calculating and comparing intrinsic dynamics of multiple proteins using elastic network models, as well as a selection of examples from the recent literature.

MAJOR CONCLUSIONS

The increasing interest for comparing dynamics across protein structures with various levels of similarity, has led to the establishment and validation of reliable computational strategies using ENMs. Comparing dynamics has been shown to be a viable way for gaining greater understanding for the mechanisms employed by proteins for their function. Choices of ENM parameters, structure alignment or similarity measures will likely influence the interpretation of the comparative analysis of protein motion.

GENERAL SIGNIFICANCE

Understanding the relation between protein function and dynamics is relevant to the fundamental understanding of protein structure-dynamics-function relationship. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Conformational response to solvent interaction and temperature of a protein (Histone h3.1) by a multi-grained monte carlo simulation

Interaction with the solvent plays a critical role in modulating the structure and dynamics of a protein. Because of the heterogeneity of the interaction strength, it is difficult to identify multi-scale structural response. Using a coarse-grained Monte Carlo approach, we study the structure and dynamics of a protein (H3.1) in effective solvent media. The structural response is examined as a function of the solvent-residue interaction strength (based on hydropathy index) in a range of temperatures (spanning low to high) involving a knowledge-based (Miyazawa-Jernigan(MJ)) residue-residue interaction. The protein relaxes rapidly from an initial random configuration into a quasi-static structure at low temperatures while it continues to diffuse at high temperatures with fluctuating conformation. The radius of gyration (R_g) of the protein responds non-monotonically to solvent interaction, i.e., on increasing the residue-solvent interaction strength (f_s), the increase in R_g (f_s≤f_sc) is followed by decay (f_s≥f_sc) with a maximum at a characteristic value (f_sc) of the interaction. Raising the temperature leads to wider spread of the distribution of the radius of gyration with higher magnitude of f_sc. The effect of solvent on the multi-scale (λ: residue to R_g) structures of the protein is examined by analyzing the structure factor (S(q),|q| = 2π/λ is the wave vector of wavelength, λ) in detail. Random-coil to globular transition with temperature of unsolvated protein (H3.1) is dramatically altered by the solvent at low temperature while a systematic change in structure and scale is observed on increasing the temperature. The interaction energy profile of the residues is not sufficient to predict its mobility in the solvent. Fine-grain representation of protein with two-node and three-node residue enhances the structural resolution; results of the fine-grained simulations are consistent with the finding described above of the coarse-grained description with one-node residue.

Mapping polymerization and allostery of hemoglobin S using point mutations

Hemoglobin is a complex system that undergoes conformational changes in response to oxygen, allosteric effectors, mutations, and environmental changes. Here, we study allostery and polymerization of hemoglobin and its variants by application of two previously described methods: (i) AllosMod for simulating allostery dynamics given two allosterically related input structures and (ii) a machine-learning method for dynamics- and structure-based prediction of the mutation impact on allostery (Weinkam et al. J. Mol. Biol. 2013, 425, 647-661), now applicable to systems with multiple coupled binding sites, such as hemoglobin. First, we predict the relative stabilities of substates and microstates of hemoglobin, which are determined primarily by entropy within our model. Next, we predict the impact of 866 annotated mutations on hemoglobin's oxygen binding equilibrium. We then discuss a subset of 30 mutations that occur in the presence of the sickle cell mutation and whose effects on polymerization have been measured. Seven of these HbS mutations occur in three predicted druggable binding pockets that might be exploited to directly inhibit polymerization; one of these binding pockets is not apparent in the crystal structure, but only in structures generated by AllosMod. For the 30 mutations, we predict that mutation-induced conformational changes within a single tetramer tend not to significantly impact polymerization; instead, these mutations more likely impact polymerization by directly perturbing a polymerization interface. Finally, our analysis of allostery allows us to hypothesize why hemoglobin evolved to have multiple subunits and a persistent low frequency sickle cell mutation.

Assessing the effect of loop mutations in the folding space of β2-microglobulin with molecular dynamics simulations

We use molecular dynamics simulations of a full atomistic Gō model to explore the impact of selected DE-loop mutations (D59P and W60C) on the folding space of protein human β₂-microglobulin (Hβ₂m), the causing agent of dialysis-related amyloidosis, a conformational disorder characterized by the deposition of insoluble amyloid fibrils in the osteoarticular system. Our simulations replicate the effect of mutations on the thermal stability that is observed in experiments in vitro. Furthermore, they predict the population of a partially folded state, with 60% of native internal free energy, which is akin to a molten globule. In the intermediate state, the solvent accessible surface area increases up to 40 times relative to the native state in 38% of the hydrophobic core residues, indicating that the identified species has aggregation potential. The intermediate state preserves the disulfide bond established between residue Cys25 and residue Cys80, which helps maintain the integrity of the core region, and is characterized by having two unstructured termini. The movements of the termini dominate the essential modes of the intermediate state, and exhibit the largest displacements in the D59P mutant, which is the most aggregation prone variant. PROPKA predictions of pK_a suggest that the population of the intermediate state may be enhanced at acidic pH explaining the larger amyloidogenic potential observed in vitro at low pH for the WT protein and mutant forms.

Comparing proteins by their internal dynamics: exploring structure-function relationships beyond static structural alignments

The growing interest for comparing protein internal dynamics owes much to the realisation that protein function can be accompanied or assisted by structural fluctuations and conformational changes. Analogously to the case of functional structural elements, those aspects of protein flexibility and dynamics that are functionally oriented should be subject to evolutionary conservation. Accordingly, dynamics-based protein comparisons or alignments could be used to detect protein relationships that are more elusive to sequence and structural alignments. Here we provide an account of the progress that has been made in recent years towards developing and applying general methods for comparing proteins in terms of their internal dynamics and advance the understanding of the structure-function relationship.

Surface hydration amplifies single-well protein atom diffusion propagating into the macromolecular core

The effect of surface hydration water on internal protein motion is of fundamental interest in molecular biophysics. Here, by decomposing the picosecond to nanosecond atomic motion in molecular dynamics simulations of lysozyme at different hydration levels into three components--localized single-well diffusion, methyl group rotation, and nonmethyl jumps--we show that the effect of surface hydration is mainly to increase the volume of the localized single-well diffusion. These diffusive motions are coupled in such a way that the hydration effect propagates from the protein surface into the dry core.

Electrostatics of the protein-water interface and the dynamical transition in proteins

Atomic displacements of hydrated proteins are dominated by phonon vibrations at low temperatures and by dissipative large-amplitude motions at high temperatures. A crossover between the two regimes is known as a dynamical transition. Recent experiments indicate a connection between the dynamical transition and the dielectric response of the hydrated protein. We analyze two mechanisms of the coupling between the protein atomic motions and the protein-water interface. The first mechanism considers viscoelastic changes in the global shape of the protein plasticized by its coupling to the hydration shell. The second mechanism involves modulations of the local motions of partial charges inside the protein by electrostatic fluctuations. The model is used to analyze mean-square displacements of iron of metmyoglobin reported by Mössbauer spectroscopy. We show that high displacement of heme iron at physiological temperatures is dominated by electrostatic fluctuations. Two onsets, one arising from the viscoelastic response and the second from electrostatic fluctuations, are seen in the temperature dependence of the mean-square displacements when the corresponding relaxation times enter the instrumental resolution window.

Dynamical transition in proteins and non-Gaussian behavior of low-frequency modes in self-consistent normal mode analysis

Self-consistent normal mode analysis (SCNMA) is applied to heme c type cytochrome f to study temperature-dependent protein motion. Classical normal mode analysis assumes harmonic behavior and the protein mean-square displacement has a linear dependence on temperature. This is only consistent with low-temperature experimental results. To connect the protein vibrational motions between low and physiological temperatures, we have incorporated a fitted set of anharmonic potentials into SCNMA. In addition, quantum harmonic-oscillator theory has been used to calculate the displacement distribution for individual vibrational modes. We find that the modes involving soft bonds exhibit significant non-Gaussian dynamics at physiological temperature, which suggests that it may be the cause of the non-Gaussian behavior of the protein motions probed by elastic incoherent neutron scattering. The combined theory displays a dynamical transition caused by the softening of few "torsional" modes in the low-frequency regime ( <50 cm(-1) or <6 meV or >0.6 ps). These modes change from Gaussian to a classical distribution upon heating. Our theory provides an alternative way to understand the microscopic origin of the protein dynamical transition.

The energy profiles of atomic conformational transition intermediates of adenylate kinase

The elastic network interpolation (ENI) (Kim et al., Biophys J 2002;83:1620-1630) is a computationally efficient and physically realistic method to generate conformational transition intermediates between two forms of a given protein. However it can be asked whether these calculated conformations provide good representatives for these intermediates. In this study, we use ENI to generate conformational transition intermediates between the open form and the closed form of adenylate kinase (AK). Based on C(alpha)-only intermediates, we construct atomic intermediates by grafting all the atoms of known AK structures onto the C(alpha) atoms and then perform CHARMM energy minimization to remove steric conflicts and optimize these intermediate structures. We compare the energy profiles for all intermediates from both the CHARMM force-field and from knowledge-based energy functions. We find that the CHARMM energies can successfully capture the two energy minima representing the open AK and closed AK forms, while the energies computed from the knowledge-based energy functions can detect the local energy minimum representing the closed AK form and show some general features of the transition pathway with a somewhat similar energy profile as the CHARMM energies. The combinatorial extension structural alignment (Shindyalov et al., 1998;11:739-747) and the k-means clustering algorithm are then used to show that known PDB structures closely resemble computed intermediates along the transition pathway.