A molecular dynamics computer simulation study of room-temperature ionic liquids. II. Equilibrium and nonequilibrium solvation dynamics

The molecular dynamics (MD) simulation study of solvation structure and free energetics in 1-ethyl-3-methylimidazolium chloride and 1-ethyl-3-methylimidazolium hexafluorophosphate using a probe solute in the preceding article [Y. Shim, M. Y. Choi and H. J. Kim, J. Chem. Phys. 122, 044510 (2005)] is extended to investigate dynamic properties of these liquids. Solvent fluctuation dynamics near equilibrium are studied via MD and associated time-dependent friction is analyzed via the generalized Langevin equation. Nonequilibrium solvent relaxation following an instantaneous change in the solute charge distribution and accompanying solvent structure reorganization are also investigated. Both equilibrium and nonequilibrium solvation dynamics are characterized by at least two vastly different time scales--a subpicosecond inertial regime followed by a slow diffusive regime. Solvent regions contributing to the subpicosecond nonequilibrium relaxation are found to vary significantly with initial solvation configurations, especially near the solute. If the solvent density near the solute is sufficiently high at the outset of the relaxation, subpicosecond dynamics are mainly governed by the motions of a few ions close to the solute. By contrast, in the case of a low local density, solvent ions located not only close to but also relatively far from the solute participate in the subpicosecond relaxation. Despite this difference, linear response holds reasonably well in both ionic liquids.     

Slow dynamics in protein fluctuations revealed by time-structure based independent component analysis: the case of domain motions

Protein dynamics on a long time scale was investigated using all-atom molecular dynamics (MD) simulation and time-structure based independent component analysis (tICA). We selected the lysine-, arginine-, ornithine-binding protein (LAO) as a target protein and focused on its domain motions in the open state. A MD simulation of the LAO in explicit water was performed for 600 ns, in which slow and large-amplitude domain motions of the LAO were observed. After extracting domain motions by rigid-body domain analysis, the tICA was applied to the obtained rigid-body trajectory, yielding slow modes of the LAO's domain motions in order of decreasing time scale. The slowest mode detected by the tICA represented not a closure motion described by a largest-amplitude mode determined by the principal component analysis but a twist motion with a time scale of tens of nanoseconds. The slow dynamics of the LAO were well described by only the slowest mode and were characterized by transitions between two basins. The results show that tICA is promising for describing and analyzing slow dynamics of proteins.     

Effect of ligand binding on the intraminimum dynamics of proteins

Effects of ligand binding on protein dynamics are studied via molecular dynamics (MD) simulations on two different enzymes, dihydrofolate reductase (DHFR) and triosephosphate isomerase (TIM), in their unliganded (free) and liganded states. Domain motions in MD trajectories are analyzed by collectivities and rotation angles along the principal components (PCs). DHFR in the free state has well‐defined domain rotations, whereas rotations are slightly damped in the binary complex with nicotinamide adenine dinucleotide phosphate (NADPH), and remarkably distorted in the presence of NADP⁺, showing that NADP⁺ is solely responsible for the loss of correlation of the domains in DHFR. Although mean square fluctuations of MD simulations in the same PC subspaces are similar for different ligation states, linear stochastic time series models show that backbone flexibility along the first five PCs is decreased upon NADPH and NADP⁺ binding in subpicosecond scale. This shows that mobility of the protein along the PCs is closely related with intraminimum dynamics, and alterations in ligation states may change the intraminimum dynamics significantly. Low vibrational frequencies of the alpha‐carbon atoms of DHFR are determined from the time series models of a larger number of low indexed PCs, and it is found that number of modes in the lowest frequencies is reduced upon ligand binding. A similar result is obtained for TIM in the unliganded and dihydroxyacetone phosphate bound states. We suggest that stochastic time series modeling is a promising method to be used in determining subtle perturbations in protein dynamics. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Hydration dynamics and time scales of coupled water-protein fluctuations

We report experimental and theoretical studies on water and protein dynamics following photoexcitation of apomyoglobin. Using site-directed mutation and with femtosecond resolution, we experimentally observed relaxation dynamics with a biphasic distribution of time scales, 5 and 87 ps, around the site Trp7. Theoretical studies using both linear response and direct nonequilibrium molecular dynamics (MD) calculations reproduced the biphasic behavior. Further constrained MD simulations with either frozen protein or frozen water revealed the molecular mechanism of slow hydration processes and elucidated the role of protein fluctuations. Observation of slow water dynamics in MD simulations requires protein flexibility, regardless of whether the slow Stokes shift component results from the water or protein contribution. The initial dynamics in a few picoseconds represents fast local motions such as reorientations and translations of hydrating water molecules, followed by slow relaxation involving strongly coupled water-protein motions. We observed a transition from one isomeric protein configuration to another after 10 ns during our 30 ns ground-state simulation. For one isomer, the surface hydration energy dominates the slow component of the total relaxation energy. For the other isomer, the slow component is dominated by protein interactions with the chromophore. In both cases, coupled water-protein motion is shown to be necessary for observation of the slow dynamics. Such biologically important water-protein motions occur on tens of picoseconds. One significant discrepancy exists between theory and experiment, the large inertial relaxation predicted by simulations but clearly absent in experiment. Further improvements required in the theoretical model are discussed.     

Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model alpha-helical systems

The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper, was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala(10) polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala(10) polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain-side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time.     

New Insights into the Jahn–Teller Effect through ab initio Quantum-Mechanical/Molecular-Mechanical Molecular Dynamics Simulations of CuII in Water

The Cu^II hydration shell structure has been studied by means of classical molecular dynamics (MD) simulations including three-body corrections and hybrid quantum-mechanical/molecular-mechanical (QM/MM) molecular dynamics (MD) simulations at the Hartree–Fock level. The copper(II ) ion is found to be six-fold coordinated and [Cu(H₂O)₆]²⁺ exhibits a distorted octahedral structure. The QM/MM MD approach reproduces correctly the experimentally observed Jahn–Teller effect but exhibits faster inversions (<200 fs) and a more complex behaviour than expected from experimental data. The dynamic Jahn–Teller effect causes the high lability of [Cu(H₂O)₆]²⁺ with a ligand-exchange rate constant some orders of magnitude higher than its neighbouring ions Ni^II and Zn^II. Nevertheless, no first-shell water exchange occurred during a 30-ps simulation. The structure of the hydrated ion is discussed in terms of radial distribution functions, coordination numbers, and various angular distributions and the dynamical properties as librational and vibrational motions and reorientational times were evaluated, which lead to detailed information about the first hydration shell. Second-shell water-exchange processes could be observed within the simulation time scale and yielded a mean ligand residence time of ≈20 ps.     

Ligand Binding and Release Investigated by Contact-Guided Iterative Multiple Independent Molecular Dynamics Simulations

Binding and releasing ligands are critical for the biological functions of many proteins, so it is important to determine these highly dynamic processes. Although there are experimental techniques to determine the structure of a protein-ligand complex, it only provides a static picture of the system. With the rapid increase of computing power and improved algorithms, molecular dynamics (MD) simulations have diverse of superiority in probing the binding and release process. However, it remains a great challenge to overcome the time and length scales when the system becomes large. This work presents an enhanced sampling tool for ligand binding and release, which is based on iterative multiple independent MD simulations guided by contacts formed between the ligand and the protein. From the simulation results on adenylate kinase, we observe the process of ligand binding and release while the conventional MD simulations at the same time scale cannot.     

Dynamics of proton transfer and vibrational relaxation in dilute hydrofluoric acid

The molecular mechanisms in both vibrational relaxation and proton transfer (PT) associated with infrared (IR)-induced PT in a dilute hydrofluoric acid solution at ambient temperature are studied by molecular dynamics (MD) simulations with the multistate empirical valence bond model. To investigate the solvation dynamics, a collective solvent coordinate and its perpendicular bath modes are defined from the diabatic energy gap and their motions are examined by the generalized Langevin equation (GLE) formalism. The GLE analysis using the equilibrium MD simulation shows that the major solvent reorganizations in the PT are represented by the libration and hindered translation. In particular, the libration gives the stronger coupling to the solvent reorganization and the faster relaxation. The nonequilibrium MD simulation demonstrated that both the HF stretching vibration and the solvent reorganization relax on a similar time scale and thus compete in the PT. It also supported the "presolvation mechanism" for the PT in this system.     

Molecular dynamics investigation with the time resolved optical Kerr effect on the CS2-C6H6 mixtures

An investigation of the molecular dynamics in pure liquids and in mixtures through the technique of time resolved optical Kerr effect is performed. The samples studied were the mixtures of carbon disulfide (CS(2)) with benzene (C(6)H(6)). The molecular dynamics of the pure liquids is briefly discussed while the main results are obtained for the mixtures. A slow dynamics component is observed for the optical heterodyne detected optical Kerr effect transient decaying exponentially with time constants on picosecond time scale. The fast subpicosend time relaxations are analyzed in terms of the nondiffusive component of the spectral response that is associated with the molecular dynamics. The modifications of the spectrum are quantified, and the explanation of the observed changes is given in terms of the structural interaction configurations that produced changes in the intermolecular potential within which the molecules execute librational motions.     

Implications of fast-time scale dynamics of human DNA/RNA cytosine methyltransferases (DNMTs) for protein function

The role of protein dynamics in the control of substrate recognition, catalysis, and protein–protein interactions is often underestimated. Recently, a number of studies have examined the contribution of protein dynamics to the thermodynamics of ligand binding in detail, mostly using NMR relaxation measurements and molecular dynamics (MD) simulations. The results unequivocally demonstrate that conformational dynamics play a pivotal role in the properties and functions of proteins, and ignoring this contribution is likely to lead to substantial errors when explaining the biological function of proteins and in predictions of the binding affinities of their cognate ligands. However, the details of the interplay between structure and dynamics and the way it affects the biological function of the target protein remain poorly understood. In this study, the changes in fast (picosecond-to-nanosecond time scale) dynamics of catalytic domains of four human cytosine DNA methyltransferases (DNMTs) were studied using molecular dynamics (MD) simulations. The results provide insight into the protein dynamics changes that occur upon binding of the cofactor, S-adenosylmethionine (SAM). Contrary to expectations, increased amplitude of motions of backbone amide (N–H) and terminal heavy atom (C–C) bond vectors was observed in all studied DNMTs upon binding of SAM. These results imply that the cofactor binding causes a global increase in the extent of protein dynamics in the short time scale. This global dynamic change constitutes a favourable entropic contribution to the free energy of SAM binding. These results suggest that cytosine DNA methyltransferases may exploit changes in their fast scale dynamics to reduce the entropic cost of the substrate binding.     

Coarse-grained protein molecular dynamics simulations

A limiting factor in biological science is the time-scale gap between experimental and computational trajectories. At this point, all-atom explicit solvent molecular dynamics (MD) are clearly too expensive to explore long-range protein motions and extract accurate thermodynamics of proteins in isolated or multimeric forms. To reach the appropriate time scale, we must then resort to coarse graining. Here we couple the coarse-grained OPEP model, which has already been used with activated methods, to MD simulations. Two test cases are studied: the stability of three proteins around their experimental structures and the aggregation mechanisms of the Alzheimer's Abeta16-22 peptides. We find that coarse-grained isolated proteins are stable at room temperature within 50 ns time scale. Based on two 220 ns trajectories starting from disordered chains, we find that four Abeta16-22 peptides can form a three-stranded beta sheet. We also demonstrate that the reptation move of one chain over the others, first observed using the activation-relaxation technique, is a kinetically important mechanism during aggregation. These results show that MD-OPEP is a particularly appropriate tool to study qualitatively the dynamics of long biological processes and the thermodynamics of molecular assemblies.     

Molecular dynamics simulations of semicrystalline polymers: Crystallization,melting, and reorganization

Large‐scale molecular dynamics (MD) simulations of semicrystalline entangled polymers are carried out to explore crystallization and melting processes. Semicrystalline polymers are obtained from disordered melts via homogeneous nucleation. In the early stage of the crystallization process, the collective scattering does not show the emergence of nuclei seeds. Although the crystallization process is thermodynamically simple, the melting process is complex resulting in multiple‐peaked melting endotherms. The molecular origin is found to be the different thermal stabilities of microcrystalline domains (MCDs). Coexistence of melting and growth of different MCDs during sufficiently slow heating enlarges the difference of their thermal stabilities. An increase of stem length close to the melting point is assisted by disorder effects in particular in the surface regions of the MCDs. The number of trans–trans states is decreasing, which increases the flexibility and mobility of the crystalline stems. We have also investigated self‐seeding processes, and we show how these can be used to obtain single lamellar crystals in MD simulations. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Dielectric response of polar liquids in narrow slit pores

Based on molecular dynamics (MD) simulations and a simple (Stockmayer) model we investigate the static and dynamic dielectric response of polar liquids confined to narrow slit pores. The MD simulations are used to calculate the time-dependent polarization fluctuations along directions parallel and perpendicular to the walls, from which the components of the frequency-dependent dielectric tensor can be derived via linear response theory. Our numerical results reveal that the system's response is strongly anisotropic. The parallel dielectric function, epsilonparallel(omega), has Debye-like character very similar to the corresponding isotropic bulk function, epsilonbulk(omega), at the same chemical potential. Indeed, the main confinement effect on epsilonparallel(omega) consists in a shift toward smaller values relative to the bulk function. On the other hand, in the perpendicular direction we observe a characteristic peak in the absorption part of the dielectric function, epsilonperpendicular(omega). This peak is absent in the bulk system and reflects strongly pronounced, damped oscillations in the polarization fluctuations normal to the walls. We discuss two possible origins of the oscillations (and the resulting absorption peak), that is collective oscillations of dipoles in clusters formed parallel to the walls, and the existence of a "dipolaron mode" previously observed in MD simulations of bulk polar fluids.     

Molecular dynamics integration meets standard theory of molecular vibrations

An iterative SISM (split integration symplectic method) for molecular dynamics (MD) integration is described. This work explores an alternative for the internal coordinate system prediction in the SISM introduced by JaneZic et al. (J. Chem. Phys. 2005, 122, 174101). The SISM, which employs a standard theory of molecular vibrations, analytically resolves the internal high-frequency molecular vibrations. This is accomplished by introducing a translating and rotating internal coordinate system of a molecule and calculating normal modes of an isolated molecule only. The Eckart frame, which is usually used in the standard theory of molecular vibrations as an internal coordinate system of a molecule, is adopted to be used within the framework of the second order generalized leapfrog scheme. In the presented MD integrator the internal coordinate frame at the end of the integration step is predicted halfway through the integration step using a predictor-corrector type iterative approach thus ensuring the method's time reversibility. The iterative SISM, which is applicable to any system of molecules with one equilibrium configuration, was applied here to perform all-atom MD simulations of liquid CO2 and SO2. The simulation results indicate that for the same level of accuracy, this algorithm allows significantly longer integration time steps than the standard second-order leapfrog Verlet (LFV) method.     

Molecular dynamics study of polarizability anisotropy relaxation in aromatic liquids and its connection with local structure

The collective polarizability anisotropy dynamics in a set of three aromatic liquids, benzene (Bz), hexafluorobenzene (HFB), and 1,3,5-trifluorobenzene (TFB), has been studied by molecular dynamics simulation. These liquids have very similar shapes, but different electrostatic interactions due to opposite polarities of C-H and C-F bonds, giving rise to different local intermolecular structures in the liquid phase. We have investigated how these structural arrangements affect polarizability anisotropy dynamics observed in optical Kerr-effect (OKE) spectroscopy. We have modeled the interaction-induced polarizability with the first-order dipole-induced dipole approximation, with the molecular polarizability distributed over the carbon sites. Local contributions to the librational OKE spectrum were computed separately for molecules participating in parallel or perpendicular relative orientations within the first coordination shell. We found that the relative locations of parallel and perpendicular librational bands of the OKE spectra are closely related to the corresponding pair energy distributions of the closest four neighbors of a given molecule, corresponding to a model of a harmonic oscillator in a cage of nearest neighbors. This model predicts higher librational frequencies for more attractive intermolecular interactions, which in all three liquids correspond to parallel local arrangements. On the diffusive orientational time scale, all three liquids exhibit slower relaxation of molecules in parallel arrangements, although the difference in relaxation rates is substantial only in TFB, which has the strongest tendency toward parallel stacking. The analysis of the collective polarizability relaxation was performed using two different approaches, the projection scheme (J. Chem. Phys. 1980, 72, 2801) and the theory developed by Steele (Mol. Phys. 1987, 61, 1031) for the second time derivatives applied to collective time correlations. Both approaches allow the decomposition of the OKE response into contributions from orientational relaxation and other dynamical processes. We find that they lead to different predictions on how the response depends on collective reorientation and processes arising from fluctuations in the interaction-induced polarizability. We discuss the reasons for these differences and the advantages and disadvantages of the two analysis schemes.     

Structural dynamics of supercooled water from quasielastic neutron scattering and molecular simulations

One of the outstanding challenges presented by liquid water is to understand how molecules can move on a picosecond time scale despite being incorporated in a three-dimensional network of relatively strong H-bonds. This challenge is exacerbated in the supercooled state, where the dramatic slowing down of structural dynamics is reminiscent of the, equally poorly understood, generic behavior of liquids near the glass transition temperature. By probing single-molecule dynamics on a wide range of time and length scales, quasielastic neutron scattering (QENS) can potentially reveal the mechanistic details of water's structural dynamics, but because of interpretational ambiguities this potential has not been fully realized. To resolve these issues, we present here an extensive set of high-quality QENS data from water in the range 253-293 K and a corresponding set of molecular dynamics (MD) simulations to facilitate and validate the interpretation. Using a model-free approach, we analyze the QENS data in terms of two motional components. Based on the dynamical clustering observed in MD trajectories, we identify these components with two distinct types of structural dynamics: picosecond local (L) structural fluctuations within dynamical basins and slower interbasin jumps (J). The Q-dependence of the dominant QENS component, associated with J dynamics, can be quantitatively rationalized with a continuous-time random walk (CTRW) model with an apparent jump length that depends on low-order moments of the jump length and waiting time distributions. Using a simple coarse-graining algorithm to quantitatively identify dynamical basins, we map the newtonian MD trajectory on a CTRW trajectory, from which the jump length and waiting time distributions are computed. The jump length distribution is gaussian and the rms jump length increases from 1.5 to 1.9 A? as the temperature increases from 253 to 293 K. The rms basin radius increases from 0.71 to 0.75 A? over the same range. The waiting time distribution is exponential at all investigated temperatures, ruling out significant dynamical heterogeneity. However, a simulation at 238 K reveals a small but significant dynamical heterogeneity. The macroscopic diffusion coefficient deduced from the QENS data agrees quantitatively with NMR and tracer results. We compare our QENS analysis with existing approaches, arguing that the apparent dynamical heterogeneity implied by stretched exponential fitting functions results from the failure to distinguish intrabasin (L) from interbasin (J) structural dynamics. We propose that the apparent dynamical singularity at ～220 K corresponds to freezing out of J dynamics, while the calorimetric glass transition corresponds to freezing out of L dynamics.     

Dynamical signature of abasic damage in DNA

Time-dependent Stokes shift (TDSS) responses in proteins and DNA exhibit a broad range of long time scales (>10 ps) that are not present in bulk aqueous solution. The physical interpretation of the long TDSS time scales in biomolecular systems is a matter of considerable debate because of the many different components present in the sample (water, biomolecule, counterions), which have highly correlated motions and intrinsically different abilities to adapt to local perturbations. Here we use molecular dynamics (MD) simulations to show that the surprisingly slow (～10 ns) TDSS response of coumarin 102 (C102), a base pair replacement, reflects a distinct dynamical signature for DNA damage. When the C102 molecule is covalently incorporated into DNA, an abasic site is created on the strand opposite the C102 probe. The abasic sugar exhibits a reversible interchange between intra- and extrahelical conformations that are kinetically stable on a nanosecond time scale. This conformational change, only possible in damaged DNA, was found to be responsible for the long time scales in the measured TDSS response. For the first time, a TDSS measurement has been attributed to a specific biomolecular motion. This finding directly contradicts the prevailing notion that the TDSS response in biomolecular contexts is dominated by hydration dynamics. It also suggests that TDSS experiments can be used to study ultrafast biomolecular dynamics that are inaccessible to other techniques.     

Molecular dynamics simulation of liquid trimethylphosphine

Structural and dynamical properties of liquid trimethylphosphine (TMP), (CH(3))(3)P, as a function of temperature is investigated by molecular dynamics (MD) simulations. The force field used in the MD simulations, which has been proposed from molecular mechanics and quantum chemistry calculations, is able to reproduce the experimental density of liquid TMP at room temperature. Equilibrium structure is investigated by the usual radial distribution function, g(r), and also in the reciprocal space by the static structure factor, S(k). On the basis of center of mass distances, liquid TMP behaves like a simple liquid of almost spherical particles, but orientational correlation due to dipole-dipole interactions is revealed at short-range distances. Single particle and collective dynamics are investigated by several time correlation functions. At high temperatures, diffusion and reorientation occur at the same time range as relaxation of the liquid structure. Decoupling of these dynamic properties starts below ca. 220 K, when rattling dynamics of a given TMP molecules due to the cage effect of neighbouring molecules becomes important.     

Structure-breaking effects of solvated Rb(I) in dilute aqueous solution--an ab initio QM/MM MD approach

Structural properties of the hydrated Rb(I) ion have been investigated by ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations at the double-zeta HF quantum mechanical level. The first shell coordination number was found to be 7.1, and several other structural parameters such as angular distribution functions, radial distribution functions and tilt- and theta-angle distributions allowed the full characterization of the hydration structure of the Rb(I) ion in dilute aqueous solution. Velocity autocorrelation functions were used to calculate librational and vibrational motions, ion-ligand motions, as well as reorientation times. Different dynamical parameters such as water reorientation, mean ligand residence time, the number of ligand exchange processes, and rate constants were also analyzed. The mean ligand residence time for the first shell was determined as tau = 2.0 ps.