Insight into Protein–Polymer Conjugate Relaxation Dynamics: The Importance of Polymer Grafting

The bio and chemical physics of protein–polymer conjugates are related to parameters that characterize each component. With this work, it is intended to feature the dynamical properties of the protein–polymer conjugate myoglobin (Mb)–poly(ethyl ethylene phosphate), in the ps and ns time scales, in order to understand the respective roles of the protein and of the polymer size in the dynamics of the conjugate. Elastic and quasi‐elastic neutron scattering is performed on completely hydrogenated samples with variable number of polymer chains covalently attached to the protein. The role of the polymer length in the protein solvation and internal dynamics is investigated using two conjugates formed by polymers of different molecular weight. It is confirmed that the flexibility of the complex increases with the number of grafted polymer chains and that a sharp dynamical transition appears when either grafting density or polymer molecular weight are high. It is shown that protein size is crucial for the polymer structural organization and interaction on the protein surface and it is established that the glass properties of the polymer change upon conjugation. The results give a better insight of the equivalence of the polymer coating and the role of water on the surface of proteins.     

Conserving the linear momentum in stochastic dynamics: Dissipative particle dynamics as a general strategy to achieve local thermostatization in molecular dynamics simulations

Stochastic dynamics is a widely employed strategy to achieve local thermostatization in molecular dynamics simulation studies; however, it suffers from an inherent violation of momentum conservation. Although this short‐coming has little impact on structural and short‐time dynamic properties, it can be shown that dynamics in the long‐time limit such as diffusion is strongly dependent on the respective thermostat setting. Application of the methodically similar dissipative particle dynamics (DPD) provides a simple, effective strategy to ensure the advantages of local, stochastic thermostatization while at the same time the linear momentum of the system remains conserved. In this work, the key parameters to employ the DPD thermostats in the framework of periodic boundary conditions are investigated, in particular the dependence of the system properties on the size of the DPD‐region as well as the treatment of forces near the cutoff. Structural and dynamical data for light and heavy water as well as a Lennard–Jones fluid have been compared to simulations executed via stochastic dynamics as well as via use of the widely employed Nose–Hoover chain and Berendsen thermostats. It is demonstrated that a small size of the DPD region is sufficient to achieve local thermalization, while at the same time artifacts in the self‐diffusion characteristic for stochastic dynamics are eliminated. © 2016 Wiley Periodicals, Inc.     

Impact of anisotropy on the structure and dynamics of ionic liquids: a computational study of 1-butyl-3-methyl-imidazolium trifluoroacetate

The complex ionic network of 1-butyl-3-methyl-imidazolium trifluoroacetate was simulated by means of the molecular dynamics methods over a time period of 100 ns. The influence of the anisotropy of the shape and charge distribution of both the cations and the anions on the local (molecular) and global (collective) structure and dynamics is analyzed. The distance-dependent g coefficients of the orientational probability function g(r,Omega) were found to be an excellent way to interpret local structure. Thereby, the combination and interrelation of individual g coefficients elucidate the mutual orientation. Dynamics at the molecular level is characterized by the time correlation function of the center-of-mass corrected molecular dipole moment mucm. Upon uniting the set of molecular dipoles to a single collective rotational dipole moment, MD, dynamics on a global level is studied. Decomposing into subsets of cations and anions respective self terms as well as the prominent cross term can be extracted. This decomposition also enables a detailed peak assignment in dielectric spectra.     

Quantitative characterization of ion pairing and cluster formation in strong 1:1 electrolytes

Aqueous solutions of 1:1 strong electrolytes are considered to be the prototype for complete ionic dissociation. Nonetheless, clustering of strong 1:1 electrolytes has been widely reported in all atom molecular dynamics simulations, and their presence is indirectly implicated in a diverse range of experimental results. Is there a physical basis for nonidealities such as ion pairing and cluster formation in aqueous solutions of strong 1:1 electrolytes? We attempt to answer this question by direct comparison of results from detailed molecular dynamics simulations to experimentally observed properties of 1:1 electrolytes. We report the analysis of a series of lengthy molecular dynamics simulations of alkali-halide solutions carried out over a wide range of physiologically relevant concentrations using explicit representations of water molecules. We find evidence for pronounced nonideal behavior of ions at all concentrations in the form of ion pairs and clusters which are in rapid equilibrium with dissociated ions. The phenomenology for ion pairing seen in these simulations is congruent with the multistep scheme proposed by Eigen and Tamm based on data from ultrasonic absorption experiments. For a given electrolyte, we show that the dependence of cluster populations on concentration can be described through a single set of equilibrium constants. We assess the accuracy of calculated ion pairing constants by favorable comparison to estimates obtained by Fuoss and co-workers and based on conductometric experiments. Ion pairs and clusters form on length scales where the size of individual water molecules is as important as the hard core radius of ions. Ion pairing results as a balance between the favorable Coulomb interactions and the unfavorable partial desolvation of ions needed to form a pair.     

Hydration of alkali ions from first principles molecular dynamics revisited

Structural and dynamical properties of the hydration of Li(+), Na(+), and K(+) in liquid water at ambient conditions were studied by first principles molecular dynamics. Our simulations successfully captured the different hydration behavior shown by the three alkali ions as observed in experiments. The present analyses of the dependence of the self-diffusion coefficient and rotational correlation time of water on the ion concentration suggest that Li(+) (K(+)) is certainly categorized as a structure maker (breaker), whereas Na(+) acts as a weak structure breaker. An analysis of the relevant electronic structures, based on maximally localized Wannier functions, revealed that the dipole moment of H(2)O molecules in the first solvation shell of Na(+) and K(+) decreases by about 0.1 D compared to that in the bulk, due to a contraction of the oxygen lone pair orbital pointing toward the metal ion.     

Comparative study of normal and branched alkane monolayer films adsorbed on a solid surface. II. Dynamics

The dynamics of monolayer films of the n-alkane tetracosane (n-C24H52) and the branched alkane squalane (C30H62) adsorbed on graphite have been studied by quasielastic and inelastic neutron scattering and molecular dynamics (MD) simulations. Both molecules have 24 carbon atoms along their carbon backbone, and squalane has an additional six methyl side groups symmetrically placed along its length. The authors' principal objective has been to determine the influence of the side groups on the dynamics of the squalane monolayer and thereby assess its potential as a nanoscale lubricant. To investigate the dynamics of these monolayers they used both the disk chopper spectrometer (DCS) and the high flux backscattering spectrometer (HFBS) at the National Institute of Standards and Technology. These instruments made it possible to study dynamical processes such as molecular diffusive motions and vibrations on very different time scales: 1-40 ps (DCS) and 0.1-4 ns (HFBS). The MD simulations were done on corresponding time scales and were used to interpret the neutron spectra. The authors found that the dynamics of the two monolayers are qualitatively similar on the respective time scales and that there are only small quantitative differences that can be understood in terms of the different masses and moments of inertia of the two molecules. In the course of this study, the authors developed a procedure to separate out the low-frequency vibrational modes in the spectra, thereby facilitating an analysis of the quasielastic scattering. They conclude that there are no major differences in the monolayer dynamics caused by intramolecular branching. It remains to be seen whether this similarity in monolayer dynamics also holds for the lubricating properties of these molecules in confined geometries.     

线形、梳形和星形高分子静态和动态性质的模拟

以梳形高分子为纽带,基于粗粒化分子动力学模拟方法,研究了线形、梳形和星形拓扑结构高分子的静态和动态性质,以揭示稀溶液中高分子链行为与链拓扑结构依赖关系的一般性规律.研究结果表明,随着线形-梳形-星形的链拓扑结构转变,回转半径的标度关系由仅依赖分子聚合度转变为同时依赖链聚合度与臂数或侧链数.分析了星形高分子和梳形高分子的静态和动态性质的特征规律.星形高分子的臂数增加使其尺寸迅速减小,形状则由长椭球形转变为类球形,且扩散系数也随之增加;其均方回转半径(〈R_g〉)和扩散系数(D)与分子聚合度(N)及臂数(f)的标度规律为〈R_g〉~N~(0.581)f~(-0.402),D~N~(-0.763)f~(0.227).梳形高分子的静态与动态性质与分子聚合度及侧链数的依赖关系为〈R_g〉~N~(0.597)f~(-0.212)(每个支化点只有一条侧链)和〈R_g〉~N~(0.599)f~(-0.316)(每个支化点有多条侧链).     

Quantum mechanical/molecular mechanical simulations of the Tl(III) ion in water

Classical molecular dynamics (MD) and combined quantum mechanical/molecular mechanical (QM/MM) MD simulations have been performed to investigate the structural and dynamical properties of the Tl(III) ion in water. A six-coordinate hydration structure with a maximum probability of the Tl-O distance at 2.21 A was observed, which is in good agreement with X-ray data. The librational and vibrational spectra of water molecules in the first hydration shell are blue-shifted compared with those of pure liquid water, and the Tl-O stretching force constant was evaluated as 148 Nm(-1). Both structural and dynamical properties show a distortion of the first solvation shell structure. The second shell ligands' mean residence time was determined as 12.8 ps. The Tl(III) ion can be classified as "structure forming" ion; the calculated hydration energy of -986 +/- 9 kcal mol agrees well with the experimental value of -986 kcal mol.     

Statics and dynamics of polymer-wrapped colloids

We study the complex between a colloidal particle and a semiflexible polymer chain that "wraps" around it. Via molecular dynamics simulation we investigate statistical and dynamical properties of this system. First we establish the dependence of wrapped chain length on absorption energy and chain persistence length and obtain the distribution of wrapped-sphere positions. Then we study the length and position distributions of thermally excited loop defects. Finally we consider the repositioning dynamics of the colloid, focusing on the case where the chain stays wrapped onto the complex. Specifically we determine the mean square displacement of the central monomer of the wrapped chain and the resulting diffusion coefficient of the chain as a function of its persistence length, absorption energy, chain length, and size of the sphere. We argue that both statics and dynamics of these complexes can be mainly understood by energetic arguments, whereas entropic contributions from the chain configurations play only a minor role.     

Car-parrinello molecular dynamics simulation of liquid formic acid

First-principles molecular dynamics has been used to investigate the structural, vibrational, and energetic properties of formic acid, formic acid-formate anion dimers, and liquid formic acid in a periodically repeated box with 32 formic acid molecules. We found that in liquid formic acid the hydrogen-bonded clusters mainly consist of linear branching chains. From our simulation, we got good agreement with the available structural and dynamical data. We also studied the proton transfer in the cis-formic acid-formate anion dimer, and we showed that this proton transfer does not have any potential barrier. The hydrogen bonding statistics as well as the mean lifetime of the hydrogen bonds are analyzed.     

Structural and dynamical properties of ionic liquids: the influence of ion size disparity

The influence of ion size disparity on structural and dynamical properties of ionic liquids is systematically investigated employing molecular dynamics simulations. Ion size ratios are varied over a realistic range (from 1:1 to 5:1) while holding other important molecular and system parameters fixed. In this way we isolate and identify effects that stem from size disparity alone. In strongly size disparate systems the larger species (cations in our model) tend to dominate the structure; the anion-anion distribution is largely determined by anion-cation correlations. The diffusion coefficients of both species increase, and the shear viscosity decreases with increasing size disparity. The influence of size disparity is strongest up to a size ratio of 3:1, then decreases, and by 5:1 both the diffusion coefficients and viscosity appear to be approaching limiting values. The conventional Stokes-Einstein expression for diffusion coefficients holds reasonably well for the cations but fails for the smaller anions as size disparity increases likely due to the neglect of strong anion-cation correlations. The electrical conductivity is not a simple monotonic function of size disparity; it first increases up to size ratios of 2:1, remains nearly constant until 3:1, then decreases such that the conductivities of the 1:1 and 5:1 systems are similar. This behavior is traced to the competing influences of ion diffusion (enhancing) and ion densities (reducing) on conductivities at constant packing fraction. The temperature dependence of the transport properties is examined for the 1:1 and 3:1 systems. In accord with experiment, the temperature dependence of all transport properties is well represented by the Vogel-Fulcher-Tammann equation. The dependence of the diffusion coefficients on the temperature/viscosity ratio is well described by the fractional Stokes-Einstein relation D proportional to (T/eta)(beta) with beta approximately = 0.8, consistent with the exponent observed for many molten inorganic salts.     

Molecular dynamics simulations of phospholipid bilayers: Influence of artificial periodicity, system size, and simulation time

This article investigates the convergence of structural and dynamical properties with system size and with time in molecular dynamics simulations of solvated phospholipid bilayers performed at constant volume under periodic boundary conditions using lattice-sum electrostatics. The electron density profile across the bilayer, the carbon-deuterium order parameters, and the surface tension are shown to be converged for a bilayer containing 36 lipids per leaflet and simulated over a period of 3-4 ns. Reasonable estimates for these properties can already be obtained from a system containing 16 lipids per leaflet. The convergence limit of 36 lipids per leaflet and the investigation of the correlation between lipid headgroup dipoles suggest a correlation length of about 3-5 nm in the lateral directions for a hydrated DPPC bilayer in the liquid-crystalline phase. Although these (relatively small) system sizes and (relatively short) time scales appear sufficient to obtain converged collective structural properties at constant volume, two restrictions should be kept in mind: (i) the relaxation times associated with the motion of individual lipids may be much longer and (ii) simulated properties converge significantly faster under constant volume conditions as compared to constant pressure conditions. Therefore, an accurate assessment of the dynamical properties of the system or of the relaxation of the bilayer under constant pressure conditions may require longer simulation time scales.     

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.     

Crystal water dynamics of guanosine dihydrate: analysis of atomic displacement parameters, time profile of hydrogen-bonding probability, and translocation of water by MD simulation

The dynamics of crystal water molecules of guanosine dihydrate are investigated in detail by molecular dynamics (MD) simulation. A 2 ns simulation is performed using a periodic boundary box composed of 4 x 5 x 8 crystallographic unit cells and using the particle-mesh Ewald method for calculation of electrostatic energy. The simulated average atomic positions and atomic displacement parameters are remarkably coincident with the experimental values determined by X-ray analysis, confirming the high accuracy of this simulation. The dynamics of crystal water are analyzed in terms of atomic displacement parameters, orientation vectors, order parameters, self-correlation functions of the orientation vectors, time profiles of hydrogen-bonding probability, and translocations. The simulation clarifies that the average structure is composed of various stable and transient structures of the molecules. The simulated guanosine crystal forms a layered structure, with four water sites per asymmetric unit, classified as either interlayer water or intralayer water. From a detailed analysis of the translocations of water molecules in the simulation, columns of intralayer water molecules along the c axis appear to represent a pathway for hydration and dehydration by a kind of molecular valve mechanism.     

Spatial correlations of a flexible-chain oligomer in an ionic liquid

The effect of the length of the cationic tail of an ionic liquid on the dependence of the scale of structural heterogeneities of a flexible-chain oligomer dissolved in the liquid on the oligomer concentration is studied in terms of the integral equation theory. The structure of the ionic-liquid-oligomer mixture is analyzed with the use of the calculated partial structure factors. The effect of the alkyl chain length of the cation on the dependence of the characteristic scale of ordering of the oligomer chains on their concentration in the solution is the most significant for an ionic liquid with medium-length and long cationic tails. It is shown that the behavior of this dependence is affected by the type of ordering of the ionic-liquid ions. For comparison, a similar dependence for an oligomer in a molecular solvent is calculated and analyzed.     

A classical point charge model study of system size dependence of oxidation and reorganization free energies in aqueous solution

The response of water to a change of charge of a solvated ion is, to a good approximation, linear for the type of iron-like ions frequently used as a model system in classical force field studies of electron transfer. Free energies for such systems can be directly calculated from average vertical energy gaps. Exploiting this feature, we have computed the free energy and the reorganization energy of the M2+/M3+ and M1+/M2+ oxidations in a series of model systems all containing a single Mn+ ion and an increasing number of simple point charge water molecules. Long-range interactions are taken into account by Ewald summation methods. Our calculations confirm the observation made by Hummer, Pratt, and Garcia (J. Phys. Chem. 1996, 100, 1206) that the finite size correction to the estimate of solvation energy (and hence oxidation free energy) in such a setup is effectively proportional to the inverse third power (1/L3) of the length L of the periodic cell. The finite size correction to the reorganization energy is found to scale with 1/L. These simulation results are analyzed using a periodic generalization of the Born cavity model for solvation, yielding three different estimates of the cavity radius, namely, from the infinite system size extrapolation of oxidation free energy and reorganization energy, and from the slope of the linear dependence of oxidation free energy on 1/L3. The cavity radius for the reorganization energy is found to be significantly larger compared to the radius for the oxidation (solvation) free energy. The radius controlling the 1/L3 dependence of oxidation free energy is found to be comparable to the radius for reorganization. The implication of these results for density functional theory-based ab initio molecular dynamics calculation of redox potentials is discussed.     

Dynamical motions of lipids and a finite size effect in simulations of bilayers

Molecular dynamics (MD) simulations of dipalmitoylphosphatidylcholine bilayers composed of 72 and 288 lipids are used to examine system size dependence on dynamical properties associated with the particle mesh Ewald (PME) treatment of electrostatic interactions. The lateral diffusion constant Dl is 2.92 x 10(-7) and 0.95 x 10(-7) cm2/s for 72 and 288 lipids, respectively. This dramatic finite size effect originates from the correlation length of lipid diffusion, which extends to next-nearest neighbors in the 288 lipid system. Consequently, diffusional events in smaller systems can propagate across the boundaries of the periodic box. The internal dynamics of lipids calculated from the PME simulations are independent of the system size. Specifically, reorientational correlation functions for the slowly relaxing phosphorus-glycerol hydrogen, phosphorus-nitrogen vectors, and more rapidly relaxing CH vectors in the aliphatic chains are equivalent for the 72 and 288 lipid simulations. A third MD simulation of a bilayer with 72 lipids using spherical force-shift electrostatic cutoffs resulted in interdigitated chains, thereby rendering this cutoff method inappropriate.     

Molecular dynamics study of the liquid-vapor interface of acetonitrile: equilibrium and dynamical properties

The equilibrium and dynamical properties of the liquid-vapor interface of pure acetonitrile are studied by means of molecular dynamics simulations. Both nonpolarizable and polarizable models are employed in the present study. For the nonpolarizable model, the simulations are carried out for two different system sizes and at two different temperatures whereas the simulation with the polarizable model is done for a single system. The inhomogeneous density, anisotropic orientational profile, the width of the interface, and also the surface tension are calculated at room temperature and also at a lower temperature of 273 K. The dynamical aspects of the interface are investigated in terms of the single-particle dynamical properties such as the relaxation of velocity autocorrelation and the translational diffusion coefficients along the perpendicular and parallel directions and the dipole orientational relaxation of the interfacial acetonitrile molecules. The results of the interfacial dynamics are compared with those of the corresponding bulk phases at both temperatures. The convergence of the calculated results with respect to the length of simulation runs and the system size are also discussed.     

Very fast tunneling in the early stage of reaction dynamics

The difference between quantum and classical survival probabilities for molecular dissociation dynamics in the time domain, which arises mainly from quantum mechanical tunneling, has interesting characteristics that are not noticed through the counterpart in energy domain. It is shown that the early stage undergoes a fast tunneling, while the later stage is characterized with a long-lasting slow tunneling. The mechanism of this behavior is analyzed in terms of a quasi-semiclassical theory featuring the geometrical distribution of the so-called tunneling points. In particular, the role of dynamical tunneling is discussed as a phenomenon that typifies the time dependence of tunneling dynamics. It is predicted that these tunneling characteristics will be reflected in the isotope effect and should be experimentally observable.