Isothermal-isobaric Molecular Dynamics Simulations Research Articles

FF12MC: A revised AMBER forcefield and new protein simulation protocol.

ABSTRACTSpecialized to simulate proteins in molecular dynamics (MD) simulations with explicit solvation, FF12MC is a combination of a new protein simulation protocol employing uniformly reduced atomic masses by tenfold and a revised AMBER forcefield FF99 with (i) shortened C—H bonds, (ii) removal of torsions involving a nonperipheral sp3 atom, and (iii) reduced 1–4 interaction scaling factors of torsions ϕ and ψ. This article reports that in multiple, distinct, independent, unrestricted, unbiased, isobaric–isothermal, and classical MD simulations FF12MC can (i) simulate the experimentally observed flipping between left‐ and right‐handed configurations for C14–C38 of BPTI in solution, (ii) autonomously fold chignolin, CLN025, and Trp‐cage with folding times that agree with the experimental values, (iii) simulate subsequent unfolding and refolding of these miniproteins, and (iv) achieve a robust Z score of 1.33 for refining protein models TMR01, TMR04, and TMR07. By comparison, the latest general‐purpose AMBER forcefield FF14SB locks the C14–C38 bond to the right‐handed configuration in solution under the same protein simulation conditions. Statistical survival analysis shows that FF12MC folds chignolin and CLN025 in isobaric–isothermal MD simulations 2–4 times faster than FF14SB under the same protein simulation conditions. These results suggest that FF12MC may be used for protein simulations to study kinetics and thermodynamics of miniprotein folding as well as protein structure and dynamics. Proteins 2016; 84:1490–1516. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

Prediction of self diffusion coefficients of selected solvents in poly(vinyl alcohol) using lattice-free volume theory

The free volume model is probably the most successful model for predicting the diffusivity of small molecules in polymers. However, the experimental procedure for parameterizing the model is not trivial and in fact extremely time consuming. In this work, we propose a much less time consuming approach for the parameterization step. In particular, we carried out isobaric-isothermal molecular dynamics simulations to generate thermodynamic data of a few selected polymer/solvent systems and used the data to parameterize the corresponding Sanchez–Lacombe equation of state (SLEOS). The characteristic parameters of the SLEOS were then used in the parameterization of the lattice free volume (LFV) model so that diffusivity of the solvents in a polymer was then determined. To illustrate the newly proposed approach, we used poly(vinyl alcohol) and water, ethanol and benzene over a concentration range of 1–20 wt% and a temperature range of 270–370 K. We found that the LFV model was much easier to be parametrized in the aforementioned approach and yielded predictions much better than those of the well-known Mackie-Meares model. We also demonstrated that the two adjustable parameters of the LFV model are related to the size of the solvent molecules and their interaction with the polymer.

Molecular dynamics study of the diffusivity of a hydrophobic drug Cucurbitacin B in pseudo-poly(ethylene oxide-b-caprolactone) micelle environments.

Isobaric-isothermal molecular dynamics simulation was used to study the diffusion of a hydrophobic drug Cucurbitacin B (CuB) in pseudomicelle environments consisting of poly(ethylene oxide-b-caprolactone) (PEO-b-PCL) swollen by various amounts of water. Two PEO-b-PCL configurations, linear and branched, with the same total molecular weight were used. For the branched configuration, the block copolymer contained one linear block of PEO with the same molecular weight as that of the PEO block used in the linear configuration but with one end connecting to three PCL blocks with the same chain length, hereafter denoted PEO-b-3PCL. Regardless of the configuration, the simulation results showed that the diffusivity of CuB was insensitive to the water concentration up to ∼8 wt % while that of water decreased with an increasing water concentration. The diffusivity of CuB (10(-8) cm(2)/s) was 3 orders of magnitude lower than that of water (10(-5) cm(2)/s). This is attributed to the fact that CuB relied on the wiggling motion of the block copolymers to diffuse while water molecules diffused via a hopping mechanism. The rates at which CuB and water diffused into PEO-b-PCL were twice those in PEO-b-3PCL because the chain mobility and the degree of swelling are higher and there are fewer intermolecular hydrogen bonds in the case of PEO-b-PCL. The velocity autocorrelation functions of CuB show that the free volume holes formed by PEO-b-3PCL are more rigid than those formed by PEO-b-PCL, making CuB exhibit higher-frequency collision motion in PEO-b-3PCL than in PEO-b-PCL, and the difference in frequency is insensitive to water concentration.

Intercalation of dodecylamine into kaolinite and its layering structure investigated by molecular dynamics simulation

Dodecylamine was successfully intercalated into the layer space of kaolinite by utilizing the methanol treated kaolinite–dimethyl sulfoxide (DMSO) intercalation complex as an intermediate. The basal spacing of kaolinite, measured by X-ray diffraction (XRD), increased from 0.72nm to 4.29nm after the intercalation of dodecylamine. Also, the significant variation observed in the Fourier Transform Infrared Spectroscopy (FTIR) spectra of kaolinite when intercalated with dodecylamine verified the feasibility of intercalation of dodecylamine into kaolinite. Isothermal-isobaric (NPT) molecular dynamics simulation with the use of Dreiding force field was performed to probe into the layering behavior and structure of nanoconfined dodecylamine in the kaolinite gallery. The concentration profiles of the nitrogen atom, methyl group and methylene group of intercalated dodecylamine molecules in the direction perpendicular to the kaolinite basal surface indicated that the alkyl chains within the interlayer space of kaolinite exhibited an obvious layering structure. However, the unified bilayer, pseudo-trilayer, or paraffin-type arrangements of alkyl chains deduced based on their chain length combined with the measured basal spacing of organoclays were not found in this study. The alkyl chains aggregated to a mixture of ordered paraffin-type-like structure and disordered gauche conformation in the middle interlayer space of kaolinite, and some alkyl chains arranged in two bilayer structures, in which one was close to the silica tetrahedron surface, and the other was close to the alumina octahedron surface with their alkyl chains parallel to the kaolinite basal surface.

The effect of urea in the nucleation process of CO2 clathrate hydrates

The role of urea in the promotion and stability of CO2 clathrate hydrates in the context of nucleation was investigated through isothermal–isobaric molecular dynamics simulations. A comparison of structural and dynamic properties was made for aqueous solutions of CO2 interstitial to model montmorillonite surfaces in the presence and absence of urea. The results showed that meta-stable amorphous hydrates associated through proximity interact through cross-relaxation of H-bonds. Urea appears to mediate this effect by functioning as a bridge for thermal fluctuations of H-bond networks between nearby CO2 hydrates. The implications have significant bearing in the modification of solution properties for the enhancement of clathrate hydrate formation in geologic and aquatic sediments through the control and stabilization of nucleation using organic matter.

Force field comparison and thermodynamic property calculation of supercritical CO2 and CH4 using molecular dynamics simulations

Thermodynamic properties of carbon dioxide and methane have been calculated under supercritical conditions up to 900K and 100MPa using isothermal-isobaric molecular dynamics simulations and the multistate Bennett acceptance ratio (MBAR) technique. Seven different carbon dioxide force fields (two single-site models, three rigid three-site models, and two fully flexible three-site models) were considered for preliminary density calculation. Those showing better accuracy when compared to experimental results were used to calculate the volume expansivity, isothermal compressibility, isobaric and isochoric heat capacities, Joule–Thomson coefficient, and speed of sound. The same properties were also calculated for methane using two different single-site models.The results show that force fields originally parameterized and optimized to reproduce vapor–liquid coexistence curves may be able to give accurate predictions of other thermodynamic properties in an extended temperature and pressure range. The results obtained with molecular simulations are generally more accurate than predictions with the Peng–Robinson equation of state, especially near critical conditions and at high pressures. Furthermore, the MBAR technique is successfully applied to improve the accuracy of results, decrease calculation uncertainties and reduce the number of simulations required to provide reliable property predictions over a range of temperatures and pressures. Recommendations are made as to which force fields are most accurate for the set of properties computed here.

CO32–Mobility in Carbonate Apatite As Revealed by Density Functional Modeling

Carbonate apatite is a material of the utmost importance as it represents the inorganic fraction of biological hard tissues in bones and teeth. Here we study the static and dynamic features of CO32– ion in the apatitic channel of carbonate apatite (A-type substitution), by applying both static and dynamic quantum mechanical calculations based on density functional methods with B3LYP-D* and PBE functionals. The static calculations reveal a number of almost energetically equivalent carbonate configurations in the channel, leading to cell parameters compatible with the P3 space group assigned by the experimental X-ray structure determination. Ab initio isothermal–isobaric molecular dynamics simulations provide insights on the CO32– mobility, showing that at the temperature of the experimental structural determination the CO32– moiety undergoes a dynamic disorder, as the carbonate group is almost free to move within the apatitic channel enhancing its exchangeability with other anions.

Aqueous CO2 Solutions at Silica Surfaces and within Nanopore Environments. Insights from Isobaric–Isothermal Molecular Dynamics

We present a detailed molecular-based characterization via isobaricisothermal molecular dynamics simulation of the microstructure and dynamics of water-rich aqueous CO2 solutions at silica surfaces and under extreme confinement between finite silica plates at state conditions relevant to geologic capture and sequestration of carbon dioxide. The study comprises three types of slit-pore plates to represent two extreme cases of surface polarity, and a mismatched pair of plates, to interrogate the fluid behavior at and confined between heterogeneous surfaces. We found layer formation of H2O and CO2 whose strength depends on the nature of the plate surface, i.e., stronger H2O layering at hydrophilic than at hydrophobic plates with a simultaneous weaker water mediated CO2 /hydrophilic-surface interactions. We observed the opposite behavior with the hydrophobic plates where the weaker water layering results from the CO2 mediated H2O/hydrophobicsurface interactions. Moreover, we illustrated how the interplay between these types of interactions and extreme fluid confinement, i.e., strong overlapping of interfacial structures, can induce a drying out of the pore environment whose immediate consequence is a significant CO2 concentration enhancement relative to that of the bulk environment. Finally, we assessed the effect of the nature of the plate surfaces on the translational diffusion coefficient of water,more » where we found that this property changes 2 monotonically at purely interfacial regions, but non-monotonically under confinement.« less

Local segmental dynamics of cis-1,4-polybutadiene, polypropylene and polyethylene terephthalate via molecular dynamics simulations

The local segmental dynamics of cis-1,4-polybutadiene, polypropylene and polyethylene terephthalate have been investigated via isothermal-isobaric molecular dynamics simulations. The simulation pressure was 1 atm for all systems, with all simulation temperatures being at least 150 K above the polymer's glass transition temperature. The trajectories have been analysed via autocorrelation functions (ACFs) of chord vectors spanning different number of chain backbone bonds. Inverse Laplace transformations of these ACFs using the CONTIN algorithm afforded the corresponding distribution of relaxation times (DRTs) for the simulated dynamics. All DRTs illustrated a peak on fast timescales corresponding to short length scale segmental motion and a peak at longer timescales corresponding to longer length scale relaxations. A third peak, intermediate between the fast and slow processes, appears as the relaxation of chord vectors spanning increasing number of backbone bonds is considered. The temperature dependence of the relaxation dynamics is also investigated.

Structure and Dynamics of Aqueous Solutions of Electrolytes in Confined Space

We perform isothermal-isobaric molecular dynamics simulations of aqueous solutions of potassium and chloride ions with varying tube diameter. An equilibrium state is attained within 1 ns, but the relaxation time to equilibrium is dependent on the initial arrangement of ions. When the tube diameter is larger than 1 nm, ions exchange their axial positions in few tens of picosecond to be the most stable configuration in which counterions are lined up alternately. However, ions in a tube narrower than 1 nm cannot exchange the mutual positions in axial-coordinate within an order of nano second. The axial self-diffusion coefficients are also examined. It is found that they increase with increasing the tube size once an equilibrium is attained. These results suggest the partial hydration and dehydration play a certain role in diffusion of the electrolytes in confined space like tubes and channels.

Molecular simulation study of cavity-generated instabilities in the superheated Lennard-Jones liquid

Previous equilibrium-based density-functional theory (DFT) analyses of cavity formation in the pure component superheated Lennard-Jones (LJ) liquid [S. Punnathanam and D. S. Corti, J. Chem. Phys. 119, 10224 (2003); M. J. Uline and D. S. Corti, Phys. Rev. Lett. 99, 076102 (2007)] revealed that a thermodynamic limit of stability appears in which no liquidlike density profile can develop for cavity radii greater than some critical size (being a function of temperature and bulk density). The existence of these stability limits was also verified using isothermal-isobaric Monte Carlo (MC) simulations. To test the possible relevance of these limits of stability to a dynamically evolving system, one that may be important for homogeneous bubble nucleation, we perform isothermal-isobaric molecular dynamics (MD) simulations in which cavities of different sizes are placed within the superheated LJ liquid. When the impermeable boundary utilized to generate a cavity is removed, the MD simulations show that the cavity collapses and the overall density of the system remains liquidlike, i.e., the system is stable, when the initial cavity radius is below some certain value. On the other hand, when the initial radius is large enough, the cavity expands and the overall density of the system rapidly decreases toward vaporlike densities, i.e., the system is unstable. Unlike the DFT predictions, however, the transition between stability and instability is not infinitely sharp. The fraction of initial configurations that generate an instability (or a phase separation) increases from zero to unity as the initial cavity radius increases over a relatively narrow range of values, which spans the predicted stability limit obtained from equilibrium MC simulations. The simulation results presented here provide initial evidence that the equilibrium-based stability limits predicted in the previous DFT and MC simulation studies may play some role, yet to be fully determined, in the homogeneous nucleation and growth of embryos within metastable fluids.

Polarization behavior of water in extreme aqueous environments: A molecular dynamics study based on the Gaussian charge polarizable water model

We study the polarization behavior of water under geologically relevant extreme aqueous environments along four equidistant supercritical isotherms, 773<or=T(K)<or=1373, and over a wide pressure range, 0<P(GPa)<or=30, by isobaric-isothermal molecular dynamics simulations of the Gaussian charge polarizable water model, to unravel and discuss the underlying link between two precisely defined orientational order parameters and the magnitude of the average induced dipole moment of water. The predicted behavior indicates an isothermal linear dependence (a) between the magnitude of the average induced dipole moment mu(ind) and the average system density rho, (b) between the magnitude of the average induced dipole mu(ind) and that of the total dipole mu(tot), resulting from (c), a compensating (inverse) dependence between the permanent-to-induced dipolar angle theta and the magnitude of the average induced dipole moment mu(ind). Moreover, we interpret this behavior in terms of the evolution of the state dependent tetrahedral order parameter q(T) and the corresponding bond-order parameter Q(6), supplemented by the microstructural analysis based on the three site-site radial distribution functions of water and the distance-ranked nearest-neighbor distributions. Finally, we show that while water exhibits a dramatic microstructural transformation from an open four-coordinated hydrogen-bonded network at normal conditions to a quasi-close-packed coordination, it still preserves a significant degree of hydrogen bonding.

Ab initio and molecular dynamics studies of solid β-HMX: effects of hydrostatic pressure and high temperature

Using first-principles density functional theory and classical molecular dynamics (MD), the structural, electronic and mechanical properties of the energetic material β-HMX have been studied. The crystal structure optimised by the local density approximation calculations compares reasonably with the experimental data. Electronic band structure and density of states indicate that β-HMX is an insulator with a band gap of 3.059 eV. The pressure effect on the crystal structure and physical properties has been investigated in the range of 0–40 GPa. The crystal structure and electronic properties change slightly as the pressure increases from 0 to 2.5 GPa; when the pressure is above 2.5 GPa, further increment of the pressure results in significant changes in crystal structure. There is a larger compression along the b-axis than along the a- and c-axes. Isothermal–isobaric MD simulations on β-HMX were performed in the temperature range of 5–400 K. Phase transition at 360 K, corresponding to a volume interrupt, was found. The computed thermal expansion coefficients show anisotropic behaviour with a slightly larger expansion along the b- and c-axes than along the a-axis. In the temperature range of 5–360 K, β-HMX possesses good plasticity and its stiffness decreases with increasing the temperature.

The director and molecular dynamics of the field-induced alignment of a Gay–Berne nematic phase: An isothermal-isobaric nonequilibrium molecular dynamics simulation study

Isothermal-isobaric molecular dynamics simulations have been performed for the generic Gay–Berne (GB) mesogen, GB(4.4, 20.0, 1, 1), to investigate director and molecular rotational motion during the field-induced alignment of a nematic. The alignment process for the director is discussed within the context of a hydrodynamic analysis based on the Ericksen–Leslie theory and this is found to predict the simulated behavior well. The dependence of the relaxation time for the alignment on the field strength is also in good accord with the theory. The rotational viscosity coefficient estimated from the simulation is smaller than that typically observed for real nematics and the possible reasons for this are discussed. However, the simulation results are found to follow not only the theory but also the experiments, at least qualitatively. No significant variation in the local and long-range structure of the nematic phase is found during the field-induced alignment process. In addition, we have explored the molecular dynamics in the nematic phase in the presence of the field using the first- and second-rank time autocorrelation functions. More importantly we are able to show that the director relaxation time is longer than that for molecular rotation. It is also possible to use the two orientational correlation times to explore the relationship between the rotational viscosity coefficient and the rotational diffusion constant. The diffusion constants determined from the orientational correlation times, based on the short-time expansion of the autocorrelation functions, are found to be significantly different. In consequence it is not possible to test, unambiguously, the relationship between the rotational viscosity coefficient and the rotational diffusion constant. However, it would seem that the second-rank rotational correlation time provides the most reliable route to the rotational viscosity coefficient.

Solvation and ion pair association in aqueous metal sulfates: Interpretation of NDIS raw data by isobaric–isothermal molecular dynamics simulation

We analyzed the solvation behavior of aqueous lithium, nickel, and ytterbium sulfates at ambient conditions in terms of the relevant radial distributions functions and the corresponding first-order difference of the sulfur-site neutron-weighted distribution functions generated by isothermal-isobaric molecular dynamics simulation. We determined the partial contributions to the neutron-weighted distribution functions, to identify the main contributing peaks of the corresponding radial distribution functions, and the effect of the contact ion-pair configuration on the resulting water’s hydrogen coordination around the sulfate’s sulfur site. Finally, we assessed the extent of the ion-pair formation according to Poirier–DeLap formalism and highlighted the significant increase of the ion-pair association exhibited by these salts with cation charge.

The pressure-induced phase transition of the solid β–HMX

The structural, vibrational and thermodynamic properties of β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β–HMX) crystal have been studied using the isothermal-isobaric molecular dynamics (NPT-MD) simulations. The variations of cell volume, lattice constants and molecular geometry of solid β–HMX are presented and discussed at different pressure and temperature. It was found that the N–N bond is significantly lengthened with increasing temperature, which suggests that it is relevant to the initial decomposition. An abrupt change at 27 Gpa for the volume and internal geometrical parameters was observed. This is in good accord with the experimental observation that there is a phase transition at 27 GPa, which is clearly due to conformational change, not chemical reaction. The vibrational frequencies at ambient conditions agree well with experimental results, and the pressure/temperature-induced frequency shifts of these modes are discussed. Frequency discontinuity was also observed at pressure when the phase transition occurred. The Grüneisen parameter was obtained using the vibrational frequency.

Isothermal isobaric molecular dynamics simulation of water

A series of isothermal isobaric molecular dynamics simulation are carried out on a system made up of 210 molecules at normal temperature and pressure ( T = 298 K, P = 1 bar) and at high pressure ( T = 298 K, P = 2.1 kbar). The physical model is based upon the tetrahedral cluster architecture composed of one central molecule (20% of the sample) and four outer molecules (80%). This theoretical approach of the liquid water structure and description was recently strengthened by spectroscopy measurements (Raman spectrometry, X-ray and neutron scattering) on the three-dimensional network of hydrogen bond at the femto second time scale [Ph. Wernet, D. Nordlund, U. Bergmann, M. Cavalleri, M. Odelius, H. Ogasawara, L.A. Naslund, T.K. Hirsch, L. Ojamae, P. Glatzel, L.G.M. Pettersson, A. Nilsson, Science 304 (2004) 995; Jared D. Smith, Christopher D. Cappa, Benjamin M. Messer, Walter S. Drisdell, Ronald C. Cohen, Richard J. SayKally, J. Phys. Chem. B 110 (2006) 20038; Jared D. Smith, Christopher D. Cappa, Kevin R. Wilson, Ronald C. Cohen, Phillip L. Geissler, Science 306 (2004)]. This work corroborates that the number of water molecules having two and four hydrogen bonds in liquid water represents the relative molecular composition of 20% and 80%, respectively, and improves our previous mixture model [M. Amrani, W. Sellaoui, M. Belhakem, A. Krallafa, D. Bormann, J. Soc. Algiers Chim. 13(2) (2003) 227–237] of water, focusing in particular on the charge asymmetry and distribution of water molecules within the liquid. For that purpose, investigations of the influence of the charge delocalization on the central molecule of our pentamer upon various calculated data are performed. A high pressure is applied to highlight optimal selective polarization on the hydrogen bond network forming the Walrafen’s cluster [D. Eizenberg, W. Kauzmann, The Structure and the Properties of Water, Springer, 1968] at room temperature. A complementary series of molecular dynamics simulation are carried out in the temperature range T = 270–285 K under atmospheric pressure for the optimal charge delocalisation and results are compared to the experimental data. Data reported in the present work such as structural data (molecular density or lacunar index, pair distribution function, hydrogen bond arrangements…), transport and thermodynamic properties are found to be in very good agreement with experimental data.

Molecular Dynamics Simulation Study for Transport Properties of Diatomic Liquids

We present results for transport properties of diatomic fluids by isothermal-isobaric (NpT) equilibrium molecular dynamics (EMD) simulations using Green-Kubo and Einstein formulas. As the molecular elongation of diatomic molecules increases from the spherical monatomic molecule, the diffusion coefficient increases, indicating that longish shape molecules diffuse more than spherical molecules, and the rotational diffusion coefficients are almost the same in the statistical error since random rotation decreases. The calculated translational viscosity decreases with the molecular elongation of diatomic molecule within statistical error bar, while the rotational viscosity increases. The total thermal conductivity decreases as the molecular elongation increases. This result of thermal conductivity for diatomic molecules by EMD simulations is again inconsistent with the earlier results of those by non-equilibrium molecular dynamics (NEMD) simulations even though the missing terms related to rotational degree of freedom into the Green-Kubo and Einstein formulas with regard to the calculation of thermal conductivity for molecular fluids are included.

The glass transition temperatures of amorphous trehalose–water mixtures and the mobility of water: an experimental and in silico study

Isothermal–isobaric molecular dynamics simulations are used to calculate the specific volume of models of trehalose and three amorphous trehalose–water mixtures (2.9%, 4.5% and 5.3% (w/w) water, respectively) as a function of temperature. Plots of specific volume versus temperature exhibit a characteristic change in slope when the amorphous systems change from the glassy to the rubbery state and the intersection of the two regression lines provides an estimate of the glass transition temperature T g. A comparison of the calculated and experimental T g values, as obtained from differential scanning calorimetry, shows that despite the predicted values being systematically higher (about 21–26 K), the trend and the incremental differences between the T g values have been computed correctly: T g 5.3 % ( w/w ) < T g 4.5 % ( w/w ) < T g 2.9 % ( w/w ) < T g 0.0 % ( w/w ) . The mobility of water has been investigated over temperature ranges covering the rubbery and the glassy phases of the trehalose–water mixtures by calculating the diffusion coefficients of water. The temperature dependence of the diffusion coefficient changes in the region of the glass transition and can be used as well to estimate T g values. The activation energies for water diffusion were found to be independent of the amount of water in amorphous trehalose.

Glass Transition Temperature of Glucose, Sucrose, and Trehalose: An Experimental and in Silico Study

Isothermal-isobaric molecular dynamics simulations are used to calculate the specific volume of models of different amorphous carbohydrates (glucose, sucrose, and trehalose) as a function of temperature. Plots of specific volume vs temperature exhibit a characteristic change in slope when the amorphous systems change from the glassy to the rubbery state. The intersection of the regression lines of data below (glassy state) and above (rubbery state) the change in slope provides the glass transition temperature (T(g)). These predicted glass transition temperatures are compared to experimental T(g) values as obtained from differential scanning calorimetry measurements. As expected, the predicted values are systematically higher than the experimental ones (about 12-34 K) as the cooling rates of the modeling methods are about a factor of 10(12) faster. Nevertheless, the calculated trend of T(g) values agrees exactly with the experimental trend: T(g)(glucose) < T(g)(sucrose) < T(g)(trehalose). Furthermore, the relative differences between the glass transition temperatures were also computed precisely, implying that atomistic molecular dynamics simulations can reproduce trends of T(g) values in amorphous carbohydrates with high quality.