Reaction Field Simulations of Monatomic and Diatomic Dipolar Fluids

Firstly, the conditions are explored for which molecular dynamics simulations yield reliable thermodynamic results when the reaction field method is applied for dipolar fluids. The influence of the system size, of the scaling method for avoiding the total energy updrift, and of the reaction field dielectric constant are studied. With appropriate conditions, the results for the Stockmayer fluid when compared to previous results show excellent agreement up to very high dipole moments. In the next step the method is applied to two-centre Lennard-Jones plus ideal axial dipole (2CLJD) molecules of elongation L = 0.505. For one state point, the influence of the molecular shape as well as of the dipolar strength on energy and pressure is studied in detail. Finally, in the project of developing a physically based equation of state for polar fluids, thermodynamic results are presented for 2CLJD fluids of elongation L = 0.505 for four different dipole moments at 29 state points in a temperature and density grid. For these 116 runs which all were performed with vectorized codes on a CYBER 205 also the uncertainties in the results are given as have been estimated from the running averages.     

Electrostatics of proteins: Description in terms of two dielectric constants simultaneously

In the semi-continuum treatment of the energetics of charge formation (or transfer) inside a protein, two components of the energy are inevitably present: the energy of interaction of the ion with the pre-existing intraprotein electric field, and the energy due to polarization of the medium by the newly formed charge. The pre-existing field is set up by charges (partial or full) of the protein atoms fixed in a definite structure. The calculation of this field involves only the electronic polarization (the optical dielectric constant ϵ_o) of the protein because the polarization due to shifts of heavy atoms has already been accounted for by their equilibrium coordinates. At the same time, the aqueous surroundings should be described by the static constant ϵ_sw, as the positions of water molecules are not fixed. The formation of a new charge, absent in the equilibrium X-ray structure, results in shifts of electrons and polar atoms, i.e., it involves all kinds of medium polarization described by the static dielectric constant of protein ϵ_s. Thus, in calculations of the total energy, two different dielectric constants of the protein are operative simultaneously. This differs from a widely used algorithm employing one effective dielectric constant for both components of the ion's energy. Proteins: 28:174–182, 1997. © 1997 Wiley-Liss Inc.     

Gibbs-Ensemble Molecular Dynamics: Liquid-Gas Equilibria for Lennard-Jones Spheres and n-Hexane

Abstract

We present a novel method to simulate phase equilibria in atomic and molecular systems. The method is a Molecular Dynamics version of the Gibbs-Ensemble Monte Carlo technique, which has been developed some years ago for the direct simulation of phase equilibria in fluid systems. The idea is to have two separate simulation boxes, which can exchange particles (or molecules) in a thermodynamically consistent fashion. Here we pres the derivation of the generalized equations of motion and discuss the relation of the resulting trajectory averages to the relevant ensemble. We test this Gibbs-Ensemble Molecular Dynamics algorithm by applying it to an atomic and a molecular system, i.e. to the liquid-gas coexistence in a Lennard-Jones fluid and in n-hexane. In both cases our results are in good accord with previous mean field and Gibbs-Ensemble Monte Carlo results as well as with the experimental data in the case of hexane. We also show that our Gibbs-Ensemble Molecular Dynamics algorithm like other Molecular Dynamics techniques can be used to study the dynamics of the system. Self-diffusion coefficients calculated with this method are in agreement with the result of conventional constant temperature Molecular Dynamics.     

Molecular dynamics simulations of ion separation in nano-channel water flows using an electric field

ABSTRACT

Removal of undesired substances from water is a field of investigation recently focused at the nanoscale. Towards this direction, molecular dynamics simulations are conducted in this paper to investigate unwanted ion removal in nanochannel flows. The simulation method incorporates a Poiseuille-like water/ion flow system at the nanoscale where an electric field, of various magnitudes in the range of E?=?0.25–1.5?V/Å, is applied perpendicular to the flow, leading anions and cations close to the wall regions, similar to the Capacitive De-Ionization method. The time needed for ions to reach equilibrium, i.e. to flow in the region near the walls while pure water flows in the channel interior, is t?=?1.3?ns when E?=?1.5?V/Å and t?=?4.0?ns when E?=?0.25?V/Å, showing a dependency on the value of the electric field. Calculations on density, velocity, and temperature values report on fluid properties to be used in the proposed desalination configuration and could act as a basis to guide novel technological applications and extend to higher scales.     

Structure of Supercritical Fluid Krypton at Small Scattering Angle Using Parallel Molecular Dynamics Simulation

Abstract

We present a parallel algorithm for molecular dynamics involving short-range two- and three-body potentials and the pair-correlation function, g(r). The method is based on a spatial decomposition of the simulation box that takes advantage of a linked-cell list, and allows a load balanced partition of the computations of both the forces and g(r) over the processors. The tests of the program is conducted by evaluating the efficiency for both the thermalization phase and the production phase of the simulation. This method is successfully applied to the calculation of the direct correlation function of fluid krypton at small scattering angle along the T = 297 K supercritical isotherm.     

Phase Equilibria of Quadrupolar Fluids by Simulation in the Gibbs Ensemble

Abstract

Vapour-liquid phase diagrams for pure fluids and mixtures of molecules with Lennard-Jones plus quadrupole-quadrupole interaction potentials were determined by Monte Carlo simulation in the Gibbs ensemble [1]. This is the first reported application of the method to molecular fluids. We have demonstrated that the Gibbs method works reliably for strongly interacting molecular fluids at liquid densities. Pure fluid calculations were performed for reduced quadrupole strengths, Q* = Q/(εσ⁵)^1/2 equal to 1 and √2, typical of molecules like C₂H₂ and C₂H₄. It was found that the critical temperature of the quadrupolar fluid increased rapidly with increasing quadrupolar strength, in good agreement with previous computer simulation and theoretical results. A single mixture with components characterized by identical Lennard-Jones parameters and Q*₁ = + 1, Q*₂ = - 1 was studied at three temperatures. A negative azeotrope was observed at the lowest temperature studied, as seen experimentally in the CO₂/C₂H₂ mixture. The perturbation theory calculations are in good agreement with the simulation results for all properties except coexisting liquid densities. The results illustrate some of the strengths and limitations of perturbation theories based on the Padé approximant for the free energy of polar fluids.     

A Modified Gibbs Ensemble Method for Calculating Fluid Phase Equilibria

Abstract

A modification of the Gibbs ensemble Monte Carlo computer simulation method for fluid phase equilibrium is described. The modification, which is based on the assumption of a thermodynamic model for the vapor phase, reduces the computational time for the simulation as compared to the original Gibbs ensemble methods. Since the computational time is largely proportional to the number of particle-particle interactions, avoiding the direct simulation of the vapor phase typically leads to a thirty to forty percent reduction in computational time. For a pure Leonard-Jones-(12,6) fluid the results obtained at moderate reduced temperatures, T/T_c < 0.8, are in good agreement with the full Gibbs ensemble method.     

Molecular dynamics simulation and nmr study of a blood group H trisaccharide

Molecular dynamics simulations in vacuum and solution have been carried out on 2′-α-L -fucosyllactitol, a model for blood group H in conjunction with two-dimensional nmr measurements on the same compound. Three independent starting conformations for the dynamics were chosen from low energy conformations obtained by a ?/ψ grid search. Nine 5 ns vacuum simulations of the trisaccharide were performed, employing three different ways to treat electrostatic interactions for each starting conformation: distance-dependent dielectric with ε = r, constant dielectric with ε = 1, or constant dielectric with ε = 80. In vacuum, transitions of ? and ψ for the α-L -Fuc-(1 → 2)-β-D -Gal element occur in a cooperative manner. The virtual distance obtained for H1 in fucose to H2 in galactose from nuclear Overhauser effect spectroscopy experiments agree with one of the conformations of the trisaccharide in one of the three 100 ps aqueous simulations (?/ψ ca. ?100°/150°), indicating this may be a dominant solution conformation. The rms fluctuations of the ?- and ψ-dihedral angles were ～ 10° for a conformational state, both in the vacuum and the aqueous simulations. For the simulations in vacuum, the agreement with experimental NOE data is reasonable when a constant dielectric of 1 is used (major conformers having ?/ψ ca. ?100°/150° and ?140°/100°), whereas the agreement was poor with a constant dielectric of 80. Translational diffusion coefficients calculated from the simulation of the oligosaccharides were 0.12–0.18 × 10^?5 cm²/s and from nmr measurements 0.27 × 10^?5 cm²/s. © 1994 John Wiley & Sons, Inc.     

Batch and fed-batch fermentation of optically pure D (-) lactic acid from Kodo millet (Paspalum scrobiculatum) bran residue hydrolysate: growth and inhibition kinetic modeling

Abstract

A low-cost Kodo millet bran residue was utilized as feedstock for the production of D (?) lactic acid (DLA) using Lactobacillus delbrueckii NBRC3202 under anaerobic condition. Data culled from a series of batch fermentation processes with different initial Kodo millet bran residue hydrolysate (KMBRH) and DLA concentrations were used for kinetic model development. Both simulated and experimental data were in good agreement for cell growth, KMBRH utilization, and DLA formation. The values of kinetic constants specific growth rate, (μ_m = 0.17?h^?1); growth (α_P = 0.96?g.g^?1) and non-growth (β_P = 1.19?g.g^?1.h^?1) associated constant for DLA production and the maximum specific KMBRH utilization rate, (q_{G, max} = 1.18?g.g^?1.h^?1) were in good agreement with the literature reports. Kinetic analysis elucidated that L. delbrueckii growth was predominantly influenced by KMBRH limitation and highly sensitive to DLA inhibition. Fed-batch fermentation studies demonstrated the existence of substrate and product inhibition paving the scope for process intensification.     

Comparison of end-point continuum-solvation methods for the calculation of protein-ligand binding free energies

We have compared the predictions of ligand‐binding affinities from several methods based on end‐point molecular dynamics simulations and continuum solvation, that is, methods related to MM/PBSA (molecular mechanics combined with Poisson–Boltzmann and surface area solvation). Two continuum‐solvation models were considered, viz., the Poisson–Boltzmann (PB) and generalised Born (GB) approaches. The nonelectrostatic energies were also obtained in two different ways, viz., either from the sum of the bonded, van der Waals, nonpolar solvation energies, and entropy terms (as in MM/PBSA), or from the scaled protein–ligand van der Waals interaction energy (as in the linear interaction energy approach, LIE). Three different approaches to calculate electrostatic energies were tested, viz., the sum of electrostatic interaction energies and polar solvation energies, obtained either from a single simulation of the complex or from three independent simulations of the complex, the free protein, and the free ligand, or the linear‐response approximation (LRA). Moreover, we investigated the effect of scaling the electrostatic interactions by an effective internal dielectric constant of the protein (?_int). All these methods were tested on the binding of seven biotin analogues to avidin and nine 3‐amidinobenzyl‐1H‐indole‐2‐carboxamide inhibitors to factor Xa. For avidin, the best results were obtained with a combination of the LIE nonelectrostatic energies with the MM+GB electrostatic energies from a single simulation, using ?_int = 4. For fXa, standard MM/GBSA, based on one simulation and using ?_int = 4–10 gave the best result. The optimum internal dielectric constant seems to be slightly higher with PB than with GB solvation. © Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Electrical properties of hydrated collagen. I. Dielectric properties

The effect of water on the low-frequency (10²-10⁵ H_z) complex permittivitv of native, sold-state collagen has been investigated experimentally. Measurements at ambient temperature show that dry collagen exhibits essentially no frequency or temperature dependence. As water is absorbed, both dielectric constant and loss factor increase simultaneously and rise sharply upward at a hydration level which may be associated with the completion of the primary absorption layer as determined from independent water absorption studies. The behaviour is qualitatively identical to that observed for other proteins and related materials. Temperature-dependent measurements made under vacuum conditions in the range ?196°C to +100°C are characteristic of the dielectric properties of the water in the sample. Dehydration produced by successive temperature recycling to the maximum temperature effectively eliminates any temperature or frequency dependence. A maximum in the temperature-dependent curves is found at about +40°C and is explained as the superposition of two processes: (1) the transition of water molecules from bound to free states, and (2) the difffusion of water molecules out of the system. The dielectric constant of dry collagen, after desorption at ambient temperature, is about 4.5. Desorption at elevated temperatures reduced the room temperature value to about 2.3 and the liquid nitrogen temperature value to a number indistinguishable from the optical value of n² = 2.16.     

Calculations of the φ -ψ Conformational Contour Maps for N-Acetyl Alanine N'-Methyl Amide and of the Characteristic Ratios of Poly-L-alanine Using Various Molecular Mechanics Forcefields

Abstract

We generated φ -ψ conformational energy contour maps for the of N-acetyl alanine N'-methyl amide using the molecular mechanics forcefields AMBER, AMBER3, BI085, CFF91, CVFF, MM2, MM3, MM+, and SYBYL. With MM2, MM3, and MM+, we used a dielectric constant of ? = 1.5, the default effective value for these forcefields. With the other forcefields we used ? = 1 and 4, except with SYBYL, which, in Spartan 3.1, has no electrostatic term. All forcefields yielded the C^eq ₇ conformation as a low-energy minimum or the global minimum. Most of the forcefields also yielded a minimum-energy conformation in the C₅,α_R, and α_t. regions of the φ -ψ contour map. Fewer of the forcefields yielded a minimum in the C^ax ₇ region; however, adiabatic relaxation frequently lowered the relative energy of this region. Based on the appearance of the φ -ψ maps, the following pairs of forcefields were broadly similar (but not identical) to each other but dissimilar to the other pairs: AMBER3 and AMBER, BI085 and CHARMM, MM+ and MM2, SYBYL and ECEPP, and CFF91 and MM3. We used the data from the φ -ψ contour maps to compute the characteristic ratio of poly-L-alanine. Most of the computed values deviated significantly from the experimental value. Only the computed characteristic ratio of CFF91 without adiabatic relaxation at ? = 4 and MM3 without adiabatic relaxation at ? = 1.5 agreed with the experimental value.     

Calculation of protonation patterns in proteins with structural relaxation and molecular ensembles – application to the photosynthetic reaction center

The conventional method to determine protonation patterns of proteins was extended by explicit consideration of structural relaxation. The inclusion of structural relaxation was achieved by alternating energy minimization with the calculation of protonation pattern in an iterative manner until consistency of minimized structure and protonation pattern was reached. We applied this method to the bacterial photosynthetic reaction center (bRC) of Rps. viridis and could show that the relaxation procedure accounts for the nuclear polarization and therefore allows one to lower the dielectric constant for the protein from the typically chosen value of ɛ _p = 4 to a value of ɛ _p = 2 without fundamentally changing the results. Owing to the lower dielectric shielding at ɛ _p = 2, the charges of the titratable groups interact more strongly, which leads to sampling problems during Monte Carlo titration. We solved this problem by introducing triple moves in addition to the conventional single and double moves. We also present a new method that considers ensembles of protein conformations for the calculation of protonation patterns. Our method was successfully applied to calculate the redox potential differences of the quinones in the bRC using the relaxed structures for the different redox states of the quinones. Received: 30 October 1997 / Revised version: 2 March 1998 / Accepted: 7 March 1998     

Effect of water on piezoelectric,dielectric, and elastic properties of bone

The complex piezoelectric constant (d = d′ ? id″), elastic constant (c = c′ + ic″), and dielectric constant (ε = ε′ ? iε″) were measured at a frequency of 10 Hz over the temperature range from ?150 to 50°C and for a range of hydration up to 0.26 g/g for decalcified bone and up to 0.084 g/g for bone. For decalcified bone, ε′ and ε″ increased with increasing hydration with a deflection at the critical hydration h_c = 0.08 g/g;d′ at ?150°C increased below h_c but decreased above h_c with increasing hydration; c′ increased below ?60°C but decreased above ?60°C with increasing hydration; and the peak temperatures of ε″, d″, and c″ below ?50°C agree with each other and decreased with increasing hydration with a deflection at h_c. For bone, similar hydration and temperature dependences were observed for ε and c. However, the dependence of d on hydration and temperature was different from that of decalcified bone, reflecting a two-phase structure consisting of collagen fibers and mineral hydroxyapatite. The critical hydration for bone was 0.04 g/g.     

The Application of the Reaction-Field Method to the Calculation of Dielectric Constants

Abstract

The behaviour of the popular TIP3P water model has been investigated using both molecular dynamics and Monte Carlo simulation procedures. Long-range electrostatic interactions were included through a reaction-field treatment, and the nonbonded interactions were either truncated at the cutoff distance, or smoothly scaled to zero using a switching function. The thermodynamic observables, and in particular the dipole-dipole correlation functions, are found to differ between the two simulation techniques if a rigid nonbonded cutoff is applied. However, use of a switching function gives exact agreement between the simulation methodologies. This difference is ascribed to the effect of energy pumping in the molecular dynamics simulations, and suggests that dielectric constants calculated using this simulation method with the fluctuation procedure in conjunction with a reaction field should be reappraised. Thus the Monte Carlo simulation procedure offers a number of intrinsic advantages over molecular dynamics for the calculation of dielectric constants with a reaction field. The most precise value for the dielectric constant of TIP3P is calculated to be 102 ± 3 at 298 K.     

Molecular Dynamics Study of High Temperature Phase-Separation in a H2O/N2 Mixture with Exp-6 Interactions

Abstract

Equimolar H₂O/N₂ fluid mixture was studied by molecular dynamics simulations for NVT ensemble. Calculations were performed with the modified Buckingham (exp-6) potentials at T = 2000 K. Particular attention was given to the phase separation at very high pressures relevant to a detonation environment. Calculations of pair correlation functions and local mole fractions clearly indicated the occurrence of the fluid separation into N₂-rich and H₂O-rich phase. The density at the phase boundary between homogeneous and inhomogeneous phase-separated state was determined to be p = 1.35 g/cm³ on the basis of the static cross correlation factor which is defined by the sum of the local mole fractions. The ratio of the self-diffusion coefficients of N₂ and H₂O at p < 1.35 g/cm³ was found to be approximately equal to the value predicted by the kinetic theory of the ideal gas, whereas the ratio was close to unity at the phase-separated state (p > 1.35 g/cm³). In addition, two distinctive behaviors of the system could be observed for the relaxation from the initial uniform mixture to the phase-separated fluid: at lower densities (1.35 < p < 2.0 g/cm³) the fluid mixture began to relax into the phase-separated system without obvious incubation time, while clear incubation period was associated for the separation at higher densities. During this incubation period, discontinuous jumps in the mean square displacements were found.     

Design,synthesis and biological evaluation of novel 1H-1,2,4-triazole,benzothiazole and indazole-based derivatives as potent FGFR1 inhibitors viafragment-based virtual screening

Abstract

Fibroblast growth-factor receptor (FGFR) is a potential target for cancer therapy. We designed three novel series of FGFR1 inhibitors bearing indazole, benzothiazole, and 1H-1,2,4-triazole scaffold via fragment-based virtual screening. All the newly synthesised compounds were evaluated in vitro for their inhibitory activities against FGFR1. Compound 9d bearing an indazole scaffold was first identified as a hit compound, with excellent kinase inhibitory activity (IC₅₀ = 15.0?nM) and modest anti-proliferative activity (IC₅₀ = 785.8?nM). Through two rounds of optimisation, the indazole derivative 9?u stood out as the most potent FGFR1 inhibitors with the best enzyme inhibitory activity (IC₅₀ = 3.3?nM) and cellular activity (IC₅₀ = 468.2?nM). Moreover, 9?u also exhibited good kinase selectivity. In addition, molecular docking study was performed to investigate the binding mode between target compounds and FGFR1.     

An electrostatic model for the dielectric effects,the adsorption of multivalent ions,and the bending of B-DNA

We have studied electrostatic properties of DNA with a discrete charge model consisting of a cylindrical dielectric core with a radius of 8 Å and a dielectric constant D_i = 4, surrounded by two helical strings of phosphate point charges at 10 Å from the axis, immersed in an aqueous medium with dielectric constant D_w = 78.54. Eliminating the dielectric core makes potentials in the phosphate surface less negative by about 0.5 kT/e. Salt effects are evaluated for the model without a dielectric core, using the shielded Coulomb potential. Smearing the phosphate charges increases their potential by about 2.5 kT/e, due mostly to the self-potential of the smeared charge. Potentials in the center of the minor and major grooves vary less than 0.02 kT/e along their helical path. The potential in the center of the minor groove is from 1.0 to 1.7 kT/e, more negative than in the center of the major groove, depending on dielectric core and salt concentration. So multivalent cations and also larger cationic ligands, such as some antibiotics, are likely to adsorb in the minor groove, in agreement with earlier computations by A. and B. Pullman. Dielectric effects on the surface potential and the local potential variations are found to be relatively small. Bending of DNA is studied by placing a multivalent cation, M^Z+, in the center of the minor or major groove, curving DNA around it for a certain length, and calculating the free energy difference between the bent and the straight configuration. Boltzmann averaged bending angles, 〈β〉, are found to be maximal in 0.03M monovalent salt, for a length of about 50 or 25 Å of curved DNA when an M^Z+ ion is adsorbed in the minor or the major groove, respectively. When the dielectric constant of water is used throughout the calculation, we find maximal bends of 〈β〉 = 11° for M²⁺ and 〈β〉 = 16° for M³⁺ in the minor groove, 〈β〉 = 13° for M³⁺ in the major groove. The absence of bends in DNA adsorbed to mica in the presence of Mg salts supports the role of Mg²⁺ in “ion bridging” between DNA and mica. The treatment of the effective dielectric constant between two points outside a dielectric cylinder in water is appended. © 1998 John Wiley & Sons, Inc. Biopoly 46: 503–516, 1998     

Temperature dependence of the polarization and the dielectric constant near the paraelectric-ferroelectric transitions in BaTiO3

Temperature dependences of the spontaneous polarization and the dielectric constant are calculated near the paraelectric-ferroelectric (cubic-tetragonal) transition in BaTiO₃ using our mean field model. By expanding the free energy in terms of the spontaneous polarization (order parameter), expressions for the temperature dependence of the spontaneous polarization and the dielectric constant are derived. By considering the temperature dependence of the Raman frequencies for the lattice mode (～310 cm^?1) which is related to the spontaneous polarization, the experimental data from the literature is analyzed near the first order paraelectric-ferroelectric transition in BaTiO₃. The dielectric constant is then calculated as a function of temperature for the cubic-tetragonal transition in BaTiO₃. Our results show that the observed behavior of the spontaneous polarization in the ferroelectric phase (T<T_C) and that of the dielectric constant in both paraelectric (T>T_C) and ferroelectric phases, can be described adequately by the mean field model studied here for BaTiO₃.     

On the Implementation of Friedman Boundary Conditions in Liquid Water Simulations

Abstract

We have applied the image approximation to the reaction field as suggested by H.L. Friedman [Mol. Phys., 29, 1533 (1975)] by investigating appropriate cavity sizes and system parameters for use in molecular simulations. The energy of and the structure around a central simple point charge (SPC) water molecule in a dielectric cavity was found to be in good agreement with the properties of a liquid sample. To confine the water molecules within the cavity, we introduced a short-range repulsion between a real charge and its image as the Lennard-Jones repulsive potential between oxygen atoms of the SPC potential. For a system of 65 water molecules a cavity radius of 10.45 Å is appropriate; this radius is altered to 12.00 Å for a cavity surrounding 113 molecules. The effect of the boundary is restricted to the outer-most water layer which is in contact with the dielectric continuum.