Molecular dynamics simulations for the prediction of the dielectric spectra of alcohols,glycols and monoethanolamine

The response of molecular systems to electromagnetic radiation in the microwave region (0.3–300 GHz) has been principally studied experimentally, using broadband dielectric spectroscopy. However, relaxation times corresponding to reorganisation of molecular dipoles due to their interaction with electromagnetic radiation at microwave frequencies are within the scope of modern molecular simulations. In this work, fluctuations of the total dipole moment of a molecular system, obtained through molecular dynamics simulations, are used to determine the dielectric spectra of water, a series of alcohols and glycols, and monoethanolamine. Although the force fields employed in this study have principally been developed to describe thermodynamic properties, most them give fairly good predictions of this dynamical property for these systems. However, the inaccuracy of some models and the long simulation times required for the accurate estimation of the static dielectric constant can sometimes be problematic. We show that the use of the experimental value for the static dielectric constant in the calculations, instead of the one predicted by the different models, yields satisfactory results for the dielectric spectra, and hence the heat absorbed from microwaves, avoiding the need for extraordinarily long simulations or re-calibration of molecular models.     

Dielectric relaxation of DNA solutions. III. Effects of DNA concentration, protein contamination, and mixed solvents

As a continuation of previous papers [Biopolymers (1976) 15 , 879; (1978) 17 , 1508], the low-frequency dielectric relaxation of DNA solutions was studied with a four-electrode cell and the simultaneous two-frequency measurement. Below a critical concentration, the dielectric relaxation time agrees with the rotational relaxation time estimated from the reduced viscosity and is almost independent of DNA concentration C_p, and the dielectric increment is proportional to C_p. The critical concentration is approximately 0.02% of DNA for molecular weight M_r 2 × 10⁶ and 0.2% for M_r 4.5 × 10⁵ in 1 mM NaCl. Dielectric relaxations are compared for samples before and after deproteinization, and the protein contamination is found to have a minor effect on the dipole moment of DNA. The effect of a mixed solvent of water and ethanol on the dielectric relaxation of DNA is well interpreted in terms of changes in viscosity and the dielectric constant of the solvent, assuming that the relaxation arises from rotation of the molecule with a quasi-permanent dipole due to counterion fluctuation.     

Molecular dynamics studies of a DNA-binding protein: 2. An evaluation of implicit and explicit solvent models for the molecular dynamics simulation of the Escherichia coli trp repressor.

Although aqueous simulations with periodic boundary conditions more accurately describe protein dynamics than in vacuo simulations, these are computationally intensive for most proteins. Trp repressor dynamic simulations with a small water shell surrounding the starting model yield protein trajectories that are markedly improved over gas phase, yet computationally efficient. Explicit water in molecular dynamics simulations maintains surface exposure of protein hydrophilic atoms and burial of hydrophobic atoms by opposing the otherwise asymmetric protein-protein forces. This properly orients protein surface side chains, reduces protein fluctuations, and lowers the overall root mean square deviation from the crystal structure. For simulations with crystallographic waters only, a linear or sigmoidal distance-dependent dielectric yields a much better trajectory than does a constant dielectric model. As more water is added to the starting model, the differences between using distance-dependent and constant dielectric models becomes smaller, although the linear distance-dependent dielectric yields an average structure closer to the crystal structure than does a constant dielectric model. Multiplicative constants greater than one, for the linear distance-dependent dielectric simulations, produced trajectories that are progressively worse in describing trp repressor dynamics. Simulations of bovine pancreatic trypsin were used to ensure that the trp repressor results were not protein dependent and to explore the effect of the nonbonded cutoff on the distance-dependent and constant dielectric simulation models. The nonbonded cutoff markedly affected the constant but not distance-dependent dielectric bovine pancreatic trypsin inhibitor simulations. As with trp repressor, the distance-dependent dielectric model with a shell of water surrounding the protein produced a trajectory in better agreement with the crystal structure than a constant dielectric model, and the physical properties of the trajectory average structure, both with and without a nonbonded cutoff, were comparable.     

Molecular Dynamics Simulations of a DMPC Bilayer Using Nonadditive Interaction Models

We present a polarizable force field based on the charge-equilibration formalism for molecular dynamics simulations of phospholipid bilayers. We discuss refinement of headgroup dihedral potential parameters to reproduce ab initio conformational energies of dimethylphosphate calculated at the MP2/cc-pVTZ level of theory. We also address the refinement of electrostatic and Lennard-Jones (van der Waals) parameters to reproduce ab initio polarizabilities and water interaction energies of dimethylphosphate and tetramethylammonium. We present results of molecular dynamics simulations of a solvated dimyristoylphosphatidylcholine bilayer using this polarizable force field as well as the nonpolarizable, fixed-charge CHARMM27 and CHARMM27r force fields for comparison. Calculated atomic and electron-density profiles, deuterium order parameters, and headgroup orientations are found to be consistent with previous simulations and with experiment. Polarizable interaction models for solvent and lipid exhibit greater water penetration into the lipid interior; this is due to the variation of water molecular dipole moment from a bulk value of 2.6 Debye to a value of 1.9 Debye in the membrane interior. The reduction in the electrostatic component of the desolvation free-energy penalty allows for greater water density. The surface dipole potential predicted by the polarizable model is 0.95 V compared to the value of 0.8 V based on nonpolarizable force-field calculations. Effects of inclusion of explicit polarization are discussed in relation to water dipole moment and varying charge distributions. Dielectric permittivity profiles for polarizable and nonpolarizable interactions exhibit subtle differences arising from the nature of the individual component parameterizations; for the polarizable force field, we obtain a bulk dielectric permittivity of 79, whereas the nonpolarizable force field plateaus at 97 (the value for pure TIP3P water). In the membrane interior, both models predict unit permittivities, with the polarizable models contributing from one to two more units due to the optical dielectric (high-frequency dipole fluctuations). This contribution is a step toward the continuing development of a CHARMM (Chemistry at Harvard Molecular Mechanics) polarizable force field for simulations of biomacromolecular systems.     

Comparison of the potentials of mean force for alanine tetrapeptide between integral equation theory and simulation.

The dielectrically consistent reference interaction site model (DRISM) integral equation theory is applied to determine the potential of mean force (PMF) for an alanine tetramer. A stochastic dynamics simulation of the alanine tetramer using this PMF is then compared with an explicit water molecular dynamics simulation. In addition, comparison is also done with simulations using other solvent models like the extended reference interaction site model (XRISM) theory, constant dielectric and linear distance-dependent dielectric models. The results show that the DRISM method offers a fairly accurate and computationally inexpensive alternative to explicit water simulations for studies on small peptides.     

The optical birefringence of DNA solutions induced by oscillatory electric and hydrodynamic fields

The optical birefringence induced in DNA solutions by both oscillating hydrodynamic fields (flow birefringence) and oscillating electric fields (Kerr effect) is measured over a wide frequency range. The observed frequency response of the birefrigence is compared with theories for rigid ellipsoidal particles and for Gaussian chains. DNA at 6 × 10⁵ molecular weight is found to exhibit rigid particle hydrodynamic behavior, while DNA at 5 × 10⁶ molecular weight behaves like a flexible chain. Characterization of the hydrodynamic relaxation spectra for the DNA's by oscillatory flow birefringence allows precise comparison between theory and the experimental Kerr effect response. The dielectric model for DNA contains both permanent and dispersionless induced dipole moments. The dielectric behavior of DNA has the character of a permanent dipole but with anomalous low-frequency dispersion in the Kerr effect. The existing theories do not adequately describe this dispersion. A fluctuation dipole mechanism with relaxation times comparable to those associated with the hydrodynamic motion could possibly demonstrate the observed polar behavior.     

Solvent influence on base stacking.

In this paper we present a detailed analysis of the base-stacking phenomenon in different solvents, using nanosecond molecular dynamics simulations. The investigation focuses on deoxyribo- and ribodinucleoside monophosphates in aqueous and organic solutions. Organic solvents with a low dielectric constant, such as chloroform, and solvents with intermediate dielectric constants, such as dimethyl sulfoxide and methanol, were analyzed. This was also done for water, which is highly polar and has a high dielectric constant. Structural parameters such as the sugar puckering and the base-versus-base orientations, as well as the energetics of the solute-solvent interactions, were examined in the different solvents. The obtained data demonstrate that base stacking is favored in the high dielectric aqueous solution, followed by methanol and dimethyl sulfoxide with intermediate dielectric constants, and chloroform, with a low dielectric constant.     

Study of dielectric behavior of DNA in shear gradient

The dielectric behavior of the DNA molecule is investigated in the presence of mechanical force as well as the electrical field. In the present experiment, the direction of the electrical field is perpendicular to that of the mechanical force. The dipole moment of polar molecules manifest itself as dielectric increment at low frequencies or as the conductance increment at high frequencies. These two quantities are closely related to each other by Eq. (1) in the text. Because of the difficulty due to electrode polarization at low frequencies, no useful information was obtained by investigating the dielectric increment in the present system. Therefore, the effect of shear gradient was studied by measuring the conductance increment at high frequencies with various velocity gradients. The conductance increment decreased when the shear was applied perpendicular to the electrical field. The conductance change is converted into the unit of dielectric constant; it was found that the dielectric increment of DNA solution decreases by as much as 85 percent. From these observations, it is concluded that the direction of the dipole moment in DNA is longitudinal rather than transverse. The same experiment was repeated with the random coil DNA and no anisotropy in the dielectric increment was observed.     

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.     

Dielectric constant dependence of biological oxidation-reduction. 1. A model of polarity-dependent ferrocytochrome c oxidation

A theoretical model for the effect of the dielectric constant (c) of the solvent medium on ferrocytochrome c oxidation by ferricyanide is developed to account for the observed variations of the rate constant (k) of reactions in aqueous binary mixtures with alcohols (less than 5-10 mol% ethanol and propranolol). A correlation between k and c is found if ln k is expressed as a function of the Kirkwood parameter (c-1)(2c+1). The results of calculations indicate that the use of the 'overall dipole moment' of cytochrome c in oxidoreduction studies is likely to be unreliable. Instead, the decrease in k in alcohol/water mixtures is best explained--in conformity with Onsager's theory of the reaction field--by a polarity effect on the dipole moment of the cytochrome c heme upon diffusion of the polar solvent molecules into the low dielectric constant heme crevice.     

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.     

Dielectric relaxation in proteins: the computational perspective

In photoexcitation and electron transfer, a new dipole or charge is introduced, and the structure is adjusted. This adjustment represents dielectric relaxation, which is the focus of this review. We concentrate on a few selected topics. We discuss linear response theory, as a unifying framework and a tool to describe non-equilibrium states. We review recent, molecular dynamics simulation studies that illustrate the calculation of dynamic and thermodynamic properties, such as Stokes shifts or reorganization free energies. We then turn to the macroscopic, continuum electrostatic view. We recall the physical definition of a dielectric constant and revisit the decomposition of the free energy into a reorganization and a static term. We review some illustrative continuum studies and discuss some difficulties that can arise with the continuum approach. In conclusion, we consider recent developments that will increase the accuracy and broaden the scope of all these methods.     

Dielectric relaxation of DNA solutions. II

Real and imaganiry parts of complex dielectric constant of dilute solutions of DNA in 10^?3M NaCl with molecular weight ranging from 0.4 × 10⁶ to 4 × 10⁶ were measured at frequencies from 0.2 Hz to 30 kHz. Dielectric increments Δε were obtained from Cole-Cole plots and relaxation times τ_D from the loss maximum frequency. The τ_D of all samples agrees well with twice of the maximum viscoelastic relexation time in the Zimm theory, indicating that the low-frequency dielectric relaxiation should be ascribed to be the rotation of DNA. The rms dipole moment, which was obtained from Δε, agree well with that calculated from the counterion fluctuation theory. The dielectric increment was found to be greatly depressed in MgCl₂, which is resonably interpreted in terms of a strong binding of Mg⁺⁺ ions with DNA.     

The dielectric properties of water within model transbilayer pores.

Ion channels contain extended columns of water molecules within their transbilayer pores. The dynamic properties of such intrapore water have been shown to differ from those of water in its bulk state. In previous molecular dynamics simulations of two classes of model pore (parallel bundles of Ala20 alpha-helices and antiparallel barrels of Ala10 beta-strands), a substantially reduced translational and rotational mobility of waters was observed within the pore relative to bulk water. Molecular dynamics simulations in the presence of a transpore electrostatic field (i.e., a voltage drop along the pore axis) have been used to estimate the resultant polarization (due to reorientation) of the intrapore water, and hence to determine the local dielectric behavior within the pore. It is shown that the local dielectric constant of water within a pore is reduced for models formed by parallel alpha-helix bundles, but not by those formed by beta-barrels. This result is discussed in the context of electrostatics calculations of ion permeation through channels, and the effect of the local dielectric of water within a helix bundle pore is illustrated with a simple Poisson-Boltzmann calculation.     

What are the dielectric “constants” of proteins and how to validate electrostatic models?

Implicit models for evaluation of electrostatic energies in proteins include dielectric constants that represent effect of the protein environment. Unfortunately, the results obtained by such models are very sensitive to the value used for the dielectric constant. Furthermore, the factors that determine the optimal value of these constants are far from being obvious. This review considers the meaning of the protein dielectric constants and the ways to determine their optimal values. It is pointed out that typical benchmarks for validation of electrostatic models cannot discriminate between consistent and inconsistent models. In particular, the observed pK(a) values of surface groups can be reproduced correctly by models with entirely incorrect physical features. Thus, we introduce a discriminative benchmark that only includes residues whose pK(a) values are shifted significantly from their values in water. We also use the semimacroscopic version of the protein dipole Langevin dipole (PDLD/S) formulation to generate a series of models that move gradually from microscopic to fully macroscopic models. These include the linear response version of the PDLD/S models, Poisson Boltzmann (PB)-type models, and Tanford Kirkwwod (TK)-type models. Using our different models and the discriminative benchmark, we show that the protein dielectric constant, epsilon(p), is not a universal constant but simply a parameter that depends on the model used. It is also shown in agreement with our previous works that epsilon(p) represents the factors that are not considered explicitly. The use of a discriminative benchmark appears to help not only in identifying nonphysical models but also in analyzing effects that are not reproduced in an accurate way by consistent models. These include the effect of water penetration and the effect of the protein reorganization. Finally, we show that the optimal dielectric constant for self-energies is not the optimal constant for charge-charge interactions.     

The ELBA force field for coarse-grain modeling of lipid membranes

A new coarse-grain model for molecular dynamics simulation of lipid membranes is presented. Following a simple and conventional approach, lipid molecules are modeled by spherical sites, each representing a group of several atoms. In contrast to common coarse-grain methods, two original (interdependent) features are here adopted. First, the main electrostatics are modeled explicitly by charges and dipoles, which interact realistically through a relative dielectric constant of unity (ε(r) = 1). Second, water molecules are represented individually through a new parametrization of the simple Stockmayer potential for polar fluids; each water molecule is therefore described by a single spherical site embedded with a point dipole. The force field is shown to accurately reproduce the main physical properties of single-species phospholipid bilayers comprising dioleoylphosphatidylcholine (DOPC) and dioleoylphosphatidylethanolamine (DOPE) in the liquid crystal phase, as well as distearoylphosphatidylcholine (DSPC) in the liquid crystal and gel phases. Insights are presented into fundamental properties and phenomena that can be difficult or impossible to study with alternative computational or experimental methods. For example, we investigate the internal pressure distribution, dipole potential, lipid diffusion, and spontaneous self-assembly. Simulations lasting up to 1.5 microseconds were conducted for systems of different sizes (128, 512 and 1058 lipids); this also allowed us to identify size-dependent artifacts that are expected to affect membrane simulations in general. Future extensions and applications are discussed, particularly in relation to the methodology's inherent multiscale capabilities.     

Molecular dynamics simulation of α-melanocyte stimulating hormone in a water-membrane model interface

The conformation of the tridecapeptide α-melanocyte stimulating hormone in the presence of a double water-membrane interface was studied by molecular dynamics simulation, using the computational package THOR. In this program the solvent is represented by a continuous medium with dielectric constant ɛ, and the interface between different media is simulated by a surface of discontinuity of the dielectric constant. The electrostatic image method was used to write down the terms, added to the force field, that describe the polarisation effects induced in the interface by the atomic charges. The program was further improved by the introduction of a second surface, parallel to the first one, to mimic the membrane. A conformational search using the software Prelude was employed to find an initial geometry for the peptide in water. The molecular dynamics simulation performed during 10 ns showed that the peptide structure is flexible in water, without stabilisation of any preferential conformation. In the presence of the model membrane, the peptide moved to the medium representing the interior of the membrane. Inside the low dielectric constant medium, the structure of the peptide showed a turn in the central sequence of amino acids and a packed conformation remained stabilised during more than 7.0 ns of simulation. Received: 27 November 1998 / Revised version: 11 March 1999 / Accepted: 8 April 1999     

Long time dynamics of Met-enkephalin: comparison of explicit and implicit solvent models

Met-enkephalin is one of the smallest opiate peptides. Yet, its dynamical structure and receptor docking mechanism are still not well understood. The conformational dynamics of this neuron peptide in liquid water are studied here by using all-atom molecular dynamics (MD) and implicit water Langevin dynamics (LD) simulations with AMBER potential functions and the three-site transferable intermolecular potential (TIP3P) model for water. To achieve the same simulation length in physical time, the full MD simulations require 200 times as much CPU time as the implicit water LD simulations. The solvent hydrophobicity and dielectric behavior are treated in the implicit solvent LD simulations by using a macroscopic solvation potential, a single dielectric constant, and atomic friction coefficients computed using the accessible surface area method with the TIP3P model water viscosity as determined here from MD simulations for pure TIP3P water. Both the local and the global dynamics obtained from the implicit solvent LD simulations agree very well with those from the explicit solvent MD simulations. The simulations provide insights into the conformational restrictions that are associated with the bioactivity of the opiate peptide dermorphin for the delta-receptor.