Monte Carlo Study of Structural and Thermodynamic Properties of Liquid Chloroform Using a Five Site Model

A five site potential model combining Lennard–Jones plus Coulomb potential functions has been developed for chloroform molecule. The partial charges needed for Coulombic interactions were derived using the chelpg procedure implemented in the gaussian 92 program. These calculations were performed at the MP2 level with MC-311G* basis set for Cl and 6-311G** for C and H atoms. The parameters for the Lennard–Jones potentials were optimized to reproduce experimental values for the density and enthalpy of vaporization of the pure liquid at 298 K and 1 atm. The statistical mechanics calculations were performed with the Monte Carlo method in the isothermic and isobaric (NpT) ensemble. Besides the values obtained for density, ρ, and molar enthalpy of vaporization at constant pressure, Δ H_V, for liquid chloroform, results for molar volume, V_m, molar heat capacity, C_p, isobaric thermal expansivity, α_p, and isothermal compressibility, κ_T, for this pure liquid are also in very good agreement with experimental observations. Size effects on the values of thermodynamic properties were investigated. The potential model was also tested by computing the free energy for solvating one chloroform molecule into its own liquid at 298 K using a statistical perturbation approach. The result obtained compares well with the experimental value. Site–site pair correlation functions were calculated and are in good accordance with theoretical results available in the literature. Dipole–dipole correlation functions for the present five site model were also calculated at different carbon–carbon distances. These correlations were compared to those obtained using the four site model reported in the literature. An investigation of the solvent dependence of the relative free energy for cis/trans conversion of a hypothetical solute in TIP4P water and chloroform was accomplished. The results show strong interaction of water and chloroform molecules with the gauche conformer. The value obtained for the free energy barrier for cis/trans rotation in TIP4P water is higher than that for chloroform. This result is in agreement with the continuous theory for solvation as the conformer with higher dipole moment is more favoured by the solvent with higher dieletric constant. The results also show an increase in entropy as the solute goes from the cis to the trans geometry and this result is more appreciable in the aqueous solution. This revised version was published online in June 2006 with corrections to the Cover Date.     

Study of Bound Water of Poly-Adenine Using High Frequency Dielectric Measurements

The high frequency dielectric constant of poly-adenine (poly-A) was measured between 1 MHz and 1 GHz. The purpose of these experiments was to investigate the state of water molecules that are bound to the charged groups of the poly-A molecule. Analysis of the data using the Maxwell's mixture equation revealed the dielectric constant of bound water higher than we expected. Using Onsager's internal field in Debye's equation, we calculated the dielectric constant of water in the vicinity of a charged ion. The result of this computation demonstrates that the dielectric constant of bound water is much smaller than the normal value only in the immediate proximity of charged ions (within 2 Å). The dielectric constant increases rapidly to the normal value as the distance increases from 2 to 4 Å. This observation indicates that charged sites of polyions have only short range interactions with the surrounding water molecules. However, this conclusion pertains only to rotary diffusion of bound water since dielectric measurement is unable to detect translational diffusion.     

Molecular modeling of hair keratin/peptide complex: Using MM-PBSA calculations to describe experimental binding results

Molecular dynamics simulations of a keratin/peptide complex have been conducted to predict the binding affinity of four different peptides toward human hair. Free energy calculations on the peptides' interaction with the keratin model demonstrated that electrostatic interactions are believed to be the main driving force stabilizing the complex. The molecular mechanics-Poisson-Boltzmann surface area methodology used for the free energy calculations demonstrated that the dielectric constant in the protein's interior plays a major role in the free energy calculations, and the only way to obtain accordance between the free energy calculations and the experimental binding results was to use the average dielectric constant.     

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.     

Estimating the dielectric constant of the channel protein and pore

When modelling biological ion channels using Brownian dynamics (BD) or Poisson–Nernst–Planck theory, the force encountered by permeant ions is calculated by solving Poisson’s equation. Two free parameters needed to solve this equation are the dielectric constant of water in the pore and the dielectric constant of the protein forming the channel. Although these values can in theory be deduced by various methods, they do not give a reliable answer when applied to channel-like geometries that contain charged particles. To determine the appropriate values of the dielectric constants, here we solve the inverse problem. Given the structure of the MthK channel, we attempt to determine the values of the protein and pore dielectric constants that minimize the discrepancies between the experimentally-determined current–voltage curve and the curve obtained from BD simulations. Two different methods have been applied to determine these values. First, we use all possible pairs of the pore dielectric constant of water, ranging from 20 to 80 in steps of 10, and the protein dielectric constant of 2–10 in steps of 2, and compare the simulated results with the experimental values. We find that the best agreement is obtained with experiment when a protein dielectric constant of 2 and a pore water dielectric constant of 60 is used. Second, we employ a learning-based stochastic optimization algorithm to pick out the optimum combination of the two dielectric constants. From the algorithm we obtain an optimum value of 2 for the protein dielectric constant and 64 for the pore dielectric constant.     

A fast and simple method to calculate protonation states in proteins.

A simple model for electrostatic interactions in proteins, based on a distance and position dependent screening of the electrostatic potential, is presented. It is applied in conjunction with a Monte Carlo algorithm to calculate pK(alpha) values of ionizable groups in proteins. The purpose is to furnish a simple, fast, and sufficiently accurate model to be incorporated into molecular dynamic simulations. This will allow for dynamic protonation calculations and for coupling between changes in structure and protonation state during the simulation. The best method of calculating protonation states available today is based on solving the linearized Poisson-Boltzmann equation on a finite difference grid. However, this model consumes far too much computer time to be a practical alternative. Tests are reported for fixed structures on bacteriorhodopsin, lysozyme, myoglobin, and calbindin. The studies include comparisons with Poisson-Boltzmann calculations with dielectric constants 4 and 20 inside the protein, a model with uniform dielectric constant 80 and distance-dependent dielectric models. The accuracy is comparable to that of Poisson-Boltzmann calculations with dielectric constant 20, and it is considerably better than that with epsilon = 4. The time to calculate the protonation at one pH value is at least 100 times less than that of a Poisson-Boltzmann calculation. Proteins 1999;36:474-483.     

The properties of liquid water in electric and magnetic fields

A new model of liquid water is proposed, which involves the liquid-crystalline phase, namely, the presence of linearly ordered chains of water molecules and large clusters of these molecules. The presence of linearly ordered chains and clusters in liquid water makes itself evident after the exposure of water to low-frequency electromagnetic radiation. The kinetics of the linearly ordered chains is described by nonlinear excitations (solitons). A hydrodynamic equation describing the behavior of this model system was derived. On the basis of the model, the dimensions of clusters were determined (approximately 600 A). The calculated values of dielectric permeability in the range of low frequencies appeared to be close to their experimentally obtained values. A tenfold increase in the stationary value of dielectric permeability compared with the known value of the dielectric constant in the frequency range of 10(4)-10(6) Hz was predicted. The frequency dependence of dielectric permeability in this range was studied.     

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.     

Modeling loop reorganization free energies of acetylcholinesterase: a comparison of explicit and implicit solvent models

The treatment of hydration effects in protein dynamics simulations varies in model complexity and spans the range from the computationally intensive microscopic evaluation to simple dielectric screening of charge-charge interactions. This paper compares different solvent models applied to the problem of estimating the free-energy difference between two loop conformations in acetylcholinesterase. Molecular dynamics (MD) simulations were used to sample potential energy surfaces of the two basins with solvent treated by means of explicit and implicit methods. Implicit solvent methods studied include the generalized Born (GB) model, atomic solvation potential (ASP), and the distance-dependent dieletric constant. By using the linear response approximation (LRA), the explicit solvent calculations determined a free-energy difference that is in excellent agreement with the experimental estimate, while rescoring the protein conformations with GB or the Poisson equation showed inconsistent and inferior results. While the approach of rescoring conformations from explicit water simulations with implicit solvent models is popular among many applications, it perturbs the energy landscape by changing the solvent contribution to microstates without conformational relaxation, thus leading to non-optimal solvation free energies. Calculations applying MD with a GB solvent model produced results of comparable accuracy as observed with LRA, yet the electrostatic free-energy terms were significantly different due to optimization on a potential energy surface favored by an implicit solvent reaction field. The simpler methods of ASP and the distance-dependent scaling of the dielectric constant both produced considerable distortions in the protein internal free-energy terms and are consequently unreliable.     

High apparent dielectric constant inside a protein reflects structural reorganization coupled to the ionization of an internal Asp

The dielectric properties of proteins are poorly understood and difficult to describe quantitatively. This limits the accuracy of methods for structure-based calculation of electrostatic energies and pK(a) values. The pK(a) values of many internal groups report apparent protein dielectric constants of 10 or higher. These values are substantially higher than the dielectric constants of 2-4 measured experimentally with dry proteins. The structural origins of these high apparent dielectric constants are not well understood. Here we report on structural and equilibrium thermodynamic studies of the effects of pH on the V66D variant of staphylococcal nuclease. In a crystal structure of this protein the neutral side chain of Asp-66 is buried in the hydrophobic core of the protein and hydrated by internal water molecules. Asp-66 titrates with a pK(a) value near 9. A decrease in the far UV-CD signal was observed, concomitant with ionization of this aspartic acid, and consistent with the loss of 1.5 turns of alpha-helix. These data suggest that the protein dielectric constant needed to reproduce the pK(a) value of Asp-66 with continuum electrostatics calculations is high because the dielectric constant has to capture, implicitly, the energetic consequences of the structural reorganization that are not treated explicitly in continuum calculations with static structures.     

Solvent reorganization contribution to the transfer thermodynamics of small nonpolar molecules.

The experimental thermodynamic data for the dissolution of five simple hydrocarbon molecules in water were combined with the solute-solvent interaction energy from a computer simulation study to yield data on the enthalpy change of solvent reorganization. Similar data were generated for dissolving these same solute molecules in their respective neat solvents using the equilibrium vapor pressure and the heat of vaporization data for the pure liquid. The enthalpy and the free energy changes upon cavity formation were also estimated using the temperature dependence of the solute-solvent interaction energy. Both the enthalpy and T delta S for cavity formation rapidly increase with temperature in both solvent types, and the free energy of cavity formation can be reproduced accurately by the scaled particle theory over the entire temperature range in all cases. These results indicate that the characteristic structure formation around an inert solute molecule in water produces compensating changes in enthalpy and entropy, and that the hydrophobicity arises mainly from the difference in the excluded volume effect.     

Behavior of κ-carrageenan in glycerol and sorbitol solutions

The solubility of κ-carrageenan in low water-content solvents is important in food applications where complete solubilization is required for proper development of structure and rheology. The effect of glycerol and sorbitol on the gelation and conformational helix transition of κ-carrageenan was studied using rheology and optical rotation. Glycerol/water solutions from 0–100 wt% glycerol and sorbitol solutions from 0–100% saturation were studied over the temperature range 0–90°C. The results were analyzed in terms of solvent solubility parameters, water chemical potential, and solvent dielectric constant. Effective cohesive energy density parameters could not be inferred for the carrageenan, but the gelation temperature could be correlated with solvent dielectric constant. Hydrogen bonding interactions control the carrageenan helix formation. The cohesive energy density as a measure of solvent quality accounts for hydrogen bonding but not Coulombic interactions, and the Coulombic interactions scale on dielectric constant. This indicates the dominant role of electrostatics on the gelation process.     

Control of the redox potential of cytochrome c and microscopic dielectric effects in proteins

X-ray structural information provides the opportunity to explore quantitatively the relation between the microenvironments of heme proteins and their redox potentials. This can be done by considering the protein as a "solvent" for its redox center and calculating the difference between the electrostatic energy of the reduced and oxidized heme. Such calculations are presented here, applying the protein dipoles-Langevin dipoles (PDLD) model to cytochrome c. The calculations focus on an evaluation of the difference between the redox potentials of cytochrome c and the octapeptide-methionine complex formed by hydrolysis of cytochrome c. The corresponding difference (approximately 7 kcal/mol) is accounted for by the PDLD calculations. It is found that the protein provides basically a low dielectric environment for the heme, which destabilizes the oxidized heme (relative to its energy in water). The effect of the charged propionic acids on the heme is examined in a preliminary way. It is found that the negative charges of these groups are in a hydrophilic rather than a hydrophobic environment and that the protein-water system provides an effective high dielectric constant for their interaction with the heme. The dual nature of the dielectric effect of the cytochrome (a low dielectric constant for the self-energy of the heme and a high dielectric constant for charge-charge interactions) is discussed. The findings of this work are consistent with the difference between the folding energies of the reduced and oxidized cytochrome c.     

Changes in stability upon charge reversal and neutralization substitution in staphylococcal nuclease are dominated by favorable electrostatic effects

Single site mutations that reverse or neutralize a surface charge were made at 22 ionizable residues in staphylococcal nuclease. Unfolding free energies were obtained by guanidine hydrochloride denaturation. These data, in conjunction with previously obtained stabilities of the corresponding alanine mutants, unequivocally show that the dominant contribution to stability for virtually all of the wild-type side chains examined is the electrostatic effect associated with each residue's charged group. With only a few exceptions, these charges stabilize the native state, with an average loss of 0.5 kcal/mol of stability upon neutralization of a charge. When the charge is reversed, the average destabilization is doubled. Structure-based calculations of electrostatic free energy with the continuum method based on the finite difference solution to the linearized Poisson-Boltzmann equation reproduce the observed energetics when the polarizability in the protein interior is represented with a dielectric constant of 20. However, in some cases, large differences are found, giving insight into possible areas for improvement of the calculations. In particular, it appears that the assumptions made in the calculations about the absence of electrostatic interactions in the denatured state and the energetic consequences of dynamic fluctuations in the native state will have to be further explored.     

Sequestered water and binding energy are coupled in complexes of lambda Cro repressor with non-consensus binding sequences

We use the osmotic pressure dependence of dissociation rates and relative binding constants to infer differences in sequestered water among complexes of lambda Cro repressor with varied DNA recognition sequences. For over a 1000-fold change in association constant, the number of water molecules sequestered by non-cognate complexes varies linearly with binding free energy. One extra bound water molecule is coupled with the loss of approximately 150 cal/mol complex in binding free energy. Equivalently, every tenfold decrease in binding constant at constant salt and temperature is associated with eight to nine additional water molecules sequestered in the non-cognate complex. The relative insensitivity of the difference in water molecules to the nature of the osmolyte used to probe the reaction suggests that the water is sterically sequestered. If the previously measured changes in heat capacity for lambda Cro binding to different non-cognate sequences are attributed solely to this change in water, then the heat capacity change per incorporated water is almost the same as the difference between ice and water. The associated changes in enthalpies and entropies, however, indicate that the change in complex structure involves more than a simple incorporation of fixed water molecules that act as adaptors between non-complementary surfaces.     

Ordering in aqueous polysaccharide solutions. II. Optical rotation and heat capacity of aqueous solutions of a triple-helical polysaccharide schizophyllan

Deuterium oxide solutions of schizophyllan, a triple-helical polysaccharide, undergoing an order-disorder transition centered at 17 degrees C, were studied by optical rotation (OR) and heat capacity (C(p)) to elucidate the molecular mechanism of the transition and water structure in the solution and frozen states. The ordered structure at low temperature consisted of the side chains and water in the vicinity forming an ordered hydrogen-bonded network surrounding the helix core and was disordered at higher temperature. In the solution state appeared clearly defined transition curves in both the OR and C(p) data. The results for three samples of different molecular weights were analyzed theoretically, treating this transition as a typical linear cooperative transition from the ordered to disordered states and explained quantitatively if the molecular weight polydispersity of the sample was considered. The excess heat capacity C(EX)(p) defined as the C(p) minus the contributions from schizophyllan and D(2)O was estimated. In the frozen state it increased with raising temperature above 150 K until the mixture melted. This was compared with the dielectric increment observed in this temperature range and ascribed to unfreezable water. From the heat capacity and dielectric data, unfreezable water is mobile but more ordered than free water. In the solution state, the excess heat capacity originates from the interactions of D(2)O molecules as bound water and structured water, and so forth. Thus the schizophyllan triple helix molds water into various structures of differing orders in solution and in the solid state.     

Heat capacity and conformation of proteins in the denatured state

Heat capacity, intrinsic viscosity and ellipticity of a number of globular proteins (pancreatic ribonuclease A, staphylococcal nuclease, hen egg-white lysozyme, myoglobin and cytochrome c) and a fibrillar protein (collagen) in various states (native, denatured, with and without disulfide crosslinks or a heme) have been studied experimentally over a broad range of temperatures. It is shown that the partial heat capacity of denatured protein significantly exceeds the heat capacity of native protein, especially in the case of globular proteins, and is close to the value calculated for an extended polypeptide chain from the known heat capacities of individual amino acid residues. The significant residual structure that appears at room temperature in the denatured states of some globular proteins (e.g. myoglobin and lysozyme) at neutral pH results in a slight decrease of the heat capacity, probably due to partial screening of the protein non-polar groups from water. The heat capacity of the unfolded state increases asymptotically, approaching a constant value at about 100 degrees C. The temperature dependence of the heat capacity of the native state, which can be determined over a much shorter range of temperature than that of the denatured state and, correspondingly, is less certain, appears to be linear up to 80 degrees C. Therefore, the denaturational heat capacity increment seems to be temperature-dependent and is likely to decrease to zero at about 140 degrees C.     

On the mechanism of the cold ethanol precipitation method of plasma protein fractionation

Given the negligible difference in the value of the dielectric constant of water at 20°C and that of ethanol solutions at low temperatures, the often advanced expanation for the precipitation of plasma proteins by the cold ethanol process, as being due to a reduction of the dielectric constant and the resulting increase in interprotein charge interactions, is not tenable. It is shown by a surface-thermodynamic approach that, upon dehydration by ethanol, isoelectric serum albumin molecules as well as isoelectric serum gamma globulin molecules will attract each other to a sufficient degree by van der Waals forces to become insoluble in the ethanol-water mixtures used.     

Allowance for spatial dispersion of dielectric permittivity in polyelectrolyte model of DNA.

In order to allow for real dielectric properties of a solvent in calculating of electrostatic characteristics of strongly charged polyions such as DNA in salt solution we consider a simple model of linear dielectric response of a medium. The interactions between charged particles are treated in the framework of self-consistent-field approximation. The basic characteristic of the problem, electrostatic potential, can be found from the solution of non-linear integro-differential equation. Specifically we consider so-called quasimacroscopic model where dielectric response of a medium depends only on the distance from the polyion. Application of the approach for calculating of the B-to-Z free energy qualitatively retains the main conclusion obtained previously within the model with fixed dielectric constant: non-monotonous behavior of the free energy differences as a function of ionic strength. At the same time, essential sensitivity of the results to specific values of dielectric parameters is observed.