A challenging system: free energy prediction for factor Xa

Factor Xa (fXa) is a promising target for antithrombotic drugs. Recently, we presented a molecular dynamics study on fXa, which highlighted the need for a careful system setup to obtain stable simulations. Here, we show that these simulations can be used to predict the free energy of binding of several fXa inhibitors. We tested molecular mechanics/Poisson-Boltzmann surface area, molecular mechanics/Generalized Born surface area, and linear interaction energy (LIE) on a small data set of fXa ligands. The continuum solvent approaches only yield satisfying correlations to the experimental results if some of the water molecules are explicitly included in the free energy calculations. LIE gave reasonable results if a sufficiently large data set is used. In general, our procedure of setting up the fXa simulation system enabled MD simulations, which produce adequate ensembles for free energy calculations.     

Parametrization strategy for the MolFESD concept: quantitative surface representation of local hydrophobicity

We derive a new model for the established concept of the molecular free energy surface density (MolFESD) yielding a more rigorous representation of local surface contributions to the overall hydrophobicity of a molecule. The model parametrization makes efficient use of both local and global information about solvation thermodynamics, as formulated earlier for the problem of predicting free energies of hydration. The free energy of transfer is separated into an interaction contribution and a term related to the cavity formation. Interaction and cavity components are obtained from the statistical three-dimensional (3D) free energy density and a linear combination of surface and volume terms, respectively. An appropriate molecular interaction field generated by the program Grid is used as an approximate representation of the interaction part of the 3D free energy density. We further compress the 3D density by means of a linear combination of localized surface functions allowing for the derivation of local hydrophobic contributions in the form of a free energy surface density. For a set of 400 compounds our model yields significant correlation (R(2) = 0.95, sigma = 0.57) between experimental and calculated log P values. The final model is applied to establish a correlation between partial free energies of transfer for a series of sucrose derivatives and their relative sweetness, as studied earlier in the group of the authors. We find considerable improvement regarding the rms error of the regression thus validating the presented approach.     

Free energy of binding of a small molecule to an amorphous polymer in a solvent

Crystallization is a commonly used purification process in industrial practice. It usually begins with heterogeneous nucleation on a foreign surface. The complicated mechanism of heterogeneous nucleation is not well understood, but we hypothesize that a possible correlation between binding affinity to a surface and nucleation enhancement might exist. Amorphous polymers have been used in controlling crystallization. However, to our knowledge, no attempt has been made to calculate the free energy of binding of a small molecule to an amorphous polymer in a solvent, and to characterize the binding sites/conformations of this system at a molecular level. We developed a two-step approach, first using Adsorption Locator to identify probable binding sites and molecular dynamics to screen for the best binding sites and then using the Blue-Moon Ensemble method to compute the free energy of binding. A system of ethylene glycol, polyvinyl alcohol (PVA), and heavy water (D(2)O) was used for validation, since experimental data exists on a related system. Looking at four independently constructed surfaces, we found that ethylene glycol binds to an indentation on the surface or in a hole beneath the surface. We focused on the indentation binding sites because they are easily accessible and do not have large free energy barriers. The closest system for which experimental data on binding energetics exists is ethylene glycol on PVA in aqueous solutions/gels, and the magnitudes of the free energy of binding to the three best indentation binding sites are close to the experimental value, 0.4-3.7 kcal/mol higher. Our approach offers a way to compute the free energy of binding and characterize the binding sites/conformations, and is general enough to apply to other small molecule/amorphous polymer/solvent systems.     

Surface free energy of ladderlike polyepoxysiloxane–diamine reaction systems

We studied three kinds of ladderlike polyepoxysiloxanes, which have different side groups grafted on the ladderlike backbones. 1,3‐Bis(aminopropyl)tetramethyl disiloxane (diamine) was used as the curing agent. The reaction between ladderlike polyepoxysiloxanes and diamine was investigated by contact angle measurements and surface free energy study. Several factors such as diamine amount, reaction time, and temperature can affect the systems' surface tension (or surface free energy), which were determined by two‐liquid geometric and three‐liquid acid‐base methods. The experimental results showed that an increase in the diamine amount in the reaction systems results in an increase in the polar part of surface free energy because of electron donate characteristics of the diamine. However, because epoxy (electron acceptor) and diamine (electron donor) react fast at elevated temperatures, increasing reaction temperature decreases the polar part of the surface free energy, while increases the nonpolar part of the surface free energy. The evolution of surface free energy with time for various epoxy–diamine reaction systems at various temperatures has also been studied. It was found that it took a relatively long time (50–60 h) to reach the equilibrium state. The experimental results can be well interpreted by the epoxy–diamine reaction mechanism and van Oss–Good's Lewis acid‐base theory. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1449–1460, 2000     

Confinement free energy of surfaces bearing end-grafted polymers in the mushroom regime and local measurement of the polymer density

End-tethered polymer chains usually adopt mushroomlike structures on the surface when their density is low. The behaviors of these surface-attached hemicoils are described by existing polymer theory. Dolan and Edwards derived the free energy of a single polymer chain confined between two planar surfaces. Their theory was used to approximate the steric interaction free energy, E, of two identical surfaces bearing polymers in the mushroom regime and to compare with experimental data obtained from surface force measurements. However, because of a mislabeled plot in the original paper, experimental force profiles did not seem to fit the free energy approximation satisfactorily. We have correctly relabeled the involved plot and derived a new simple expression for E. In order to verify this expression, we have performed experiments on PEG45 polymers incorporated in lipid bilayers using a surface force apparatus. The measured force profiles are in perfect agreement with the prediction. We show that such measurements can be used to determine the local density of grafted polymer with good precision.     

Zeta potential and surface free energy changes of solid-supported phospholipid (DPPC) layers caused by the enzyme phospholipase A2 (PLA2)

Stability and wetting properties changes of systems formed of phospholipid DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine) layers covering silica particles or glass slides due to the phospholipase A₂ (PLA₂) action were determined by zeta potential measurements and the surface free energy evaluation, respectively. The comparison of the zeta potential and surface free energy, which was evaluated from advancing and receding contact angles via applying models of interfacial interactions, i.e. van Oss et al. (LWAB) and contact angle hysteresis (CAH), was found to be helpful for better understanding the mechanism of PLA₂ action on the lipid layers, what is discussed in the paper.     

Comparison of Dorris-Gray and Schultz methods for the calculation of surface dispersive free energy by inverse gas chromatography

Inverse gas chromatography (IGC) is an important technique for the characterization of surface properties of solid materials. A standard method of surface characterization is that the surface dispersive free energy of the solid stationary phase is firstly determined by using a series of linear alkane liquids as molecular probes, and then the acid-base parameters are calculated from the dispersive parameters. However, for the calculation of surface dispersive free energy, generally, two different methods are used, which are Dorris-Gray method and Schultz method. In this paper, the results calculated from Dorris-Gray method and Schultz method are compared through calculating their ratio with their basic equations and parameters. It can be concluded that the dispersive parameters calculated with Dorris-Gray method will always be larger than the data calculated with Schultz method. When the measuring temperature increases, the ratio increases large. Compared with the parameters in solvents handbook, it seems that the traditional surface free energy parameters of n-alkanes listed in the papers using Schultz method are not enough accurate, which can be proved with a published IGC experimental result.     

Topography and surface free energy of DPPC layers deposited on a glass, mica, or PMMA support

An investigation of energetic properties of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) layers deposited on glass, mica, and PMMA (poly(methyl methacrylate)) surfaces was carried out by means of contact angles measurements (advancing and receding) for three probe liquids (diiodomethane, water, and formamide). DPPC was deposited on the surfaces from water (on glass and mica) or methanol (on PMMA) solutions. The topography of the tested surfaces was determined with a help of scanning electron microscopy (SEM) and atomic force microscopy (AFM). Using the measured contact angles, the total apparent surface free energy and its components of the studied layers were determined from van Oss et al.'s (Lifshitz-van der Waals and acid-base components, LWAB) and contact angle hysteresis (CAH) approaches. It allowed us to learn about changes in the surface free energy of the layers (hydrophobicity/hydrophilicity) depending on their number and kind of support. It was found that the changes in the energy greatly depended on the surface properties of the substrate as well as the statistical number of monolayers of DPPC. However, principal changes took place for first three monolayers.     

Surface Tension Calculations for Liquid Metals

Abstract

We present a class of models for the surface of a liquid metal, which may be part of an electrochemical interface. The particles of the system, for the purpose of derivation of thermodynamic properties, are the charged ion cores, while the energy of the electrons is evaluated using the electron density functional formalism, previously principally applied to solids. An expression for the surface energy U^s , defined as the energy required to create unit area of surface by separation of a volume of homogeneous metal into two parts, is derived (Eqs. 18–20). The surface tension γ is obtained by differentiating the Helmholtz free energy with respect to the area of the system, keeping volume and particle number constant (Eqs. 27–37). The surface tension is also equal to the difference between the free energy of the system containing a surface and the free energy of a reference system. It thus defines a surface energy through the Gibbs-Helmholtz equation, and this surface energy is shown to be identical to U^s .

The expressions for U^s and γ are made explicit (Eqs. 45–57) by insertion of particular assumptions for the ion-density profile, the electron-density profile, the interionic interaction and pair distribution function, and the electronic energy. Only information about bulk liquid metal is used. The parameter in the electron-density profile is obtained by minimizing the surface energy. The simplest assumption for the interionic interaction, hard-sphere and Coulombic repulsions, requires a choice for the hard-sphere diameter, which is made such that the pressure of bulk metals is given correctly (52–55). For the alkali metals, the surface tension calculated from this model is about half the experimental value in each case, while calculated surface energies are too high (1/5 too high for Cs, but three times too high for Li). For the electrical potential difference between the inside and the outside of a metal, and for the electrochemical potential, agreement with experiment is good. The main reason for the disagreements in the other properties is traced to the simple form used for the ion pair distribution function.     

Contact angle hysteresis on polymer substrates established with various experimental techniques, its interpretation, and quantitative characterization

The effect of contact angle hysteresis (CAH) was studied on various polymer substrates with traditional and new experimental techniques. The new experimental technique presented in the article is based on the slow deformation of the droplet, thus CAH is studied under the constant volume of the drop in contrast to existing techniques when the volume of the drop is changed under the measurement. The energy of hysteresis was calculated in the framework of the improved Extrand approach. The advancing contact angle established with a new technique is in a good agreement with that measured with the needle-syringe method. The receding angles measured with three experimental techniques demonstrated a very significant discrepancy. The force pinning the triple line responsible for hysteresis was calculated.     

The generalized Born/volume integral implicit solvent model: estimation of the free energy of hydration using London dispersion instead of atomic surface area

A new generalized Born model for estimating the free energy of hydration is presented. The new generalized Born/volume integral (GB/VI) estimates the free energy of hydration as a classical electrostatic energy plus a cavitation energy that is not based upon atomic surface area (SA) used in GB/SA hydration models but on a VI London dispersion energy estimated from quantities already calculated in the classical electrostatic energy. The (relatively few) GB/VI model parameters are fitted to experimental data, and parameterizations for two different atomic partial charge models are presented. Comparison of the calculated and experimental free energies of hydration for 560 small molecules (both neutral and charged) shows good agreement (r(2) = 0.94).     

Development of surface-SFED models for polar solvents

We developed surface grid-based solvation free energy density (Surface-SFED) models for 36 commonly used polar solvents. The parametrization was performed with a large and diverse set of experimental solvation free energies mainly consisting of combinations of polar solvent and multipolar solute. Therefore, the contribution of hydrogen bonds was dominant in the model. In order to increase the accuracy of the model, an elaborate version of a previous hydrogen bond acidity and basicity prediction model was introduced. We present two parametrizations for use with experimentally determined (Surface-SFED/HB(exp)) and empirical (Surface-SFED/HB(cal)) hydrogen bond acidity and basicity values. Our computational results agreed well with experimental results, and inaccuracy of empirical hydrogen bond acidity and basicity values was the main source of error in Surface-SFED/HB(cal). The mean absolute errors of Surface-SFED/HB(exp) and Surface-SFED/HB(cal) were 0.49 and 0.54 kcal/mol, respectively.     

Metadynamics in essential coordinates: free energy simulation of conformational changes

We propose an approach that combines an extraction of collective motions of a molecular system with a sampling of its free energy surface. A recently introduced method of metadynamics allows exploration of the free energy surface of a molecular system by means of coarse-grained dynamics with flooding of free energy minima. This free energy surface is defined as a function of a set of collective variables (e.g., interatomic distances, angles, torsions, and others). In this study, essential coordinates determined by essential dynamics (principle component analysis) were used as collective variables in metadynamics. First, dynamics of the model system (explicitly solvated alanine dipeptide, Ace-Ala-Nme) was simulated by a classical molecular dynamics simulation. The trajectory (1 ns) was then analyzed by essential dynamics to obtain essential coordinates. The free energy surface as a function of the first and second essential coordinates was then explored by metadynamics. The resulting free energy surface is in agreement with other studies of this system. We propose that a combination of these two methods (metadynamics and essential dynamics) has great potential in studies of conformational changes in peptides and proteins.     

自由能微扰法研究系列烷基芳基磺酸盐的胶束化焓-熵补偿现象

为了研究不同结构的表面活性剂分子在水溶液中的胶束化焓-熵补偿现象, 采用自由能微扰(FEP)法计算了系列烷基芳基磺酸盐的溶剂化自由能, 并根据胶团化过程的质量作用模型讨论了相关热力学性质. 结果表明: 自由能微扰法得到的溶剂化自由能大小与用传统热力学表面张力法测定的吉布斯自由能相近, 能够用于比较不同结构的烷基芳基磺酸盐间胶束化能力; 烷基芳基磺酸盐在水溶液中的胶束化过程是自发进行的, 且存在焓-熵补偿现象, 补偿温度范围均在(302±2) K; 随着分子结构中芳环向长烷基链中间位置移动, 胶束化能力和胶束的稳定性均下降; 而随着芳环上短烷基链或长烷基链碳数的增加, 形成胶束的能力与稳定性均提高.     

Melting temperature of Pb nanostructural materials from free energy calculation

The thermodynamic properties of lead, including the entropy, heat capacity, Gibbs free energy, and surface free energy have been studied. Based on bulk thermodynamic properties of lead, Gibbs free energy for nanostructural materials is obtained and used to calculate the size-dependent melting point depression for lead nanostructural materials. The studies indicate that the surface free energy difference between solid phase and liquid phase is a decisive factor for the size-dependent melting of nanostructural materials. The calculated results are in agreement with recent experimental values and the available molecular dynamics simulation data.     

An efficient method for computing excess free energy of liquid

We present a new theoretical method for efficient calculation of free energy of liquid. This interaction entropy method allows one to compute entropy and free energy of liquid from standard single step MD (molecular dynamics) simulation directly in liquid state without the need to perform MD simulations at many intermediate states as required in thermodynamic integration or free energy perturbation methods. In this new approach, one only needs to evaluate the interaction energy of a single (fixed) liquid molecule with the rest of liquid molecules as a function of time from a standard MD simulation of liquid and the fluctuation of distribution of this interaction energy is then used to calculate the interaction entropy of the liquid. Explicit theoretical derivation of this interaction entropy approach is provided and numerical calculations for the benchmark liquid water system were carried out using three different water models. Numerical analysis of the result was performed and comparison of the computational result with experimental data and other theoretical results were provided. Excellent agreement of calculated free energies with the experimental data using TIP4P model is obtained for liquid water.     

Microtextured superhydrophobic surfaces: a thermodynamic analysis

Superhydrophobic surfaces with a contact angle (CA) larger than 150 degrees have recently attracted great interest in both academic research and practical applications due to their water-repellent or self-cleaning properties. However, thermodynamic mechanisms responsible for the effects of various factors such as surface geometry and chemistry, liquids, and environmental sources have not been well understood. In this study, a pillar microtexture, which has been intensively investigated in experiments, is chosen as a typical example and thermodynamically analyzed in detail. To gain a comprehensive insight into superhydrophobic behavior, the roles of pillar height, width and spacing (or roughness and solid fraction), intrinsic CA, drop size, and vibrational energy are systematically investigated. Free energy (FE) and free energy barrier (FEB) are calculated using a simple and robust model. Based on the calculations of FE and FEB, various CAs, including apparent, equilibrium (stable), advancing and receding CAs, and contact angle hysteresis (CAH) can be determined. Especially, the design of practical superhydrophobic surfaces is emphasized in connection with the transition between noncomposite and composite states; a criterion for judging such transition is proposed. The theoretical results are consistent with the Wenzel's and the Cassie's equations for equilibrium CA values and experimental observations. Furthermore, based on these results and the proposed criterion, some general principles to achieve superhydrophobic performance are suggested.     

Covalently Attached Liquids: Instant Omniphobic Surfaces with Unprecedented Repellency

Recent strategies to prepare “omniphobic” surfaces have demonstrated that minimizing contact angle hysteresis (CAH) is the key criterion for effectiveness. CAH is affected by chemistry and topography defects at the molecular and higher levels, thus most surfaces exhibit significant CAH. Preparative methods for stable coatings on smooth substrates with negligible CAH (<2°) for a broad range of liquids have not been reported. In this work, we describe a simple and rapid procedure to prepare omniphobic surfaces that are stable under pressure and durable at elevated temperatures. Consistent with theory, they exhibit sliding angles that decrease with liquid surface tension. Slippery omniphobic covalently attached liquid (SOCAL) surfaces are obtained through acid‐catalyzed graft polycondensation of dimethyldimethoxysilane. The smooth, stable, and temperature‐resistant coatings show extremely low CAH (≤1°) and low sliding angles for liquids that span surface tensions from 78.2 to 18.4 mN m^?1.     

Free energy of solvation from molecular dynamics simulation applying Voronoi-Delaunay triangulation to the cavity creation

The free energy of solvation for a large number of representative solutes in various solvents has been calculated from the polarizable continuum model coupled to molecular dynamics computer simulation. A new algorithm based on the Voronoi-Delaunay triangulation of atom-atom contact points between the solute and the solvent molecules is presented for the estimation of the solvent-accessible surface surrounding the solute. The volume of the inscribed cavity is used to rescale the cavitational contribution to the solvation free energy for each atom of the solute atom within scaled particle theory. The computation of the electrostatic free energy of solvation is performed using the Voronoi-Delaunay surface around the solute as the boundary for the polarizable continuum model. Additional short-range contributions to the solvation free energy are included directly from the solute-solvent force field for the van der Waals-type interactions. Calculated solvation free energies for neutral molecules dissolved in benzene, water, CCl4, and octanol are compared with experimental data. We found an excellent correlation between the experimental and computed free energies of solvation for all the solvents. In addition, the employed algorithm for the cavity creation by Voronoi-Delaunay triangulation is compared with the GEPOL algorithm and is shown to predict more accurate free energies of solvation, especially in solvents composed by molecules with nonspherical molecular shapes.