SAMPL6 host–guest blind predictions using a non equilibrium alchemical approach

In this paper, we compute, by means of a non equilibrium alchemical technique, called fast switching double annihilation methods (FSDAM), the absolute standard dissociation free energies of the the octa acids host–guest systems in the SAMPL6 challenge initiative. FSDAM is based on the production of canonical configurations of the bound and unbound states via enhanced sampling and on the subsequent generation of hundreds of fast non-equilibrium ligand annihilation trajectories. The annihilation free energies of the ligand when bound to the receptor and in bulk solvent are obtained from the collection of work values using an estimate based on the Crooks theorem for driven non equilibrium processes. The FSDAM blind prediction, relying on the normality assumption for the annihilation work distributions, ranked fairly well among the submitted blind predictions that were not adjusted with a linear corrections obtained from retrospective data on similar host guest systems. Improved results for FSDAM can be obtained by post-processing the work data assuming mixtures of normal components.     

Estimation of adsorption parameters from temperature-programmed-desorption thermograms: application to the adsorption of carbon dioxide onto Na- and H-mordenite

In this work, a model is proposed for the estimation of the adsorption parameters from TPD thermograms when the adsorption cell can be modeled as a well-mixed reactor, evaluating the adsorption and desorption rate constants from statistical thermodynamics. The estimation procedure consists of fitting the model to the experimental TPD thermograms using numerical methods. The study of the effect of readsorption in this system reveals that this effect must be taken into account in most cases. Only with high activation energies of adsorption may this effect be negligible. The model is used to estimate the adsorption parameters of the systems CO(2)-Na-mordenite and CO(2)-H-mordenite, including an analysis about the degrees of freedom of the adsorbed phase. The estimated values of the adsorption enthalpy have been compared with the ones obtained from adsorption equilibrium data.     

"Exact" surface free energies of iron surfaces using a modified embedded atom method potential and lambda integration

Previously a new universal lambda-integration path and associated methodology was developed for the calculation of "exact" surface and interfacial free energies of solids. Such a method is in principle applicable to any intermolecular potential function, including those based on ab initio methods, but in previous work the method was only tested using a relatively simple embedded atom method iron potential. In this present work we apply the new methodology to the more sophisticated and more accurate modified embedded atom method (MEAM) iron potential, where application of other free- energy methods would be extremely difficult due to the complex many-body nature of the potential. We demonstrate that the new technique simplifies the process of obtaining "exact" surface free energies by calculating the complete set of these properties for the low index surface faces of bcc and fcc solid iron structures. By combining these data with further calculations of liquid surface tensions we obtain the first complete set of exact surface free energies for the solid and liquid phases of a realistic MEAM model system. We compare these predictions to various experimental and theoretical results.     

A general method of calculating phase equilibria in a multicomponent system by means of a hill-climbing minimization procedure

A generalization of the method of calculating the state of equilibrium of a multicomponent system, using a hill-climbing minimization procedure, is proposed. Moreover, an original method of calculating values for partial free energies from the state of equilibrium has been made an essential part of the general schedule.     

Calcul des stabilites relatives d'hydrocarbures derives du bicyclo[2.2.1]heptane. Mise en evidence,de torsions induites par les substituants et d'inte

The ΔG° standard free enthalpy différences between isomeric bicyclo-heptane hydrocarbons derivatives have been calculated via molecular mechanics calculation of the equilibrium geometry of each isomer, calculation of energies using PCILO method, and estimation of entropy values. The calculated ΔG° values are in good agreement with experimental values measured for mono and dimethyl bicyclo[2.2.1]heptane at equilibrium.     

Determining equilibrium constants for dimerization reactions from molecular dynamics simulations

With today's available computer power, free energy calculations from equilibrium molecular dynamics simulations "via counting" become feasible for an increasing number of reactions. An example is the dimerization reaction of transmembrane alpha-helices. If an extended simulation of the two helices covers sufficiently many dimerization and dissociation events, their binding free energy is readily derived from the fraction of time during which the two helices are observed in dimeric form. Exactly how the correct value for the free energy is to be calculated, however, is unclear, and indeed several different and contradictory approaches have been used. In particular, results obtained via Boltzmann statistics differ from those determined via the law of mass action. Here, we develop a theory that resolves this discrepancy. We show that for simulation systems containing two molecules, the dimerization free energy is given by a formula of the form ΔG ∝ ln(P(1) /P(0) ). Our theory is also applicable to high concentrations that typically have to be used in molecular dynamics simulations to keep the simulation system small, where the textbook dilute approximations fail. It also covers simulations with an arbitrary number of monomers and dimers and provides rigorous error estimates. Comparison with test simulations of a simple Lennard Jones system with various particle numbers as well as with reference free energy values obtained from radial distribution functions show full agreement for both binding free energies and dimerization statistics.     

The fixed rotor approximation in the vibronic semi-classical treatment of atom—molecule collisions

Calculations for non-adiabatic atom—molecule collisions at low energies frequently make use of a sudden approximation vis-à-vis the molecule rotation. The present work investigates the effect on vibronic excitation and charge-transfer processes of freeing the rotation of the molecule during the collision. This is achieved in a semi-classical framework. The H⁺+O₂ collisional system is selected for this study in view of the strong anisotropy of the relevant interactions and on account of the availability of fixed rotor data for this system. Results obtained in the 1 eV/amu energy range and higher generally confirm the validity of the fixed rotor approximation. For this energy range sizeable deviations of free rotor from fixed rotor results appear in exceptional cases for impact parameters of the order of the molecule's bond distance. At lower energies (⩽0.2 eV/amu) the fixed rotor approximation becomes questionable.     

Comparison of free energy methods for molecular systems

We present a detailed comparison of computational efficiency and precision for several free energy difference (DeltaF) methods. The analysis includes both equilibrium and nonequilibrium approaches, and distinguishes between unidirectional and bidirectional methodologies. We are primarily interested in comparing two recently proposed approaches, adaptive integration, and single-ensemble path sampling to more established methodologies. As test cases, we study relative solvation free energies of large changes to the size or charge of a Lennard-Jones particle in explicit water. The results show that, for the systems used in this study, both adaptive integration and path sampling offer unique advantages over the more traditional approaches. Specifically, adaptive integration is found to provide very precise long-simulation DeltaF estimates as compared to other methods used in this report, while also offering rapid estimation of DeltaF. The results demonstrate that the adaptive integration approach is the best overall method for the systems studied here. The single-ensemble path sampling approach is found to be superior to ordinary Jarzynski averaging for the unidirectional, "fast-growth" nonequilibrium case. Closer examination of the path sampling approach on a two-dimensional system suggests it may be the overall method of choice when conformational sampling barriers are high. However, it appears that the free energy landscapes for the systems used in this study have rather modest configurational sampling barriers.     

Free energy for protein folding from nonequilibrium simulations using the Jarzynski equality

The equilibrium free energy difference between two long-lived molecular species or "conformational states" of a protein (or any other molecule) can in principle be estimated by measuring the work needed to shuttle the system between them, independent of the irreversibility of the process. This is the meaning of the Jarzynski equality (JE), which we test in this paper by performing simulations that unfold a protein by pulling two atoms apart. Pulling is performed fast relative to the relaxation time of the molecule and is thus far from equilibrium. Choosing a simple protein model for which we can independently compute its equilibrium properties, we show that the free energy can be exactly and effectively estimated from nonequilibrium simulations. To do so, one must carefully and correctly determine the ensemble of states that are pulled, which is more important the farther from equilibrium one performs simulations; this highlights a potential problem in using the JE to extract the free energy from forced unfolding experiments. The results presented here also demonstrate that the free energy difference between the native and denatured states of a protein measured in solution is not always equal to the free energy profile that can be estimated from forced unfolding simulations (or experiments) using the JE.     

Comparison of efficiency and bias of free energies computed by exponential averaging, the Bennett acceptance ratio, and thermodynamic integration

Recent work has demonstrated the Bennett acceptance ratio method is the best asymptotically unbiased method for determining the equilibrium free energy between two end states given work distributions collected from either equilibrium and nonequilibrium data. However, it is still not clear what the practical advantage of this acceptance ratio method is over other common methods in atomistic simulations. In this study, we first review theoretical estimates of the bias and variance of exponential averaging (EXP), thermodynamic integration (TI), and the Bennett acceptance ratio (BAR). In the process, we present a new simple scheme for computing the variance and bias of many estimators, and demonstrate the connections between BAR and the weighted histogram analysis method. Next, a series of analytically solvable toy problems is examined to shed more light on the relative performance in terms of the bias and efficiency of these three methods. Interestingly, it is impossible to conclusively identify a "best" method for calculating the free energy, as each of the three methods performs more efficiently than the others in at least one situation examined in these toy problems. Finally, sample problems of the insertion/deletion of both a Lennard-Jones particle and a much larger molecule in TIP3P water are examined by these three methods. In all tests of atomistic systems, free energies obtained with BAR have significantly lower bias and smaller variance than when using EXP or TI, especially when the overlap in phase space between end states is small. For example, BAR can extract as much information from multiple fast, far-from-equilibrium simulations as from fewer simulations near equilibrium, which EXP cannot. Although TI and sometimes even EXP can be somewhat more efficient in idealized toy problems, in the realistic atomistic situations tested in this paper, BAR is significantly more efficient than all other methods.     

The Confine-and-Release Method: Obtaining Correct Binding Free Energies in the Presence of Protein Conformational Change

Free energy calculations are increasingly being used to estimate absolute and relative binding free energies of ligands to proteins. However, computed free energies often appear to depend on the initial protein conformation, indicating incomplete sampling. This is especially true when proteins can change conformation on ligand binding, as free energies associated with these conformational changes are either ignored or assumed to be included by virtue of the sampling performed in the calculation. Here, we show that, in a model protein system (a designed binding site in T4 Lysozyme), conformational changes can make a difference of several kcal/mol in computed binding free energies, and that they are neglected in computed binding free energies if the system remains kinetically trapped in a particular metastable state on simulation timescales. We introduce a general "confine-and-release" framework for free energy calculations that accounts for these free energies of conformational change. We illustrate its use in this model system by demonstrating that an umbrella sampling protocol can obtain converged binding free energies that are independent of the starting protein structure and include these conformational change free energies.     

Level-Set Variational Implicit-Solvent Modeling of Biomolecules with the Coulomb-Field Approximation

Central in the variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett.2006, 96, 087802 and J. Chem. Phys.2006, 124, 084905] of molecular solvation is a mean-field free-energy functional of all possible solute-solvent interfaces or dielectric boundaries. Such a functional can be minimized numerically by a level-set method to determine stable equilibrium conformations and solvation free energies. Applications to nonpolar systems have shown that the level-set VISM is efficient and leads to qualitatively and often quantitatively correct results. In particular, it is capable of capturing capillary evaporation in hydrophobic confinement and corresponding multiple equilibrium states as found in molecular dynamics (MD) simulations. In this work, we introduce into the VISM the Coulomb-field approximation of the electrostatic free energy. Such an approximation is a volume integral over an arbitrary shaped solvent region, requiring no solutions to any partial differential equations. With this approximation, we obtain the effective boundary force and use it as the "normal velocity" in the level-set relaxation. We test the new approach by calculating solvation free energies and potentials of mean force for small and large molecules, including the two-domain protein BphC. Our results reveal the importance of coupling polar and nonpolar interactions in the underlying molecular systems. In particular, dehydration near the domain interface of BphC subunits is found to be highly sensitive to local electrostatic potentials as seen in previous MD simulations. This is a first step toward capturing the complex protein dehydration process by an implicit-solvent approach.     

The equilibrium shapes of crystals and of cavities in crystals

Surface free energies are assumed to be the sum of the excess free energies of bonding of molecules in or near the surface, and the stable form of a crystal or cavity is assumed to be the form that makes the sum of these excess free energies a minimum. When only plane surfaces are allowed, this model predicts the same shapes for crystals as an equation of Wulff (2. Kristallogr. 34, 449 (1901)), which is based on the macroscopic thermodynamic relation of Gibbs (“The Collected Works, Vol. 1.: Thermodynamics,” Longmans, Green, New York (1931)). The model predicts rounding of edges and corners of kinds which are not allowed by the Wulff relation and predicts that spherical forms of particles and cavities can be stable despite anisotropic surface free energies. The model provides a useful framework for analysis of whether unstable crystal or cavity shapes will evolve into stable or metastable forms. Some crystals and cavities that have been assumed to have equilibrium shapes instead have metastable shapes.     

Hydrolytic polymerization of caprolactam. II. Vapor–liquid equilibria

The system water–caprolactam–polymer at equilibrium is regarded as a solution consisting of two solvents (water and caprolactam) and one solute (polymer). The activities of water and caprolactam in equilibrium at 270°C in the range of 2–10 wt-% total water content have been determined by vapor-pressure measurements. Water shows large negative deviations from Raoult's law, as a consequence of the different size of water and polymer molecules. The partial molar free energies of mixing are compared with the expressions derived from the Flory-Huggins theory of polymer solutions; the results are not conclusive, but seem to indicate a qualitative agreement with the theory. The increase in vapor pressure during polymerization in sealed systems and the water dependence of the polycondensation equilibrium are discussed and explained in terms of water activity changes.     

支化高分子溶胶-凝胶相变的热力学

以典型的Aa-Bb型缩聚反应为例, 应用统计力学和热力学的基本原理对反应体系的一些平衡特征进行研究. 基于从两种不同角度所构造的正则配分函数, 导出反应体系的平衡自由能以及质量作用定律的解析形式, 同时指出获得数量分布函数的新方法, 并通过计算反应体系的等温压缩系数从而得到反应体系的凝胶化条件. 进一步利用数量分布函数的不变性, 给出临界点后溶胶相和凝胶相的平衡自由能, 探讨了溶胶-凝胶相变的相关问题.     

Operations and Thermodynamics of an Artificial Rotary Molecular Motor in Solution

A general framework is provided that makes possible the estimation of time‐dependent properties of a stochastic system moving far from equilibrium. The process is investigated and discussed in general terms of nonequilibrium thermodynamics. The approach is simple and can be exploited to gain insight into the dynamics of any molecular‐level machine. As a case study, the dynamics of an artificial molecular rotary motor, similar to the inversion of a helix, which drives the motor from a metastable state to equilibrium, are examined. The energy path that the motor walks was obtained from the results of atomistic calculations. The motor undergoes unidirectional rotation and its entropy, internal energy, free energy, and net exerted force are given as a function of time, starting from the solution of Smoluchowski’s equation. The rather low value of the organization index, that is, the ratio of the work done by the particle against friction during the unidirectional motion per available free energy, reveals that the motion is mainly subject to randomness, and the amount of energy converted to heat due to the directional motion is very small.     

乙烯-丙烯气相共聚动力学研究

应用自行设计的烯烃气相聚合半连续反应装置 ,对乙烯 丙烯气相共聚动力学进行了研究 .并结合传质研究结果 ,求得了乙 丙共聚反应速率常数、竞聚率及其与温度的关系     

NMR spectroscopic study of rotation around CC and C?N bonds in diene δ-aminocarbonyl compounds

A relatively fast rotation around the α,β carbon–carbon double bond at the equilibrium of geometrical isomers and a comparatively slow rotation around the carbon-nitrogen single bond in compounds of the type (X₁, X₂ are electron-attracting substituents) were detected and investigated by the NMR technique. The relationships between the free energies of activation for these rotational processes and the character of the substituents, the number of double bonds, solvents and concentration were studied.     

Estimation of relative binding free energy based on a free energy variational principle for the FKBP-ligand system

Predicting an accurate binding free energy between a target protein and a ligand can be one of the most important steps in a drug discovery process. Often, many molecules must be screened to find probable high potency ones. Thus, a computational technique with low cost is highly desirable for the estimation of binding free energies of many molecules. Several techniques have thus far been developed for estimating binding free energies. Some techniques provide accurate predictions of binding free energies but high large computational cost. Other methods give good predictions but require tuning of some parameters to predict them with high accuracy. In this study, we propose a method to predict relative binding free energies with accuracy comparable to the results of prior methods but with lower computational cost and with no parameter needing to be carefully tuned. Our technique is based on the free energy variational principle. FK506 binding protein (FKBP) with 18 ligands is taken as a test system. Our results are compared to those from other widely used techniques. Our method provides a correlation coefficient (r ² ) of 0.80 between experimental and calculated relative binding free energies and yields an average absolute error of 0.70 kcal/mol compared to experimental values. These results are comparable to or better than results from other techniques. We also discuss the possibility to improve our method further.