Thermodynamic cycle integration by computer simulation as a tool for obtaining free energy differences in molecular chemistry

Summary A new and promising development in the field of computer simulation of molecular systems is the socalled thermodynamic cycle integration technique, which combines well-known results from statistical thermodynamics with powerful computer simulation methods. The basic formulas, the development and the applications in the areas of drug design, protein engineering and conformational analysis of this elegant technique are discussed.     

Calculating zeros: Non-equilibrium free energy calculations

Free energy calculations on three model processes with theoretically known free energy changes have been performed using short simulation times. A comparison between equilibrium (thermodynamic integration) and non-equilibrium (fast growth) methods has been made in order to assess the accuracy and precision of these methods. The three processes have been chosen to represent processes often observed in biomolecular free energy calculations. They involve a redistribution of charges, the creation and annihilation of neutral particles and conformational changes. At very short overall simulation times, the thermodynamic integration approach using discrete steps is most accurate. More importantly, reasonable accuracy can be obtained using this method which seems independent of the overall simulation time. In cases where slow conformational changes play a role, fast growth simulations might have an advantage over discrete thermodynamic integration where sufficient sampling needs to be obtained at every λ-point, but only if the initial conformations do properly represent an equilibrium ensemble. From these three test cases practical lessons can be learned that will be applicable to biomolecular free energy calculations.     

Molecular Dynamics Simulation of Aqueous Solutions Using Interaction Energy Components: Application to the Solvation Gibbs Energy

Molecular dynamics simulations of aqueous solutions of the solutes acetamide (AcNH₂), acetic acid (AcOH), and acetaldehyde (AcH) were made using Lennard–Jones 12-6-1 potentials to describe the solute–solvent interactions. The Morokuma decomposition scheme and the ESIE solute atomic charges were used to reproduce the exchange, polarization, and electrostatic components of the solute–water interaction energy. A nonlinear perturbation was incorporated into the “slow-growth” technique in order to improve the results for the solvation Gibbs energy that were found to be in agreement with the available experimental and theoretical values.     

Evaluation of the contribution to hydration of nonelectrolytes from the hydrophobic effect

A new method was suggested for estimating the hydrophobic effect of contributions to the Gibbs energies and enthalpies of hydration of hydrocarbons, inorganic gases and rare gases. In accordance with this method the hydrophobic effect contribution to the Gibbs energy was evaluated from the difference between the hydration Gibbs energy of a solute and the non hydrophobic contribution. To estimate the latter value, the known dependence connecting the Gibbs energies of solvation of a solute in a number of aprotic solvents to the Hildebrand solubility parameter for these solvents was used. The non hydrophobic contribution to the Gibbs energy of hydration was calculated for various solutes from such dependences extended to water as solvent. The Hildebrand solubility parameter for water used in the calculation was corrected for the effect of association through hydrogen bonding. This correction was made by subtraction of the water self-association enthalpy from the enthalpy of vaporization of water. The evaluated Gibbs energies of the hydrophobic effect are positive for saturated hydrocarbons, inorganic gases and rare gases and linearly depend on the solute molecular refraction. The hydrophobic contribution to the hydration enthalpies of the solutes was calculated in the same manner as was made to calculate the hydrophobic contribution to Gibbs energies of hydration. Enthalpies of the hydrophobic effect for the solutes under study are negative.     

Relationship between molecular connectivity indices of barbiturates and chromatographic parameters

Summary 166 data sets of different chromatographic parameters for barbiturates taken from the literature were correlated with the first order valence connectivity indices. The most significant correlations were found for HPLC. The correlations depend on the structure of the substituents and the substitution mode of the barbituric acid ring.Preliminary results of this work have been published at the Annual Meeting of the Polish Chemical Society, in Krakow, September 17–20, 1980.     

A model for the Gibbs energy of aqueous solutions of polyelectrolytes

A new model for the excess Gibbs energy of aqueous solutions of polyelectrolytes is presented and applied for the correlation of the activity of water in aqueous solutions of polyelectrolytes without as well as with an added (single) salt. The model considers the phenomenon of counterion condensation, i.e., the partial dissociation of highly charged polyelectrolytes in water. Three parameters (a binary interaction parameter between polymer segments, the equilibrium constant of the dissociation reaction and a parameter which accounts for the polymer configuration) were fitted to the experimental results. The model allows for a reliable correlation of experimental results for the osmotic coefficient of aqueous solutions of a single polyelectrolyte (without as well as with an added salt).     

AM1-SM2 and PM3-SM3 parameterized SCF solvation models for free energies in aqueous solution

Summary Two new continuum solvation models have been presented recently, and in this paper they are explained and reviewed in detail with further examples. Solvation Model 2 (AM1-SM2) is based on the Austin Model 1 and Solvation Model 3 (PM3-SM3) on the Parameterized Model 3 semiempirical Hamiltonian. In addition to the incorporation of phosphorus parameters, both of these new models address specific deficiencies in the original Solvation Model 1 (AM1-SM1), viz., (1) more accurate account is taken of the hydrophobic effect of hydrocarbons, (2) assignment of heavy-atom surface tensions is based on the presence or absence of bonded hydrogen atoms, and (3) the treatment of specific hydration-shell water molecules is more consistent. The new models offer considerably improved performance compared to AM1-SM1 for neutral molecules and essentially equivalent performance for ions. The solute charges within the Parameterized Model 3 Hamiltonian limit the utility of PM3-SM3 for compounds containing nitrogen and possibly phosphorus. For other systems both AM1-SM2 and PM3-SM3 give realistic results, but AM1-SM2 in general outperforms PM3-SM3. Key features of the models are discussed with respect to alternative approaches.     

A Gibbs free energy correlation for automated docking of carbohydrates

Thermodynamic information can be inferred from static atomic configurations. To model the thermodynamics of carbohydrate binding to proteins accurately, a large binding data set has been assembled from the literature. The data set contains information from 262 unique protein-carbohydrate crystal structures for which experimental binding information is known. Hydrogen atoms were added to the structures and training conformations were generated with the automated docking program AutoDock 3.06, resulting in a training set of 225,920 all-atom conformations. In all, 288 formulations of the AutoDock 3.0 free energy model were trained against the data set, testing each of four alternate methods of computing the van der Waals, solvation, and hydrogen-bonding energetic components. The van der Waals parameters from AutoDock 1 produced the lowest errors, and an entropic model derived from statistical mechanics produced the only models with five physically and statistically significant coefficients. Eight models predict the Gibbs free energy of binding with an error of less than 40% of the error of any similar models previously published.     

Thermodynamic stability and hydration enthalpy of strontium cerate doped with yttrium

The standard molar enthalpy of formation of SrY_0.05Ce_0.95O_2.975 has been derived by combining the enthalpy of solution in 1 M HCl + 0.1 KI with auxiliary literature data, Δ_fH° (SrY_0.05Ce_0.95O_2.975, s, 298.15 K) = −1720.4 ± 3.4 kJ/mol. The formation enthalpy of SrY_0.05Ce_0.95O_2.975 from the mixture of binary oxides is Δ_oxH° (298.15 K) = −45.9 ± 3.4 kJ/mol and the enthalpy of reaction of SrY_0.05Ce_0.95O_2.975 with water forming Sr(OH)₂, CeO₂, and Y₂O₃ is Δ_rH° (298.15 K) = −85.5 ± 3.4 kJ/mol. Our data and the entropies of different substances show that SrY_0.05Ce_0.95O_2.975 is thermodynamically stable with respect to a mixture of SrO, Y₂O₃, CeO₂ and that the reaction of SrY_0.05Ce_0.95O_2.975 with water is thermodynamically favourable.     

Relationship between heat of immersion and surface Gibbs energy of fluorite and cassiterite

Calorimetric measurements were made of the heat of immersion in water of cassiterite that was either untreated or treated with 60% HNO₃. The heats of immersion of cassiterite and fluorite were also calculated theoretically from the surface Gibbs energy components, and compared with the heat of immersion measured for cassiterite and that taken from the literature for fluorite. The results of the measurements and calculation revealed that the heat of immersion depends on the degree of hydration of the surface of cassiterite and fluorite. It was also found that it is possible to predict the heats of immersion in water of cassiterite and fluorite from the Lifshitz-van der Waals and acid-base components of the surface Gibbs energy.     

Gibbs free energy of formation of calcium rhodite

The Gibbs free energy of formation of CaRh₂O₄(s) has been determined using two techniques viz., quadrupole mass spectrometer coupled to a Knudsen cell and solid-state cell incorporating CaF₂(s) as the solid electrolyte. In the former method, equilibrium O₂(g) pressures were measured over the phase field Rh(s)+Rh₂O₃(s), in the temperature range 793.7-909.1 K and over the three phase mixture CaRh₂O₄(s)+Rh(s)+CaO(s) was measured from 862.1 to 1022.7 K.The Gibbs free energy of formation of Rh₂O₃(s) from elements in their standard state can be given by

     

Excess Gibbs free energy and kinetics of grain growth of nanostructured silver

Samples of nanostructured silver were prepared by a mechanochemical technique and by electrodeposition. In the former, the microstructure was stabilized by intergranular cosegregation of Mg and O atoms. The excess Gibbs free energy of these samples was investigated by e.m.f. measurements at 453 K in a solid state electrochemical cell with AgI as a solid electrolyte. Electrodeposited pure silver samples had a labile microstructure even at 298 K. Their structural relaxation process was monitored in situ by chronopotentiometric measurements in an aqueous iodoargentate electrolyte. The time dependence of the e.m.f. could be quantitatively described by a parabolic law of grain growth without any adjustable parameter. Received: 13 January 2000 / Accepted: 8 February 2000     

An extension of the Pitzer equation for the excess Gibbs energy of aqueous electrolyte systems to aqueous polyelectrolyte solutions

Pitzer's equation for the excess Gibbs energy of aqueous solutions of low-molecular electrolytes is extended to aqueous solutions of polyelectrolytes. The model retains the original form of Pitzer's model (combining a long-range term, based on the Debye–Hückel equation, with a short-range term similar to the virial equation where the second osmotic virial coefficient depends on the ionic strength). The extension consists of two parts: at first, it is assumed that a constant fraction of the monomer units of the polyelectrolyte is dissociated, i.e., that fraction does not depend on the concentration of the polyelectrolyte, and at second, a modified expression for the ionic strength (wherein each charged monomer group is taken into account individually) is introduced. This modification is to account for the presence of charged polyelectrolyte chains, which cannot be regarded as punctual charges. The resulting equation was used to correlate osmotic coefficient data of aqueous solutions of a single polyelectrolyte as well as of binary mixtures of a single polyelectrolyte and a salt with low-molecular weight. It was additionally applied to correlate liquid–liquid equilibrium data of some aqueous two-phase systems that might form when a polyelectrolyte and another hydrophilic but neutral polymer are simultaneously dissolved in water. A good agreement between the experimental data and the correlation result is observed for all investigated systems.     

KBPh4由水到系列水-醇混合溶剂的迁移自由能

由于四苯硼盐在分析化学、生物学、电化学等各领域中的广泛用途及其大阴离子在研究与计算单个离子迁移热力学函数中所具有的特殊作用,人们对四苯硼盐的溶液热力学性质进行了广泛研究,特别是对四苯硼钠和可作为参考电解质的四苯硼盐进行了深入细致的研究 [1, 2],得到了一些重要的的结论,为溶液理论的研究提供了有力的实验基础 .但是文献中对难溶碱金属四苯硼盐由单一到不同混合溶剂中的迁移热力学性质的系统研究较少 .在前文 [3]对 KBPh4由水到水-异丙醇和由甲醇到甲醇-异丙醇混合溶剂的迁移自由能进行研究的基础上,我们系统地对 KB…     

气流床粉煤气化的Gibbs自由能最小化模拟

用Gibbs自由能最小化方法对粉煤气化过程进行了热力学平衡分析。对一混合煤种,在3.0 MPa和气化温度限制在1 200 ℃～1 450 ℃时,研究了氧-煤比、蒸气-煤比对气化炉出口气体组成、温度和有效气产率的影响,并由此确定了可行的操作域是氧-煤比545m3/t～605 m3/t、蒸气-煤比为152.64 kg/t～313.92 kg/t及其对应的工艺指标。从操作域中选择有代表性的工艺条件为氧-煤比578 m3/t、蒸气-煤比为187 kg/t,对应的气化炉出口温度1 358 ℃,CO+H2干基体积分数为91.5%,有效气产率为2.123(CO+H2)m3/kg。同时,研究了碳转化率和热损失对气化工艺指标的影响,其影响是显著的。     

Molecular dynamics simulation of the renin inhibitor H142 in water

Summary H142 is a synthetic decapeptide designed to inhibit renin, an enzyme acting in the regulation of blood pressure. The inhibiting effect of H142 is caused by a reduction of a-Leu-Val-peptide bond (i. e. C(=O)-NHCH₂-NH). The conformational and dynamical properties of H142 and its unreduced counterpart (H142n) was modelled by means of molecular dynamics simulations. Water was either included explicitly in the simulations or as a dielectric continuum. When water molecules surround the peptides, they remain in a more or less extended conformation through the simulation. If water is replaced by a dielectric continuum, the peptides undergo a conformational change from an extended to a folded state. It is not clear whether this difference is a consequence of a too short simulation time for the water simulations, a force-field artifact promoting extended conformations, or if the extended conformation represents the true conformational state of the peptide. A number of dynamic properties were evaluated as well, such as overall rotation, translational diffusion, side-chain dynamics and hydrogen bonding.     

An approximate but efficient method to calculate free energy trends by computer simulation: Application to dihydrofolate reductase-inhibitor complexes

Summary Derivatives of free energy differences have been calculated by molecular dynamics techniques. The systems under study were ternary complexes of Trimethoprim (TMP) with dihydrofolate reductases of E. coli and chicken liver, containing the cofactor NADPH. Derivatives are taken with respect to modification of TMP, with emphasis on altering the 3-, 4- and 5-substituents of the phenyl ring. A linear approximation allows the encompassing of a whole set of modifications in a single simulation, as opposed to a full perturbation calculation, which requires a separate simulation for each modification. In the case considered here, the proposed technique requires a factor of 1000 less computing effort than a full free energy perturbation calculation. For the linear approximation to yield a significant result, one has to find ways of choosing the perturbation evolution, such that the initial trend mirrors the full calculation. The generation of new atoms requires a careful treatment of the singular terms in the non-bonded interaction. The result can be represented by maps of the changed molecule, which indicate whether complex formation is favoured under movement of partial charges and change in atom polarizabilities. Comparison with experimental measurements of inhibition constants reveals fair agreement in the range of values covered. However, detailed comparison fails to show a significant correlation. Possible reasons for the most pronounced deviations are given.