Experimental Free Energies Research Articles

A simplification of gas clathrate hydrate thermochemistry using the Thermodynamic Difference Rule (TDR). Part 3. Heat capacity prediction as compared with experimental C values – Towards further validation of the TDR approach

Abstract To date the Thermodynamic Difference Rule (TDR) has proved itself to be highly satisfactory as a means of establishing unknown thermodynamic data. In Parts 1 (Jenkins, 2017) and 2 (Jenkins, 2017) we demonstrated the successful prediction of ΔfHo data for gas clathrate hydrates using TDR. In the absence of any experimental standard Gibbs free energy, ΔfGo or standard entropy, S298o data suggestions were made (based on experience with conventional inorganic hydrates) of likely forms of TDR equations which might predict these missing thermodynamic values. In the present paper, in view of the availability of a few experimental heat capacity values, we test the applicability of a similar suggested form of TDR for Cp prediction against the experimental values. Despite the fact that an absolute comparison cannot actually be achieved, closeness of predicted and (extrapolated) experimental values compare well. The result suggests that our previous TDR equations for the prediction of ΔfGo and S298o are likely to be highly reliable.

The Origin of Chalcogen-Bonding Interactions.

Favorable molecular interactions between group 16 elements have been implicated in catalysis, biological processes, and materials and medicinal chemistry. Such interactions have since become known as chalcogen bonds by analogy to hydrogen and halogen bonds. Although the prevalence and applications of chalcogen-bonding interactions continues to develop, debate still surrounds the energetic significance and physicochemical origins of this class of σ-hole interaction. Here, synthetic molecular balances were used to perform a quantitative experimental investigation of chalcogen-bonding interactions. Over 160 experimental conformational free energies were measured in 13 different solvents to examine the energetics of O···S, O···Se, S···S, O···HC, and S···HC contacts and the associated substituent and solvent effects. The strongest chalcogen-bonding interactions were found to be at least as strong as conventional H-bonds, but unlike H-bonds, surprisingly independent of the solvent. The independence of the conformational free energies on solvent polarity, polarizability, and H-bonding characteristics showed that electrostatic, solvophobic, and van der Waals dispersion forces did not account for the observed experimental trends. Instead, a quantitative relationship between the experimental conformational free energies and computed molecular orbital energies was consistent with the chalcogen-bonding interactions being dominated by n → σ* orbital delocalization between a lone pair (n) of a (thio)amide donor and the antibonding σ* orbital of an acceptor thiophene or selenophene. Interestingly, stabilization was manifested through the same acceptor molecular orbital irrespective of whether a direct chalcogen···chalcogen or chalcogen···H-C contact was made. Our results underline the importance of often-overlooked orbital delocalization effects in conformational control and molecular recognition phenomena.

Efficient Implicit Solvation Method for Full Potential DFT.

With the advent of efficient electronic structure methods, effective continuum solvation methods have emerged as a way to, at least partially, include solvent effects into simulations without the need for expensive sampling over solvent degrees of freedom. The multipole moment expansion (MPE) model, while based on ideas initially put forward almost 100 years ago, has recently been updated for the needs of modern electronic structure calculations. Indeed, for an all-electron code relying on localized basis sets and-more importantly-a multipole moment expansion of the electrostatic potential, the MPE method presents a particularly cheap way of solving the macroscopic Poisson equation to determine the electrostatic response of a medium surrounding a solute. In addition to our implementation of the MPE model in the FHI-aims electronic structure theory code [ Blum , V. ; Comput. Phys. Commun. 2009 , 180 , 2175 - 2196 , DOI: 10.1016/j.cpc.2009.06.022 ], we describe novel algorithms for determining equidistributed points on the solvation cavity-defined as a charge density isosurface-and the determination of cavity surface and volume from just this collection of points and their local density gradients. We demonstrate the efficacy of our model on an analytically solvable test case, against high-accuracy finite-element calculations for a set of ≈140000 2D test cases, and finally against experimental solvation free energies of a number of neutral and singly charged molecular test sets [ Andreussi , O. ; J. Chem. Phys. 2012 , 136 , 064102 , DOI: 10.1063/1.3676407 ; Marenich , A. V. ; Minnesota Solvation Database , Version 2012; University of Minnesota : Minneapolis, MN, USA , 2012 . ]. In all test cases we find that our MPE approach compares very well with given references at computational overheads < 20% and sometimes much smaller compared to a plain self-consistency cycle.

New Coarse Variables for the Accurate Determination of Standard Binding Free Energies.

To improve sampling of the configurational entropy change upon protein-ligand binding, we have introduced a new set of coarse variables describing the relative orientation and position of the ligand via a global macromolecular orientational procedure, onto which geometrical restraints are applied. Evaluating the potential of mean force for the different coarse variables, the experimental standard binding free energy for three decapeptides associated with the SH3 domain of the Abl kinase is reproduced quantitatively.

A component analysis of the free energies of folding of 35 proteins: A consensus view on the thermodynamics of folding at the molecular level.

What factors favor protein folding? This is a textbook question. Parsing the experimental free energies of folding/unfolding into diverse enthalpic and entropic components of solute and solvent favoring or disfavoring folding is not an easy task. In this study, we present a computational protocol for estimating the free energy contributors to protein folding semi-quantitatively using ensembles of unfolded and native states generated via molecular dynamics simulations. We tested the methodology on 35 proteins with diverse structural motifs and sizes and found that the calculated free energies correlate well with experiment (correlation coefficient ∼ 0.85), enabling us to develop a consensus view of the energetics of folding. As a more sensitive test of the methodology, we also investigated the free energies of folding of an additional 33 single point mutants and obtained a correlation coefficient of 0.8. A notable observation is that the folding free energy components appear to carry signatures of the fold (SCOP classification) of the protein. © 2017 Wiley Periodicals, Inc.

Protein surface roughness accounts for binding free energy of Plasmepsin II-ligand complexes.

The calculation of absolute binding affinities for protein-inhibitor complexes remains as one of the main challenges in computational structure-based ligand design. The present work explored the calculations of surface fractal dimension (as a measure of surface roughness) and the relationship with experimental binding free energies of Plasmepsin II complexes. Plasmepsin II is an attractive target for novel therapeutic compounds to treat malaria. However, the structural flexibility of this enzyme is a drawback when searching for specific inhibitors. Concerning that, we performed separate explicitly solvated molecular dynamics simulations using the available high-resolution crystal structures of different Plasmepsin II complexes. Molecular dynamics simulations allowed a better approximation to systems dynamics and, therefore, a more reliable estimation of surface roughness. This constitutes a novel approximation in order to obtain more realistic values of fractal dimension, because previous works considered only x-ray structures. Binding site fractal dimension was calculated considering the ensemble of structures generated at different simulation times. A linear relationship between binding site fractal dimension and experimental binding free energies of the complexes was observed within 20ns. Previous studies of the subject did not uncover this relationship. Regression model, coined FD model, was built to estimate binding free energies from binding site fractal dimension values. Leave-one-out cross-validation showed that our model reproduced accurately the absolute binding free energies for our training set (R2 =0.76; <|error|>=0.55kcal/mol; SDerror =0.19kcal/mol). The fact that such a simple model may be applied raises some questions that are addressed in the article.

Solvation free energies and partition coefficients with the coarse-grained and hybrid all-atom/coarse-grained MARTINI models

We present the estimation of solvation free energies of small solutes in water, n-octanol and hexane using molecular dynamics simulations with two MARTINI models at different resolutions, viz. the coarse-grained (CG) and the hybrid all-atom/coarse-grained (AA/CG) models. From these estimates, we also calculate the water/hexane and water/octanol partition coefficients. More than 150 small, organic molecules were selected from the Minnesota solvation database and parameterized in a semi-automatic fashion. Using either the CG or hybrid AA/CG models, we find considerable deviations between the estimated and experimental solvation free energies in all solvents with mean absolute deviations larger than 10 kJ/mol, although the correlation coefficient is between 0.55 and 0.75 and significant. There is also no difference between the results when using the non-polarizable and polarizable water model, although we identify some improvements when using the polarizable model with the AA/CG solutes. In contrast to the estimated solvation energies, the estimated partition coefficients are generally excellent with both the CG and hybrid AA/CG models, giving mean absolute deviations between 0.67 and 0.90 log units and correlation coefficients larger than 0.85. We analyze the error distribution further and suggest avenues for improvements.

How fast monoamine oxidases decompose adrenaline? Kinetics of isoenzymes A and B evaluated by empirical valence bond simulation.

This work scrutinizes kinetics of decomposition of adrenaline catalyzed by monoamine oxidase (MAO) A and B enzymes, a process controlling the levels of adrenaline in the central nervous system and other tissues. Experimental kinetic data for MAO A and B catalyzed decomposition of adrenaline are reported only in the form of the maximum reaction rate. Therefore, we estimated the experimental free energy barriers form the kinetic data of closely related systems using regression method, as was done in our previous study. By using multiscale simulation on the Empirical Valence Bond (EVB) level, we studied the chemical reactivity of the MAO A catalyzed decomposition of adrenaline and we obtained a value of activation free energy of 17.3 ± 0.4 kcal/mol. The corresponding value for MAO B is 15.7 ± 0.7 kcal/mol. Both values are in good agreement with the estimated experimental barriers of 16.6 and 16.0 kcal/mol for MAO A and MAO B, respectively. The fact that we reproduced the kinetic data and preferential catalytic effect of MAO B over MAO A gives additional support to the validity of the proposed hydride transfer mechanism. Furthermore, we demonstrate that adrenaline is preferably involved in the reaction in a neutral rather than in a protonated form due to considerably higher barriers computed for the protonated adrenaline substrate. The results are discussed in the context of chemical mechanism of MAO enzymes and possible applications of multiscale simulation to rationalize the effects of MAO activity on adrenaline level.

Statistical Analysis on the Performance of Molecular Mechanics Poisson–Boltzmann Surface Area versus Absolute Binding Free Energy Calculations: Bromodomains as a Case Study

Binding free energy calculations that make use of alchemical pathways are becoming increasingly feasible thanks to advances in hardware and algorithms. Although relative binding free energy (RBFE) calculations are starting to find widespread use, absolute binding free energy (ABFE) calculations are still being explored mainly in academic settings due to the high computational requirements and still uncertain predictive value. However, in some drug design scenarios, RBFE calculations are not applicable and ABFE calculations could provide an alternative. Computationally cheaper end-point calculations in implicit solvent, such as molecular mechanics Poisson–Boltzmann surface area (MMPBSA) calculations, could too be used if one is primarily interested in a relative ranking of affinities. Here, we compare MMPBSA calculations to previously performed absolute alchemical free energy calculations in their ability to correlate with experimental binding free energies for three sets of bromodomain–inhibitor pairs. Different MMPBSA approaches have been considered, including a standard single-trajectory protocol, a protocol that includes a binding entropy estimate, and protocols that take into account the ligand hydration shell. Despite the improvements observed with the latter two MMPBSA approaches, ABFE calculations were found to be overall superior in obtaining correlation with experimental affinities for the test cases considered. A difference in weighted average Pearson () and Spearman () correlations of 0.25 and 0.31 was observed when using a standard single-trajectory MMPBSA setup ( = 0.64 and = 0.66 for ABFE; = 0.39 and = 0.35 for MMPBSA). The best performing MMPBSA protocols returned weighted average Pearson and Spearman correlations that were about 0.1 inferior to ABFE calculations: = 0.55 and = 0.56 when including an entropy estimate, and = 0.53 and = 0.55 when including explicit water molecules. Overall, the study suggests that ABFE calculations are indeed the more accurate approach, yet there is also value in MMPBSA calculations considering the lower compute requirements, and if agreement to experimental affinities in absolute terms is not of interest. Moreover, for the specific protein–ligand systems considered in this study, we find that including an explicit ligand hydration shell or a binding entropy estimate in the MMPBSA calculations resulted in significant performance improvements at a negligible computational cost.

Extensive Assessment of Various Computational Methods for Aspartate's pKa Shift.

A series of computational methods for pKa shift prediction are extensively tested on a set of benchmark protein systems, aiming at identifying pitfalls and evaluating their performance on high variants. Including 19 ASP residues in 10 protein systems, the benchmark set consists of both residues with highly shifted pKa values as well as those varying little from the reference value, with an experimental RMS free energy differences of 2.49 kcal/mol with respect to blocked amino acid, namely the RMS pKa shift being 1.82 pKa units. The constant pH molecular dynamics (MD), alchemical methods, PROPKA3.1, and multiconformation continuum electrostatics give RMSDs of 1.52, 2.58, 1.37, and 3.52 pKa units, respectively, on the benchmark set. The empirical scoring method is the most accurate one with extremely low computational cost, and the pH-dependent model is also able to provide accurate results, while the accuracy of MD sampling incorporating alchemical free energy simulation is prohibited by convergence achievement and the performance of conformational search incorporating multiconformation continuum electrostatics is bad. Former research works did not define statistical uncertainty with care and yielded the questionable conclusion that alchemical methods perform well in most benchmarks. In this work the traditional alchemical methods are thoroughly tested for high variants. We also performed the first application of nonequilibrium alchemical methods to the pKa cases.

An effective tridental molecular clip for fullerenes

AbstractBy means of density functional calculations, we studied the performance of 2 fullerene receptors that contain 3 corannulene or triphenylene pincers. For the first time, we found a receptor that has a small tendency to form intramolecular stacks between the 3 corannulene pincers. After comparing their ability to trap fullerenes, with that of buckycatcher, buckycatcher‐II, and the Venus flytrap, we conclude that a record‐breaking association constant is expected for the receptor with 3 corannulene pincers. Although triphenylene is less effective than the corannulene units in forming inclusion complexes with C60, the triphenylene‐based host is also expected to have a high association constant. Finally, we discuss the theoretical problems found in reproducing the experimental free energy changes in solution for buckycatcher, buckycatcher‐II, and the Venus flytrap.

Free-Energy Calculations of Ionic Hydration Consistent with the Experimental Hydration Free Energy of the Proton

Computational free-energy correction strategies and the choice of experimental proton hydration free energy, ΔGs*(H+), are analyzed to investigate the apparent controversy in experimental thermodynamics of ionic hydration. Without corrections, the hydration free-energy (ΔGhyd) calculations match experiments with ΔGs*(H+) = -1064 kJ/mol as reference. Using the Galvani surface potential the resulting (real) ΔGhyd are consistent with ΔGs*(H+) = -1098 kJ/mol. When applying, in an ad hoc manner, the discrete solvent correction, ΔGhyd matching the "consensus" ΔGs*(H+) of -1112 kJ/mol are obtained. This analysis rationalizes reports on ΔGhyd calculations for ions using different experimental references. For neutral amino acid side chains ΔGhyd are independent of the water model, whereas there are large differences in ΔGhyd due to the water model for charged species, suggesting that long-range ordering of water around ions yields an important contribution to the ΔGhyd. These differences are reduced significantly when applying consistent corrections, but to obtain the most accurate results it is recommended to use the water model belonging to the force field.

Attach-Pull-Release Calculations of Ligand Binding and Conformational Changes on the First BRD4 Bromodomain.

Bromodomains, protein domains involved in epigenetic regulation, are able to bind small molecules with high affinity. In the present study, we report free energy calculations for the binding of seven ligands to the first BRD4 bromodomain, using the attach-pull-release (APR) method to compute the reversible work of removing the ligands from the binding site and then allowing the protein to relax conformationally. We test three different water models, TIP3P, TIP4PEw, and SPC/E, as well as the GAFF and GAFF2 parameter sets for the ligands. Our simulations show that the apo crystal structure of BRD4 is only metastable, with a structural transition happening in the absence of the ligand typically after 20 ns of simulation. We compute the free energy change for this transition with a separate APR calculation on the free protein and include its contribution to the ligand binding free energies, which generally causes an underestimation of the affinities. By testing different water models and ligand parameters, we are also able to assess their influence in our results and determine which one produces the best agreement with the experimental data. Both free energies associated with the conformational change and ligand binding are affected by the choice of water model, with the two sets of ligand parameters affecting their binding free energies to a lesser degree. Across all six combinations of water model and ligand potential function, the Pearson correlation coefficients between calculated and experimental binding free energies range from 0.55 to 0.83, and the root-mean-square errors range from 1.4–3.2 kcal/mol. The current protocol also yields encouraging preliminary results when used to assess the relative stability of ligand poses generated by docking or other methods, as illustrated for two different ligands. Our method takes advantage of the high performance provided by graphics processing units and can readily be applied to other ligands as well as other protein systems.

Improved Electrochemical Phase Diagrams from Theory and Experiment: The Ni–Water System and Its Complex Compounds

Electrode potential–pH (Pourbaix) diagrams provide a phase map of the most stable compounds of a metal, its corrosion products, and associated ions in solution. The utility of these phase diagrams is that they enable the assessment of electrochemical stabilities, for example, of Ni metal and its derived oxides, hydroxides, and oxyhydroxides, against corrosion in aqueous environments. Remarkably, the Ni Pourbaix diagrams reported over the last 50 years are largely inconsistent with various electrochemical observations, which may be attributed to inaccurate experimental free energies of formation (ΔfG) for the complex Ni-based compounds used in producing the available diagrams. Here we show that state-of-the-art density-functional theory (DFT) can be used to obtain accurate ΔfG values, which lead to Ni Pourbaix diagrams that are more consistent with direct electrochemical experiments: Electrochemical impedance spectroscopy and surface-enhanced Raman spectroscopy are used to characterize the electrochemical ...

Insights into Supramolecular Sites Responsible for Complete Separation of Biomass-Derived Phenolics and Glucose in Metal–Organic Framework NU-1000

The molecular origins of adsorption of lignin-derived phenolics to metal-organic framework NU-1000 are investigated from aqueous solution as well as in competitive mode with glucose present in the same aqueous mixture. A comparison of adsorption equilibrium constants (Kads) for phenolics functionalized with either carboxylic acid or aldehyde substituents demonstrated only a slight increase (less than a factor of 6) for the former according to both experiments and calculations. This small difference in Kads between aldehyde and carboxylic-acid substituted adsorbates is consistent with the pyrene unit of NU-1000 as the adsorption site, rather than the zirconia nodes, while at saturation coverage, the adsorption capacity suggests multiple guests per pyrene. Experimental standard free energies of adsorption directly correlated with the molecular size and electronic structure calculations confirmed this direct relationship, with the pyrene units as adsorption site. The underlying origins of this relationship are grounded in noncovalent π-π interactions as being responsible for adsorption, the same interactions present in the condensed phase of the phenolics, which to a large extent govern their heat of vaporization. Thus, NU-1000 acts as a preformed aromatic cavity for driving aromatic guest adsorption from aqueous solution and does so specifically without causing detectable glucose adsorption from aqueous solution, thereby achieving complete glucose-phenolics separations. The reusability of NU-1000 during an adsorption/desorption cycle was good, even with some of the phenolic compounds with greatest affinity not easiliy removed with water and ethanol washes at room temperature. A competitive adsorption experiment gave an upper bound for Kads for glucose of at most 0.18 M-1, which can be compared with Kads for the phenolics investigated here, which fell in the range of 443-42 639 M-1. The actual value of Kads for glucose may be much closer to zero given the lack of observed glucose uptake with NU-1000 as adsorbent.

A Comprehensive Docking and MM/GBSA Rescoring Study of Ligand Recognition upon Binding Antithrombin.

Background: A high-throughput virtual screening pipeline has been extended from single energetically minimized structure Molecular Mechanics/Generalized Born Surface Area (MM/GBSA) rescoring to ensemble-average MM/GBSA rescoring. The correlation coefficient (R2) of calculated and experimental binding free energies for a series of antithrombin ligands has been improved from 0.36 to 0.69 when switching from the single-structure MM/GBSA rescoring to ensemble-average one. The electrostatic interactions in both solute and solvent are identified to play an important role in determining the binding free energy after the decomposition of the calculated binding free energy. The increasing negative charge of the compounds provides a more favorable electrostatic energy change but creates a higher penalty for the solvation free energy. Such a penalty is compensated by the electrostatic energy change, which results in a better binding affinity. A highly hydrophobic ligand is determined by the docking program to be a non-specific binder.Results: Our results have demonstrated that it is very important to keep a few top poses for rescoring, if the binding is non-specific or the binding mode is not well determined by the docking calculation.

A Hybrid Knowledge-Based and Empirical Scoring Function for Protein–Ligand Interaction: SMoG2016

We present the third generation of our scoring function for the prediction of protein-ligand binding free energy. This function is now a hybrid between a knowledge-based potential and an empirical function. We constructed a diversified set of ∼1000 complexes from the PDBBinding-CN database for the training of the function, and we show that this number of complexes generates enough data to build the potential. The occurrence of 420 different types of atomic pairwise interactions is computed in up to five different ranges of distances to derive the knowledge-based part. All of the parameters were optimized, and we were able to considerably improve the accuracy of the scoring function with a Pearson correlation coefficient against experimental binding free energies of up to 0.57, which ranks our new scoring function as one of the best currently available and the second-best in terms of standard deviation (SD = 1.68 kcal/mol). The function was then further improved by inclusion of different terms taking into account repulsion and loss of entropy upon binding, and we show that it is capable of recovering native binding poses up to 80% of the time. All of the programs, tools, and protein sets are released in the Supporting Information or as open-source programs.

Snare Proteins Entropically Expand Membrane Fusion Pores

Neurotransmitters and hormones are released through fusion pores whose dynamics are a critical determinant of the release amount and rate. Fusion pores may flicker repeatedly, before resealing (“kiss & run” fusion) or dilating irreversibly (full fusion). These dynamics are physiologically regulated, but the mechanisms are not understood. Prior studies either monitored single exocytotic pores in live cells with uncontrolled biochemistry, or used in vitro reconstitutions lacking single pore sensitivity. The unavailability of key parameters has hampered development of meaningful models to describe pore dynamics.Here we combine mathematical modeling and single pore measurements to investigate regulation of pore dilation. Experimentally, we measured individual pore conductances with controlled SNARE copy number for the first time. Reconstituting v-SNAREs into ∼23 nm diameter nanolipoprotein particles (discs), we fused discs with patch-clamped cells expressing complementary t-SNAREs and measured currents.We found that SNARE numbers dramatically affected pore size. Just ∼2 SNAREs nucleated pores, but with increasing numbers of SNAREs pores became progressively more dilated. We determined pore size distributions and free energy versus pore size.We developed a coarse-grained mathematical model that reproduced the experimental free energy profiles. Free energies were averaged over fusion pore shapes and configurations of SNARE complexes which could zipper at the pore waist or roam unzippered. Protein-free pores resisted expansion with force ∼19 pN due to membrane tension and bending, close to the experimental value. With SNAREs, zippering drove SNARE assembly at the pore, where SNARE crowding generated entropic pore expansion forces, since bigger pores gave zippered SNAREs more entropy. With 15 SNAREs the entropic expansion force of 14 pN was close to the 19 pN resistance.Our results suggest that SNAREs critically regulate pores post-fusion by entropic expansion forces. Several SNAREs are required to fully dilate pores for efficient contents release.

Effect of Humidity and Cathodic Current on Chromium Poisoning of Sr-Doped LaMnO3-Based Cathode in Anode-Supported Solid Oxide Fuel Cells

Anode-supported solid oxide fuel cells (SOFCs), which were comprised of a Sr-doped LaMnO3 (LSM) + yttria-stabilized zirconia (YSZ) cathode active layer and a LSM cathode current collector layer, were fabricated. Electrochemical performance tests of the cells with and without chromia-forming alloy interconnect at 800 °C were conducted, under different cathode atmospheres (dry air or 10% humidified air) and current conditions (no current or 0.75 A/cm2). It was found that both humidity and cathodic current promote chromium (Cr) poisoning which has a detrimental effect on cathode performance. Major amounts of Cr-containing deposits were observed at the cathode/electrolyte interfaces of the cells tested with cathodic current and/or humidity. Based on the experimental results and free energy minimization calculations, a mechanism associated to Cr vapor species dissociation at the cathode/electrolyte interface is proposed.

Modeling DNA oxidation in water.

A novel set of hole-site energies and electronic coupling parameters to be used, in the framework of the simplest tight-binding approximation, for predicting DNA hole trapping efficiencies and rates of hole transport in oxidized DNA is proposed. The novel parameters, significantly different from those previously reported in the literature, have been inferred from reliable density functional calculations, including both the sugar-phosphate ionic backbone and the effects of the aqueous environment. It is shown that most of the experimental oxidation free energies of DNA tracts and of oligonucleotides available from photoelectron spectroscopy and voltammetric measurements are reproduced with great accuracy, without the need for introducing sequence dependent parameters.