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This article provides an overview of various methods for calculating free energy in the interactions between biomolecules and nanomaterials. The authors discuss the advantages and limitations of these methods and their applicability to different systems. The article aims to guide future research in this field and emphasizes the need for further improvements in force fields, software, and the use of machine learning. The document also includes a list of references to scientific articles related to drug discovery, computational methods, and the calculation of free energy in molecular systems. These articles provide valuable insights and techniques for researchers in these fields. Additionally, there are references to two specific articles that discuss the use of machine learning in drug discovery and the computational characterization of membrane proteins as potential targets for anticancer treatments. [Extracted from the article]

[Display omitted] Dielectric effects and the coupled electrostatics between the nanoconfined and the internal/external aqueous media contribute to the observed deviations of chemistry within the nanoconfined environment when compared with unconfined systems. A systematic understanding has remained elusive, especially with respect to background salt concentration and boundary condition effects like the nanopore surface chemistry and the reference state used to calculate free energies. We utilize molecular dynamics simulations along with thermodynamic integration to determine the free energy difference associated with acid-base chemistry in 2 nm and 4 nm slit pores open to a bulk-like reservoir. pK a increases are predicted when confining acetic acid, formic acid, and bicarbonate in the slits at infinite dilution conditions. We find that confinement weakens the acids, and the modulation of outer pore surface dipole magnitudes can tune the pK a shift values, suggesting that purely "intrinsic" electrostatic effect on confinement may not exist. At sufficiently high salt concentrations, the dielectric/electrostatic effects on pK a values diminish due to charge screening effects. These discoveries enable future modifications of nanopore chemistries to achieve desirable properties for industrial applications. [ABSTRACT FROM AUTHOR]

In computational chemistry and molecular modeling, the interactions between biomolecules (BMs) and nanomaterials (NMs) play a crucial role in various physical and biological processes, and have significant implications in material discovery and development. While there is extensive literature on free energy calculations for drug-target interactions, reviews specifically addressing BM-NM interactions are relatively scarce. This manuscript aims to fill in this gap by presenting a comprehensive overview of the most widely used and well-established methods for free energy calculations. It provides a detailed analysis of the advantages and limitations of these methods and discusses their applicability to BM-NM systems. This work is intended to offer insights into free energy calculations and serve as a guide for future research in this field.

Rational protein engineering has often focused on increasing the thermal stability of proteins by incorporating stabilising mutations. Introducing fluorinated amino acids into proteins has been used to enhance protein stability. Free energy simulations of the immunoglobulin binding domain of streptococcal protein G in both the folded and unfolded states were performed to understand the detailed mechanism of the effect of fluorinated aromatic and aliphatic amino acid side chains on the stability of Leu → Hfl (hexafluoroleucine) and Phe → Pff (pentafluorophenylalanine) mutations at the solvent-exposed position of the globular protein. Our simulated free energy differences (ΔΔG) for the Leu → Hfl and Phe → Pff mutations are −0.43 ± 0.14 kcal/mol and −0.45 ± 0.20 kcal/mol, respectively. These calculated free energy differences are in excellent agreement with the corresponding reported experimental values. Surprisingly, a significant contribution to the increased stability of the Hfl-containing fluorinated protein comes from van der Waals interactions and, in the case of Pff, electrostatic interactions. The simulated quantitative agreement with experimental values validates the free energy simulation method to elucidate the effect of fluorination on protein stability. The implications of the simulation results for our understanding of the effect of fluorination on protein stability are discussed. [ABSTRACT FROM AUTHOR]

In Bayesian inference, we are usually interested in the numerical approximation of integrals that are posterior expectations or marginal likelihoods (a.k.a., Bayesian evidence). In this paper, we focus on the computation of the posterior expectation of a function f (x) . We consider a target-aware scenario where f (x) is known in advance and can be exploited in order to improve the estimation of the posterior expectation. In this scenario, this task can be reduced to perform several independent marginal likelihood estimation tasks. The idea of using a path of tempered posterior distributions has been widely applied in the literature for the computation of marginal likelihoods. Thermodynamic integration, path sampling and annealing importance sampling are well-known examples of algorithms belonging to this family of methods. In this work, we introduce a generalized thermodynamic integration (GTI) scheme which is able to perform a target-aware Bayesian inference, i.e., GTI can approximate the posterior expectation of a given function. Several scenarios of application of GTI are discussed and different numerical simulations are provided. [ABSTRACT FROM AUTHOR]

Comprehensive and accurate measurements of the speed of sound in liquid water are reported. The measurements were carried out by a double-path-length pulse-echo technique and cover the temperature range from 273.65 K to 368.15 K with pressures up to 100 MPa. The relative expanded ( k = 2 ) uncertainties are 2.1 mK in temperature, 45 parts-per-million (ppm) in pressure, and between 40 ppm and 70 ppm in speed of sound. Furthermore, values for the density and specific isobaric and isochoric heat capacities were derived from the speed of sound data in the measured temperature range up to 100 MPa by the method of thermodynamic integration. Very accurate values for the derived properties were obtained by using density data of Takenaka and Masui (Metrologia 27:165–171, 1990) and isobaric heat capacity data of Osborne et al. (J Res Natl Bur Stand 23:197, 1939) at ambient pressure as initial values in combination with an accurate correlation of our speed of sound. The relative expanded ( k = 2 ) uncertainties of the derived properties are 2 ppm in density, 0.11% in isobaric heat capacity, and 0.12% in isochoric heat capacity. The experimental speeds of sound and derived properties are compared with experimental data of other authors from the literature, the IAPWS-95 (International Association of the Properties of Water and Steam) formulation for the thermodynamic properties of water, and a recent equation of state for supercooled water. [ABSTRACT FROM AUTHOR]

ABSTRACTEnormous progress has been made in high-pressure research over the last decades in both, experiments and computer simulations, many challenges still remain. This is evidenced by controversial experimental and numerical data even for the simplest atomic systems exhibiting different types of bonding. Here we discuss the determination of the solid–liquid co-existence (melting) lines reviewing the computational techniques for studying the high-pressure melting of atomic systems based on molecular dynamic or Monte Carlo algorithms. Some emphasis is put on presenting the parallel-tempering Monte Carlo method that gives direct access to heat capacity curves and entropic information as a function of temperature allowing for an easy detection and interpretation of the melting transition. For molecular dynamics simulations there exist a variety of methods to extract melting information – here we include a more thorough discussion of thermodynamic integration as it is frequently used for high-pressure melting. Applications of these techniques and discussion for different atomic systems are presented including an overview of experimental and numerical results of the weakly, van-der-Waals bond noble gases, of diamond as a representative for covalent bonding and of alkali metals and iron. We conclude by summarizing some outstanding problems and challenges for numerical simulations.

Alchemical free energy calculations are widely used in predicting p K a , and binding free energy calculations in biomolecular systems. These calculations are carried out using either Free Energy Perturbation (FEP) or Thermodynamic Integration (TI). Numerous efforts have been made to improve the accuracy and efficiency of such calculations, especially by boosting conformational sampling. In this paper, we use a technique that enhances the conformational sampling by temperature acceleration of collective variables for alchemical transformations and applies it to the prediction of p K a of the buried Asp 26 residue in thioredoxin protein. We discuss the importance of enhanced sampling in the p K a calculations. By using a computational technique that enhances the conformational sampling and alchemical transformation, we predict the pKa shift of the buried Asp26 residue in thioredoxin protein. [ABSTRACT FROM AUTHOR]

Flavodoxins are enzymes that contain the redox-active flavin mononucleotide (FMN) cofactor and play a crucial role in numerous biological processes, including energy conversion and electron transfer. Since the redox characteristics of flavodoxins are significantly impacted by the molecular environment of the FMN cofactor, the evaluation of the interplay between the redox properties of the flavin cofactor and its molecular surroundings in flavoproteins is a critical area of investigation for both fundamental research and technological advancements, as the electrochemical tuning of flavoproteins is necessary for optimal interaction with redox acceptor or donor molecules. In order to facilitate the rational design of biomolecular devices, it is imperative to have access to computational tools that can accurately predict the redox potential of both natural and artificial flavoproteins. In this study, we have investigated the feasibility of using non-equilibrium thermodynamic integration protocols to reliably predict the redox potential of flavodoxins. Using as a test set the wild-type flavodoxin from Clostridium Beijerinckii and eight experimentally characterized single-point mutants, we have computed their redox potential. Our results show that 75% (6 out of 8) of the calculated reaction free energies are within 1 kcal/mol of the experimental values, and none exceed an error of 2 kcal/mol, confirming that non-equilibrium thermodynamic integration is a trustworthy tool for the quantitative estimation of the redox potential of this biologically and technologically significant class of enzymes. [ABSTRACT FROM AUTHOR]

Noble gas solubility in silicate melts has provided important insights into how these gases are incorporated into the Earth's interior and how they can be used as tracers of geochemical processes. However, previous studies have shown conflicting results regarding the noble gas solubility in silicate melts at high pressures. Some suggest that a drastic drop in solubility occurs above 5 GPa, while others indicate that maximum solubility is reached at this pressure but the solubility keeps unchanged when the pressure further increases. To clarify this discrepancy and gain a better understanding of the underlying mechanisms, we conducted a solubility investigation using the thermodynamic integration (TI) method and molecular dynamics (MD) simulations based on a machine-learning based force-field called deep potential (DP), which was trained by density functional theory (DFT) calculations. The effects of temperature, pressure and melt composition were investigated up to ∼30 GPa, 2500 K for the melt of model basalt, olivine and enstatite. Our results showed that the solubility of all noble gases (He, Ne and Ar) increased with temperature, while they increased with pressure until maximum solubility was reached at around 5 GPa. Beyond this pressure, solubility gradually decreased as pressure continued to increase. The structural and dynamic analysis of silicate melts revealed an abnormal increase in the self-diffusivity of oxygen atoms in silicate melts from ambient pressure to ∼5–8 GPa, which can be attributed to the formation of Si/Al-O 5-6 in the melts upon compression. Interestingly, the upper limit pressure (5–8 GPa) for this abnormal increase in oxygen diffusivity was also the pressure at which noble gas solubilities reached their maximum. Our findings suggest that the maximum noble gas solubility at around 5 GPa may be a universal phenomenon in silicate melts. However, the specific values and changing trends of solubility depend on the specific melt compositions and noble gases. The complexity of noble gas solubility in silicate melts at high temperatures and pressures suggests that there is significant potential for improving the high-pressure noble gas partition coefficients between minerals, silicate melts, and even the Earth's core. Such improvements would extend our understanding of the behavior of noble gases in the Earth's interior and their role in tracing geodynamic processes. [ABSTRACT FROM AUTHOR]

In this article, a multivariate count distribution with Conway-Maxwell (COM)-Poisson marginals is proposed. To do this, we develop a modification of the Sarmanov method for constructing multivariate distributions. Our multivariate COM-Poisson (MultCOMP) model has desirable features such as (i) it admits a flexible covariance matrix allowing for both negative and positive nondiagonal entries; (ii) it overcomes the limitation of the existing bivariate COM-Poisson distributions in the literature that do not have COM-Poisson marginals; (iii) it allows for the analysis of multivariate counts and is not just limited to bivariate counts. Inferential challenges are presented by the likelihood specification as it depends on a number of intractable normalizing constants involving the model parameters. These obstacles motivate us to propose Bayesian inferential approaches where the resulting doubly intractable posterior is handled with via the noisy exchange algorithm or the Grouped Independence Metropolis–Hastings algorithm. Numerical experiments based on simulations are presented to illustrate the proposed Bayesian approach. We demonstrate the potential of the MultCOMP model through a real data application on the numbers of goals scored by the home and away teams in the English Premier League from 2018 to 2021. Here, our interest is to assess the effect of a lack of crowds during the COVID-19 pandemic on the well-known home team advantage. A MultCOMP model fit shows that there is evidence of a decreased number of goals scored by the home team, not accompanied by a reduced score from the opponent. Hence, our analysis suggests a smaller home team advantage in the absence of crowds, which agrees with the opinion of several football experts. for this article are available online. [ABSTRACT FROM AUTHOR]

There has been a long debate on the stable phase of iron under the Earth's inner core conditions. Because of the solid‐liquid coexistence at the inner core boundary, the thermodynamic stability of solid phases directly relates to their melting temperatures, which remains considerable uncertainty. In the present study, we utilized a semi‐empirical potential fitted to high‐temperature ab initio data to perform a thermodynamic integration from classical systems described by this potential to ab initio systems. This method provides a smooth path for thermodynamic integration and significantly reduces the uncertainty caused by the finite‐size effect. Our results suggest the hcp phase is the stable phase of pure iron under the inner core conditions, while the free energy difference between the hcp and bcc phases is tiny, on the order of 10 s meV/atom near the melting temperature. Plain Language Summary: The structure of Earth's solid inner core is a fundamental question in understanding the Earth's interior. Fe is the major element in the Earth's solid inner core, while its stable phase under inner core conditions is still under debate. The inaccuracy of present ab initio free energy calculations was too large to estimate the small free energy difference between different Fe phases, making this debate unsolved. In this paper, we developed a method to determine Fe's melting temperatures from ab initio calculations. This was achieved by utilizing a potential fitted to high‐temperature ab initio data and performing a thermodynamic integration from classical systems described by this potential to ab initio systems. This method significantly reduces the uncertainty caused by the finite size effect in the ab initio calculations. Using this method, we calculated the free energy difference and melting temperatures of hcp and bcc Fe under inner‐core boundary and center conditions. We show that the hcp phase is the stable phase of pure Fe throughout the inner core condition. However, the bcc and hcp phases show a very small free energy difference that may be altered by other elements in the inner core. Key Points: Thermodynamic integration with a potential fitted to high‐temperature ab initio data allows precise melting temperature determinationsHcp and bcc Fe's melting temperatures are computed at the same ab initio accuracy at 323 and 360 GPaBcc Fe is metastable while its free energy is only ∼10 meV/atom higher than the stable hcp phase under inner core conditions [ABSTRACT FROM AUTHOR]

Bayesian evidence is a key tool in model selection, allowing a comparison of models with different numbers of parameters. Its use in the analysis of cosmological models has been limited by difficulties in calculating it, with current numerical algorithms requiring supercomputers. In this paper we give exact formulae for the Bayesian evidence in the case of Gaussian likelihoods with arbitrary correlations and top-hat priors, and approximate formulae for the case of likelihood distributions with leading non-Gaussianities (skewness and kurtosis). We apply these formulae to cosmological models with and without isocurvature components, and compare with results we previously obtained using numerical thermodynamic integration. We find that the results are of lower precision than the thermodynamic integration, while still being good enough to be useful. [ABSTRACT FROM AUTHOR]

Solubility in water, free energy of solvation (ΔG s o l v ) and free energy of hydration (ΔG h y d ) were determined for 86 organic liquids using Molecular Dynamics simulations in order to find out the relation among these properties. Both, correlation between ΔG h y d and solubility and correlation between ΔG s o l v and solubility are not clearly defined. However, by defining Δ s =ΔG s o l v − Δ G h y d , it is found a numerical relation between Δ s and solubility. This result was verified for pentane, ethanol and, hexanol of three different force fields (TraPPE-UA, CHARMM and, GROMOS). Also, it was studied the relation of these properties by increasing hydrophobicity in a functional group through the number of carbon atoms of the hydrocarbon chain. In this last case, the mentioned relation was also found. [ABSTRACT FROM AUTHOR]

Recently, we have investigated the cucurbit[7]uril (CB7) recognition of the α- and β-anomers of neutral, protonated, and acetylated forms of glucosamine in water. In the present work, we employed molecular dynamics (MD) and thermodynamic integration methods (TI) to investigate the recognition of these molecules by cucurbit[6]uril (CB6) and cucurbit[8]uril (CB8). MD revealed the formation of stable 1:1 inclusion complexes by all studied molecules with cucurbit[n]urils (CBn), and 2:1 complex by the α-anomer of the acetylated form of glucosamine with the large homologue CB8. CB6 forms roughly twice as many hydrogen bonds with the guest molecules as CB8. MM-PBSA results indicated that the electrostatic contribution to the binding free energy of each guest:CB complex was larger for CB6 than for CB8, and that CB6 and CB8 have lower affinity toward the different forms of glucosamine compared to CB7. Furthermore, TI was used to estimate the relative affinities of CB6 and CB8 toward the α- and β-anomers for each form of the studied glucosamine and compare with CB7.

Abstract There has been a long debate on the stable phase of iron under the Earth’s inner core conditions. Because of the solid‐liquid coexistence at the inner core boundary, the thermodynamic stability of solid phases directly relates to their melting temperatures, which remains considerable uncertainty. In the present study, we utilized a semi‐empirical potential fitted to high‐temperature ab initio data to perform a thermodynamic integration from classical systems described by this potential to ab initio systems. This method provides a smooth path for thermodynamic integration and significantly reduces the uncertainty caused by the finite‐size effect. Our results suggest the hcp phase is the stable phase of pure iron under the inner core conditions, while the free energy difference between the hcp and bcc phases is tiny, on the order of 10 s meV/atom near the melting temperature.

Cardiac troponin C (cTnC) is the critical Ca2+‐sensing component of the troponin complex. Binding of Ca2+ to cTnC triggers a cascade of conformational changes within the myofilament that culminate in force production. Hypertrophic cardiomyopathy (HCM)‐associated TNNC1 variants generally induce a greater degree and duration of Ca2+ binding, which may underly the hypertrophic phenotype. Regulation of contraction has long been thought to occur exclusively through Ca2+ binding to site II of cTnC. However, work by several groups including ours suggest that Mg2+, which is several orders of magnitude more abundant in the cell than Ca2+, may compete for binding to the same cTnC regulatory site. We previously used isothermal titration calorimetry (ITC) to demonstrate that physiological concentrations of Mg2+ may decrease site II Ca2+‐binding in both N‐terminal and full‐length cTnC. Here, we explore the binding of Ca2+ and Mg2+ to cTnC harbouring a series of TNNC1 variants thought to be causal in HCM. ITC and thermodynamic integration (TI) simulations show that A8V, L29Q and A31S elevate the affinity for both Ca2+ and Mg2+. Further, L48Q, Q50R and C84Y that are adjacent to the EF hand binding motif of site II have a more significant effect on affinity and the thermodynamics of the binding interaction. To the best of our knowledge, this work is the first to explore the role of Mg2+ in modifying the Ca2+ affinity of cTnC mutations linked to HCM. Our results indicate a physiologically significant role for cellular Mg2+ both at baseline and when elevated on modifying the Ca2+ binding properties of cTnC and the subsequent conformational changes which precede cardiac contraction. [ABSTRACT FROM AUTHOR]

Prediction of ligand-receptor complex structure is important in both the basic science and the industry such as drug discovery. We report various computation molecular docking methods: fundamental in silico (virtual) screening, ensemble docking, enhanced sampling (generalized ensemble) methods, and other methods to improve the accuracy of the complex structure. We explain not only the merits of these methods but also their limits of application and discuss some interaction terms which are not considered in the in silico methods. In silico screening and ensemble docking are useful when one focuses on obtaining the native complex structure (the most thermodynamically stable complex). Generalized ensemble method provides a free-energy landscape, which shows the distribution of the most stable complex structure and semi-stable ones in a conformational space. Also, barriers separating those stable structures are identified. A researcher should select one of the methods according to the research aim and depending on complexity of the molecular system to be studied. [ABSTRACT FROM AUTHOR]

Human transthyretin (TTR) is a homotetrameric plasma protein associated with a high percentage of β‐sheet, which forms amyloid fibrils and accumulates in tissues or extracellular matrix to cause amyloid diseases. Free energy simulations based on all‐atom molecular dynamics simulations were carried out to analyze the effects of the His88 → Arg, Phe, and Tyr mutations on the stability of human TTR. The calculated free energy change differences (ΔΔG) caused by the His → Arg, Phe, and Tyr mutations at position 88 are 6.48 ± 0.45, −9.99 ± 0.54, and 2.66 ± 0.33 kcal/mol, respectively. These calculated free energy change differences between wild type and the mutants are in excellent agreement with prior experimental values. Our simulation results show that the wild type of the TTR is more stable than H88R and H88Y mutants, whereas it is less stable than the H88F mutant. The free energy component analysis shows that the primary contribution to the free energy change difference (ΔΔG) for the His → Arg mutation arises from electrostatic interaction; the ΔΔG for the His → Phe mutation is from van der Waals and electrostatic interactions and that for the His → Tyr mutation from covalent interaction. The simulation results show that the free energy calculation with thermodynamic integration is beneficial for understanding the detailed microscopic mechanism of protein stability. The implications of the results for understanding stabilizing and destabilizing effect of the mutation and the contribution to protein stability are discussed. [ABSTRACT FROM AUTHOR]

Flavodoxins are enzymes that contain the redox-active flavin mononucleotide (FMN) cofactor and play a crucial role in numerous biological processes, including energy conversion and electron transfer. Since the redox characteristics of flavodoxins are significantly impacted by the molecular environment of the FMN cofactor, the evaluation of the interplay between the redox properties of the flavin cofactor and its molecular surroundings in flavoproteins is a critical area of investigation for both fundamental research and technological advancements, as the electrochemical tuning of flavoproteins is necessary for optimal interaction with redox acceptor or donor molecules. In order to facilitate the rational design of biomolecular devices, it is imperative to have access to computational tools that can accurately predict the redox potential of both natural and artificial flavoproteins. In this study, we have investigated the feasibility of using non-equilibrium thermodynamic integration protocols to reliably predict the redox potential of flavodoxins. Using as a test set the wild-type flavodoxin from Clostridium Beijerinckii and eight experimentally characterized single-point mutants, we have computed their redox potential. Our results show that 75% (6 out of 8) of the calculated reaction free energies are within 1 kcal/mol of the experimental values, and none exceed an error of 2 kcal/mol, confirming that non-equilibrium thermodynamic integration is a trustworthy tool for the quantitative estimation of the redox potential of this biologically and technologically significant class of enzymes.

The protonation state of molecules and surfaces is pivotal in various disciplines, including (electro-)catalysis, geochemistry, biochemistry, and pharmaceutics. Accurately and efficiently determining acidity constants is critical yet challenging, particularly when explicitly considering the electronic structure, thermal fluctuations, anharmonic vibrations, and solvation effects. In this research, we employ thermodynamic integration accelerated by com- mittee Neural Network potentials, training a single machine learning model that accurately describes the relevant protonated, deprotonated, and intermediate states. We investigate two deprotonation reactions at the BiVO4 (010)-water interface, a promising candidate for efficient photocatalytic water splitting. Our results illustrate the convergence of the required ensemble averages over simulation time and of the final acidity constant as a function of the Kirkwood coupling parameter. We demonstrate that simulation times on the order of nanoseconds are required for statistical convergence. This time scale is currently unachievable with explicit ab-initio molecular dynamics simulations at the hybrid DFT level of theory. In contrast, our machine learning workflow only requires a few hundred DFT single point calculations for training and testing. Exploiting the extended time scales accessible, we furthermore asses the effect of commonly applied bias potentials. Thus, our study significantly advances calculating free energy differences with ab-initio accuracy., (© 2024 Wiley‐VCH GmbH.)

Lidocaine and bupivacaine are local anaesthetics used clinically to numb tissue in a specific area. The anaesthetic effect of lidocaine starts twice as fast as bupivacaine, although it lasts half as long or less. It is still unclear why there is an offset of action and different numbing effect duration between these two drugs. In this work, we investigate the thermodynamic cause of such a difference on the anaesthetic effects of the ionised forms of lidocaine and bupivacaine. We applied the Membrane Multi-Phase Solvation Model (MMPSM) to estimate the free energy and partition coefficient of transferring the drugs from the aqueous environment to the membrane interior. The thermodynamic analysis shows that lidocaine diffuses into the membrane faster (higher probability), but bupivacaine takes longer to diffuse outside the membrane (lower probability). These results provide a plausible explanation of the differences in the anaesthesia onset and duration. [ABSTRACT FROM AUTHOR]

Point defects are crucial in determining the quality of germanium crystals. A quantitative understanding of the thermodynamic formation properties of the point defects is necessary for the subsequent control of the defect formation during crystal growth. Here, molecular dynamics simulations were employed to investigate the formation energies, total formation free energies and formation entropies of the point defects in a germanium crystal. As far as we know, this is the first time that the total formation free energies of point defects in a germanium crystal have been reported in the literature. We found that the formation energies increased slightly with temperature. The formation free energies decreased significantly with an increase in temperature due to the increase in entropy. The estimated total formation free energies at the melting temperature are ~1.3 eV for self-interstitial and ~0.75 eV for vacancy, corresponding to a formation entropy of ~15 kB for both types of point defects. [ABSTRACT FROM AUTHOR]

The method of thermodynamic integration is applied to calculate accurate data for the density and isobaric and isochoric heat capacity of toluene and n-butane from speed of sound data sets measured previously in our laboratory. Values for the density and isobaric heat capacity on the initial isobar for the integration are derived from very accurate density and speed of sound data sets using well-known thermodynamic relations. The relative expanded uncertainties (at the 0.95 confidence level) in the derived values for the density and isobaric and isochoric heat capacities are estimated to be 0.011 %, 0.3 %, and 0.4 % for toluene and 0.02 %, 0.5 %, and 0.7 % for n-butane, respectively. Comparisons with experimental data, values of other authors derived by the thermodynamic integration, and equations of state show that our values for both fluids are more accurate than most data available in the literature. Moreover, the domain of the thermodynamic integration for toluene extends down to 240 K and covers lower temperatures than recently considered by other authors. The derived values for the isobaric heat capacity of n-butane fill a gap as this property has hitherto only been measured at ambient pressure. Because of their low uncertainty, the values of the derived properties reported in this work in combination with recent data of other authors are useful for developing new and improved equations of state for both fluids. [ABSTRACT FROM AUTHOR]

Tuberculosis is an ancient disease of mankind, and its causative bacterium is Mycobacterium tuberculosis. Isoniazid is one of the most effective first‐line antituberculosis drugs. As prodrugs, it and its derivative ethionamide act on enoyl‐acyl carrier protein reductase (InhA) after being oxidized in bacteria, and kill the bacteria by inhibiting the formation of M. tuberculosis cell walls. However, the S94A mutation of InhA causes M. tuberculosis to develop cross‐resistance to isoniazid and ethionamide. This work is dedicated to studying the cross‐resistance mechanism of isoniazid and ethionamide through theoretical calculations. First, thermodynamic integral simulations are used to accurately calculate the relative binding energy of two drugs in the mutant and wild‐type system. Furthermore, through classic molecular dynamic simulations and molecular mechanics generalized‐Born surface area calculation, some key residues are identified and the binding affinity of isoniazid and ethionamide reduced by 9–13 kcal/mol due to S94A mutation. The hydrogen bond between Ala94 and isoniazid (ethionamide) disappeared and the energy contribution of Ala94 decreased after the mutation. In addition, the dynamic network analysis indicated that the mutation of Ser94 also indirectly affected the conformation of key residues such as Met147, Thr196, and Leu97, resulting in a reduction in the energy contribution of these residues. Finally, the binding conformation of isoniazid and ethionamide has also undergone major changes. The obtained results could provide valuable information for the future molecular design to overcome the drug resistance. [ABSTRACT FROM AUTHOR]

Protein-ligand binding is among the most fundamental phenomena underlying all molecular biology, and a greater ability to more accurately and robustly predict the binding free energy of a small molecule ligand for its cognate protein is expected to have vast consequences for improving the efficiency of pharmaceutical drug discovery. We briefly reviewed a number of scientific and technical advances that have enabled alchemical free energy calculations to recently emerge as a preferred approach, and critically considered proper validation and effective use of these techniques. In particular, we characterized a selection bias effect which may be important in prospective free energy calculations, and introduced a strategy to improve the accuracy of the free energy predictions.

The paper presents analysis of precision of a phonon-based free energy calculation technique (Temperature Dependent Effective Potential method) in comparison with the thermodynamic integration method within classical molecular dynamics. It is shown that the use of the second order force constants is insufficient for accurate calculations of free energies at elevated temperatures due to noticeable anharmonic contributions to lattice vibrations. On the other hand, reliable calculations of the crystal phase equilibrium lines requires free energy accuracy better than 1–3 meV per atom. Based upon the obtained results the Temperature Dependent Effective Potential technique is applied to the detailed study of the solid-state Zr phase diagram from ab initio molecular dynamics that may be achieved if force constants up to the fourth order are used. The calculated zirconium phase diagram is in good agreement with experiment. The α − β − ω triple point was determined at P ≈ 6. 74 GPa, T ≈ 837 K. [Display omitted] [ABSTRACT FROM AUTHOR]

Bayesian evidence is a key tool in model selection, allowing a comparison of models with different numbers of parameters. Its use in the analysis of cosmological models has been limited by difficulties in calculating it, with current numerical algorithms requiring supercomputers. In this paper we give exact formulae for the Bayesian evidence in the case of Gaussian likelihoods with arbitrary correlations and top-hat priors, and approximate formulae for the case of likelihood distributions with leading non-Gaussianities (skewness and kurtosis). We apply these formulae to cosmological models with and without isocurvature components, and compare with results we previously obtained using numerical thermodynamic integration. We find that the results are of lower precision than the thermodynamic integration, while still being good enough to be useful.

During the demethylation of 5‐methyl cytosine residues in duplex DNAs, formyl or carboxyl cytosines are produced and these modified cytosines are preferentially recognized and excised by the thymine DNA glycosylase (TDG). It has been suggested that the TDG detects a soft spot created by weakening of the hydrogen bond of a G·C base pair (bp). Such bp destabilization is ascribed to the presence of electron‐withdrawing 5‐formyl or 5‐carboxyl group in the modified cytosine. Previously, this bp weakening was linked to reduced pKa values of nucleoside molecules. However, the pKa values of nucleosides can deviate from those of duplex DNAs. Thus, to improve agreement with experiments, the corresponding pKa values for DNA environments are needed. In this computational study, we report two pKa values of the N3‐ and the C5‐carboxyl sites in the 5‐carboxyl cytosine residue in a duplex DNA that enable more reasonable interpretations of previous experimental data. [ABSTRACT FROM AUTHOR]

The anomalies properties of water have been interpreted theoretically using several all-atom and coarse-grained water models. Here we use a robust and traditional free energy approach to develop the solid-liquid coexistence curve for water using coarse-grained monatomic mW and machine-learned bond order potential (ML-BOP) water models. We employ the pseudo-supercritical thermodynamic path in combining multiple histogram reweighting (MHR) and Gibbs-Duhem integration. The ML-BOP model has a broad density-temperature hysteresis loop and shows lower maximum and minimum densities as compared to the mW model. The computed excess Helmholtz free energy and the Gibbs free energy at the approximate melting temperature are higher for the ML-BOP model in comparison with the mW model. The pressure dependence fusion curve for both water models aligns with the literature. This analysis indicates that the free energy method accurately captures the solid-liquid transformation and the thermodynamic melting point of water. [Display omitted] [ABSTRACT FROM AUTHOR]

Experimental binding free energies of 27 adamantyl amines against the influenza M2(22-46) WT tetramer, in its closed form at pH 8, were measured by ITC in DPC micelles. The measured K d 's range is ~44 while the antiviral potencies (IC 50) range is ~750 with a good correlation between binding free energies computed with K d and IC 50 values (r = 0.76). We explored with MD simulations (ff19sb, CHARMM36m) the binding profile of complexes with strong, moderate and weak binders embedded in DMPC, DPPC, POPC or a viral mimetic membrane and using different experimental starting structures of M2. To predict accurately differences in binding free energy in response to subtle changes in the structure of the ligands, we performed 18 alchemical perturbative single topology FEP/MD NPT simulations (OPLS2005) using the BAR estimator (Desmond software) and 20 dual topology calculations TI/MD NVT simulations (ff19sb) using the MBAR estimator (Amber software) for adamantyl amines in complex with M2(22-46) WT in DMPC, DPPC, POPC. We observed that both methods with all lipids show a very good correlation between the experimental and calculated relative binding free energies (r = 0.77–0.87, mue = 0.36–0.92 kcal mol-1) with the highest performance achieved with TI/MBAR and lowest performance with FEP/BAR in DMPC bilayers. When antiviral potencies are used instead of the K d values for computing the experimental binding free energies we obtained also good performance with both FEP/BAR (r = 0.83, mue = 0.75 kcal mol-1) and TI/MBAR (r = 0.69, mue = 0.77 kcal mol-1). [Display omitted] • We measured K d values for 27 adamantyl amines to influenza A M2TM WT measured with ITC in DPC micelles pH 8, differing by a factor of ~44. • The compounds antiviral potencies (IC 50 s) range was ~750 and there is a good correlation (r = 0.76) between Δ G b s computed with K d s and IC 50 s. • We investigated with MD simulations and ff19sb, CHARMM36m force fields the binding profile of the adamantyl amines. • In MD simulations were tested DMPC, DPPC, POPC or viral mimetic membranes and different experimental starting structures. • FEP/BAR and TI/MBAR binding free energy calculations based on K d values in the tested lipid systems show r = 0.77–0.87, mue = 0.36–0.92 kcal mol−1. • The highest performance was achieved with TI/MBAR and lowest performance with FEP/BAR for M2TM WT complexes in DMPC bilayers. • FEP/BAR or TI/MBAR showed good performance based on IC 50 values, r = 0.69, mue = 0.77 kcal mol−1 or r = 0.83, mue = 0.75 kcal mol−1. [ABSTRACT FROM AUTHOR]

Point defects are crucial in determining the quality of germanium crystals. A quantitative understanding of the thermodynamic formation properties of the point defects is necessary for the subsequent control of the defect formation during crystal growth. Here, molecular dynamics simulations were employed to investigate the formation energies, total formation free energies and formation entropies of the point defects in a germanium crystal. As far as we know, this is the first time that the total formation free energies of point defects in a germanium crystal have been reported in the literature. We found that the formation energies increased slightly with temperature. The formation free energies decreased significantly with an increase in temperature due to the increase in entropy. The estimated total formation free energies at the melting temperature are ~1.3 eV for self-interstitial and ~0.75 eV for vacancy, corresponding to a formation entropy of ~15 kB for both types of point defects.

A full Bayesian statistical treatment of complex pharmacokinetic or pharmacodynamic models, in particular in a population context, gives access to powerful inference, including on model structure. Markov Chain Monte Carlo (MCMC) samplers are typically used to estimate the joint posterior parameter distribution of interest. Among MCMC samplers, the simulated tempering algorithm (TMCMC) has a number of advantages: it can sample from sharp multi-modal posteriors; it provides insight into identifiability issues useful for model simplification; it can be used to compute accurate Bayes factors for model choice; the simulated Markov chains mix quickly and have assured convergence in certain conditions. The main challenge when implementing this approach is to find an adequate scale of auxiliary inverse temperatures (perks) and associated scaling constants. We solved that problem by adaptive stochastic optimization and describe our implementation of TMCMC sampling in the GNU MCSim software. Once a grid of perks is obtained, it is easy to perform posterior-tempered MCMC sampling or likelihood-tempered MCMC (thermodynamic integration, which bridges the joint prior and the posterior parameter distributions, with assured convergence of a single sampling chain). We compare TMCMC to other samplers and demonstrate its efficient sampling of multi-modal posteriors and calculation of Bayes factors in two stylized case-studies and two realistic population pharmacokinetic inference problems, one of them involving a large PBPK model. [ABSTRACT FROM AUTHOR]

Thermodynamic integration (TI), a powerful formalism for computing Gibbs free energy, has been implemented for many biophysical processes with alchemical schemes that require delicate human efforts to choose/design biasing potentials for sampling the desired biophysical events and to remove their artifactitious consequences afterwards. Theoretically, an alchemical scheme is exact but practically, an unsophisticated implementation of this exact formula can cause error amplifications. Small relative errors in the input parameters can be amplified many times in their propagation into the computed free energy [due to subtraction of similar numbers such as (105±5)−(100±5) = 5±7]. In this paper, we present an unsophisticated implementation of TI in 3n dimensions (3nD) (n = 1, 2, 3…) for the potential of mean force along a 3nD path connecting one state in the bound state ensemble to one state in the unbound state ensemble. Fluctuations in these 3nD are integrated in the bound and unbound state ensembles but not along the 3nD path. Using TI3nD, we computed the standard binding free energies of three protein complexes: trometamol in Salmonella effector SpvD (n = 1), biotin-avidin (n = 2), and Colicin E9 endonuclease with cognate immunity protein Im9 (n = 3). We employed three different protocols in three independent computations of E9-Im9 to show TI3nD's robustness. We also computed the hydration energies of 10 biologically relevant compounds (n = 1 for water, acetamide, urea, glycerol, trometamol, ammonium and n = 2 for erythritol, 1,3-propanediol, xylitol, biotin). Each of the 15 computations is accomplishable within 1 (for hydration) to 10 (for E9-Im9) days on an inexpensive GPU workstation. The computed results all agree with the available experimental data.

Acid dissociation, and thus liberation of excess protons in small water droplets, impacts on diverse fields such as interstellar, atmospheric or environmental chemistry. At cryogenic temperatures below 1 K, it is now well established that as few as four water molecules suffice to dissociate the generic strong acid HCl, yet temperature‐driven recombination sets in simply upon heating that cluster. Here, the fundamental question is posed of how many more water molecules are required to stabilize a hydrated excess proton at room temperature. Ab initio path integral simulations disclose that not five, but six water molecules are needed at 300 K to allow for HCl dissociation independently from nuclear quantum effects. In order to provide the molecular underpinnings of these observations, the classical and quantum free energy profiles were decomposed along the dissociation coordinate in terms of the corresponding internal energy and entropy profiles. What decides in the end about acid dissociation, and thus ion pair formation, in a specific microsolvated water cluster at room temperature is found to be a fierce competition between classical configurational entropy and internal energy, where the former stabilizes the undissociated state whereas the latter favors dissociation. It is expected that these are generic findings with broad implications on acid–base chemistry depending on temperature in small water assemblies. [ABSTRACT FROM AUTHOR]

The decoupling approach to solvation free energy calculations requires scaling the interactions between the solute and the solution with all intramolecular interactions preserved. This paper reports a new procedure that makes it possible to these calculations in LAMMPS. The procedure is tested against built-in GROMACS capabilities. The model compounds chosen to test our methodology are ethanol and biphenyl. The LAMMPS and GROMACS results obtained are in good agreement with each other. This work should help perform solvation free energy calculations in LAMMPS and/or other molecular dynamics software having no built-in functions to implement the decoupling approach. [ABSTRACT FROM AUTHOR]

Molecular dynamics calculations of a mixed micelle composed of sodium dodecyl sulfate (SDS) and octaethylene glycol monododecyl ether (C12E8) were performed for six compositions (SDS/C12E8 = 100/0, 80/20, 60/40, 40/60, 20/80, and 0/100) to investigate the composition dependence of the mixed micelle structure and solubilization of cyclohexane, benzene, and phenol molecules by the micelle. The radial density distribution of the hydrophilic polyoxyethylene (POE) group of C12E8 as a function of distance from the micelle center is very sharp for micelles with high SDS content because the POE group captures a Na+ ion in solution and wraps around it to form a compact crown‐ether‐like complex. The hydrophobic dodecyl groups of SDS and C12E8 were separately distributed in the mixed micelle core. ΔG(r) evaluated for each solute showed that despite the structural changes of the micelle the binding strength of the solute molecules to the micelle did not change significantly. © 2019 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

In the framework of the 2018 Drug Design Data Resource grand challenge 4, blinded predictions on relative binding free energy were performed for a set of 39 ligands of the Cathepsin S protein. We leveraged the GPU-accelerated thermodynamic integration of Amber 18 to advance our computational prediction. When our entry was compared to experimental results, a good correlation was observed (Kendall's τ: 0.62, Spearman's ρ: 0.80 and Pearson's R: 0.82). We designed a parallelized transformation map that placed ligands into several groups based on common alchemical substructures; TI transformations were carried out for each ligand to the relevant substructure, and between substructures. Our calculations were all conducted using the linear potential scaling scheme in Amber TI because we believe the softcore potential/dual-topology approach as implemented in current Amber TI is highly fault-prone for some transformations. The issue is illustrated by using two examples in which typical preparation for the dual-topology approach of Amber TI fails. Overall, the high accuracy of our prediction is a result of recent advances in force fields (ff14SB and GAFF), as well as rapid calculation of ensemble averages enabled by the GPU implementation of Amber. The success shown here in a blinded prediction strongly suggests that alchemical free energy calculation in Amber is a promising tool for future commercial drug design. [ABSTRACT FROM AUTHOR]

Knowledge of the abundance and distribution of light elements in the core is fundamental to the understanding of the Earth and other planetary systems. Recent studies (Li et al., 2018; Mashino et al., 2019) suggest the particular importance of carbon for explaining core properties, yet knowledge of carbon partitioning between the outer and inner core is unknown. By using the quasiharmonic approximation, ab initio molecular dynamics, and thermodynamic integration techniques, we have computed the chemical potential of carbon in liquid Fe and solid hcp‐Fe at core conditions. We find that substitutional carbon is more stable than interstitial carbon and other carbon defect cluster structures in solid Fe. Lattice strain and overcoordination effects lead to a high chemical potential of C in solid Fe compared to the liquid, and consequently carbon partitions almost completely into the liquid. We find that carbon can account for most of the density jump at the inner‐core boundary. This provides an alternative mechanism to the necessity of an oxygen‐rich outer core and may have significant implications for the composition and structure of the deep Earth. Key Points: The chemical potential of C in solid and liquid Fe was calculated using ab initio methodsC almost completely partitions into liquid iron in the Fe‐C binary system at Earth's core conditionsThe presence of C in the outer core may account for most of the density jump at the ICB [ABSTRACT FROM AUTHOR]