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1.  Vapor pressures and sublimation enthalpies of seven heteroatomic aromatic hydrocarbons measured using the Knudsen effusion technique 
The vapor pressures of seven heteroatom-containing cyclic aromatic hydrocarbons, ranging in molecular weight from (168.19 to 208.21) grams⊕mol−1 were measured over the temperature range of (301 to 486) Kelvin using the isothermal Knudsen effusion technique. The compounds measured include: anthraquinone, 9-fluorenone, 9-fluorenone oxime, phenoxazine, phenoxathiin and 9H-pyrido[3,4-b]indole. These solid-state sublimation measurements provided values that are compared to vapor pressures of parent aromatic compounds (anthracene and fluorene) and to others with substituent groups in order to examine the effects of alcohol, ketone, pyridine, and pyrrole functionality on this property. The enthalpies and entropies of sublimation for each compound were determined from the Clausius-Clapeyron equation. Though there is no consistent trend in terms of the effects of substitutions on changes in the enthalpy or entropy of sublimation, we note that the prevalence of enthalpic or entropic driving forces on vapor pressure depend on molecule-specific factors and not merely molecular weight of the substituents.
PMCID: PMC2856104  PMID: 20414454
2.  Towards Accurate Microscopic Calculation of Solvation Entropies: Extending the Restraint Release Approach to Studies of Solvation Effects 
The journal of physical chemistry. B  2009;113(20):7372-7382.
The evaluation of the solvation entropies is a major conceptual and practical challenge. On the one hand, it is interesting to quantify the factors that are responsible for the solvation entropies in solutions, while on the other, it is essential to be able to assess the contributions of the solvation entropies to the binding free energies and related properties. In fact, the solvation entropies are neglected in almost all the studies of the binding entropies. The main problem is that widely used approaches, such as the quasiharmonic (QH) approximation do not provide reliable results particularly, in cases of shallow potential and multidimensional surfaces while brute force evaluations of the entropic effects by simulating temperature dependence of the free energy converges very slowly. This paper addresses the above issue by starting with an analysis of the factors that are responsible for the negative solvation entropy of ions, showing that it is not due to the change in the solvent vibration modes or to the solvent force constant but to the changes in the solvent configurational space upon change in the solute charges. We begin by clarifying that when one deals with aqueous solutions, it is easy to evaluate the corresponding entropic effect by the Langevin dipole(LD) treatment. However, in this work we are interested in developing a general microscopic tool that can be used to study similar effects in the proteins. To this end, we explore the ability of our restraint release (RR) approach to evaluate the solvation entropy. We start this analysis by reviewing the foundation of this approach and in particular, the requirements of minimizing the enthalpy contribution to the RR free energy. We then establish that our approach is not a specialized harmonic treatment but a rather powerful approach. Moving to the main topic of this work, we demonstrate that the RR approach provides quantitative results for the solvation entropies of monovalent and divalent ions and effectively captures the physics of these entropic effects. The success of the current approach indicates that it should be applicable to the studies of the solvation entropies in the proteins and also, in examining hydrophobic effects. Thus, we believe that the RR approach provides a powerful tool for evaluating the corresponding contributions to the binding entropies and eventually, to the binding free energies. This holds promise for extending the information theory modeling to proteins and protein-ligand complexes in aqueous solutions and consequently, facilitating computer-aided drug design.
PMCID: PMC2738853  PMID: 19402609
Langevin dipole; Restraint release; Molecular dynamics; Quasiharmonic approximation; Drug design
3.  Drug-binding energetics of human α-1-acid glycoprotein assessed by isothermal titration calorimetry and molecular docking simulations 
This study utilizes sensitive, modern isothermal titration calorimetric (ITC) methods to characterize the microscopic thermodynamic parameters that drive the binding of basic drugs to α-1-acid glycoprotein (AGP) and thereby rationalize the thermodynamic data in relation to docking models and crystallographic structures of the drug-AGP complexes. The binding of basic compounds from the tricyclic antidepressant series, together with miaserine, chlorpromazine, disopyramide and cimetidine all displayed an exothermically driven binding interaction with AGP. The impact of protonation/deprotonation events, ionic strength, temperature and the individual selectivity of the A and F1*S AGP variants on drug-binding thermodynamics were characterized. A correlation plot of the thermodynamic parameters for all of the test compounds revealed enthalpy-entropy compensation is in effect. The exothermic binding energetics of the test compounds were driven by a combination of favorable (negative) enthalpic (ΔH°) and favorable (positive) entropic (ΔS°) contributions to the Gibbs free energy (ΔG°). Collectively, the data imply that the free energies that drive drug binding to AGP and its relationship to drug-serum residency evolve from the complex interplay of enthalpic and entropic forces from interactions with explicit combinations of hydrophobic and polar side-chain sub-domains within the multi-lobed AGP ligand binding cavity.
PMCID: PMC3513776  PMID: 23192962
human α-1-acid glycoprotein; thermodynamics; drug binding
4.  Influence of Position and Size of Substituents on the Mechanism of Partitioning: A Thermodynamic Study on Acetaminophens, Hydroxybenzoic Acids, and Parabens 
AAPS PharmSciTech  2008;9(1):205-216.
The objective of the present investigation was to study the influence of size, nature, and topology of substituents on the thermodynamic characteristics of sublimation, fusion, solubility, solvation, and partitioning processes of some drug and druglike molecules. Thermodynamic functions of sublimation process 2-acetaminophen and 3-acetaminophen were obtained on the basis of temperature dependencies of vapor pressure by the transpiration method. Thermodynamic characteristics of solubility processes in water, n-octanol, and n-hexane were calculated from the temperature dependencies of solubility using the solubility saturation method. For evaluation of fusion parameters, differential scanning calorimetry was used. A new approach to distinguishing specific and nonspecific energetic terms in the crystal lattice was developed. Specific and nonspecific solvation terms were distinguished using the transfer from the “inert” n-hexane to the other solvents. For the acetaminophen compounds and for some related drug molecules, the correlation between melting points and a parameter describing the ratio between specific and nonspecific interaction in the crystal lattices was obtained. A diagram enabling analysis of the mechanism of the partitioning process was applied. It was found that for isomers of benzoic acids and for acetaminophens, the position of substituents affects the mechanism of the partitioning process but not the extent of partitioning (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta G_{{\text{tr}}}^{\text{0}}$$\end{document} values). In contrast to this, an increased size of substituents (parabens) leads to essential changes in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta G_{{\text{tr}}}^{\text{0}}$$\end{document} values, but the mechanism of the partitioning process stays the same.
PMCID: PMC2976908  PMID: 18446483
partitioning; solubility; solvation; sublimation; thermodynamics; transfer
5.  Thermodynamics of Aryl-Dihydroxyphenyl-Thiadiazole Binding to Human Hsp90 
PLoS ONE  2012;7(5):e36899.
The design of specific inhibitors against the Hsp90 chaperone and other enzyme relies on the detailed and correct understanding of both the thermodynamics of inhibitor binding and the structural features of the protein-inhibitor complex. Here we present a detailed thermodynamic study of binding of aryl-dihydroxyphenyl-thiadiazole inhibitor series to recombinant human Hsp90 alpha isozyme. The inhibitors are highly potent, with the intrinsic Kd approximately equal to 1 nM as determined by isothermal titration calorimetry (ITC) and thermal shift assay (TSA). Dissection of protonation contributions yielded the intrinsic thermodynamic parameters of binding, such as enthalpy, entropy, Gibbs free energy, and the heat capacity. The differences in binding thermodynamic parameters between the series of inhibitors revealed contributions of the functional groups, thus providing insight into molecular reasons for improved or diminished binding efficiency. The inhibitor binding to Hsp90 alpha primarily depended on a large favorable enthalpic contribution combined with the smaller favorable entropic contribution, thus suggesting that their binding was both enthalpically and entropically optimized. The enthalpy-entropy compensation phenomenon was highly evident when comparing the inhibitor binding enthalpies and entropies. This study illustrates how detailed thermodynamic analysis helps to understand energetic reasons for the binding efficiency and develop more potent inhibitors that could be applied for therapeutic use as Hsp90 inhibitors.
PMCID: PMC3360036  PMID: 22655030
6.  Sublimation characterization and vapor pressure estimation of an HIV nonnucleoside reverse transcriptase inhibitor using thermogravimetric analysis 
AAPS PharmSciTech  2003;4(2):99-108.
The purpose of this research is to investigate the sublimation process of DPC 963, a second-generation nonnucleoside reverse transcriptase inhibitor for HIV-1 retrovirus, and to better understant the effect of sublimation during active pharmaceutical ingredient (API) manufacture and formulation development, especially the drying processes. Sublimation of DPC 963 at 150°C and above was determined by thermogravimetric analysis-Fourier transform infrared (TGA-FTIR). The rates of sublimation at different temperatures were measured using isothermal TGA. Condensed material was collected and analyzed by differential scanning calorimetry (DSC), x-ray powder diffraction (XRPD), and infrared (IR) spectrometry. Benzoic acid was used as a reference standard to derive a linear logarithmic relationship between sublimation/evaporation rate and vapor pressure specific to the TGA system used in this study. Sublimation and evaporation of DPC 963 were found to follow apparent zero-order kinetics. Using the Eyring equation, the enthalpy and entropy of the sublimation and evaporation processes were obtained. The enthalpies of sublimation and evaporation were found to be 29 and 22 kcal/mol, respectively. The condensed material from the vapor phase was found to exist in 2 physical forms, amorphous and crystalline. Using benzoic acid as a reference standard, vapor pressure of DPC 963 at different temperatures was calculated using the linear logarithmic relationship obtained. DPC 963 undergoes sublimation at appreciable rates at 150°C and above but this is not likely to pose a serious issue during the manufacturing process. Vapor pressure estimation using thermogravimetric analysis provided sufficient accuracy to be used as a fast, simple, and safe alternative to the traditional methods of vapor pressure determination.
PMCID: PMC2750601  PMID: 12916905
sublimation; vapor pressure; thermogravimetric analysis-infrared (TGA-IR)
7.  Thermodynamic properties of 5(nitrophenyl) furan-2-carbaldehyde isomers 
The aim of the current work was to determine thermo dynamical properties of 5(2-nitro phenyl)-furan-2-carbaldehyde, 5(3-nitro phenyl)-furan-2-carbaldehyde and 5(4-nitro phenyl)-furan-2-carbaldehyde.
The temperature dependence of saturated vapor pressure of 5(2-nitro phenyl)-furan-2-carbaldehyde, 5(3-nitro phenyl)-furan-2-carbaldehyde and 5(4-nitro phenyl)-furan-2-carbaldehyde was determined by Knudsen’s effusion method. The results are presented by the Clapeyron–Clausius equation in linear form, and via this form, the standard enthalpies, entropies and Gibbs energies of sublimation and evaporation of compounds were calculated at 298.15 K. The standard molar formation enthalpies of compounds in crystalline state at 298.15 K were determined indirectly by the corresponding standard molar combustion enthalpy, obtained using bomb calorimetry combustion.
Determination of the thermodynamic properties for these compounds may contribute to solving practical problems pertaining optimization processes of their synthesis, purification and application and it will also provide a more thorough insight regarding the theoretical knowledge of their nature.Graphical abstract:Generalized structural formula of investigated compounds and their formation enthalpy determination scheme in the gaseous state
PMCID: PMC4674947  PMID: 26664456
5(2-Nitrophenyl)-furan-2-carbaldehydes; Vapor pressure; Combustion enthalpy; Formation enthalpy; Vaporization enthalpy; Sublimation enthalpy; Isomerisation enthalpy
8.  DNA Plasticity Is a Key Determinant of the Energetics of Binding of Jun-Fos Heterodimeric Transcription Factor to Genetic Variants of TGACGTCA Motif† 
Biochemistry  2009;48(51):12213-12222.
The Jun-Fos heterodimeric transcription factor is a target of a diverse array of signaling cascades that initiate at the cell surface and converge in the nucleus and ultimately result in the expression of genes involved in a multitude of cellular processes central to health and disease. Here, using isothermal titration calorimetry in conjunction with circular dichroism, we report the effect of introducing single nucleotide variations within the TGACGTCA canonical motif on the binding of bZIP domains of Jun-Fos heterodimer to DNA. Our data reveal that the Jun-Fos heterodimer exhibits differential energetics in binding to such genetic variants in the physiologically relevant micromolar-submicromolar range with the TGACGTCA canonical motif affording the highest affinity. Although binding energetics are largely favored by enthalpic forces and accompanied by entropic penalty, neither the favorable enthalpy nor the unfavorable entropy correlate with overall free energy of binding in agreement with enthalpy-entropy compensation phenomenon widely observed in biological systems. However, a number of variants including the TGACGTCA canonical motif bind to the Jun-Fos heterodimer with high affinity through having overcome such enthalpy-entropy compensation barrier, arguing strongly that better understanding of the underlying invisible forces driving macromolecular interactions may be the key to future drug design. Our data also suggest that the Jun-Fos heterodimer has a preference for binding to TGACGTCA variants with higher AT content, implying that the DNA plasticity may be an important determinant of protein-DNA interactions. This notion is further corroborated by the observation that the introduction of genetic variations within the TGACGTCA motif allows it to sample a much greater conformational space. Taken together, these new findings further our understanding of the role of DNA sequence and conformation on protein-DNA interactions in thermodynamic terms.
PMCID: PMC2807364  PMID: 19921846
AP1-DNA thermodynamics; Jun-Fos heterodimer; bZIP domain; Single nucleotide variants; DNA plasticity
9.  Solvated Crystalline Forms of Nevirapine: Thermoanalytical and Spectroscopic Studies 
AAPS PharmSciTech  2010;11(3):1328-1339.
The study is aimed at exploring the utility of thermoanalytical methods in the solid-state characterization of various crystalline forms of nevirapine. The different forms obtained by recrystallization of nevirapine from various solvents were identified using differential scanning calorimetry and thermogravimetric analysis (TGA). The appearance of desolvation peak accompanied by weight loss in TGA indicated the formation of solvates: hemi-ethanolate (Form I), hemi-acetonitrilate (Form II), hemi-chloroformate (Form III), hemi-THF solvate (Form IV), mixed hemi-ethanolate hemi-hydrate (Form V), and hemi-toluenate (Form VI). The higher desolvation temperatures of all the solvates except toluenate than their respective boiling point indicate tighter binding of solvent. Emphasis has been laid on the determination of heat capacity and heat of solution utilizing microreaction calorimeter to further distinguish the various forms. The enthalpy of solution (ΔHsol), an indirect measure of the lattice energy of a solid, was well correlated with the crystallinity of all the solid forms obtained. The magnitude of ΔHsol was found to be −14.14 kJ/mol for Form I and −2.83 kJ/mol for Form V in phosphate buffer of pH 2, exhibiting maximum ease of molecular release from the lattice in Form I. The heat capacity for solvation (ΔCp) was found to be positive, providing information about the state of solvent molecules in the host lattice. The solubility and dissolution rate of the forms were also found to be in agreement with their enthalpy of solution. Form (I), being the most exothermic, was found to be the most soluble of all the forms.
PMCID: PMC2974108  PMID: 20737259
calorimetry; enthalpy of solution; heat capacity; recrystallization; solvates
10.  Some Binding-Related Drug Properties are Dependent on Thermodynamic Signature 
Chemical biology & drug design  2011;77(3):161-165.
The binding affinity is determined by the Gibbs energy of binding (ΔG) which is the sum of enthalpic (ΔH) and entropic (-TΔS) contributions. Because the enthalpy and entropy contribute in an additive way to the binding energy, the same binding affinity can be achieved by many different combinations of enthalpic and entropic contributions; however, do compounds with similar binding affinities but different thermodynamic signatures (i.e. different ΔH, -TΔS combinations) exhibit the same functional effects? Are there characteristics of compounds that can be modulated by modifying their thermodynamic signatures? In this paper, we consider the minimization of unwanted conformational effects arising during the development of CD4/gp120 inhibitors, a new class of HIV-1 cell entry inhibitors. Competitive inhibitors of protein/protein interactions run the risk of triggering the very same signals that they are supposed to inhibit. Here, we show that for CD4/gp120 inhibitors the magnitude of those unwanted effects is related to the proportion in which the enthalpy and entropy changes contribute to the binding affinity. The thermodynamic optimization plot (TOP) previously proposed to optimize binding affinity can also be used to obtain appropriate enthalpy/entropy combinations for drug candidates.
PMCID: PMC3079564  PMID: 21288305
Binding Affinity; Enthalpy; Entropy; Thermodynamic Optimization; Isothermal Titration Calorimetry
11.  PHOENIX: A Scoring Function for Affinity Prediction Derived Using High-Resolution Crystal Structures and Calorimetry Measurements 
Binding affinity prediction is one of the most critical components to computer-aided structure-based drug design. Despite advances in first-principle methods for predicting binding affinity, empirical scoring functions that are fast and only relatively accurate are still widely used in structure-based drug design. With the increasing availability of X-ray crystallographic structures in the Protein Data Bank and continuing application of biophysical methods such as isothermal titration calorimetry to measure thermodynamic parameters contributing to binding free energy, sufficient experimental data exists that scoring functions can now be derived by separating enthalpic (ΔH) and entropic (TΔS) contributions to binding free energy (ΔG). PHOENIX, a scoring function to predict binding affinities of protein-ligand complexes, utilizes the increasing availability of experimental data to improve binding affinity predictions by the following: model training and testing using high-resolution crystallographic data to minimize structural noise, independent models of enthalpic and entropic contributions fitted to thermodynamic parameters assumed to be thermodynamically biased to calculate binding free energy, use of shape and volume descriptors to better capture entropic contributions. A set of 42 descriptors and 112 protein-ligand complexes were used to derive functions using partial least squares for change of enthalpy (ΔH) and change of entropy (TΔS) to calculate change of binding free energy (ΔG), resulting in a predictive r2 (r2pred) of 0.55 and a standard error (SE) of 1.34 kcal/mol. External validation using the 2009 version of the PDBbind “refined set” (n = 1612) resulted in a Pearson correlation coefficient (Rp) of 0.575 and a mean error (ME) of 1.41 pKd. Enthalpy and entropy predictions were of limited accuracy individually. However, their difference resulted in a relatively accurate binding free energy. While the development of an accurate and applicable scoring function was an objective of this study, the main focus was evaluation of the use of high-resolution X-ray crystal structures with high-quality thermodynamic parameters from isothermal titration calorimetry for scoring function development. With the increasing application of structure-based methods in molecular design, this study suggests that using high-resolution crystal structures, separating enthalpy and entropy contributions to binding free energy, and including descriptors to better capture entropic contributions may prove to be effective strategies towards rapid and accurate calculation of binding affinity.
PMCID: PMC3046228  PMID: 21214225
12.  Global analysis of riboswitches by small-angle X-ray scattering and calorimetry 
Biochimica et biophysica acta  2014;1839(10):1020-1029.
Riboswitches are phylogenetically widespread non-coding mRNA domains that directly bind cellular metabolites and regulate transcription, translation, RNA stability or splicing via alternative RNA structures modulated by ligand binding. The details of ligand recognition by many riboswitches have been elucidated using X-ray crystallography and NMR. However, the global dynamics of riboswitch-ligand interactions and their thermodynamic driving forces are less understood. By compiling the work of many laboratories investigating riboswitches using small-angle X-ray scattering (SAXS) and isothermal titration calorimetry (ITC), we uncover general trends and common themes. There is a pressing need for community-wide consensus experimental conditions to allow results of riboswitch studies to be compared rigorously. Nonetheless, our meta-analysis reveals considerable diversity in the extent to which ligand binding reorganizes global riboswitch structures. It also demonstrates a wide spectrum of enthalpy-entropy compensation regimes across riboswitches that bind a diverse set of ligands, giving rise to a relatively narrow range of physiologically relevant free energies and ligand affinities. From the strongly entropy-driven binding of glycine to the predominantly enthalpy-driven binding of c-di-GMP to their respective riboswitches, these distinct thermodynamic signatures reflect the versatile strategies employed by RNA to adapt to the chemical natures of diverse ligands. Riboswitches have evolved to use a combination of long-range tertiary interactions, conformational selection, and induced fit to work with distinct ligand structure, charge, and solvation properties.
PMCID: PMC4177933  PMID: 24769285
13.  Intrinsic Thermodynamics and Structure Correlation of Benzenesulfonamides with a Pyrimidine Moiety Binding to Carbonic Anhydrases I, II, VII, XII, and XIII 
PLoS ONE  2014;9(12):e114106.
The early stage of drug discovery is often based on selecting the highest affinity lead compound. To this end the structural and energetic characterization of the binding reaction is important. The binding energetics can be resolved into enthalpic and entropic contributions to the binding Gibbs free energy. Most compound binding reactions are coupled to the absorption or release of protons by the protein or the compound. A distinction between the observed and intrinsic parameters of the binding energetics requires the dissection of the protonation/deprotonation processes. Since only the intrinsic parameters can be correlated with molecular structural perturbations associated with complex formation, it is these parameters that are required for rational drug design. Carbonic anhydrase (CA) isoforms are important therapeutic targets to treat a range of disorders including glaucoma, obesity, epilepsy, and cancer. For effective treatment isoform-specific inhibitors are needed. In this work we investigated the binding and protonation energetics of sixteen [(2-pyrimidinylthio)acetyl]benzenesulfonamide CA inhibitors using isothermal titration calorimetry and fluorescent thermal shift assay. The compounds were built by combining four sulfonamide headgroups with four tailgroups yielding 16 compounds. Their intrinsic binding thermodynamics showed the limitations of the functional group energetic additivity approach used in fragment-based drug design, especially at the level of enthalpies and entropies of binding. Combined with high resolution crystal structural data correlations were drawn between the chemical functional groups on selected inhibitors and intrinsic thermodynamic parameters of CA-inhibitor complex formation.
PMCID: PMC4262373  PMID: 25493428
14.  Characterization of Promiscuous Binding of Phosphor Ligands to Breast-Cancer-Gene 1 (BRCA1) C-Terminal (BRCT): Molecular Dynamics, Free Energy, Entropy and Inhibitor Design 
PLoS Computational Biology  2016;12(8):e1005057.
Inhibition of the protein-protein interaction (PPI) mediated by breast-cancer-gene 1 C-terminal (BRCT) is an attractive strategy to sensitize breast and ovarian cancers to chemotherapeutic agents that induce DNA damage. Such inhibitors could also be used for studies to understand the role of this PPI in DNA damage response. However, design of BRCT inhibitors is challenging because of the inherent flexibility associated with this domain. Several studies identified short phosphopeptides as tight BRCT binders. Here we investigated the thermodynamic properties of 18 phosphopeptides or peptide with phosphate mimic and three compounds with phosphate groups binding to BRCT to understand promiscuous molecular recognition and guide inhibitor design. We performed molecular dynamics (MD) simulations to investigate the interactions between inhibitors and BRCT and their dynamic behavior in the free and bound states. MD simulations revealed the key role of loops in altering the shape and size of the binding site to fit various ligands. The mining minima (M2) method was used for calculating binding free energy to explore the driving forces and the fine balance between configuration entropy loss and enthalpy gain. We designed a rigidified ligand, which showed unfavorable experimental binding affinity due to weakened enthalpy. This was because it lacked the ability to rearrange itself upon binding. Investigation of another phosphate group containing compound, C1, suggested that the entropy loss can be reduced by preventing significant narrowing of the energy well and introducing multiple new compound conformations in the bound states. From our computations, we designed an analog of C1 that introduced new intermolecular interactions to strengthen attractions while maintaining small entropic penalty. This study shows that flexible compounds do not always encounter larger entropy penalty, compared with other more rigid binders, and highlights a new strategy for inhibitor design.
Author Summary
Promiscuous proteins are commonly observed in biological systems, such as modular domains that recognize phosphopeptides during signal transduction. The use of phosphopeptides and compounds with phosphate groups as inhibitors to protein–protein interactions have attracted increasing interest for years. By using atomistic molecular dynamics simulations, we are able to perform detailed analyses of the dihedral space to explore protein fluctuation upon ligand binding to better understand promiscuous molecular recognition. Free energy calculation can further provide insights into the mechanism of binding, including both enthalpic and entropic contributions for molecular recognition, which assist in inhibitor design. Our calculation results show that pre-rigidifying a ligand is not always advantageous, suggesting the challenge in retaining optimized intermolecular interactions in pre-rigidified ligand. Instead, certain flexible ligands with multiple binding conformations can reduce entropic penalty, and therefore improves binding affinity. According to our computations, we can introduce new intermolecular interactions to flexible ligand to strengthen attractions while maintaining small entropic penalty by retaining its plasticity in the bound conformation. The study might cast light on a new general strategy for designing inhibitors targeting promiscuous modular domains and protein–protein interactions.
PMCID: PMC4999267  PMID: 27560145
15.  Characterisation and evaluation of pharmaceutical solvates of Atorvastatin calcium by thermoanalytical and spectroscopic studies 
Atorvastatin calcium (ATC), an anti-lipid biopharmaceutical class II drug, is widely prescribed as a cholesterol-lowering agent and is presently the world’s best-selling medicine. A large number of crystalline forms of ATC have been published in patents. A variety of solid forms may give rise to different physical properties. Therefore, the discovery of new forms of this unusual molecule, ATC, may still provide an opportunity for further improvement of advantageous properties.
In the present work, eight new solvates (Solvate I-VIII) have been discovered by recrystallization method. Thermal behaviour of ATC and its solvates studied by DSC and TGA indicate similar pattern suggesting similar mode of entrapment of solvent molecules. The type of solvent present in the crystal lattice of the solvates is identified by GC-MS analysis and the stoichiometric ratio of the solvents is confirmed by 1HNMR. The high positive value of binding energy determined from thermochemical parameters indicates deep inclusion of the solvent molecules into the host cavity. The XRPD patterns point towards the differences in their crystallanity, however, after desolvation solvate II, III, IV, V and VIII transform to isostructral amorphous desolvated solvates. The order of crystallinity was confirmed by solution calorimetric technique as the enthalpy of solution is an indirect measure of lattice energy. All the solvates behaved endothermically following the order solvate-VIII (1-butanol solvate) < solvate-I (isoproplyate) < solvate-V (methanol solvate) < solvate-III (ethonalate) < solvate-VI (acetone ethanol solvate) < solvate-IV (t-butanol solvate) < solvate-II (THF solvate) < solvate-VII (mixed hemi-ethanol hydrate). The positive value of the heat capacity of the solvate formation provides information about the state of solvent molecules in the host lattice. The solvents molecules incorporated in the crystal lattice induced local chemical environment changes in the drug molecules which are observed in 13CP/MAS NMR spectral changes.
Aqueous solubility of solvate-VIII was found to be maximum, however, solvate-I and VIII showed better reduction in total cholesterol and triglyceride levels as compared to atorvastatin against triton-induced dyslipidemia.
PMCID: PMC3547732  PMID: 23039933
Solvate; Recrystalliztion; Heat capacity; Calorimetry; 13C /MAS solid state NMR
16.  What Drives Proteins into the Major or Minor Grooves of DNA? 
Journal of molecular biology  2006;365(1):1-9.
The energetic profiles of a significant number of protein-DNA systems at 20°C reveal that, despite comparable Gibbs free energies, association with the major groove is primarily an enthalpy driven process, whereas binding to the minor groove is characterized by an unfavorable enthalpy that is compensated by favorable entropic contributions. These distinct energetic signatures for major versus minor groove binding are irrespective of the magnitude of DNA bending and/or the extent of binding-induced protein refolding. The primary determinants of their different energetic profiles appear to be the distinct hydration properties of the major and minor grooves, namely that the water in the AT-rich minor groove is in a highly ordered state and its removal results in a substantial positive contribution to the binding entropy. Since the entropic forces driving protein binding into the minor groove are a consequence of displacing water ordered by the regular arrangement of polar contacts, they cannot be regarded as hydrophobic.
PMCID: PMC1934558  PMID: 17055530
DNA binding; DNA grooves; hydration; thermodynamics; electrostatics
17.  Prediction of cyclin-dependent kinase 2 inhibitor potency using the fragment molecular orbital method 
The reliable and robust estimation of ligand binding affinity continues to be a challenge in drug design. Many current methods rely on molecular mechanics (MM) calculations which do not fully explain complex molecular interactions. Full quantum mechanical (QM) computation of the electronic state of protein-ligand complexes has recently become possible by the latest advances in the development of linear-scaling QM methods such as the ab initio fragment molecular orbital (FMO) method. This approximate molecular orbital method is sufficiently fast that it can be incorporated into the development cycle during structure-based drug design for the reliable estimation of ligand binding affinity. Additionally, the FMO method can be combined with approximations for entropy and solvation to make it applicable for binding affinity prediction for a broad range of target and chemotypes.
We applied this method to examine the binding affinity for a series of published cyclin-dependent kinase 2 (CDK2) inhibitors. We calculated the binding affinity for 28 CDK2 inhibitors using the ab initio FMO method based on a number of X-ray crystal structures. The sum of the pair interaction energies (PIE) was calculated and used to explain the gas-phase enthalpic contribution to binding. The correlation of the ligand potencies to the protein-ligand interaction energies gained from FMO was examined and was seen to give a good correlation which outperformed three MM force field based scoring functions used to appoximate the free energy of binding. Although the FMO calculation allows for the enthalpic component of binding interactions to be understood at the quantum level, as it is an in vacuo single point calculation, the entropic component and solvation terms are neglected. For this reason a more accurate and predictive estimate for binding free energy was desired. Therefore, additional terms used to describe the protein-ligand interactions were then calculated to improve the correlation of the FMO derived values to experimental free energies of binding. These terms were used to account for the polar and non-polar solvation of the molecule estimated by the Poisson-Boltzmann equation and the solvent accessible surface area (SASA), respectively, as well as a correction term for ligand entropy. A quantitative structure-activity relationship (QSAR) model obtained by Partial Least Squares projection to latent structures (PLS) analysis of the ligand potencies and the calculated terms showed a strong correlation (r2 = 0.939, q2 = 0.896) for the 14 molecule test set which had a Pearson rank order correlation of 0.97. A training set of a further 14 molecules was well predicted (r2 = 0.842), and could be used to obtain meaningful estimations of the binding free energy.
Our results show that binding energies calculated with the FMO method correlate well with published data. Analysis of the terms used to derive the FMO energies adds greater understanding to the binding interactions than can be gained by MM methods. Combining this information with additional terms and creating a scaled model to describe the data results in more accurate predictions of ligand potencies than the absolute values obtained by FMO alone.
PMCID: PMC3032746  PMID: 21219630
18.  Enthalpic and Entropic Contributions to Hydrophobicity 
Hydrophobic hydration plays a key role in a vast variety of biological processes, ranging from the formation of cells to protein folding and ligand binding. Hydrophobicity scales simplify the complex process of hydration by assigning a value describing the averaged hydrophobic character to each amino acid. Previously published scales were not able to calculate the enthalpic and entropic contributions to the hydrophobicity directly. We present a new method, based on Molecular Dynamics simulations and Grid Inhomogeneous Solvation Theory, that calculates hydrophobicity from enthalpic and entropic contributions. Instead of deriving these quantities from the temperature dependence of the free energy of hydration or as residual of the free energy and the enthalpy, we directly obtain these values from the phase space occupied by water molecules. Additionally, our method is able to identify regions with specific enthalpic and entropic properties, allowing to identify so-called “unhappy water” molecules, which are characterized by weak enthalpic interactions and unfavorable entropic constraints.
PMCID: PMC5024328  PMID: 27442443
19.  Water-Membrane Partition Thermodynamics of an Amphiphilic Lipopeptide: An Enthalpy-Driven Hydrophobic Effect 
Biophysical Journal  2008;95(7):3269-3277.
To shed light on the driving force for the hydrophobic effect that partitions amphiphilic lipoproteins between water and membrane, we carried out an atomically detailed thermodynamic analysis of a triply lipid modified H-ras heptapeptide anchor (ANCH) in water and in a DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) bilayer. Combining molecular mechanical and continuum solvent approaches with an improved technique for solute entropy calculation, we obtained an overall transfer free energy of ∼−13 kcal mol−1. This value is in qualitative agreement with free energy changes derived from a potential of mean force calculation and indirect experimental observations. Changes in free energies of solvation and ANCH conformational reorganization are unfavorable, whereas ANCH-DMPC interactions—especially van der Waals—favor insertion. These results are consistent with an enthalpy-driven hydrophobic effect, in accord with earlier calorimetric data on the membrane partition of other amphiphiles. Furthermore, structural and entropic analysis of molecular dynamics-generated ensembles suggests that conformational selection may play a hitherto unappreciated role in membrane insertion of lipid-modified peptides and proteins.
PMCID: PMC2547422  PMID: 18621822
20.  Binding of the Biogenic Polyamines to Deoxyribonucleic Acids of Varying Base Composition: Base Specificity and the Associated Energetics of the Interaction 
PLoS ONE  2013;8(7):e70510.
The thermodynamics of the base pair specificity of the binding of the polyamines spermine, spermidine, putrescine, and cadaverine with three genomic DNAs Clostridium perfringens, 27% GC, Escherichia coli, 50% GC and Micrococcus lysodeikticus, 72% GC have been studied using titration calorimetry and the data supplemented with melting studies, ethidium displacement and circular dichroism spectroscopy results.
Methodology/Principal Findings
Isothermal titration calorimetry, differential scanning calorimetry, optical melting studies, ethidium displacement, circular dichroism spectroscopy are the various techniques employed to characterize the interaction of four polyamines, spermine, spermidine, putersine and cadaverine with the DNAs. Polyamines bound stronger with AT rich DNA compared to the GC rich DNA and the binding varied depending on the charge on the polyamine as spermine>spermidine >putrescine>cadaverine. Thermodynamics of the interaction revealed that the binding was entropy driven with small enthalpy contribution. The binding was influenced by salt concentration suggesting the contribution from electrostatic forces to the Gibbs energy of binding to be the dominant contributor. Each system studied exhibited enthalpy-entropy compensation. The negative heat capacity changes suggested a role for hydrophobic interactions which may arise due to the non polar interactions between DNA and polyamines.
From a thermodynamic analysis, the AT base specificity of polyamines to DNAs has been elucidated for the first time and supplemented by structural studies.
PMCID: PMC3722294  PMID: 23894663
21.  The Thermochemistry of London Dispersion-Driven Transition Metal Reactions: Getting the ‘Right Answer for the Right Reason’ 
ChemistryOpen  2014;3(5):177-189.
Reliable thermochemical measurements and theoretical predictions for reactions involving large transition metal complexes in which long-range intramolecular London dispersion interactions contribute significantly to their stabilization are still a challenge, particularly for reactions in solution. As an illustrative and chemically important example, two reactions are investigated where a large dipalladium complex is quenched by bulky phosphane ligands (triphenylphosphane and tricyclohexylphosphane). Reaction enthalpies and Gibbs free energies were measured by isotherm titration calorimetry (ITC) and theoretically ‘back-corrected’ to yield 0 K gas-phase reaction energies (ΔE). It is shown that the Gibbs free solvation energy calculated with continuum models represents the largest source of error in theoretical thermochemistry protocols. The (‘back-corrected’) experimental reaction energies were used to benchmark (dispersion-corrected) density functional and wave function theory methods. Particularly, we investigated whether the atom-pairwise D3 dispersion correction is also accurate for transition metal chemistry, and how accurately recently developed local coupled-cluster methods describe the important long-range electron correlation contributions. Both, modern dispersion-corrected density functions (e.g., PW6B95-D3(BJ) or B3LYP-NL), as well as the now possible DLPNO-CCSD(T) calculations, are within the ‘experimental’ gas phase reference value. The remaining uncertainties of 2–3 kcal mol−1 can be essentially attributed to the solvation models. Hence, the future for accurate theoretical thermochemistry of large transition metal reactions in solution is very promising.
PMCID: PMC4234214  PMID: 25478313
density functional theory; isothermal titration calorimetry; local coupled cluster; London dispersion interactions; transition metal reactions
22.  Membrane Partitioning: “Classical” and “Nonclassical” Hydrophobic Effects 
The Journal of Membrane Biology  2010;239(1-2):5-14.
The free energy of transfer of nonpolar solutes from water to lipid bilayers is often dominated by a large negative enthalpy rather than the large positive entropy expected from the hydrophobic effect. This common observation has led to the idea that membrane partitioning is driven by the “nonclassical” hydrophobic effect. We examined this phenomenon by characterizing the partitioning of the well-studied peptide melittin using isothermal titration calorimetry (ITC) and circular dichroism (CD). We studied the temperature dependence of the entropic (−TΔS) and enthalpic (ΔH) components of free energy (ΔG) of partitioning of melittin into lipid membranes made of various mixtures of zwitterionic and anionic lipids. We found significant variations of the entropic and enthalpic components with temperature, lipid composition and vesicle size but only small changes in ΔG (entropy–enthalpy compensation). The heat capacity associated with partitioning had a large negative value of about −0.5 kcal mol−1 K−1. This hallmark of the hydrophobic effect was found to be independent of lipid composition. The measured heat capacity values were used to calculate the hydrophobic-effect free energy ΔGhΦ, which we found to dominate melittin partitioning regardless of lipid composition. In the case of anionic membranes, additional free energy comes from coulombic attraction, which is characterized by a small effective peptide charge due to the lack of additivity of hydrophobic and electrostatic interactions in membrane interfaces [Ladokhin and White J Mol Biol 309:543–552, 2001]. Our results suggest that there is no need for a special effect—the nonclassical hydrophobic effect—to describe partitioning into lipid bilayers.
PMCID: PMC3030945  PMID: 21140141
Heat capacity; Hydrophobic effect; “Nonclassical” hydrophobic effect
23.  Constraining binding hot spots: NMR and MD simulations provide a structural explanation for enthalpy-entropy compensation in SH2-ligand binding 
Journal of the American Chemical Society  2010;132(32):11058-11070.
NMR spectroscopy and molecular dynamics (MD) simulations were used to probe the structure and dynamics of complexes of three phosphotyrosine-derived peptides with the Src SH2 domain in an effort to uncover a structural explanation for enthalpy-entropy compensation observed in the binding thermodynamics. The series of phosphotyrosine peptide derivatives comprises the natural pYEEI Src SH2 ligand, a constrained mimic, in which the phosphotyrosine (pY) residue is preorganized in the bound conformation for the purpose of gaining an entropic advantage to binding, and a flexible analog of the constrained mimic. The expected gain in binding entropy of the constrained mimic was realized; however, a balancing loss in binding enthalpy was also observed that could not be rationalized from the crystallographic structures. We examined protein dynamics to evaluate whether the observed enthalpic penalty might be the result of effects arising from altered motions in the complex. 15N-relaxation studies and positional fluctuations from molecular dynamics indicate that the main-chain dynamics of the protein show little variation among the three complexes. Root mean squared (RMS) coordinate deviations vary by less than 1.5 Å for all non-hydrogen atoms for the crystal structures and in the ensemble average structures calculated from the simulations. In contrast to this striking similarity in the structures and dynamics, there are a number of large chemical shift differences from residues across the binding interface, but particularly from key Src SH2 residues that interact with pY, the ‘hot spot’ residue, which contributes about half of the binding free energy. Rank order correlations between chemical shifts and ligand binding enthalpy for several pY-binding residues, coupled with available mutagenesis and calorimetric data, suggest that subtle structural perturbations (< 1 Å) from the conformational constraint of the pY residue sufficiently alter the geometry of enthalpically critical interactions in the binding pocket to cause the loss of binding enthalpy, leading to the observed entropy-enthalpy compensation. We find no evidence to support the premise that enthalpy-entropy compensation is an inherent property and conclude that preorganization of Src SH2 ligand residues involved in binding hot spots may eventuate in suboptimal interactions with the domain. We propose that introducing constraints elsewhere in the ligand could minimize entropy-enthalpy compensation effects. The results illustrate the utility of the NMR chemical shift to highlight small, but energetically significant, perturbations in structure that might otherwise go unnoticed in an apparently rigid protein.
PMCID: PMC2943377  PMID: 20698672
computational binding enthalpy; NMR chemical shift perturbation; SH2 binding specificity
24.  Thermodynamics of Binding of Structurally Similar Ligands to Histone Deacetylase 8 Sheds Light on Challenges in the Rational Design of Potent and Isozyme-Selective Inhibitors of the Enzyme 
Biochemistry  2014;53(48):7445-7458.
Among the different histone deacetylase (HDAC) isozymes, HDAC8 is the most highly malleable enzyme, and it exhibits the potential to accommodate structurally diverse ligands (albeit with moderate binding affinities) in its active site pocket. To probe the molecular basis of this feature, we performed detailed thermodynamic studies of the binding of structurally similar ligands, which differed with respect to the “cap”, “linker”, and “metal-binding” regions of the suberoylanilide hydroxamic acid (SAHA) pharmacophore, to HDAC8. The experimental data revealed that although the enthalpic (ΔH°) and entropic (ΔS°) changes for the binding of individual SAHA analogues to HDAC8 were substantially different, their binding free energies (ΔG°) were markedly similar, conforming to a strong enthalpy–entropy compensation effect. This effect was further observed in the temperature-dependent thermodynamics of binding of all SAHA analogues to the enzyme. Notably, in contrast to other metalloenzymes, our isothermal titration calorimetry experiments (performed in different buffers of varying ionization enthalpies) suggest that depending on the ligand, its zinc-binding group may or may not be deprotonated upon the binding to HDAC8. Furthermore, the heat capacity changes (ΔCp°) associated with the ligand binding to HDAC8 markedly differed from one SAHA analogue to the other, and such features could primarily be rationalized in light of the dynamic flexibility in the enzyme structure in conjunction with the reorganization of the active site resident water molecules. Arguments are presented that although the binding thermodynamic features described above would facilitate identification of weak to moderately tight-binding HDAC8 inhibitors (by a high-throughput and/or virtual screening of libraries of small molecules), they would pose major challenges for the structure-based rational design of highly potent and isozyme-selective inhibitors of human HDAC8.
PMCID: PMC4263425  PMID: 25407689
25.  Estimation of Solvation Entropy and Enthalpy via Analysis of Water Oxygen–Hydrogen Correlations 
A statistical-mechanical framework for estimation of solvation entropies and enthalpies is proposed, which is based on the analysis of water as a mixture of correlated water oxygens and water hydrogens. Entropic contributions of increasing order are cast in terms of a Mutual Information Expansion that is evaluated to pairwise interactions. In turn, the enthalpy is computed directly from a distance-based hydrogen bonding energy algorithm. The resulting expressions are employed for grid-based analyses of Molecular Dynamics simulations. In this first assessment of the methodology, we obtained global estimates of the excess entropy and enthalpy of water that are in good agreement with experiment and examined the method’s ability to enable detailed elucidation of solvation thermodynamic structures, which can provide valuable knowledge toward molecular design.
Graphical abstract
PMCID: PMC4877138  PMID: 26574307

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