Insights into Modeling Approaches in Chemistry: Assessing Ligand-Protein Binding Thermodynamics Based on Rigid-Flexible Model Molecules

In the field of chemistry, model compounds find extensive use for investigating complex objects. One prime example of such object is the protein-ligand supramolecular interaction. Prediction the enthalpic and entropic contribution to the free energy associated with this process, as well as the structural and dynamic characteristics of protein-ligand complexes poses considerable challenges. This review exemplifies modeling approaches used to study protein-ligand binding (PLB) thermodynamics by employing pairs of conformationally constrained/flexible model molecules. Strategically designing the model molecules can reduce the number of variables that influence thermodynamic parameters. This enables scientists to gain deeper insights into the enthalpy and entropy of PLB, which is relevant for medicinal chemistry and drug design. The model studies reviewed here demonstrate that rigidifying ligands may induce compensating changes in the enthalpy and entropy of binding. Some “rules of thumb” have started to emerge on how to minimize entropy-enthalpy compensation and design efficient rigidified or flexible ligands.     

The effect of water displacement on binding thermodynamics: concanavalin A

Interactions at the binding interface of biomolecular complexes are often mediated by ordered water molecules. In this work, we considered two concanavalin A-carbohydrate complexes. In the first, a water molecule is buried at the binding interface. In the second, this water molecule is displaced by a modification of the ligand (Clarke, C.; Woods, R. J.; Gluska, J.; Cooper, A.; Nutley, M. A.; Boons, G. J. J. Am. Chem. Soc. 2001, 123, 12238-12247). We computed the contribution of this water molecule to the thermodynamic properties using statistical mechanical formulas for the energy and entropy and molecular dynamics simulations. Other contributions to the binding affinity, including desolvation, entropy of conformational restriction, and interaction between the ligand and protein, were also computed. The thermodynamic consequences of displacement of the ordered water molecule by ligand modification were in qualitative agreement with experimental data. The free energy contribution of the water molecule (-17.2 kcal/mol; -19.2 enthalpic and +2 entropic) was nearly equivalent to the additional protein-ligand interactions in trimannoside 2 (-18.9 kcal/mol). The two structural ions interact more strongly with the water than with the hydroxyl of trimannoside 2, thus favoring trimannoside 1. The contributions from desolvation and conformational entropy are much smaller but significant, compared to the binding free energy difference. The picture that emerges is that the final outcome of water displacement is sensitive to the details of the binding site and cannot be predicted by simple empirical rules.     

Enthalpy and entropy of nanoparticle association from temperature-dependent cryo-TEM

Quantum dots form equilibrium structures in liquid dispersions, due to thermodynamic forces that are often hard to quantify. Analysis of these structures, visualized using cryogenic electron microscopy, yields their formation free energy. Here we show that the nanoparticle interaction free energy can be further separated into the enthalpic and entropic contributions, using the temperature dependence of the assembled structures. Monodisperse oleic acid-capped PbSe nanoparticles dispersed in decalin were used as a model system, and the temperature-dependent equilibrium structures were imaged by cryo-TEM, after quenching from different initial temperatures. The interaction enthalpy and entropy follow from van 't Hoff's exact equation for the temperature dependence of thermodynamic equilibria, now applied to associating nanoparticles. The enthalpic component gives the magnitude of the contact interaction, which is crucial information in understanding the energetics of the self-assembly of nanoparticles into ordered structures.     

Enthalpy-entropy contributions to the potential of mean force of nanoscopic hydrophobic solutes

Entropic and enthalpic contributions to the hydrophobic interaction between nanoscopic hydrophobic solutes, modeled as graphene plates in water, have been calculated using molecular dynamics simulations in the isothermal-isobaric (NPT) ensemble with free energy perturbation methodology. We find the stabilizing contribution to the free energy of association (contact pair formation) to be the favorable entropic part, the enthalpic contribution being highly unfavorable. The desolvation barrier is dominated by the unfavorable enthalpic contribution, despite a fairly large favorable entropic compensation. The enthalpic contributions, incorporating the Lennard-Jones solute-solvent terms, largely determine the stability of the solvent separated configuration. We decompose the enthalpy into a direct solute-solute term, the solute-solvent interactions, and the remainder that contains pressure-volume work as well as contributions due to solvent reorganization. The enthalpic contribution due to changes in water-water interactions arising from solvent reorganization around the solute molecules is shown to have major contribution in the solvent induced enthalpy change.     

A Mixed QM/MM Scoring Function to Predict Protein-Ligand Binding Affinity

Computational methods for predicting protein-ligand binding free energy continue to be popular as a potential cost-cutting method in the drug discovery process. However, accurate predictions are often difficult to make as estimates must be made for certain electronic and entropic terms in conventional force field based scoring functions. Mixed quantum mechanics/molecular mechanics (QM/MM) methods allow electronic effects for a small region of the protein to be calculated, treating the remaining atoms as a fixed charge background for the active site. Such a semi-empirical QM/MM scoring function has been implemented in AMBER using DivCon and tested on a set of 23 metalloprotein-ligand complexes, where QM/MM methods provide a particular advantage in the modeling of the metal ion. The binding affinity of this set of proteins can be calculated with an R(2) of 0.64 and a standard deviation of 1.88 kcal/mol without fitting and 0.71 and a standard deviation of 1.69 kcal/mol with fitted weighting of the individual scoring terms. In this study we explore using various methods to calculate terms in the binding free energy equation, including entropy estimates and minimization standards. From these studies we found that using the rotational bond estimate to ligand entropy results in a reasonable R(2) of 0.63 without fitting. We also found that using the ESCF energy of the proteins without minimization resulted in an R(2) of 0.57, when using the rotatable bond entropy estimate.     

Listening to PS II: enthalpy, entropy, and volume changes

Photosystem II, located in the thylakoid membranes of green plants, algae, and cyanobacteria, uses sunlight to split water into protons, electrons, and a dioxygen molecule. The mechanism of its electron transfers and oxygen evolution including the structure of the protein and rates of the S-state cycle has been extensively investigated. Substantial progress has been made; however, the thermodynamics of PS II electron transfer and of the oxygen cycle are poorly understood. Recent progress in thermodynamic measurements in photosynthesis provides novel insights on the enthalpic and entropic contribution to electron transfer in proteins. In this review the thermodynamic parameters including quantum yield, enthalpy, entropy, and volume changes of PS II photochemistry determined by photoacoustics and other laser techniques are summarized and evaluated. Light-driven volume changes via electrostriction are directly related to the photoreaction in PS II and thus can be a useful measurement of PS II activity and function. The enthalpy changes of the reactions observed can be directly measured by photoacoustics. The apparent reaction entropy can also be estimated when the free energy is known. Dissecting the free energy of a photoreaction into enthalpic and entropic components provides critical information about mechanisms of PS II function. Potential limitations and future direction of the study of the thermodynamics of PS II electron transfer and oxygen evolution are presented.     

Thermodynamics of buried water clusters at a protein-ligand binding interface

The structure of the complex of cyclophilin A (CypA) with cyclosporin A (CsA, 1) shows a cluster of four water molecules buried at the binding interface, which is rearranged when CsA is replaced by (5-hydroxynorvaline)-2-cyclosporin (2). The thermodynamic contributions of each bound water molecule in the two complexes are explored with the inhomogeneous fluid solvation theory and molecular dynamics simulations. Water (WTR) 133 in complex 1 contributes little to the binding affinity, while WTR6 and 7 in complex 2 play an essential role in mediating protein-ligand binding with a hydrogen bond network. The calculations reveal that the rearrangement of the water molecules contributes favorably to the binding affinity, even though one of them is displaced going from ligand 1 to 2. Another favorable contribution comes from the larger protein-ligand interactions of ligand 2. However, these favorable contributions are not sufficient to overcome the unfavorable desolvation free energy change and the conformational entropy of the hydroxylpropyl group of ligand 2 in the complex, leading to a lower binding affinity of ligand 2. These physical insights may be useful in the development of improved scoring functions for binding affinity prediction.     

Water‐Restructuring Mutations Can Reverse the Thermodynamic Signature of Ligand Binding to Human Carbonic Anhydrase

This study uses mutants of human carbonic anhydrase (HCAII) to examine how changes in the organization of water within a binding pocket can alter the thermodynamics of protein–ligand association. Results from calorimetric, crystallographic, and theoretical analyses suggest that most mutations strengthen networks of water‐mediated hydrogen bonds and reduce binding affinity by increasing the enthalpic cost and, to a lesser extent, the entropic benefit of rearranging those networks during binding. The organization of water within a binding pocket can thus determine whether the hydrophobic interactions in which it engages are enthalpy‐driven or entropy‐driven. Our findings highlight a possible asymmetry in protein–ligand association by suggesting that, within the confines of the binding pocket of HCAII, binding events associated with enthalpically favorable rearrangements of water are stronger than those associated with entropically favorable ones.     

PLASS: Protein-ligand affinity statistical score – a knowledge-based force-field model of interaction derived from the PDB

We have developed PLASS (Protein-Ligand Affinity Statistical Score), a pair-wise potential of mean-force for rapid estimation of the binding affinity of a ligand molecule to a protein active site. This scoring function is derived from the frequency of occurrence of atom-type pairs in crystallographic complexes taken from the Protein Data Bank (PDB). Statistical distributions are converted into distance-dependent contributions to the Gibbs free interaction energy for 10 atomic types using the Boltzmann hypothesis, with only one adjustable parameter. For a representative set of 72 protein-ligand structures, PLASS scores correlate well with the experimentally measured dissociation constants: a correlation coefficient R of 0.82 and RMS error of 2.0 kcal/mol. Such high accuracy results from our novel treatment of the volume correction term, which takes into account the inhomogeneous properties of the protein-ligand complexes. PLASS is able to rank reliably the affinity of complexes which have as much diversity as in the PDB.     

Additivity and the physical basis of multivalency effects: a thermodynamic investigation of the calcium EDTA interaction

To better understand the origin of multivalency effects in ligand binding, the binding of a series of mono-, bi-, tri- and tetravalent carboxylate ligands to Ca(II) was examined by isothermal titration calorimetry (ITC). The data are inconsistent with an entropic origin of enhanced affinity, but rather show that at least in this instance the multivalency effect is enthalpic in origin. Analysis of binding data using the Jencks model shows the addition of incremental carboxylate "ligands" produces an unfavorable interaction entropy that is more than offset by a strongly favorable interaction enthalpy. The most likely source of this interaction enthalpy is the relief of repulsive Coulombic interactions in the unbound state. The conformational entropy penalty arising from the restriction of flexible dihedrals is negligible, within experimental error. On the other hand, an enthalpic contribution from linker restriction contributes strongly to the overall thermodynamics of ligand binding. Together, these data suggest that enthalpic effects dominate ligand binding, and design strategies should seek to optimize these interactions. The incorporation of unfavorable interactions in the unbound ligand that are relieved during binding provides an important mechanism by which to enhance ligand affinities.     

Calculation of Host-Guest Binding Affinities Using a Quantum-Mechanical Energy Model

The prediction of protein-ligand binding affinities is of central interest in computer-aided drug discovery, but it is still difficult to achieve a high degree of accuracy. Recent studies suggesting that available force fields may be a key source of error motivate the present study, which reports the first mining minima (M2) binding affinity calculations based on a quantum mechanical energy model, rather than an empirical force field. We apply a semi-empirical quantum-mechanical energy function, PM6-DH+, coupled with the COSMO solvation model, to 29 host-guest systems with a wide range of measured binding affinities. After correction for a systematic error, which appears to derive from the treatment of polar solvation, the computed absolute binding affinities agree well with experimental measurements, with a mean error 1.6 kcal/mol and a correlation coefficient of 0.91. These calculations also delineate the contributions of various energy components, including solute energy, configurational entropy, and solvation free energy, to the binding free energies of these host-guest complexes. Comparison with our previous calculations, which used empirical force fields, point to significant differences in both the energetic and entropic components of the binding free energy. The present study demonstrates successful combination of a quantum mechanical Hamiltonian with the M2 affinity method.     

Thermodynamics of Hydrophobic Interactions: Entropic Recognition of a Hydrophobic Moiety by Poly(Ethylene Oxide)–Zinc Porphyrin Conjugates

The recognition of 4‐alkylpyridines by water‐soluble poly(ethylene oxide)–zinc porphyrin conjugates was studied with a focus on the thermodynamic parameters of binding. Microcalorimetric studies indicated that binding of the alkyl group of the guest in water is driven by the entropic term (δΔH⁰=ΔH⁰(4‐pentylpyridine)? ΔH⁰(4‐methylpyridine)=+1.7 kJ mol^?1, δTΔS⁰=TΔS⁰(4‐pentylpyridine)? TΔS⁰(4‐methylpyridine)=+11.8 kJ mol^?1 at 298 K), thus showing the significance of water reorganization during host–guest interaction. The enthalpy–entropy compensation temperature of binding of 4‐alkylpyridines was as low as 38 K; only below this temperature could the enthalpic term be a driving force. The binding affinity was modulated by the addition of cations and by varying the degree of polymerization of poly(ethylene oxide), which suggests that guest binding is coupled with polymer conformation.     

Temperature effects on chiral microemulsion electrokinetic chromatography employing the chiral surfactant dodecoxycarbonylvaline

Dodecoxycarbonylvaline (DDCV) microemulsions (1% and 4%, w/v) were employed to evaluate the retention mechanism of a series of enantiomers over a temperature range of 15-35 degrees C. From the acquired retention data, van't Hoff plots were constructed and enthalpy and entropy of transfer were calculated from the slope and intercept, respectively. Resolution, enantioselectivity, distribution coefficients and Gibb's free energy were also calculated, as well as between enantiomer differences in enthalpy, entropy and Gibb's free energy. Finally, comparisons were made between the microemulsion thermodynamic data and a corresponding set of micellar data. While the 4% DDCV microemulsion did not provide a linear van't Hoff relationship, the 1% DDCV microemulsion was linear over a temperature range of 15-30 degrees C. For the 1% DDCV microemulsion, the enthalpic contribution to retention was consistently favorable (deltaH < 0), whereas the entropic contribution varied from compound to compound. Finally, while the achiral attraction of the analytes was greater for the micellar phase, the microemulsion seemed to provide a suitable difference in entropy (and Gibb's free energy) between enantiomers to achieve chiral discrimination.     

Prediction of trypsin/molecular fragment binding affinities by free energy decomposition and empirical scores

Two families of binding affinity estimation methodologies are described which were utilized in the SAMPL3 trypsin/fragment binding affinity challenge. The first is a free energy decomposition scheme based on a thermodynamic cycle, which included separate contributions from enthalpy and entropy of binding as well as a solvent contribution. Enthalpic contributions were estimated with PM6-DH2 semiempirical quantum mechanical interaction energies, which were modified with a statistical error correction procedure. Entropic contributions were estimated with the rigid-rotor harmonic approximation, and solvent contributions to the free energy were estimated with several different methods. The second general methodology is the empirical score LISA, which contains several physics-based terms trained with the large PDBBind database of protein/ligand complexes. Here we also introduce LISA+, an updated version of LISA which, prior to scoring, classifies systems into one of four classes based on a ligand's hydrophobicity and molecular weight. Each version of the two methodologies (a total of 11 methods) was trained against a compiled set of known trypsin binders available in the Protein Data Bank to yield scaling parameters for linear regression models. Both raw and scaled scores were submitted to SAMPL3. Variants of LISA showed relatively low absolute errors but also low correlation with experiment, while the free energy decomposition methods had modest success when scaling factors were included. Nonetheless, re-scaled LISA yielded the best predictions in the challenge in terms of RMS error, and six of these models placed in the top ten best predictions by RMS error. This work highlights some of the difficulties of predicting binding affinities of small molecular fragments to protein receptors as well as the benefit of using training data.     

Solvated interaction energy (SIE) for scoring protein-ligand binding affinities. 2. Benchmark in the CSAR-2010 scoring exercise

Solvated interaction energy (SIE) is an end-point physics-based scoring function for predicting binding affinities from force-field nonbonded interaction terms, continuum solvation, and configurational entropy linear compensation. We tested the SIE function in the Community Structure-Activity Resource (CSAR) scoring challenge consisting of high-resolution cocrystal structures for 343 protein-ligand complexes with high-quality binding affinity data and high diversity with respect to protein targets. Particular emphasis was placed on the sensitivity of SIE predictions to the assignment of protonation and tautomeric states in the complex and the treatment of metal ions near the protein-ligand interface. These were manually curated from an originally distributed CSAR-HiQ data set version, leading to the currently distributed CSAR-NRC-HiQ version. We found that this manual curation was a critical step for accurately testing the performance of the SIE function. The standard SIE parametrization, previously calibrated on an independent data set, predicted absolute binding affinities with a mean-unsigned-error (MUE) of 2.41 kcal/mol for the CSAR-HiQ version, which improved to 1.98 kcal/mol for the upgraded CSAR-NRC-HiQ version. Half-half retraining-testing of SIE parameters on two predefined subsets of CSAR-NRC-HiQ led to only marginal further improvements to an MUE of 1.83 kcal/mol. Hence, we do not recommend altering the current default parameters of SIE at this time. For a sample of SIE outliers, additional calculations by molecular dynamics-based SIE averaging with or without incorporation of ligand strain, by MM-PB(GB)/SA methods with or without entropic estimates, or even by the linear interaction energy (LIE) formalism with an explicit solvent model, did not further improve predictions.     

Supramolecular Binding Thermodynamics by Dispersion‐Corrected Density Functional Theory

The equilibrium association free enthalpies ΔG_a for typical supramolecular complexes in solution are calculated by ab initio quantum chemical methods. Ten neutral and three positively charged complexes with experimental ΔG_a values in the range 0 to ?21 kcal mol^?1 (on average ?6 kcal mol^?1) are investigated. The theoretical approach employs a (nondynamic) single‐structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion corrected density functional theory (DFT‐D3) with extended basis sets (triple‐ζ and quadruple‐ζ quality) is used to determine structures and gas‐phase interaction energies (ΔE), the COSMO‐RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro‐vibrational enthalpic/entropic contributions are obtained from harmonic frequency calculations. Low‐lying vibrational modes are treated by a free‐rotor approximation. The accurate account of London dispersion interactions is mandatory with contributions in the range ?5 to ?60 kcal mol^?1 (up to 200 % of ΔE). Inclusion of three‐body dispersion effects improves the results considerably. A semilocal (TPSS) and a hybrid density functional (PW6B95) have been tested. Although the ΔG_a values result as a sum of individually large terms with opposite sign (ΔE vs. solvation and entropy change), the approach provides unprecedented accuracy for ΔG_a values with errors of only 2 kcal mol^?1 on average. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramolecular chemistry and can be applied routinely to semirigid systems with 300–400 atoms. The various contributions to binding and enthalpy–entropy compensations are discussed.     

Entropy-Driven Cooperativity in the Guest Binding of an Octaphosphonate Bis-cavitand

Uncommon entropy-driven cooperativity is reported in the guest binding of an octaphosphonate bis-cavitand. Isothermal titration calorimetry determined the thermodynamic parameters for the 1:2 host–guest binding of bis-cavitands with ammonium guests in methanol, ethanol, 2-propanol, and chloroform. Chloroform drove uncommon entropy-driven cooperative binding, whereas the alcohols resulted in enthalpy-driven noncooperative binding. ¹H NMR studies revealed that each cavity contained six water molecules in chloroform, which were liberated on guest binding. The enthalpy–entropy compensation relationship produced a large positive intrinsic entropy in chloroform, which implies that water desolvation causes a considerable entropic gain by paying an enthalpic penalty due to breaking the hydrogen-bonding networks of the water clusters.     

Surface tension of aqueous electrolyte solutions. Thermodynamics

A thermodynamic theory is developed for obtaining the enthalpic and entropic contributions to the surface excess Gibbs energy of electrolyte solutions from the dependence of the surface tension on concentration and temperature. For elaboration, accurate activity coefficients in solution as functions of concentration and temperature are required. The theory is elaborated for (1-1) electrolytes and applied to HClO(4), HNO(3), NaCl, NaBr, and LiCl, of which the first two adsorb positively and the other three negatively. One of the conspicuous outcomes is that in all cases, the surface excess entropies slightly decrease with electrolyte activity but remain close to that of pure water, whereas the enthalpy is different from that. The implication is that the driving force for positive or negative adsorption must have an enthalpic origin. This finding can be useful in developing and evaluating theoretical models for the interpretation of surface tensions of electrolyte solutions.