Enthalpy–Entropy Compensation upon Molecular Conformational Changes

Using Implicit-Solvent Potentials to Extract Water Contributions to Enthalpy-Entropy Compensation in Biomolecular Associations

Biomolecular assembly typically exhibits enthalpy-entropy compensation (EEC) behavior whose molecular origin remains a long-standing puzzle. While water restructuring is believed to play an important role in EEC, its contribution to the entropy and enthalpy changes, and how these changes relate to EEC, remains poorly understood. Here, we show that water reorganization entropy/enthalpy can be obtained by exploiting the temperature dependence in effective, implicit-solvent potentials. We find that the different temperature dependencies in the hydrophobic interaction, rooted in water reorganization, result in substantial variations in the entropy/enthalpy change, which are responsible for EEC. For lower-critical-solution-temperature association, water reorganization entropy dominates the free-energy change at the expense of enthalpy; for upper-critical-solution-temperature association, water reorganization enthalpy drives the process at the cost of entropy. Other effects, such as electrostatic interaction and conformation change of the macromolecules, contribute much less to the variations in entropy/enthalpy.

The Role of Packing, Dispersion, Electrostatics, and Solvation in High-Affinity Complexes of Cucurbit[n]urils with Uncharged Polar Guests

The rationalization of non‐covalent binding trends is both of fundamental interest and provides new design concepts for biomimetic molecular systems. Cucurbit[n]urils (CBn) are known for a long time as the strongest synthetic binders for a wide range of (bio)organic compounds in water. However, their host‐guest binding mechanism remains ambiguous despite their symmetric and simple macrocyclic structure and the wealth of literature reports. We herein report experimental thermodynamic binding parameters (ΔG, ΔH, TΔS) for CB7 and CB8 with a set of hydroxylated adamantanes, di‐, and triamantanes as uncharged, rigid, and spherical/ellipsoidal guests. Binding geometries and binding energy decomposition were obtained from high‐level theory computations. This study reveals that neither London dispersion interactions, nor electronic energies or entropic factors are decisive, selectivity‐controlling factors for CBn complexes. In contrast, peculiar host‐related solvation effects were identified as the major factor for rationalizing the unique behavior and record‐affinity characteristics of cucurbit[n]urils.

Characterizing Protein Protonation Microstates Using Monte Carlo Sampling

Proteins are polyelectrolytes with acidic and basic amino acids Asp, Glu, Arg, Lys, and His, making up ≈25% of the residues. The protonation state of residues, cofactors, and ligands defines a "protonation microstate". In an ensemble of proteins some residues will be ionized and others neutral, leading to a mixture of protonation microstates rather than in a single one as is often assumed. The microstate distribution changes with pH. The protein environment also modifies residue proton affinity so microstate distributions change in different reaction intermediates or as ligands are bound. Particular protonation microstates may be required for function, while others exist simply because there are many states with similar energy. Here, the protonation microstates generated in Monte Carlo sampling in MCCE are characterized in HEW lysozyme as a function of pH and bacterial photosynthetic reaction centers (RCs) in different reaction intermediates. The lowest energy and highest probability microstates are compared. The ΔG, ΔH, and ΔS between the four protonation states of Glu35 and Asp52 in lysozyme are shown to be calculated with reasonable precision. At pH 7 the lysozyme charge ranges from 6 to 10, with 24 accepted protonation microstates, while RCs have ≈50,000. A weighted Pearson correlation analysis shows coupling between residue protonation states in RCs and how they change when the quinone in the Q_B site is reduced. Protonation microstates can be used to define input MD parameters and provide insight into the motion of protons coupled to reactions.

Thermodynamic, kinetic, and structural parameterization of human carbonic anhydrase interactions toward enhanced inhibitor design

The aim of rational drug design is to develop small molecules using a quantitative approach to optimize affinity. This should enhance the development of chemical compounds that would specifically, selectively, reversibly, and with high affinity interact with a target protein. It is not yet possible to develop such compounds using computational (i.e., in silico) approach and instead the lead molecules are discovered in high-throughput screening searches of large compound libraries. The main reason why in silico methods are not capable to deliver is our poor understanding of the compound structure-thermodynamics and structure-kinetics correlations. There is a need for databases of intrinsic binding parameters (e.g., the change upon binding in standard Gibbs energy (ΔGint), enthalpy (ΔHint), entropy (ΔSint), volume (ΔVintr), heat capacity (ΔCp,int), association rate (ka,int), and dissociation rate (kd,int)) between a series of closely related proteins and a chemically diverse, but pharmacophoric group-guided library of compounds together with the co-crystal structures that could help explain the structure-energetics correlations and rationally design novel compounds. Assembly of these data will facilitate attempts to provide correlations and train data for modeling of compound binding. Here, we report large datasets of the intrinsic thermodynamic and kinetic data including over 400 primary sulfonamide compound binding to a family of 12 catalytically active human carbonic anhydrases (CA). Thermodynamic parameters have been determined by the fluorescent thermal shift assay, isothermal titration calorimetry, and by the stopped-flow assay of the inhibition of enzymatic activity. Kinetic measurements were performed using surface plasmon resonance. Intrinsic thermodynamic and kinetic parameters of binding were determined by dissecting the binding-linked protonation reactions of the protein and sulfonamide. The compound structure-thermodynamics and kinetics correlations reported here helped to discover compounds that exhibited picomolar affinities, hour-long residence times, and million-fold selectivities over non-target CA isoforms. Drug-lead compounds are suggested for anticancer target CA IX and CA XII, antiglaucoma CA IV, antiobesity CA VA and CA VB, and other isoforms. Together with 85 X-ray crystallographic structures of 60 compounds bound to six CA isoforms, the database should be of help to continue developing the principles of rational target-based drug design.

The Enthalpy-entropy Compensation Phenomenon. Limitations for the Use of Some Basic Thermodynamic Equations

The thermodynamic analyses of proteins, protein-ligands and protein-nucleic acid complexes involves the entropy-enthalpy (S-H) compensation phenomenon. We have examined the question whether the observed compensation is artificial or reflects anything more than the well-known laws of statistical thermodynamics (so-called extra-thermodynamic compensation). We have shown that enthalpy- entropy compensation (EEC) is mainly the trivial consequence of the basic thermodynamic laws and there are no experimental evidences for existence of the extra-thermodynamic compensation. In most cases EEC obtained in the experiments through the plot enthalpies (ΔH) and entropies (TΔS) versus one another is meaningless due to the large correlated errors in ΔH and TΔS, unless special measures are taken to minimize, quantify and propagate these errors. Van't Hoff equation can be used for entropy calculation in limited cases when enthalpy is measured in independent experiments. Eyring equation cannot be used for calculation of entropy in any case and should be excluded from scientific use. Both equation, Van't Hoff and Eyring cannot be used for simultaneous calculation of the enthalpy and entropy values using one set of data. All the data obtained in this way should be recognized as erroneous.

Relative Principal Components Analysis: Application to Analyzing Biomolecular Conformational Changes

A new method termed “Relative Principal Components Analysis” (RPCA) is introduced that extracts optimal relevant principal components to describe the change between two data samples representing two macroscopic states. The method is widely applicable in data-driven science. Calculating the components is based on a physical framework that introduces the objective function (the Kullback–Leibler divergence) appropriate for quantifying the change of the macroscopic state affected by the changes in the microscopic features. To demonstrate the applicability of RPCA, we analyze the thermodynamically relevant conformational changes of the protein HIV-1 protease upon binding to different drug molecules. In this case, the RPCA method provides a sound thermodynamic foundation for analyzing the binding process and thus characterizing both the collective and the locally relevant conformational changes. Moreover, the relevant collective conformational changes can be reconstructed from the informative latent variables to exhibit both the enhanced and the restricted conformational fluctuations upon ligand association.

Assessing the performance of MM/PBSA and MM/GBSA methods. 7. Entropy effects on the performance of end-point binding free energy calculation approaches

Entropy effects play an important role in drug-target interactions, but the entropic contribution to ligand-binding affinity is often neglected by end-point binding free energy calculation methods, such as MM/GBSA and MM/PBSA, due to the expensive computational cost of normal mode analysis (NMA). Here, we systematically investigated entropy effects on the prediction power of MM/GBSA and MM/PBSA using >1500 protein-ligand systems and six representative AMBER force fields. Two computationally efficient methods, including NMA based on truncated structures and the interaction entropy approach, were used to estimate the entropic contributions to ligand-target binding free energies. In terms of the overall accuracy, we found that, for the minimized structures, in most cases the inclusion of the conformational entropies predicted by truncated NMA (enthalpynmode_min_9Å) compromises the overall accuracy of MM/GBSA and MM/PBSA compared with the enthalpies calculated based on the minimized structures (enthalpymin). However, for the MD trajectories, the binding free energies can be improved by the inclusion of the conformation entropies predicted by either truncated-NMA for a relatively high dielectric constant (εin = 4) or the interaction entropy method for εin = 1-4. In terms of reproducing the absolute binding free energies, the binding free energies estimated by including the truncated-NMA entropies based on the MD trajectories (ΔGnmode_md_9Å) give the lowest average absolute deviations against the experimental data among all the tested strategies for both MM/GBSA and MM/PBSA. Although the inclusion of the truncated NMA based on the MD trajectories (ΔGnmode_md_9Å) for a relatively high dielectric constant gave the overall best result and the lowest average absolute deviations against the experimental data (for the ff03 force field), it needs too much computational time. Alternatively, considering that the interaction entropy method does not incur any additional computational cost and can give comparable (at high dielectric constant, εin = 4) or even better (at low dielectric constant, εin = 1-2) results than the truncated-NMA entropy (ΔGnmode_md_9Å), the interaction entropy approach is recommended to estimate the entropic component for MM/GBSA and MM/PBSA based on MD trajectories, especially for a diverse dataset. Furthermore, we compared the predictions of MM/GBSA with six different AMBER force fields. The results show that the ff03 force field (ff03 for proteins and gaff with AM1-BCC charges for ligands) performs the best, but the predictions given by the tested force fields are comparable, implying that the MM/GBSA predictions are not very sensitive to force fields.

The Molecular Origin of Enthalpy/Entropy Compensation in Biomolecular Recognition

Biomolecular recognition can be stubborn; changes in the structures of associating molecules, or the environments in which they associate, often yield compensating changes in enthalpies and entropies of binding and no net change in affinities. This phenomenon—termed enthalpy/entropy (H/S) compensation—hinders efforts in biomolecular design, and its incidence—often a surprise to experimentalists—makes interactions between biomolecules difficult to predict. Although characterizing H/S compensation requires experimental care, it is unquestionably a real phenomenon that has, from an engineering perspective, useful physical origins. Studying H/S compensation can help illuminate the still-murky roles of water and dynamics in biomolecular recognition and self-assembly. This review summarizes known sources of H/ S compensation (real and perceived) and lays out a conceptual framework for understanding and dissecting—and, perhaps, avoiding or exploiting—this phenomenon in biophysical systems.

Effect of heating and ionic strength on the interaction of bovine serum albumin and the antinutrients tannic and phytic acids, and its influence on in vitro protein digestibility

Bioavailability of food nutrients can be reduced in the presence of antinutrients such as phytates and tannins. This work aimed to study bovine serum albumin binding to phytic acid and tannic acid, and its influence on in vitro protein digestibility. The effect of autoclaving and boiling on protein digestibility and the microstructure of complexes was also evaluated. Results showed that high ionic strength promotes greater affinity between tannic acid and bovine serum albumin, and decreases in vitro protein digestibility. For phytic acid and bovine serum albumin, the opposite behavior is observed because interactions are governed by electrostatic forces. A rise in temperature above that causing denaturation of the protein favors its interaction with phytic acid, and disfavors that with tannic acid, probably due to different protein binding site exposure. For both antinutrients, heating treatment increased protein hydrolysis, the size of complexes and their fragility.

Systematic exploration of multiple drug binding sites

Background

Targets with multiple (prerequisite or allosteric) binding sites have an increasing importance in drug design. Experimental determination of atomic resolution structures of ligands weakly bound to multiple binding sites is often challenging. Blind docking has been widely used for fast mapping of the entire target surface for multiple binding sites. Reliability of blind docking is limited by approximations of hydration models, simplified handling of molecular flexibility, and imperfect search algorithms.

Results

To overcome such limitations, the present study introduces Wrap ‘n’ Shake (WnS), an atomic resolution method that systematically “wraps” the entire target into a monolayer of ligand molecules. Functional binding sites are extracted by a rapid molecular dynamics shaker. WnS is tested on biologically important systems such as mitogen-activated protein, tyrosine-protein kinases, key players of cellular signaling, and farnesyl pyrophosphate synthase, a target of antitumor agents.

Electronic supplementary material

The online version of this article (10.1186/s13321-017-0255-6) contains supplementary material, which is available to authorized users.

The Roles of Water in the Protein Matrix: A Largely Untapped Resource for Drug Discovery

The value of thoroughly understanding the thermodynamics specific to a drug discovery/design study is well known. Over the past decade, the crucial roles of water molecules in protein structure, function, and dynamics have also become increasingly appreciated. This Perspective explores water in the biological environment by adopting its point of view in such phenomena. The prevailing thermodynamic models of the past, where water was seen largely in terms of an entropic gain after its displacement by a ligand, are now known to be much too simplistic. We adopt a set of terminology that describes water molecules as being "hot" and "cold", which we have defined as being easy and difficult to displace, respectively. The basis of these designations, which involve both enthalpic and entropic water contributions, are explored in several classes of biomolecules and structural motifs. The hallmarks for characterizing water molecules are examined, and computational tools for evaluating water-centric thermodynamics are reviewed. This Perspective's summary features guidelines for exploiting water molecules in drug discovery.

Elucidating the energetic contributions to the binding free energy

New exact equations are derived for the terms contributing to the binding free energy (ΔG⁰) of a ligand-receptor pair using our recently introduced formalism which we here call perturbation-divergence formalism (PDF). Specifically, ΔG⁰ equals the sum of the average of the perturbation (pertaining to new interactions) and additional dissipative terms. The average of the perturbation includes the sum of the average receptor-ligand interactions and the average of the change of solvation energies upon association. The Kullback-Leibler (KL) divergence quantifies the energetically dissipative terms, which are due to the configurational changes and, using the chain rule of KL divergence, can be decomposed into (i) dissipation due to limiting the external liberation (translation and rotation) of the ligand relative to the receptor and (ii) dissipation due to conformational (internal) changes inside the receptor and the ligand. We also identify all exactly canceling energetic terms which do not contribute to ΔG⁰. Furthermore, the PDF provides a new approach towards dimensionality reduction in the representation of the association process and towards relating the dynamic (high dimensional) with the thermodynamic (one-dimensional) changes.

Solvent effects on ligand binding to a serine protease

ITC experiments and MD simulations reveal the mechanism behind enthalpy/entropy compensation upon trypsin-benzamidine binding at different solvation conditions.

Exploring the interaction of phenothiazinium dyes methylene blue, new methylene blue, azure A and azure B with tRNAPhe: spectroscopic, thermodynamic, voltammetric and molecular modeling approach

RNA targeting by small molecules.

AutoDock-GIST: Incorporating Thermodynamics of Active-Site Water into Scoring Function for Accurate Protein-Ligand Docking

Water plays a significant role in the binding process between protein and ligand. However, the thermodynamics of water molecules are often underestimated, or even ignored, in protein-ligand docking. Usually, the free energies of active-site water molecules are substantially different from those of waters in the bulk region. The binding of a ligand to a protein causes a displacement of these waters from an active site to bulk, and this displacement process substantially contributes to the free energy change of protein-ligand binding. The free energy of active-site water molecules can be calculated by grid inhomogeneous solvation theory (GIST), using molecular dynamics (MD) and the trajectory of a target protein and water molecules. Here, we show a case study of the combination of GIST and a docking program and discuss the effectiveness of the displacing gain of unfavorable water in protein-ligand docking. We combined the GIST-based desolvation function with the scoring function of AutoDock4, which is called AutoDock-GIST. The proposed scoring function was assessed employing 51 ligands of coagulation factor Xa (FXa), and results showed that both scoring accuracy and docking success rate were improved. We also evaluated virtual screening performance of AutoDock-GIST using FXa ligands in the directory of useful decoys-enhanced (DUD-E), thus finding that the displacing gain of unfavorable water is effective for a successful docking campaign.

How Molecular Conformational Changes Affect Changes in Free Energy

A simple quantitative relationship between the molecular conformational changes and the corresponding changes in the free energy is presented. The change in free energy is the sum of that part of the enthalpic change that is due to the externally applied work (perturbation) and of that part of the entropic change, termed dissipative entropy, that is related to the conformational changes. The dissipative entropy is equivalent to the relative entropy, a concept from information theory, between the distributions of the conformations in the initial and the final states. The remaining change in entropy (nondissipative) cancels exactly with the remaining enthalpic change. The calculation of the dissipative entropy is demonstrated to pose the main difficulty in free energy computation. The straightforward decomposition of the dissipative entropy into contributions from different parts of the system promises to improve the understanding of the role of conformational changes in biochemical reactions.

Experimental Binding Energies in Supramolecular Complexes

On the basis of many literature measurements, a critical overview is given on essential noncovalent interactions in synthetic supramolecular complexes, accompanied by analyses with selected proteins. The methods, which can be applied to derive binding increments for single noncovalent interactions, start with the evaluation of consistency and additivity with a sufficiently large number of different host-guest complexes by applying linear free energy relations. Other strategies involve the use of double mutant cycles, of molecular balances, of dynamic combinatorial libraries, and of crystal structures. Promises and limitations of these strategies are discussed. Most of the analyses stem from solution studies, but a few also from gas phase. The empirically derived interactions are then presented on the basis of selected complexes with respect to ion pairing, hydrogen bonding, electrostatic contributions, halogen bonding, π-π-stacking, dispersive forces, cation-π and anion-π interactions, and contributions from the hydrophobic effect. Cooperativity in host-guest complexes as well as in self-assembly, and entropy factors are briefly highlighted. Tables with typical values for single noncovalent free energies and polarity parameters are in the Supporting Information.

Configurational space discretization and free energy calculation in complex molecular systems

We sought to design a free energy calculation scheme with the hope of saving cost for generating dynamical information that is inherent in trajectories. We demonstrated that snapshots in a converged trajectory set are associated with implicit conformers that have invariant statistical weight distribution (ISWD). Since infinite number of sets of implicit conformers with ISWD may be created through independent converged trajectory sets, we hypothesized that explicit conformers with ISWD may be constructed for complex molecular systems through systematic increase of conformer fineness, and tested the hypothesis in lipid molecule palmitoyloleoylphosphatidylcholine (POPC). Furthermore, when explicit conformers with ISWD were utilized as basic states to define conformational entropy, change of which between two given macrostates was found to be equivalent to change of free energy except a mere difference of a negative temperature factor, and change of enthalpy essentially cancels corresponding change of average intra-conformer entropy. By implicitly taking advantage of entropy enthalpy compensation and forgoing all dynamical information, constructing explicit conformers with ISWD and counting thermally accessible number of which for interested end macrostates is likely to be an efficient and reliable alternative end point free energy calculation strategy.

The Role of Conformational Changes in Molecular Recognition

Conformational changes of molecules are crucial elements in many biochemical processes, and also in molecular recognition. Here, we present a novel exact mathematical equation for the binding free energy of a receptor-ligand pair. It shows that the energetic contribution due to conformational changes upon molecular recognition is defined by the so-called Kullback-Leibler (KL) divergence between the probability distributions of the conformational ensemble of the biomolecule in the bound and free states. We show that conformational changes always contribute positively to the change in free energy and therefore disfavor the association process. Using the example of ligands binding to a flexible cavity of T4 lysozyme, we illustrate that, due to enthalpy-entropy compensation, the conformational entropy is a misleading quantity for assessing the conformational contribution to the binding free energy, in contrast to the KL divergence, which is the correct quantity to use in this context.