Free-energy component analysis of 40 protein-DNA complexes: a consensus view on the thermodynamics of binding at the molecular level

Noncovalent association of proteins to specific target sites on DNA--a process central to gene expression and regulation--has thus far proven to be idiosyncratic and elusive to generalizations on the nature of the driving forces. The spate of structural information on protein--DNA complexes sets the stage for theoretical investigations on the molecular thermodynamics of binding aimed at identifying forces responsible for specific macromolecular recognition. Computation of absolute binding free energies for systems of this complexity transiting from structural information is a stupendous task. Adopting some recent progresses in treating atomic level interactions in proteins and nucleic acids including solvent and salt effects, we have put together an energy component methodology cast in a phenomenological mode and amenable to systematic improvements and developed a computational first atlas of the free energy contributors to binding in approximately 40 protein-DNA complexes representing a variety of structural motifs and functions. Illustrating vividly the compensatory nature of the free energy components contributing to the energetics of recognition for attaining optimal binding, our results highlight unambiguously the roles played by packing, electrostatics including hydrogen bonds, ion and water release (cavitation) in protein-DNA binding. Cavitation and van der Waals contributions without exception favor complexation. The electrostatics is marginally unfavorable in a consensus view. Basic residues on the protein contribute favorably to binding despite the desolvation expense. The electrostatics arising from the acidic and neutral residues proves unfavorable to binding. An enveloping mode of binding to short stretches of DNA makes for a strong unfavorable net electrostatics but a highly favorable van der Waals and cavitation contribution. Thus, noncovalent protein-DNA association is a system-specific fine balancing act of these diverse competing forces. With the advances in computational methods as applied to macromolecular recognition, the challenge now seems to be to correlate the differential (initial vs. final) energetics to substituent effects in drug design and to move from affinity to specificity.     

On the nonpolar hydration free energy of proteins: surface area and continuum solvent models for the solute-solvent interaction energy

Implicit solvent hydration free energy models are an important component of most modern computational methods aimed at protein structure prediction, binding affinity prediction, and modeling of conformational equilibria. The nonpolar component of the hydration free energy, consisting of a repulsive cavity term and an attractive van der Waals solute-solvent interaction term, is often modeled using estimators based on the solvent exposed solute surface area. In this paper, we analyze the accuracy of linear surface area models for predicting the van der Waals solute-solvent interaction energies of native and non-native protein conformations, peptides and small molecules, and the desolvation penalty of protein-protein and protein-ligand binding complexes. The target values are obtained from explicit solvent simulations and from a continuum solvent van der Waals interaction energy model. The results indicate that the standard surface area model, while useful on a coarse-grained scale, may not be accurate or transferable enough for high resolution modeling studies of protein folding and binding. The continuum model constructed in the course of this study provides one path for the development of a computationally efficient implicit solvent nonpolar hydration free energy estimator suitable for high-resolution structural and thermodynamic modeling of biological macromolecules.     

Selectivity of neutral/weakly basic P1 group inhibitors of thrombin and trypsin by a molecular dynamics study

Molecular dynamics (MD) simulations followed by molecular mechanics generalized Born surface area (MM-GBSA) analyses have been carried out to study the selectivity of two neutral and weakly basic P1 group inhibitors (177 and CDA) to thrombin and trypsin. Detailed binding free energies between these inhibitors and individual protein residues are calculated by using a per-residue basis decomposition method. The analysis of the detailed interaction energies provides insight on the protein-inhibitor-binding mechanism and helps to elucidate the basis for achieving selectivity through interpretation of the structural and energetic results from the simulations. The study shows that the dominant factor of selectivity for both inhibitors is van der Waals energy, which suggests better shape complementarity and packing with thrombin. Nonpolar solvation free energy and total entropy contribution are also in favor of selectivity, but the contributions are much smaller. Binding mode and structural analysis show that 177 binds to thrombin and trypsin in a similar binding mode. In contrast, the CDA binds to thrombin and trypsin in very different modes.     

Complexation forces in aqueous solution. Calorimetric studies of the association of 2-hydroxypropyl-β-cyclodextrin with monocarboxylic acids or cycloalkanols

The formation of complexes between 2-hydroxypropyl-β-cyclodextrin and monocarboxylic acids or cycloalkanols has been studied calorimetrically at 298 K in phosphate buffer, pH 11.3. The forces involved in the association process are discussed in the light of the signs and values of the thermodynamic parameters obtained: association enthalpy, binding constant, Gibbs free energy, and entropy.From this study it was inferred that (i) for monocarboxylic acids, hydrophobic interactions are the primary force determining complexation, as indicated by the small enthalpies and by the high and positive entropies. For the cycloalkanols, instead, enthalpies are negative and entropies positive or negative, depending on the solvent medium employed, namely water or phosphate buffer; (ii) the most important requirement for the formation of the complex is a good spatial fit between the two interacting molecules. A cavity elongation effect occurs because of the presence of the hydroxypropyl groups on the rim of the macrocycle. The relative contribution of hydrophobic and van der Waals interactions varies with the dimensions of the guest molecules; (iii) a linear correlation exists between enthalpy and entropy of complexation, underlying that inclusion is a process dominated by hydration phenomena and ascribed to the modifications experienced by the solvent in the hydration shells of the interacting substances.     

Can Dispersion Forces Govern Aromatic Stacking in an Organic Solvent?

Experimental support for the dominance of van der Waals dispersion forces in aromatic stacking interactions occurring in organic solution is surprisingly limited. The size‐dependence of aromatic stacking in an organic solvent was examined. The interaction energy was found to vary by about 7.5 kJ mol⁻¹ on going from a phenyl–phenyl to an anthracene–pyrene stack. Strikingly, the experimental data were highly correlated with dispersion energies determined using symmetry‐adapted perturbation theory (SAPT), while the induction, exchange, electrostatic, and solvation energy components correlated poorly. Both the experimental data and the SAPT‐dispersion energies gave high‐quality correlations with the change in solvent accessible area upon complexation. Thus, the size‐dependence of aromatic stacking interactions is consistent with the dominance of van der Waals dispersion forces even in the presence of a competing polarizable solvent.     

Can Dispersion Forces Govern Aromatic Stacking in an Organic Solvent?

Experimental support for the dominance of van der Waals dispersion forces in aromatic stacking interactions occurring in organic solution is surprisingly limited. The size‐dependence of aromatic stacking in an organic solvent was examined. The interaction energy was found to vary by about 7.5 kJ mol^?1 on going from a phenyl–phenyl to an anthracene–pyrene stack. Strikingly, the experimental data were highly correlated with dispersion energies determined using symmetry‐adapted perturbation theory (SAPT), while the induction, exchange, electrostatic, and solvation energy components correlated poorly. Both the experimental data and the SAPT‐dispersion energies gave high‐quality correlations with the change in solvent accessible area upon complexation. Thus, the size‐dependence of aromatic stacking interactions is consistent with the dominance of van der Waals dispersion forces even in the presence of a competing polarizable solvent.     

Sensitivity analysis of thermodynamic properties of liquid water: a general approach to improve empirical potentials

A sensitivity analysis of bulk water thermodynamics is presented in an effort to understand the relation between qualitative features of molecular potentials and properties that they predict. The analysis is incorporated in molecular dynamics simulations and investigates the sensitivity of the Helmholtz free energy, internal energy, entropy, heat capacity, pressure, thermal pressure coefficient, and static dielectric constant to components of the potential rather than the parameters of a given functional form. The sensitivities of the properties are calculated with respect to the van der Waals repulsive and the attractive parts, plus short- and long-range Coulomb parts of three four site empirical water potentials: TIP4P, Dang-Chang and TTM2R. The polarization sensitivity is calculated for the polarizable Dang-Chang and TTM2R potentials. This new type of analysis allows direct comparisons of the sensitivities for different potentials that use different functional forms. The analysis indicates that all investigated properties are most sensitive to the van der Waals repulsive, the short-range Coulomb and the polarization components of the potentials. When polarization is included in the potentials, the magnitude of the sensitivity of the Helmholtz free energy, internal energy, and entropy with respect to this part of the potential is comparable in magnitude to the other electrostatic components. In addition similarities in trends of observed sensitivities for nonpolarizable and polarizable potentials lead to the conclusion that the complexity of the model is not of critical importance for the calculation of these thermodynamic properties for bulk water. The van der Waals attractive and the long-range Coulomb sensitivities are relatively small for the entropy, heat capacity, thermal pressure coefficient and the static dielectric constant, while small changes in any of the potential contributions will significantly affect the pressure. The analysis suggests a procedure for modification of the potentials to improve predictions of thermodynamic properties and we demonstrate this general approach for modifying potentials for one of the potentials.     

The application of three approximate free energy calculations methods to structure based ligand design: Trypsin and its complex with inhibitors

Three approximate free energy calculation methods are examined and applied to an example ligand design problem. The first of the methods uses a single simulation to estimate the relative binding free energies for related ligands that are not simulated. The second method is similar, except that it uses only first derivatives of free energy with respect to atomic parameters (most often charge, van der Waals equilibrium distance, and van der Waals well depth) to calculate free energy differences. The last method PROFEC (Pictorial Representation of Free Energy Components), generates contour maps that show how binding free energy changes when additional particles are added near the ligand. These three methods are applied to a benzamidine/trypsin complex. They each reproduce the general trends in the binding free energies, indicating that they might be useful for suggesting how ligands could be modified to improve binding and, consequently, useful in structure-based drug design.     

Selectivity in supramolecular host-guest complexes

The background of possible selectivity-affinity correlations and their limitations is reviewed, with typical crown ether and cryptand complexes, ionic associations, hydrogen bonded complexes and complexes driven by van der Waals, stacking or hydrophobic interactions, with some additional topics including associations based on metal coordination as supplementary material. This tutorial review is addressed to students and researchers interested in molecular recognition, and relates to the design of sensors, of discriminators for separation processes, of supramolecular devices and of drug compounds. A theoretical analysis of selectivity in supramolecular host-guest complexes, defined as a difference in binding free energies for structurally related guests, as a function of total binding free energy shows that for certain types of intermolecular interactions one may observe a correlation between selectivity and affinity. Such correlation fails however if the selectivity is due to additional interactions at a secondary binding sites, which is expected in complexes with anisotropic guest molecules. Several clear examples of theoretically expected selectivity-affinity correlations are found. The influence of reaction conditions on the experimentally observed selectivity, defined as a difference in complexation degrees with different guests in the presence of added receptor, is illustrated. The importance of often neglected solvent effects on selectivity is exemplified with ionophore and hydrogen bonded complexes.     

乙酰胆碱酯酶AChE与1,7-二氮杂咔唑抑制剂的作用机理的分子动力学模拟

通过分子对接、分子动力学(MD)模拟以及成键自由能分析方法,从原子水平上模拟研究了3种1,7-二氮杂咔唑衍生物(分别记为M1、M2和M3)与ACh E的结合模式及相互作用机理,分析和讨论了研究体系的静电相互作用和范德华相互作用(vd W)。用MM-PBSA方法计算的3种抑制剂与ACh E之间的结合自由能与抑制剂的实验生物活性数据(IC50值)相对应。分析结果表明,残基S286与抑制剂之间形成的氢键作用有利于抑制剂与ACh E之间的结合。范德华相互作用,尤其是抑制剂与关键残基W279和Y334的作用,对抑制剂与ACh E之间的结合自由能有较大的贡献,在区分抑制剂M1(或M2)和M3的生物活性上发挥着重要的作用。     

乙酰胆碱酯酶AChE与1,7-二氮杂咔唑抑制剂的作用机理的分子动力学模拟

通过分子对接、分子动力学（MD）模拟以及成键自由能分析方法,从原子水平上模拟研究了3种1,7-二氮杂咔唑衍生物（分别记为M1、M2和M3）与AChE的结合模式及相互作用机理,分析和讨论了研究体系的静电相互作用和范德华相互作用（vdW）。用MM-PBSA方法计算的3种抑制剂与AChE之间的结合自由能与抑制剂的实验生物活性数据（IC₅₀值）相对应。分析结果表明,残基S286与抑制剂之间形成的氢键作用有利于抑制剂与AChE之间的结合。范德华相互作用,尤其是抑制剂与关键残基W279和Y334的作用,对抑制剂与AChE之间的结合自由能有较大的贡献,在区分抑制剂M1（或M2）和M3的生物活性上发挥着重要的作用。     

Protein-ligand binding free energy estimation using molecular mechanics and continuum electrostatics. Application to HIV-1 protease inhibitors

A method is proposed for the estimation of absolute binding free energy of interaction between proteins and ligands. Conformational sampling of the protein-ligand complex is performed by molecular dynamics (MD) in vacuo and the solvent effect is calculated a posteriori by solving the Poisson or the Poisson-Boltzmann equation for selected frames of the trajectory. The binding free energy is written as a linear combination of the buried surface upon complexation, SASbur, the electrostatic interaction energy between the ligand and the protein, Eelec, and the difference of the solvation free energies of the complex and the isolated ligand and protein, deltaGsolv. The method uses the buried surface upon complexation to account for the non-polar contribution to the binding free energy because it is less sensitive to the details of the structure than the van der Waals interaction energy. The parameters of the method are developed for a training set of 16 HIV-1 protease-inhibitor complexes of known 3D structure. A correlation coefficient of 0.91 was obtained with an unsigned mean error of 0.8 kcal/mol. When applied to a set of 25 HIV-1 protease-inhibitor complexes of unknown 3D structures, the method provides a satisfactory correlation between the calculated binding free energy and the experimental pIC5o without reparametrization.     

Calculations of solute and solvent entropies from molecular dynamics simulations

The translational, rotational and conformational (vibrational) entropy contributions to ligand-receptor binding free energies are analyzed within the standard formulation of statistical thermodynamics. It is shown that the partitioning of the binding entropy into different components is to some extent arbitrary, but an appropriate method to calculate both translational and rotational entropy contributions to noncovalent association is by estimating the configurational volumes of the ligand in the bound and free states. Different approaches to calculating solute entropies using free energy perturbation calculations, configurational volumes based on root-mean-square fluctuations and covariance matrix based quasiharmonic analysis are illustrated for some simple molecular systems. Numerical examples for the different contributions demonstrate that theoretically derived results are well reproduced by the approximations. Calculation of solvent entropies, either using total potential energy averages or van't Hoff plots, are carried out for the case of ion solvation in water. Although convergence problems will persist for large and complex simulation systems, good agreement with experiment is obtained here for relative and absolute ion hydration entropies. We also outline how solvent and solute entropic contributions are taken into account in empirical binding free energy calculations using the linear interaction energy method. In particular it is shown that empirical scaling of the nonpolar intermolecular ligand interaction energy effectively takes into account size dependent contributions to the binding free energy.     

Binding energies of five molecular pincers calculated by explicit and implicit solvent models

Molecular pincers or tweezers are designed to hold and release the target molecule. Potential applications involve drug distribution in medicine, environment technologies, or microindustrial techniques. Typically, the binding is dominated by van der Waals forces. Modeling of such complexes can significantly enhance their design; yet obtaining accurate complexation energies by theory is difficult. In this study, density functional theory (DFT) computations combined with dielectric continuum solvent model are compared with the potential of mean force approach using umbrella sampling and the weighted histogram analysis method (WHAM) with molecular dynamics (MD) simulations. For DFT, functional and basis set effects are discussed. The computed results are compared to experimental data based on NMR spectroscopic measurements of five synthesized tweezers based on the Tröger's basis. Whereas the DFT computations correctly provided the observed trends in complex stability, they failed to produce realistic magnitudes of complexation energies. Typically, the binding was overestimated by DFT if compared to experiment. The simpler semiempirical PM6‐DH2X scheme proposed lately yielded better magnitudes of the binding energies than DFT but not the right order. The MD‐WHAM simulations provided the most realistic Gibbs binding energies, although the approximate MD force fields were not able to reproduce completely the ordering of relative stabilities of model complexes found by NMR. Yet the modeling provides interesting insight into the complex geometry and flexibility and appears as a useful tool in the tweezers' design. © 2012 Wiley Periodicals, Inc.     

A model of competing van der Waals interactions for describing the physicochemical properties of binary solutions of nonelectrolytes

A model of competing van der Waals (universal) interactions was suggested for describing the excess physicochemical properties of binary systems and excess thermodynamic functions of solvation. As distinct from the Redlich-Kister and Hwang polynomials, the coefficients of this model are functionally significant and related to various mechanisms of van der Waals, in particular, electrostatic interaction manifestations as the composition of the binary solvent changes. The suggested model was used to estimate the contributions of electrostatic nonstoichiometric interactions and mutual component destructuring effects to the observed physicochemical properties of binary systems. The empirical Dimroth-Reichardt solvatochromic scale of solvent polarities for binary systems was shown to be related to the electrostatic contribution of the model.     

Binding free energy, energy and entropy calculations using simple model systems

Free energy differences are calculated for a set of two model host molecules, binding acetone and methanol. Two active sites of different characteristics were constructed based on an artificially extended C60 fullerene molecule, possibly functionalised to include polar interactions in an otherwise apolar, spherical cavity. The model host systems minimise the necessary sampling of conformational space while still capturing key aspects of ligand binding. The estimates of the free energies are split up into energetic and entropic contributions, using three different approaches investigating the convergence behaviour. For these systems, a direct calculation of the total energy and entropy is more efficient than calculating the entropy from the temperature dependence of the free energy or from a direct thermodynamic integration formulation. Furthermore, the compensating surrounding–surrounding energies and entropies are split off by calculating reduced ligand-surrounding energies and entropies. These converge much more readily and lead to properties that are more straightforwardly interpreted in terms of molecular interactions and configurations. Even though not experimentally accessible, the reduced thermodynamic properties may prove highly relevant for computational drug design, as they may give direct insights into possibilities to further optimise ligand binding while optimisation in the surrounding–surrounding energy or entropy will exactly cancel and not lead to improved affinity.     

Molecular recognition thermodynamics of pyridine derivatives by sulfonatocalixarenes at different pH values

The complex stability constants (Ka) and thermodynamic parameters (DeltaG degrees, DeltaH degrees, and TDeltaS degrees) for 1:1 complexation of water-soluble calix[4]arene, thiacalix[4]arene, and calix[5]arene sulfonates with pyridine and their methylated derivatives have been determined by means of isothermal titration calorimetry at pH 2.0 and 7.2 at 298.15 K, and their binding modes have been investigated by NMR spectroscopy. The results obtained show that sulfonatocalixarenes afford stronger binding ability toward pyridine guests at pH 2.0, attributable to the positive electrostatic interactions and the more extensive desolvation effects, but present higher molecular selectivity at pH 7.2 owing to the strengthened C-H...pi interactions. The pH-responsible binding ability and molecular selectivity are discussed from the viewpoint of electrostatic, pi-stacking, van der Waals interactions and size-fit relationship between host and guest. A close comparison further demonstrates that the C-H...pi interactions and van der Waals interactions play a more important role than pi...pi interactions in the present inclusion complexation.     

Converging free energy estimates: MM-PB(GB)SA studies on the protein-protein complex Ras-Raf

Estimating protein-protein interaction energies is a very challenging task for current simulation protocols. Here, absolute binding free energies are reported for the complex H-Ras/C-Raf1 using the MM-PB(GB)SA approach, testing the internal consistency and model dependence of the results. Averaging gas-phase energies (MM), solvation free energies as determined by Generalized Born models (GB/SA), and entropic contributions calculated by normal mode analysis for snapshots obtained from 10 ns explicit-solvent molecular dynamics in general results in an overestimation of the binding affinity when a solvent-accessible surface area-dependent model is used to estimate the nonpolar solvation contribution. Applying the sum of a cavity solvation free energy and explicitly modeled solute-solvent van der Waals interaction energies instead provides less negative estimates for the nonpolar solvation contribution. When the polar contribution to the solvation free energy is determined by solving the Poisson-Boltzmann equation (PB) instead, the calculated binding affinity strongly depends on the atomic radii set chosen. For three GB models investigated, different absolute deviations from PB energies were found for the unbound proteins and the complex. As an alternative to normal-mode calculations, quasiharmonic analyses have been performed to estimate entropic contributions due to changes of solute flexibility upon binding. However, such entropy estimates do not converge after 10 ns of simulation time, indicating that sampling issues may limit the applicability of this approach. Finally, binding free energies estimated from snapshots of the unbound proteins extracted from the complex trajectory result in an underestimate of binding affinity. This points to the need to exercise caution in applying the computationally cheaper "one-trajectory-alternative" to systems where there may be significant changes in flexibility and structure due to binding. The best estimate for the binding free energy of Ras-Raf obtained in this study of -8.3 kcal mol(-1) is in good agreement with the experimental result of -9.6 kcal mol(-1), however, further probing the transferability of the applied protocol that led to this result is necessary.     

Binding energies of tyrosine kinase inhibitors: Error assessment of computational methods for imatinib and nilotinib binding

The binding energies of imatinib and nilotinib to tyrosine kinase have been determined by quantum mechanical (QM) computations, and compared with literature binding energy studies using molecular mechanics (MM). The potential errors in the computational methods include these critical factors:

• •Errors in X-ray structures such as structural distortions and steric clashes give unrealistically high van der Waals energies, and erroneous binding energies.
• •MM optimization gives a very different configuration to the QM optimization for nilotinib, whereas the imatinib ion gives similar configurations
• •Solvation energies are a major component of the overall binding energy. The QM based solvent model (PCM/SMD) gives different values from those used in the implicit PBSA solvent MM models. A major error in inhibitor—kinase binding lies in the non-polar solvation terms.
• •Solvent transfer free energies and the required empirical solvent accessible surface area factors for nilotinib and imatinib ion to give the transfer free energies have been reverse calculated. These values differ from those used in the MM PBSA studies.
• •An intertwined desolvation—conformational binding selectivity process is a balance of thermodynamic desolvation and intramolecular conformational kinetic control.
• •The configurational entropies (TΔS) are minor error sources.