SLICK--scoring and energy functions for protein-carbohydrate interactions

Protein-carbohydrate interactions are increasingly being recognized as essential for many important biomolecular recognition processes. From these, numerous biomedical applications arise in areas as diverse as drug design, immunology, or drug transport. We introduce SLICK, a package containing a scoring and an energy function, which were specifically designed to predict binding modes and free energies of sugars and sugarlike compounds to proteins. SLICK accounts for van der Waals interactions, solvation effects, electrostatics, hydrogen bonds, and CH...pi interactions, the latter being a particular feature of most protein-carbohydrate interactions. Parameters for the empirical energy function were calibrated on a set of high-resolution crystal structures of protein-sugar complexes with known experimental binding free energies. We show that SLICK predicts the binding free energies of predicted complexes (through molecular docking) with high accuracy. SLICK is available as part of our molecular modeling package BALL (www.ball-project.org).     

Electrostatics of ligand binding: parametrization of the generalized Born model and comparison with the Poisson-Boltzmann approach

An accurate and fast evaluation of the electrostatics in ligand-protein interactions is crucial for computer-aided drug design. The pairwise generalized Born (GB) model, a fast analytical method originally developed for studying the solvation of organic molecules, has been widely applied to macromolecular systems, including ligand-protein complexes. However, this model involves several empirical scaling parameters, which have been optimized for the solvation of organic molecules, peptides, and nucleic acids but not for energetics of ligand binding. Studies have shown that a good solvation energy does not guarantee a correct model of solvent-mediated interactions. Thus, in this study, we have used the Poisson-Boltzmann (PB) approach as a reference to optimize the GB model for studies of ligand-protein interactions. Specifically, we have employed the pairwise descreening approximation proposed by Hawkins et al.(1) for GB calculations and DelPhi for PB calculations. The AMBER all-atom force field parameters have been used in this work. Seventeen protein-ligand complexes have been used as a training database, and a set of atomic descreening parameters has been selected with which the pairwise GB model and the PB model yield comparable results on atomic Born radii, the electrostatic component of free energies of ligand binding, and desolvation energies of the ligands and proteins. The energetics of the 15 test complexes calculated with the GB model using this set of parameters also agrees well with the energetics calculated with the PB method. This is the first time that the GB model has been parametrized and thoroughly compared with the PB model for the electrostatics of ligand binding.     

Specific empirical free energy function for automated docking of carbohydrates to proteins

We present an automated docking protocol specifically optimized to predict the structure and affinity of a protein-carbohydrate complex. A scoring function was developed based on a training set of 30 protein-carbohydrate complexes of known structure and affinity. Combinations of several models for hydrogen bonding, torsional entropy loss, and solvation were tested for their ability to fit the training set data, and the best model was used with AutoDock. The electrostatic empirical coefficient is larger than in a previously obtained model using a training set comprised of various types of protein-ligand complexes, indicating that electrostatic interactions play a more important role in determining the affinity between a carbohydrate and a protein. The differences in the relative weighting of the empirical coefficients in the model yields predicted free energies for the training set with a standard error of 1.403 kcal/mol. The new scoring function was tested on 17 Aspergillus niger glucoamylase inhibitors for which binding energies had been determined experimentally. Free energies of complex formation were predicted with a residual standard error of 1.101 kcal/mol. The new scoring function therefore provides a robust method for predicting free energies of formation and optimal conformations of carbohydrate-protein complexes.     

A combined treatment of hydration and dynamical effects for the modeling of host–guest binding thermodynamics: the SAMPL5 blinded challenge

As part of the SAMPL5 blinded experiment, we computed the absolute binding free energies of 22 host–guest complexes employing a novel approach based on the BEDAM single-decoupling alchemical free energy protocol with parallel replica exchange conformational sampling and the AGBNP2 implicit solvation model specifically customized to treat the effect of water displacement as modeled by the Hydration Site Analysis method with explicit solvation. Initial predictions were affected by the lack of treatment of ionic charge screening, which is very significant for these highly charged hosts, and resulted in poor relative ranking of negatively versus positively charged guests. Binding free energies obtained with Debye–Hückel treatment of salt effects were in good agreement with experimental measurements. Water displacement effects contributed favorably and very significantly to the observed binding affinities; without it, the modeling predictions would have grossly underestimated binding. The work validates the implicit/explicit solvation approach employed here and it shows that comprehensive physical models can be effective at predicting binding affinities of molecular complexes requiring accurate treatment of conformational dynamics and hydration.     

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.     

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.     

The Binding Energy Distribution Analysis Method (BEDAM) for the Estimation of Protein-Ligand Binding Affinities

The Binding Energy Distribution Analysis Method (BEDAM) for the computation of receptor-ligand standard binding free energies with implicit solvation is presented. The method is based on a well established statistical mechanics theory of molecular association. It is shown that, in the context of implicit solvation, the theory is homologous to the test particle method of solvation thermodynamics with the solute-solvent potential represented by the effective binding energy of the protein-ligand complex. Accordingly, in BEDAM the binding constant is computed by means of a weighted integral of the probability distribution of the binding energy obtained in the canonical ensemble in which the ligand is positioned in the binding site but the receptor and the ligand interact only with the solvent continuum. It is shown that the binding energy distribution encodes all of the physical effects of binding. The balance between binding enthalpy and entropy is seen in our formalism as a balance between favorable and unfavorable binding modes which are coupled through the normalization of the binding energy distribution function. An efficient computational protocol for the binding energy distribution based on the AGBNP2 implicit solvent model, parallel Hamiltonian replica exchange sampling and histogram reweighting is developed. Applications of the method to a set of known binders and non-binders of the L99A and L99A/M102Q mutants of T4 lysozyme receptor are illustrated. The method is able to discriminate without error binders from non-binders, and the computed standard binding free energies of the binders are found to be in good agreement with experimental measurements. Analysis of the results reveals that the binding affinities of these systems reflect the contributions from multiple conformations spanning a wide range of binding energies.     

Theoretical study of environmental effects on proton transfer reaction through the peptide bond in a model system

This study considered the possibility of proton transfer reactions through the peptide bond under different environments using the dipeptide and the 12-mer polyglycine α-helix models, in which diglycine is substituted by the 12-mer polyglycine helix. Ab initio molecular orbital calculations were carried out at the B3LYP/6-31+G(d) level of theory. To evaluate the free energies in solution, calculations of the solvation energies were performed using PCM. The correction functions on the calculated solvation energies were provided to reproduce experimental pKa values. The proton transfer reactions through the peptide bond are concluded to be possible in the protein for a wide range of proton acceptors. His complex has two free energy minima along a putative proton transfer pathway in spite of one minimum in the other complexes. The α-helix is estimated to suppress the proton transfer reactions through the peptide bond at the termini of the helix, although it is possible to proceed when the proton affinity of the acceptor is low. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.     

How does halogen bonding behave in solution? A theoretical study using implicit solvation model

A systematic study of halogen bonding interactions in gas phase and in solution was carried out by means of quantum chemical DFT/B3LYP method. Three solvents with different polarities (chloroform, acetone, and water) were selected, and solvation effects were considered using the polarized continuum model (PCM). For charged halogen-bonded complexes, the strength of the interactions tends to significantly weaken in solution, with a concomitant elongation of intermolecular distances. For neutral systems, halogen bond distances are shown to shorten and the interaction energies change slightly. Computations also reveal that in the gas phase the binding affinities decrease in the order Cl(-) > Br(-) > I(-), while in solution the energy gaps of binding appear limited for the three halide anions. According to free energy results, many systems under investigation are stable in solution. Particularly, calculated free energies of formation of the complexes correlate well with halogen-bonding association constants determined experimentally. The differences of the effects of solvent upon halogen and hydrogen bonding were also elucidated. This study can establish fundamental characteristics of halogen bonding in media, which would be very helpful for applying this noncovalent interaction in medicinal chemistry and material design.     

Solvation free energy of amino acids and side-chain analogues

The solvation free energies of amino acids and their side-chain analogues in water and cyclohexane are calculated by using Monte Carlo simulation. The molecular interactions are described by the OPLS-AA force field for the amino acids and the TIP4P model for water, and the free energies are determined by using the Bennett acceptance method. Results for the side-chain analogues in cyclohexane and in water are used to evaluate the performance of the force field for the van der Waals and the electrostatic interactions, respectively. Comparison of the calculated hydration free energies for the amino acid analogues and the full amino acids allows assessment of the additivity of the side chain contributions on the number of hydrating water molecules. The hydration free energies of neutral amino acids can be reasonably approximated by adding the contributions of their side chains to that of the hydration of glycine. However, significant nonadditivity in the free energy is found for the zwitterionic form of amino acids with polar side chains. In serine and threonine, intramolecular hydrogen bonds are formed between the polar side chains and backbone groups, leading to weaker solvation than for glycine. In contrast, such nonadditivity is not observed in tyrosine, in which the hydroxyl group is farther separated from, and therefore cannot form an intramolecular hydrogen bond with, the backbone. For histidine we find that a water molecule can form a bridge when the intramolecular hydrogen bond between the polar group and the backbone is broken.     

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.     

Electronic Structure Insights into the Solvation of Magnesium Ions with Cyclic and Acyclic Carbonates

A computational framework to rank the solvation behavior of Mg²⁺ in carbonates by using molecular dynamics simulations and density functional theory is reported. Based on the binding energies and enthalpies of solvation calculated at the M06‐2X/6‐311++G(d,p) level of theory and the free energies of solvation from ABF‐MD simulations, we find that ethylene carbonate (EC) and the ethylene carbonate:propylene carbonate (EC:PC) binary mixture are the best carbonate solvents for interacting with Mg²⁺. Natural bond orbital and quantum theory of atoms in molecules analyses support the thermochemistry calculations with the highest values of charge transfer, perturbative stabilization energies, electron densities, and Wiberg bond indices being observed in the Mg²⁺(EC) and Mg²⁺(EC:PC) complexes. The plots of the noncovalent interactions indicate that those responsible for the formation of Mg²⁺ carbonate complexes are strong‐to‐weak attractive interactions, depending on the regions that are interacting. Finally, density of state calculations indicate that the interactions between Mg²⁺ and the carbonate solvents affects the HOMO and LUMO states of all carbonate solvents and moves them to more negative energy values.     

Free energy perturbation calculations on models of active sites: Applications to adenosine deaminase inhibitors

Free energy perturbation calculations were performed to determine the free energy of binding associated with the presence of perhaps an unusual hydroxyl group in the transition state analog of nebularine, an inhibitor of the enzyme adenosine deaminase. The presence of a single hydroxyl group in this inhibitor has been found to contribute ?9.8 kcal/mol to the free energy of binding, with a 10⁸-fold increase in the binding affinity by the enzyme. In this work, we calculate the difference in solvation free energy for the 1,6-dihydropurine complex versus that of the 6-hydroxyl-1,6-dihydropurine complex to determine if this marked increase in binding affinity is attributed to an unusually hydrophobic hydroxyl group. The calculated ΔG associated for the solvation free energy is ?11.8 kcal/mol. This large change in the solvation free energy suggests that this hydroxyl is instead unusually hydrophilic and that the difference in free energy of interaction for the two inhibitors to the enzyme must be at least ca. 20 kcal/mol. Although the crystal structure for adenosine deaminase is currently not known, we attempt to mimic the nature of the active site by constructing models which simulate the enzyme-inhibitor complex. We present a first attempt at determining the change in free energy of binding for a system in which structural data for the enzyme is incomplete. To do this, we construct what we believe is a minimal model of the binding between adenosine deaminase and an inhibitor. The active site is simulated as a single charged carboxyl group which can form a hydrogen bond with the hydroxyl group of the analog. Two different carboxyl anion models are used. In the first model, the association is modeled between an acetic acid anion and the modified inhibitor. The second model consists of a hydrophobic amino acid pocket with an interior Glu residue in the active site. From these models we calculate the change in free energy of association and the overall change in free energy of binding. We calculate the free energies of interaction both in the absence and presence of water. We conclude from this that the presence of a single suitably placed-CO^?₂ group probably cannot explain the binding effect of the-OH group and that additional interactions will be found in the adenosine deaminase active site.     

The influence of CH…π interaction on hydrogen bonding ability of –CONH<Subscript>2</Subscript> functional group of benzamide

Interplay between CH…π and hydrogen bond interactions of benzamide has been investigated by quantum mechanical calculations. The effect of the substituents on geometrical parameters has also been studied at the B3LYP level with 6-311++G(d,p) basis set. The electron-withdrawing substituents enhance the total interaction energy of the complexes. The results indicated that the cooperativity of interactions leads to extra stability of the ternary complexes. The CH…π interaction and the hydrogen bond energies have been estimated using the electron densities calculated by the atoms in molecules (AIM) method at hydrogen bond critical points. The strength of hydrogen bonding increases in the presence of CH…π interaction in the ternary complexes. The effect of CH…π interaction on the hydrogen bond interaction has also been studied by the natural bond orbital, AIM and the molecular electrostatic potential analyses.     

β-环糊精和甾类化合物的分子动力学模拟

运用分子动力学(molecular dynamics, MD)和MM-PBSA (molecular mechanics/Poisson Boltzmann surface area)相结合的方法预测了β-环糊精(cyclodextrin, CD)和甾类客体分子包结模式. 通过重原子均方根偏差(root mean square deviation, RMSD)分析可得, 两种包结模式下客体分子都可以和β-CD形成稳定的包结. 在MD轨迹采样基础上, 采用高效MM-PBSA方法计算了两种包结模式下的包结自由能. 计算结果显示, β-CD和三个甾类客体分子包结的主要驱动力为范德华相互作用, 而溶剂化能和熵变则不利于体系的包结. 进一步分析平均构象和包结自由能发现, 对于波尼松龙, D-up (D-ring up orientation)取向为优势包结模式; 而乙炔雌二醇和雌三醇的优势包结模式均为A-up (A-ring up orientation)取向. 通过比较β-CD和三个客体分子的理论包结自由能, 预测包结稳定性的次序为乙炔雌二醇＞雌三醇＞波尼松龙, 和实验结果相一致.     

Development of surface-SFED models for polar solvents

We developed surface grid-based solvation free energy density (Surface-SFED) models for 36 commonly used polar solvents. The parametrization was performed with a large and diverse set of experimental solvation free energies mainly consisting of combinations of polar solvent and multipolar solute. Therefore, the contribution of hydrogen bonds was dominant in the model. In order to increase the accuracy of the model, an elaborate version of a previous hydrogen bond acidity and basicity prediction model was introduced. We present two parametrizations for use with experimentally determined (Surface-SFED/HB(exp)) and empirical (Surface-SFED/HB(cal)) hydrogen bond acidity and basicity values. Our computational results agreed well with experimental results, and inaccuracy of empirical hydrogen bond acidity and basicity values was the main source of error in Surface-SFED/HB(cal). The mean absolute errors of Surface-SFED/HB(exp) and Surface-SFED/HB(cal) were 0.49 and 0.54 kcal/mol, respectively.     

Solvent effects on the thermodynamics of the formation of hydrogen bonded complexes ofm-cresol III

Thermodynamic parameters for the hydrogen bonded complexes of m-cresol with various bases in the solvent benzene have been determined from calorimetric and spectroscopic data. These data were analyzed by linear solvation energy relationships. When combined with data previously determined for the same complexes in CCl₄ and cyclohexane solvents, it is shown that solvent effects on the thermodynamics of hydrogen bond formation are due to solvation of the free m-cresol and base through dipolar and perhaps donor-acceptor interactions.     

Free energy of solvation from molecular dynamics simulation applying Voronoi-Delaunay triangulation to the cavity creation

The free energy of solvation for a large number of representative solutes in various solvents has been calculated from the polarizable continuum model coupled to molecular dynamics computer simulation. A new algorithm based on the Voronoi-Delaunay triangulation of atom-atom contact points between the solute and the solvent molecules is presented for the estimation of the solvent-accessible surface surrounding the solute. The volume of the inscribed cavity is used to rescale the cavitational contribution to the solvation free energy for each atom of the solute atom within scaled particle theory. The computation of the electrostatic free energy of solvation is performed using the Voronoi-Delaunay surface around the solute as the boundary for the polarizable continuum model. Additional short-range contributions to the solvation free energy are included directly from the solute-solvent force field for the van der Waals-type interactions. Calculated solvation free energies for neutral molecules dissolved in benzene, water, CCl4, and octanol are compared with experimental data. We found an excellent correlation between the experimental and computed free energies of solvation for all the solvents. In addition, the employed algorithm for the cavity creation by Voronoi-Delaunay triangulation is compared with the GEPOL algorithm and is shown to predict more accurate free energies of solvation, especially in solvents composed by molecules with nonspherical molecular shapes.