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.     

Calculation of ligand binding free energies from molecular dynamics simulations

A recently developed method for predicting binding affinities in ligand–receptor complexes, based on interaction energy averaging and conformational sampling by molecular dynamics simulation, is presented. Polar and nonpolar contributions to the binding free energy are approximated by a linear scaling of the corresponding terms in the average intermolecular interaction energy for the bound and free states of the ligand. While the method originally assumed the validity of electrostatic linear response, we show that incorporation of systematic deviations from linear response derived from free energy perturbation calculations enhances the accuracy of the approach. The method is applied to complexes of wild-type and mutant human dihydrofolate reductases with 2,4-diaminopteridine and 2,4-diaminoquinazoline inhibitors. It is shown that a binding energy accuracy of about 1 kcal/mol is attainable even for multiply ionized compounds, such as methotrexate, for which electrostatic interactions energies are very large. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 77–88, 1998     

Calculation of binding energy differences for receptor–ligand systems using the Poisson-Boltzmann method

An approach using the finite difference solution of the Poisson-Boltzmann equation to estimate binding free energy changes for two receptor–ligand systems, arabinose binding protein and sulfate binding protein, is presented. The eight calculated binding free energy changes agree with experiment, showing a correlation coefficient of 0.92 and energy deviations of 1 kcal/mol or less. More importantly, the decomposition of solvation and assembly energies in this approach provides an understanding of binding mechanisms and therefore could suggest directions to alter binding affinities. The method is demonstrated to be useful in analyzing experimental binding structures and predicting binding effects of mutants or modified ligands for macromolecular systems, in which the electrostatic forces dominate the overall interaction and the structural perturbations upon modifications are small. © 1995 by John Wiley & Sons, Inc.     

Molecular dynamics simulations of the ligand-induced chemical information transfer in the 5-HT(1A) receptor

Comparative molecular dynamics simulations of the 5-HT(1A) receptor in its empty as well as agonist- (i.e. active) and antagonist-bound (i.e. nonactive) forms have been carried out. The agonists 5-HT and (R)-8-OH-DPAT as well as the antagonist WAY100635 have been employed. The results of this study strengthen the hypothesis that the receptor portions close to the E/DRY/W motif, with prominence to the cytosolic extensions of helices 3 and 6, are particularly susceptible to undergo structural modification in response to agonist binding. Despite the differences in the structural/dynamics behavior of the two agonists when docked into the 5-HT(1A) receptor, they both exert a destabilization of the intrahelical and interhelical interactions found in the empty and antagonist-bound receptor forms between the arginine of the E/DRY sequence and both D133(3.49) and E340(6.30). For both agonists, the chemical information transfer from the extracellular to the cytosolic domains is mediated by a cluster of aromatic amino acids in helix 6, following the ligand interaction with selected amino acids in the extracellular half of the receptor, such as D116(3.32), S199(5.42), Y195(5.38), and F361(6.51). A significant reduction in the bend at P360(6.50), as compared to the empty and the antagonist-bound receptor forms, is one of the features of the agonist-bound forms that is related to the breakage of the interhelical salt bridge between the E/DRY arginine and E340(6.30). Another structural feature, shared by the agonist-bound receptor forms and not by the empty and antagonist-bound forms, is the detachment of helices 2 and 4, as marked by the movement of W161(4.50) away from helix 2, toward the membrane space.     

Computational combinatorial ligand design: Application to human α-thrombin

Summary A new method is presented for computer-aided ligand design by combinatorial selection of fragments that bind favorably to a macromolecular target of known three-dimensional structure. Firstly, the multiple-copy simultaneous-search procedure (MCSS) is used to exhaustively search for optimal positions and orientations of functional groups on the surface of the macromolecule (enzyme or receptor fragment). The MCSS minima are then sorted according to an approximated binding free energy, whose solvation component is expressed as a sum of separate electrostatic and nonpolar contributions. The electrostatic solvation energy is calculated by the numerical solution of the linearized Poisson-Boltzmann equation, while the nonpolar contribution to the binding free energy is assumed to be proportional to the loss in solvent-accessible surface area. The program developed for computational combinatorial ligand design (CCLD) allows the fast and automatic generation of a multitude of highly diverse compounds, by connecting in a combinatorial fashion the functional groups in their minimized positions. The fragments are linked as two atoms may be either fused, or connected by a covalent bond or a small linker unit. To avoid the combinatorial explosion problem, pruning of the growing ligand is performed according to the average value of the approximated binding free energy of its fragments. The method is illustrated here by constructing candidate ligands for the active site of human -thrombin. The MCSS minima with favorable binding free energy reproduce the interaction patterns of known inhibitors. Starting from these fragments, CCLD generates a set of compounds that are closely related to high-affinity thrombin inhibitors. In addition, putative ligands with novel binding motifs are suggested. Probable implications of the MCSS-CCLD approach for the evolving scenario of drug discovery are discussed.     

Polymer-tethered ligand–receptor interactions between surfaces

We study the interaction between two parallel surfaces having a polymer-tethered ligand on one and a random distribution of receptors on the other. We examine the interplay between the specific ligand–receptor binding and the conformation degrees of freedom of the polymer tether, and address the difference between the cases of mobile (annealed) and immobile (quenched) receptors. The annealed case is solved exactly and the quenched case is treated by both Monte Carlo direct sampling and an analytical density expansion. The combination of the entropic repulsion due to chain confinement at small surface separations, and the attraction due to ligand–receptor binding which can take place at significant chain stretching, results in a minimum in the interaction free energy. For the same set of parameters, stronger binding is obtained for the annealed case than for the quenched case, reflecting the ability of the mobile receptors to migrate into the region of the ligand. In the quenched case, binding is limited by the availability of receptors within the reach of the ligand; for a given receptor density and binding energy, there exists an optimal chain length that yields the lowest minimum in the interaction free energy for the quenched case. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2621–2637, 2006     

Design of Drug Efficacy Guided by Free Energy Simulations of the β2-Adrenoceptor

G-protein-coupled receptors (GPCRs) play important roles in physiological processes and are modulated by drugs that either activate or block signaling. Rational design of the pharmacological efficacy profiles of GPCR ligands could enable the development of more efficient drugs, but is challenging even if high-resolution receptor structures are available. We performed molecular dynamics simulations of the β₂ adrenergic receptor in active and inactive conformations to assess if binding free energy calculations can predict differences in ligand efficacy for closely related compounds. Previously identified ligands were successfully classified into groups with comparable efficacy profiles based on the calculated shift in ligand affinity upon activation. A series of ligands were then predicted and synthesized, leading to the discovery of partial agonists with nanomolar potencies and novel scaffolds. Our results demonstrate that free energy simulations enable design of ligand efficacy and the same approach can be applied to other GPCR drug targets.     

应用MM/PBSA方法研究CDK2活性口袋内溶剂水分子对CDK2-配体结合自由能的影响

应用MM/PBSA方法研究了CDK2活性口袋内溶剂水分子对CDK2-配体结合自由能的影响. 结果表明, 活性口袋内溶剂水分子对CDK2-配体相互作用自由能有一定的贡献, 其贡献的大小随配体不同而有所差异, 导致这种差异的主要原因是活性位点内溶剂水分子与蛋白残基和配体之间形成了不同的氢键相互作用网络.     

Electrostatic free energy of interacting ionizable double layers

The electrostatic contribution to the interaction free energy of charge-regulating materials, similar as well as dissimilar, contains electric work as well as chemical work and can be obtained from an integration over the diffuse part of the double layer together with a summation of the surface contribution to the free energy over the two surfaces. Examples for the surface contribution are given for acid, base, zwitterionic, and amphoteric (1-pK and 2-pK) materials for a diffuse double layer and for the Stern-Gouy-Chapman model, with and without ion adsorption. For charge-regulating materials, the electrostatic contribution to the interaction free energy at contact (adhesion force of curved surfaces, or particles) is always finite and can be obtained from a simple calculation.     

Interactions between chlorinated dioxins and a positively charged molecular probe: New molecular interaction potential

Interaction with the ligand binding domain of receptors for natural chemicals present one potential mechanism for the biological effects of environmental chemicals. Evidence suggests that the electrostatic interaction between the ligand and the receptor is an important component for binding to some of the relevant receptors. The presence of charged residues near the binding site suggests that the charge distribution of the free ligand may be different from the charge distribution of the ligand as it approaches the binding domain of the protein. In this study a new type of potential is computed for a series of dibenzo-p-dioxin (dioxin) ligands. This quantum mechanically computed potential results from interaction between the ligand and a trimethyl ammonium probe at a set of grid points. This interaction potential is compared with the molecular electrostatic potential computed from the wave function of the isolated ligands. Three types of local minima are found: (1) above the oxygen; (2) above the conjugated ring; and (3) above the chlorine(s). The molecular electrostatic potential emphasizes the minima associated with the chlorine atoms and, in that potential, the minima associated with the oxygen atoms disappear with chlorination. In the new potential, the minima over the oxygen atoms are maintained even in tetrachlorodioxin. As chlorination is increased the differences between the two potentials increases. The new potential shows the influence of the π-cation interaction, which is largest when there is little substitution on the ring. The presence of the probe induces a dipole component of 1 debye perpendicular to the plane of the ligand. Local minima in the interaction potential are then used as starting structures for the determination of the most stable ligand–probe complexes. The most stable structures are obtained from the minima associated with the oxygen atoms. These structures are stabilized by a hydrogen bond formation between the probe and the oxygen and the molecule is bent by 30° about the O(SINGLE BOND)O axis. For this series of molecules, the new potential retains some of the features that determine the hydrogen bond whereas the molecular electrostatic potential does not. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 673–684, 1998     

Solvent models for protein–ligand binding: Comparison of implicit solvent poisson and surface generalized born models with explicit solvent simulations

Solvent effects play a crucial role in mediating the interactions between proteins and their ligands. Implicit solvent models offer some advantages for modeling these interactions, but they have not been parameterized on such complex problems, and therefore, it is not clear how reliable they are. We have studied the binding of an octapeptide ligand to the murine MHC class I protein using both explicit solvent and implicit solvent models. The solvation free energy calculations are more than 10³ faster using the Surface Generalized Born implicit solvent model compared to FEP simulations with explicit solvent. For some of the electrostatic calculations needed to estimate the binding free energy, there is near quantitative agreement between the explicit and implicit solvent model results; overall, the qualitative trends in the binding predicted by the explicit solvent FEP simulations are reproduced by the implicit solvent model. With an appropriate choice of reference system based on the binding of the discharged ligand, electrostatic interactions are found to enhance the binding affinity because the favorable Coulomb interaction energy between the ligand and protein more than compensates for the unfavorable free energy cost of partially desolvating the ligand upon binding. Some of the effects of protein flexibility and thermal motions on charging the peptide in the solvated complex are also considered. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 591–607, 2001     

Binding of acetylcholine and tetramethylammonium to a cyclophane receptor: anion's contribution to the cation-pi interaction

The interaction of the lipophilic cyclophane 1 with several acetylcholine (ACh) and tetramethylammonium (TMA) salts has been investigated in deuteriochloroform to ascertain the influence of the counterion on the cation-pi interaction. Reliable association constants have been measured for 17 salts of commonly used anions; corresponding binding free energies -DeltaG degrees ranged from over 8 kJ mol(-1) down to the limit of detection. The dramatic dependence of the binding energy on the anion showed that the latter takes part in the process with a passive and adverse contribution, which inhibits cation binding even to complete suppression in unfavorable cases. Thermodynamic parameters for the association of 1 with TMA picrate demonstrate that binding is enthalpic in origin, showing a substantial enthalpy gain (DeltaH degrees = -16.7 kJ mol(-1)) and an adverse entropic contribution (DeltaS degrees = -27.9 J mol(-1) K(-1)). A correlation has been found between the "goodness" of anions as binding partners and the solubility of their salts. Conversion of the anion into a more charge-dispersed species, for example, conversion of chloride into dialkyltrichlorostannate, improves cation binding substantially, indicating that charge dispersion is a main factor determining the influence of the anion on the cation-pi interaction. DFT computational studies show that the variation of the binding free energy of TMA with the counterion is closely accounted for by the electrostatic potential (EP) of the ion pair: guest binding appears to respond to the cation's charge density exposed to the receptor, which is determined by the anion's charge density through a polarization mechanism. A value of -DeltaG degrees = 38.6 kJ mol(-1) has been extrapolated for the free energy of binding of TMA to 1 in chloroform but in the absence of a counterion. The transmission of electrostatic effects from the ion pair to the cation-pi interaction demonstrates that host-guest association is governed by Coulombic attraction, as long as factors (steric, entropic, solvation, etc.) other than pure electrostatics are not prevalent.     

Ligand binding affinity prediction by linear interaction energy methods

A recent method for estimating ligand binding affinities is extended. This method employs averages of interaction potential energy terms from molecular dynamics simulations or other thermal conformational sampling techniques. Incorporation of systematic deviations from electrostatic linear response, derived from free energy perturbation studies, into the absolute binding free energy expression significantly enhances the accuracy of the approach. This type of method may be useful for computational prediction of ligand binding strengths, e.g., in drug design applications.     

Free energy simulations of uncatalyzed DNA replication fidelity: structure and stability of T.G and dTTP.G terminal DNA mismatches flanked by a single dangling nucleotide

A reference system for DNA replication fidelity was studied by free energy perturbation (FEP) and linear interaction energy (LIE) methods. The studied system included a hydrated duplex DNA with the 5'-CG dangling end of the templating strand, and dCTP4-.Mg2+ or dTTP4-.Mg2+ inserted opposite the dangling G to form a correct (i.e., Watson-Crick) or incorrect (i.e., wobble) base pair, respectively. The average distance between the 3'-terminal oxygen of the primer strand and the alpha-phosphorus of dNTP was found to be 0.2 A shorter for the correct base pair than for the incorrect base pair. Binding of the incorrect dNTP was found to be disfavored by 0.4 kcal/mol relative to the correct dNTP. We estimated that improved binding and more near-attack configurations sampled by the correct base pair should translate in aqueous solution and in the absence of DNA polymerase into a six times faster rate for the incorporation of the correct dNTP into DNA. The accuracy of the calculated binding free energy difference was verified by examining the relative free energy for melting duplex DNA containing GC and GT terminal base pairs flanked by a 5' dangling C. The calculated LIE and FEP free energies of 1.7 and 1.1 kcal/mol, respectively, compared favorably with the experimental estimate of 1.4 kcal/mol obtained using the nearest neighbor parameters. To decompose the calculated free energies into additive electrostatic and van der Waals contributions and to provide a set of rigorous theoretical data for the parametrization of the LIE method, we suggested a variant of the FEP approach, for which we coined a binding-relevant free energy (BRFE) acronym. BRFE approach is characterized by its unique perturbation pathway and by its exclusion of the intramolecular energy of a rigid part of the ligand from the total potential energy.     

Different binding orientations for the same agonist at homologous receptors: a lock and key or a simple wedge?

Using unnatural amino acid mutagenesis, the binding site for serotonin at the novel Caenorhabditis elegans receptor MOD-1 has been probed. As with the closely related serotonin receptor 5-HT3, MOD-1 makes use of a strong cation-pi interaction between the ammonium of serotonin and the indole side chain of a tryptophan. However, the specific Trp used by MOD-1 is different from that used for 5-HT3 (and the nAChR), aligning with a residue more than 40 amino acids distant in sequence space and on a different "loop" of the agonist binding site. This suggests a significant rearrangement of the ligand on binding these two closely related receptors. It is suggested that, unlike enzymes, receptors and other signaling molecules may need only to deliver an agonist to a general binding region, rather than establishing precise drug-receptor interactions.     

Comparison of methods to estimate the free energy of solvation:Importance in the modulation of the affinity of 3-benzazepines for the D1receptor

We computed the free energy of solvation for a series of ions and neutral molecules using two different continuum approaches. First, we used the AM1–SM1 technique, where the AM1 Fock matrix is modified to include a generalized Born contribution. Second, we applied the DelPhi approach, where the electrostatic component of the free energy of solvation is evaluated by resolving the Poisson–Boltzman equation by a finite difference method. Both methods appear equally reliable for ionic systems. For neutral compounds, AM1–SM1 performs better than DelPhi; however, the differences become less pronounced for compounds with larger free energies of solvation. In parallel, both methods were applied to study the influence of the solvation process in the overall drug receptor interaction for a series of closely related ligands for the D₁ dopamine receptor. An inverse linear relationship was found between the free energy of solvation and the logarithm of the affinity of the ligands; nevertheless, electrostatic properties are likely to modulate affinity as well. © 1993 John Wiley & Sons, Inc.     

Energetics of ligand binding to the DNA minor groove

In the present work the decomposition of the total Gibbs free energy of ligand-DNA binding onto various physical terms was accomplished for the group of nine DNA minor groove binders (MGB ligands) differing in both structure and charge state. The decomposition protocol includes the analysis of the most complete set of physical factors known to contribute to the complexation process, viz. the net change in the number of degrees of freedom (translational, rotational, vibrations of the chemical bonds and vibrations of the ligand as a whole within the binding site), the conformational entropy, van der Waals, electrostatic and hydrophobic interactions, the polyelectrolyte contribution and the net effect of changes in the number of hydrogen bonds. All of these processes are further decomposed into the interaction with the solvent and the interaction of the ligand with DNA. The principal outcome of the decomposition is the possibility of performing a comparative analysis of the energetic contribution of various physical terms and provide an answer to the question concerning what physical factors stabilize or destabilize the complexes of MGB ligands with DNA.     

3-D QSAR for intrinsic activity of 5-HT1A receptor ligands by the method of comparative molecular field analysis

The affinity of a ligand for a receptor is usually expressed in terms of the dissociation constant (K_i) of the drug-receptor complex, conveniently measured by the inhibition of radioligand binding. However, a ligand can be an antagonist, a partial agonist, or a full agonist, a property largely independent of its receptor affinity. This property can be quantitated as intrinsic activity (1A), which can range from 0 for a full antagonist to 1 for a full agonist. Although quantitative structure–activity relationship (QSAR) methods have been applied to the prediction of receptor affinity with considerable success, the prediction of IA, even qualitatively, has rarely been attempted. Because most traditional QSAR methods are limited to congeneric series, and there are often major structural differences between agonists and antagonists, this lack of success in predicting IA is understandable. To overcome this limitation, we used the method of comparative molecular field analysis (CoMFA), which, unlike traditional Hansch analysis, permits the inclusion of structurally dissimilar compounds in a single QSAR model. A structurally diverse set of 5-hydroxytryptamine_1A (5-HT_1A) receptor ligands, with literature IA data (determined by the inhibition of 5-HT sensitive forskolin-stimulated adenylate cyclase), was used to develop a 3-D QSAR model correlating intrinsic activity with molecular structure properties of 5HT_1A receptor ligands. This CoMFA model had a crossvalidated r² of 0.481, five components and final conventional r² of 0.943. The receptor model suggests that agonist and antagonist ligands can share parts of a common binding site on the receptor, with a primary agonist binding region that is also occupied by antagonists and a secondary binding site accommodating the excess bulk present in the sidechains of many antagonists and partial agonists. The CoMFA steric field graph clearly shows that agonists tend to be “flatter” (more coplanar) than antagonists, consistent with the difference between the 5-HT_1A agonist and antagonist pharmacophores proposed by Hibert and coworkers. The CoMFA electrostatic field graph suggests that, in the region surrounding the essential protonated aliphatic amino group, the positive molecular electrostatic potential may be weaker in antagonists as compared to agonists. Together, the steric and electrostatic maps suggest that in the secondary binding site region increased hydrophobic binding may enhance antagonist activity. These results demonstrate that CoMFA is capable of generating a statistically crossvalidated 3-D QSAR model that can successfully distinguish between agonist and antagonist 5-HT_1A ligands. To the best of our knowledge, this is the first time this or any other QSAR method has been successfully applied to the correlation of structure with IA rather than potency or affinity. The analysis has suggested various structural features associated with agonist and antagonist behaviors of 5-HT_1A ligands and thus should assist in the future design of drugs that act via 5-HT_1A receptors. © 1993 John Wiley & Sons, Inc.     

Binding free energy predictions of farnesoid X receptor (FXR) agonists using a linear interaction energy (LIE) approach with reliability estimation: application to the D3R Grand Challenge 2

Computational protein binding affinity prediction can play an important role in drug research but performing efficient and accurate binding free energy calculations is still challenging. In the context of phase 2 of the Drug Design Data Resource (D3R) Grand Challenge 2 we used our automated eTOX ALLIES approach to apply the (iterative) linear interaction energy (LIE) method and we evaluated its performance in predicting binding affinities for farnesoid X receptor (FXR) agonists. Efficiency was obtained by our pre-calibrated LIE models and molecular dynamics (MD) simulations at the nanosecond scale, while predictive accuracy was obtained for a small subset of compounds. Using our recently introduced reliability estimation metrics, we could classify predictions with higher confidence by featuring an applicability domain (AD) analysis in combination with protein–ligand interaction profiling. The outcomes of and agreement between our AD and interaction-profile analyses to distinguish and rationalize the performance of our predictions highlighted the relevance of sufficiently exploring protein–ligand interactions during training and it demonstrated the possibility to quantitatively and efficiently evaluate if this is achieved by using simulation data only.