Free energy simulations and MM-PBSA analyses on the affinity and specificity of steroid binding to antiestradiol antibody

Antiestradiol antibody 57-2 binds 17beta-estradiol (E2) with moderately high affinity (K(a) = 5 x 10(8) M(-1)). The structurally related natural estrogens estrone and estriol as well synthetic 17-deoxy-estradiol and 17alpha-estradiol are bound to the antibody with 3.7-4.9 kcal mol(-1) lower binding free energies than E2. Free energy perturbation (FEP) simulations and the molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) method were applied to investigate the factors responsible for the relatively low cross-reactivity of the antibody with these four steroids, differing from E2 by the substituents of the steroid D-ring. In addition, computational alanine scanning of the binding site residues was carried out with the MM-PBSA method. Both the FEP and MM-PBSA methods reproduced the experimental relative affinities of the five steroids in good agreement with experiment. On the basis of FEP simulations, the number of hydrogen bonds formed between the antibody and steroids, which varied from 0 to 3 in the steroids studied, determined directly the magnitude of the steroid-antibody interaction free energies. One hydrogen bond was calculated to contribute about 3 kcal mol(-1) to the interaction energy. Because the relative binding free energies of estrone (two antibody-steroid hydrogen bonds), estriol (three hydrogen bonds), 17-deoxy-estradiol (no hydrogen bonds), and 17alpha-estradiol (two hydrogen bonds) are close to each other and clearly lower than that of E2 (three hydrogen bonds), the water-steroid interactions lost upon binding to the antibody make an important contribution to the binding free energies. The MM-PBSA calculations showed that the binding of steroids to the antiestradiol antibody is driven by van der Waals interactions, whereas specificity is solely due to electrostatic interactions. In addition, binding of steroids to the antiestradiol antibody 57-2 was compared to the binding to the antiprogesterone antibody DB3 and antitestosterone antibody 3-C4F5, studied earlier with the MM-PBSA method.     

Protein docking using continuum electrostatics and geometric fit

The computer program DOT quickly finds low-energy docked structures for two proteins by performing a systematic search over six degrees of freedom. A novel feature of DOT is its energy function, which is the sum of both a Poisson-Boltzmann electrostatic energy and a van der Waals energy, each represented as a grid-based correlation function. DOT evaluates the energy of interaction for many orientations of the moving molecule and maintains separate lists scored by either the electrostatic energy, the van der Waals energy or the composite sum of both. The free energy is obtained by summing the Boltzmann factor over all rotations at each grid point. Three important findings are presented. First, for a wide variety of protein-protein interactions, the composite-energy function is shown to produce larger clusters of correct answers than found by scoring with either van der Waals energy (geometric fit) or electrostatic energy alone. Second, free-energy clusters are demonstrated to be indicators of binding sites. Third, the contributions of electrostatic and attractive van der Waals energies to the total energy term appropriately reflect the nature of the various types of protein-protein interactions studied.     

Probing the electronic structures and properties of neutral and anionic ScSi n (0,−1) (n = 1–6) clusters using ccCA-TM and G4 theory

We apply molecular docking, molecular dynamics (MD) simulation, and binding free energy calculation to investigate and reveal the binding mechanism between five xanthine inhibitors and DPP-4. The electrostatic and van der Waals interactions of the five inhibitors with DPP-4 are analyzed and discussed. The computed binding free energies using MM-PBSA method are in qualitatively agreement with experimental inhibitory potency of five inhibitors. The hydrogen bonds of inhibitors with Ser630 and Asp663 can stabilize the inhibitors in binding sites. The van der Waals interactions, especially the key contacts with His740, Asn710, Trp629, and Tyr666 have larger contributions to the binding free energy and play important roles in distinguishing the variant bioactivity of five inhibitors.     

Computational analysis of the binding affinities of the natural-product cyclopentapeptides argifin and argadin to chitinase B from Serratia marcescens

Molecular dynamics (MD) simulations and the molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) method were applied to study the interaction of the natural-product cyclopentapeptide chitinase inhibitors argifin and argadin with chitinase B (ChiB) from Serratia marcescens. Argadin inhibited ChiB with an inhibition constant (K(i)) value of 20 nM, which was three orders of magnitude greater than that of argifin (K(i)=33,000 nM). The MM-PBSA free-energy analysis provided absolute binding free energies of -6.98 and -11.16 kcal/mol for the argifin and argadin complexes, respectively. These estimates were in good agreement with the free energies derived from the experimental K(i) values (-6.36 and -10.92 kcal/mol for the argifin and argadin complexes, respectively). The energetic analysis revealed that the van der Waals and nonpolar solvation energies drove the binding of both argifin and argadin. We found that the binding of argadin gained approximately 12 kcal/mol more van der Waals energy than that of argifin, which was mainly responsible for the difference in binding free energy between argifin and argadin. In particular, W220 and W403 of ChiB were found to contribute to the more favorable van der Waals interaction with argadin. We also designed argifin derivatives with better binding affinity, in which a constituent amino-acid residue of argifin was mutated to one with a bulky side chain. The derivative in which D-Ala of argifin was replaced with D-Trp appeared to possess a binding affinity that was equally potent to that of argadin.     

Estimation of the binding affinities of FKBP12 inhibitors using a linear response method.

A series of non-immunosuppressive inhibitors of FK506 binding protein (FKBP12) are investigated using Monte Carlo statistical mechanics simulations. These small molecules may serve as scaffolds for chemical inducers of protein dimerization, and have recently been found to have FKBP12-dependent neurotrophic activity. A linear response model was developed for estimation of absolute binding free energies based on changes in electrostatic and van der Waals energies and solvent-accessible surface areas, which are accumulated during simulations of bound and unbound ligands. With average errors of 0.5 kcal/mol, this method provides a relatively rapid way to screen the binding of ligands while retaining the structural information content of more rigorous free energy calculations.     

What determines the van der Waals coefficient beta in the LIE (linear interaction energy) method to estimate binding free energies using molecular dynamics simulations?

Recently a semiempirical method has been proposed by Aqvist et al. to calculate absolute and relative binding free energies. In this method, the absolute binding free energy of a ligand is estimated as deltaGbind = alpha + beta, where Vel(bound) and Vvdw(bound) are the electrostatic and van der Waals interaction energies between the ligand and the solvated protein from an molecular dynamics (MD) trajectory with ligand bound to protein and Vel(free) and Vel(free) and Vvdw(free) are the electrostatic and van der Waals interaction energies between the ligand and the water from an MD trajectory with the ligand in water. A set of values, alpha = 0.5 and beta = 0.16, was found to give results in good agreement with experimental data. Later, however, different optimal values of beta were found in studies of compounds binding to P450cam and avidin. The present work investigates how the optimal value of beta depends on the nature of binding sites for different protein-ligand interactions. By examining seven ligands interacting with five proteins, we have discovered a linear correlation between the value of beta and the weighted non-polar desolvation ratio (WNDR), with a correlation coefficient of 0.96. We have also examined the ability of this correlation to predict optimal values of beta for different ligands binding to a single protein. We studied twelve neutral compounds bound to avidin. In this case, the WNDR approach gave a better estimate of the absolute binding free energies than results obtained using the fixed value of beta found for biotin-avidin. In terms of reproducing the relative binding free energy to biotin, the fixed-beta value gave better results for compounds similar to biotin, but for compounds less similar to biotin, the WNDR approach led to better relative binding free energies.     

Structural basis of neurophysin hormone specificity: Geometry, polarity, and polarizability in aromatic ring interactions

The structural origins of the specificity of the neurophysin hormone-binding site for an aromatic residue in peptide position 2 were explored by analyzing the binding of a series of peptides in the context of the crystal structure of liganded neurophysin. A new modeling method for describing the van der Waals surface of binding sites assisted in the analysis. Particular attention was paid to the unusually large (5 kcal/mol) difference in binding free energy between Phe and Leu in position 2, a value representing more than three times the maximum expected based on hydrophobicity alone, and additionally remarkable since modeling indicated that the Leu side chain was readily accommodated by the binding pocket. Although evidence was obtained of a weak thermodynamic linkage between the binding interactions of the residue 2 side chain and of the peptide alpha-amino group, two factors are considered central. (1) The bound Leu side chain can establish only one-third of the van der Waals contacts available to a Phe side chain. (2) The bound Phe side chain appears to be additionally stabilized relative to Leu by more favorable dipole and induced dipole interactions with nonaromatic polar and sulfur ligands in the binding pocket, as evidenced by examination of its interactions in the pocket, analysis of the detailed energetics of transfer of Phe and Leu side chains from water to other phases, and comparison with thermodynamic and structural data for the binding of residue 1 side chains in this system. While such polar interactions of aromatic rings have been previously observed, the present results suggest their potential for significant thermodynamic contributions to protein structure and ligand recognition.     

Poisson–Boltzmann model analysis of binding mRNA cap analogues to the translation initiation factor eIF4E

The electrostatic free energy of binding of two analogues of the 5′-mRNA cap, differing in size and electric charge, to the wild type and mutated eukaryotic initiation factor eIF4E was computed using the finite difference solutions to the Poisson–Boltzmann equation. Two definitions of the solute–solvent dielectric boundary were used: van der Waals model, solvent exclusion (SE) model. The computed electrostatic energies were supplemented by estimations of the non polar and entropic contributions. A comparison with experimental data for the investigated systems was done. It appears that the SE model with additional contribution fits experimental findings better than the van der Waals model does.     

Binding of small basic peptides to membranes containing acidic lipids: theoretical models and experimental results.

We measured directly the binding of Lys3, Lys5, and Lys7 to vesicles containing acidic phospholipids. When the vesicles contain 33% acidic lipids and the aqueous solution contains 100 mM monovalent salt, the standard Gibbs free energy for the binding of these peptides is 3, 5, and 7 kcal/mol, respectively. The binding energies decrease as the mol% of acidic lipids in the membrane decreases and/or as the salt concentration increases. Several lines of evidence suggest that these hydrophilic peptides do not penetrate the polar headgroup region of the membrane and that the binding is mainly due to electrostatic interactions. To calculate the binding energies from classical electrostatics, we applied the nonlinear Poisson-Boltzmann equation to atomic models of the phospholipid bilayers and the basic peptides in aqueous solution. The electrostatic free energy of interaction, which arises from both a long-range coulombic attraction between the positively charged peptide and the negatively charged lipid bilayer, and a short-range Born or image charge repulsion, is a minimum when approximately 2.5 A (i.e., one layer of water) exists between the van der Waals surfaces of the peptide and the lipid bilayer. The calculated molar association constants, K, agree well with the measured values: K is typically about 10-fold smaller than the experimental value (i.e., a difference of about 1.5 kcal/mol in the free energy of binding). The predicted dependence of K (or the binding free energies) on the ionic strength of the solution, the mol% of acidic lipids in the membrane, and the number of basic residues in the peptide agree very well with the experimental measurements. These calculations are relevant to the membrane binding of a number of important proteins that contain clusters of basic residues.     

The impact of <Emphasis Type="Italic">Trichoderma reesei</Emphasis> Cel7A carbohydrate binding domain mutations on its binding to a cellulose surface: a molecular dynamics free energy study

A critical role of the Family 7 cellobiohydrolase (Cel7A) carbohydrate binding domain (CBD) is to bind to a cellulose surface and increase the enzyme concentration on the surface. Several residues of Trichoderma reesei Cel7A CBD, including Y5, N29, Y31, Y32 and Q34, contribute to cellulose binding, as revealed by early experimental studies. To investigate the interactions between these important residues and cellulose, we applied a thermodynamic integration method to calculate the cellulose–Cel7A CBD binding free energy changes caused by Y5A, N29A, Y31A, Y32A and Q34A mutations. The experimental binding trend was successfully predicted, proving the effectiveness of the complex model. For the two polar residue mutants N29A and Q34A, the changes in the electrostatics are comparable to those of van der Waals, while for three Y to A mutants, the free energy differences mainly come from van der Waals interactions. However, in both cases, the electrostatics dominates the interactions between individual residues and cellulose. The side chains of these residues are rigidified after the complex is formed. The binding free energy changes for the two mutants Y5W and Y31W were also determined, and for these the van der Waals interaction was strengthened but the electrostatics was weakened.     

Molecular dynamics investigation on the poor sensitivity of A171T mutant NEDD8-activating enzyme (NAE) for MLN4924

MLN4924 is an adenosine sulfamate analog that generates the inhibitory NEDD8-MLN4924 covalent complex. A single nucleotide transition that changes alanine 171 to threonine (A171T) of the NAE subunit UBA3 reduces the enzyme’s sensitivity for MLN4924. Our molecular dynamics simulation study revealed that A171T transition brought remarkable conformational changes in enzyme structure (open ATP binding pocket), which reduced the interaction between MLN4924 and ATP binding pocket while wild form completely covered the MLN4924. A total difference of ?49.75?kJ/mol was noticed in interaction energy (electrostatic and van der Waals) during simulation between mutant and wild form with MLN4924. Superimposition of final 20?ns mutant structure with reference structure showed significant change in native binding position as compared to wild form. Results were found in coherence with the recently reported in vitro studies which states that A171T transition leads to change in ATP binding pocket structure.     

Influence of cation-pi interactions in different folding types of membrane proteins

Cation-pi interactions play an important role to the stability of protein structures. In this work, we analyze the influence of cation-pi interactions in three-dimensional structures of membrane proteins. We found that transmembrane strand (TMS) proteins have more number of cation-pi interactions than transmembrane helical (TMH) proteins. In TMH proteins, both the positively charged residues Lys and Arg equally experience favorable cation-pi interactions whereas in TMS proteins, Arg is more likely than Lys to be in such interactions. There is no relationship between number of cation-pi interactions and number of residues in TMH proteins whereas a good correlation was observed in TMS proteins. The average cation-pi interaction energy for TMH proteins is -16 kcal/mol and that for TMS proteins is -27 kcal/mol. The pair-wise cation-pi interaction energy between aromatic and positively charged residues showed that Lys-Trp energy is stronger in TMS proteins than TMH proteins; Arg-Phe, Arg-Tyr and Lys-Phe have higher energy in TMH proteins than TMS proteins. The decomposition of energies into electrostatic and van der Waals revealed that the contribution from electrostatic energy is twice as that from van der Waals energy in both TMH and TMS proteins. The results obtained in the present study would be helpful to understand the contribution of cation-pi interactions to the stability of membrane proteins.     

Simulation of the different biological activities of diethylstilbestrol (DES) on estrogen receptor alpha and estrogen-related receptor gamma

We describe the application of the molecular dynamics (MD) and molecular mechanics-generalized Born/surface area (MM-GB/SA) approaches to the simulation of the different biological activity of diethylstilbestrol (DES) on two highly homologous nuclear receptors-estrogen receptor alpha (ER-alpha) and estrogen-related receptor gamma (ERR-gamma). DES exerts an agonistic effect against ER-alpha and an antagonistic effect against ERR-gamma. Using the x-ray crystal structures of ER-alpha in the canonical agonist bound form (PDB code: 3ERD) and antagonist bound form (PDB code: 3ERT), ERR-gamma homology models have been constructed for the receptor in two different conformations. MM-GB/SA binding free energy calculations of DES in the ER-alpha and ERR-gamma structures suggest that DES exhibits a greater free energy of binding in the agonist bound conformation of ER-alpha, while the antagonist bound conformation is preferred for ERR-gamma. Further dissection of the free energy contributions coupled with calculation of the ligand binding pocket volume suggests that the van der Waals interactions for DES within the smaller binding pocket volume of ERR-gamma are less favorable and this is the main factor for DES antagonism in ERR-gamma. This approach has potential general applicability to the prediction of the biological activity of nuclear receptor ligands.     

Probing the structural and energetic basis of kinesin-microtubule binding using computational alanine-scanning mutagenesis

Kinesin-microtubule (MT) binding plays a critical role in facilitating and regulating the motor function of kinesins. To obtain a detailed structural and energetic picture of kinesin-MT binding, we performed large-scale computational alanine-scanning mutagenesis based on long-time molecular dynamics (MD) simulations of the kinesin-MT complex in both ADP and ATP states. First, we built three all-atom kinesin-MT models: human conventional kinesin bound to ADP and mouse KIF1A bound to ADP and ATP. Then, we performed 30 ns MD simulations followed by kinesin-MT binding free energy calculations for both the wild type and mutants obtained after substitution of each charged residue of kinesin with alanine. We found that the kinesin-MT binding free energy is dominated by van der Waals interactions and further enhanced by electrostatic interactions. The calculated mutational changes in kinesin-MT binding free energy are in excellent agreement with results of an experimental alanine-scanning study with a root-mean-square error of ~0.32 kcal/mol [Woehlke, G., et al. (1997) Cell 90, 207-216]. We identified a set of important charged residues involved in the tuning of kinesin-MT binding, which are clustered on several secondary structural elements of kinesin (including well-studied loops L7, L8, L11, and L12, helices α4, α5, and α6, and less-explored loop L2). In particular, we found several key residues that make different contributions to kinesin-MT binding in ADP and ATP states. The mutations of these residues are predicted to fine-tune the motility of kinesin by modulating the conformational transition between the ADP state and the ATP state of kinesin.     

Comparison of end-point continuum-solvation methods for the calculation of protein-ligand binding free energies

We have compared the predictions of ligand‐binding affinities from several methods based on end‐point molecular dynamics simulations and continuum solvation, that is, methods related to MM/PBSA (molecular mechanics combined with Poisson–Boltzmann and surface area solvation). Two continuum‐solvation models were considered, viz., the Poisson–Boltzmann (PB) and generalised Born (GB) approaches. The nonelectrostatic energies were also obtained in two different ways, viz., either from the sum of the bonded, van der Waals, nonpolar solvation energies, and entropy terms (as in MM/PBSA), or from the scaled protein–ligand van der Waals interaction energy (as in the linear interaction energy approach, LIE). Three different approaches to calculate electrostatic energies were tested, viz., the sum of electrostatic interaction energies and polar solvation energies, obtained either from a single simulation of the complex or from three independent simulations of the complex, the free protein, and the free ligand, or the linear‐response approximation (LRA). Moreover, we investigated the effect of scaling the electrostatic interactions by an effective internal dielectric constant of the protein (?_int). All these methods were tested on the binding of seven biotin analogues to avidin and nine 3‐amidinobenzyl‐1H‐indole‐2‐carboxamide inhibitors to factor Xa. For avidin, the best results were obtained with a combination of the LIE nonelectrostatic energies with the MM+GB electrostatic energies from a single simulation, using ?_int = 4. For fXa, standard MM/GBSA, based on one simulation and using ?_int = 4–10 gave the best result. The optimum internal dielectric constant seems to be slightly higher with PB than with GB solvation. © Proteins 2012; © 2012 Wiley Periodicals, Inc.     

A free energy analysis of nucleic acid base stacking in aqueous solution.

This paper reports a theoretical study of the free energy contributions to nucleic acid base stacking in aqueous solution. Electrostatic interactions are treated by using the finite difference Poisson-Boltzmann method and nonpolar effects are treated with explicit calculation of van der Waals interactions and/or free energy-surface area relationships. Although for some pairs of bases there is a favorable Coulombic interaction in the stacked conformation, generally the net effect of electrostatic interactions is to oppose stacking. This result is caused by the loss of favorable base-solvent electrostatic interactions, that accompany the partial removal of polar atoms from water in the stacked conformation. Nonpolar interactions, involving the hydrophobic effect and enhancement of van der Waals interactions caused by close-packing, drive stacking. The calculations qualitatively reproduce the experimental dependence of stacking free energy on purine-pyrimidine composition.     

Calculation of binding affinities of HIV-1 RT and β-secretase inhibitors using the linear interaction energy method with explicit and continuum solvation approaches

The linear interaction energy (LIE) approach has been applied to estimate the binding free energies of representative sets of HIV-1 RT and β-Secretase inhibitors, using both molecular dynamics (MD) and tethered energy minimization sampling protocols with the OPLS-AA potential, using a range of solvation methodologies. Generalized Born (GB), ‘shell’ and periodic boundary condition (PBC) solvation were used, the latter with reaction field (RF) electrostatics. Poisson-Boltzmann (PB) and GB continuum electrostatics schemes were applied to the simulation trajectories for each solvation type to estimate the electrostatic ligand-water interaction energy in both the free and bound states. Reasonable agreement of the LIE predictions was obtained with respect to experimental binding free energy estimates for both systems: for instance, ‘PB’ fits on MD trajectories carried out with PBC solvation and RF electrostatics led to models with standard errors of 1.11 and 1.03 kcal mol⁻¹ and coefficients of determination, r ² of 0.76 and 0.75 for the HIV-1 RT and β-Secretase sets. However, it was also found that results from MD sampling using PBC solvation provided only slightly better fits than from simulations using shell or Born solvation or tethered energy minimization sampling. Figure Evolution of the running averages for compound H11 (binding to HIV-1RT) of the bound state ligand-water and ligand-protein interaction energies. The ligand-water electrostatic terms are twice the corresponding GB and PB electrostatic solvation free energies. The ligand-receptor van der Waals and Coulombic interaction energies are also shown, in addition to the ligand-water van der Waals interaction term. The terms were calculated (without application of a cut-off) from a trajectory sampled under PBC solvation with reaction field electrostatics Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Computational analysis and prediction of the binding motif and protein interacting partners of the Abl SH3 domain

Protein-protein interactions, particularly weak and transient ones, are often mediated by peptide recognition domains, such as Src Homology 2 and 3 (SH2 and SH3) domains, which bind to specific sequence and structural motifs. It is important but challenging to determine the binding specificity of these domains accurately and to predict their physiological interacting partners. In this study, the interactions between 35 peptide ligands (15 binders and 20 non-binders) and the Abl SH3 domain were analyzed using molecular dynamics simulation and the Molecular Mechanics/Poisson-Boltzmann Solvent Area method. The calculated binding free energies correlated well with the rank order of the binding peptides and clearly distinguished binders from non-binders. Free energy component analysis revealed that the van der Waals interactions dictate the binding strength of peptides, whereas the binding specificity is determined by the electrostatic interaction and the polar contribution of desolvation. The binding motif of the Abl SH3 domain was then determined by a virtual mutagenesis method, which mutates the residue at each position of the template peptide relative to all other 19 amino acids and calculates the binding free energy difference between the template and the mutated peptides using the Molecular Mechanics/Poisson-Boltzmann Solvent Area method. A single position mutation free energy profile was thus established and used as a scoring matrix to search peptides recognized by the Abl SH3 domain in the human genome. Our approach successfully picked ten out of 13 experimentally determined binding partners of the Abl SH3 domain among the top 600 candidates from the 218,540 decapeptides with the PXXP motif in the SWISS-PROT database. We expect that this physical-principle based method can be applied to other protein domains as well.     

SCORE: A New Empirical Method for Estimating the Binding Affinity of a Protein-Ligand Complex

A new method is presented to estimate the binding affinity of a protein-ligand complex with known three-dimensional structure. The method, SCORE, uses an empirical scoring function to describe the binding free energy, which includes terms to account for van der Waals contact, metal-ligand bonding, hydrogen bonding, desolvation effect, and deformation penalty upon the binding process. The coefficients of each term are obtained by multivariate regressional analysis of a diverse training set of 170 protein-ligand complexes. The final scoring function reproduces the binding free energies of the whole training set with a cross-validated deviation of 6.3 kJ/mol. The predictive ability of the function is further tested by a set of 11 endothiapepsin complexes and the internal consistency of the function is demonstrated in a stepwise procedure named Evolutionary Test. A major innovation of this method is the introduction of an atomic binding score which allows the researcher to inspect and optimize the lead compound rationally in a structure-based drug design scheme.