Binding free energies for nicotine analogs inhibiting cytochrome P450 2A6 by a combined use of molecular dynamics simulations and QM/MM-PBSA calculations

Molecular dynamics (MD) simulations and hybrid quantum mechanical/molecular mechanical (QM/MM) calculations have been performed to explore the dynamic behaviors of cytochrome P450 2A6 (CYP2A6) binding with nicotine analogs (that are typical inhibitors) and to calculate their binding free energies in combination with Poisson–Boltzmann surface area (PBSA) calculations. The combined MD simulations and QM/MM-PBSA calculations reveal that the most important structural parameters affecting the CYP2A6-inhibitor binding affinity are two crucial internuclear distances, that is, the distance between the heme iron atom of CYP2A6 and the coordinating atom of the inhibitor, and the hydrogen-bonding distance between the N297 side chain of CYP2A6 and the pyridine nitrogen of the inhibitor. The combined MD simulations and QM/MM-PBSA calculations have led to dynamic CYP2A6-inhibitor binding structures that are consistent with the observed dynamic behaviors and structural features of CYP2A6-inhibitor binding, and led to the binding free energies that are in good agreement with the experimentally-derived binding free energies. The agreement between the calculated binding free energies and the experimentally-derived binding free energies suggests that the combined MD and QM/MM-PBSA approach may be used as a valuable tool to accurately predict the CYP2A6-inhibitor binding affinities in future computational design of new, potent and selective CYP2A6 inhibitors.     

Insights into protein-protein binding by binding free energy calculation and free energy decomposition for the Ras-Raf and Ras-RalGDS complexes

Absolute binding free energy calculations and free energy decompositions are presented for the protein-protein complexes H-Ras/C-Raf1 and H-Ras/RalGDS. Ras is a central switch in the regulation of cell proliferation and differentiation. In our study, we investigate the capability of the molecular mechanics (MM)-generalized Born surface area (GBSA) approach to estimate absolute binding free energies for the protein-protein complexes. Averaging gas-phase energies, solvation free energies, and entropic contributions over snapshots extracted from trajectories of the unbound proteins and the complexes, calculated binding free energies (Ras-Raf: -15.0(+/-6.3)kcal mol(-1); Ras-RalGDS: -19.5(+/-5.9)kcal mol(-1)) are in fair agreement with experimentally determined values (-9.6 kcal mol(-1); -8.4 kcal mol(-1)), if appropriate ionic strength is taken into account. Structural determinants of the binding affinity of Ras-Raf and Ras-RalGDS are identified by means of free energy decomposition. For the first time, computationally inexpensive generalized Born (GB) calculations are applied in this context to partition solvation free energies along with gas-phase energies between residues of both binding partners. For selected residues, in addition, entropic contributions are estimated by classical statistical mechanics. Comparison of the decomposition results with experimentally determined binding free energy differences for alanine mutants of interface residues yielded correlations with r(2)=0.55 and 0.46 for Ras-Raf and Ras-RalGDS, respectively. Extension of the decomposition reveals residues as far apart as 25A from the binding epitope that can contribute significantly to binding free energy. These "hotspots" are found to show large atomic fluctuations in the unbound proteins, indicating that they reside in structurally less stable regions. Furthermore, hotspot residues experience a significantly larger-than-average decrease in local fluctuations upon complex formation. Finally, by calculating a pair-wise decomposition of interactions, interaction pathways originating in the binding epitope of Raf are found that protrude through the protein structure towards the loop L1. This explains the finding of a conformational change in this region upon complex formation with Ras, and it may trigger a larger structural change in Raf, which is considered to be necessary for activation of the effector by Ras.     

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.     

Binding to DNA purine bases and amino acid residues of a ruthenium(II) antitumor complex: A density functional study

The hydrolyzed α-[Ru(azpy)₂Cl₂] (azpy is 2-(phenylazo)pyridine; α indicates that the isomer in which the coordinating pairs Cl, N(py), and N(azo) are cis, trans, and cis, respectively) binding to guanine (G), adenine (A), methionine (Met), and histidine (His) residues were investigated by using density functional theory. Reactant complexes (RC), product complexes (PC), and transition states (TS) involved were fully characterized. The calculated energy profiles showed that the activation free energies for the substitutions of hydrolyzed α-[Ru(azpy)₂Cl₂] with Met was apparently lower than those of guanine and adenine. This indicate that the hydrolyzed α-[Ru(azpy)₂Cl₂] compounds may preferentially bind to the sulfur-containing amino acids residues in vivo. Moreover, the natural orbital population analysis (NPA) showed that the Ru atom gained the greatest negative charges in the reactions of hydrolyzed α-[Ru(azpy)₂Cl₂] with Met, which may contribute to their remarkably low activation free energies partially.     

The effect of multiple binding modes on empirical modeling of ligand docking to proteins.

A popular approach to the computational modeling of ligand/receptor interactions is to use an empirical free energy like model with adjustable parameters. Parameters are learned from one set of complexes, then used to predict another set. To improve these empirical methods requires an independent way to study their inherent errors. We introduce a toy model of ligand/receptor binding as a workbench for testing such errors. We study the errors incurred from the two state binding assumption--the assumption that a ligand is either bound in one orientation, or unbound. We find that the two state assumption can cause large errors in free energy predictions, but it does not affect rank order predictions significantly. We show that fitting parameters using data from high affinity ligands can reduce two state errors; so can using more physical models that do not use the two state assumption. We also find that when using two state models to predict free energies, errors are more severe on high affinity ligands than low affinity ligands. And we show that two state errors can be diagnosed by systematically adding new binding modes when predicting free energies: if predictions worsen as the modes are added, then the two state assumption in the fitting step may be at fault.     

Estimating protein-ligand binding free energy: atomic solvation parameters for partition coefficient and solvation free energy calculation

Solvation energy calculation is one of the main difficulties for the estimation of protein-ligand binding free energy and the correct scoring in docking studies. We have developed a new solvation energy estimation method for protein-ligand binding based on atomic solvation parameter (ASP), which has been shown to improve the power of protein-ligand binding free energy predictions. The ASP set, designed to handle both proteins and organic compounds and derived from experimental n-octanol/water partition coefficient (log P) data, contains 100 atom types (united model that treats hydrogen atoms implicitly) or 119 atom types (all-atom model that treats hydrogen atoms explicitly). By using this unified ASP set, an algorithm was developed for solvation energy calculation and was further integrated into a score function for predicting protein-ligand binding affinity. The score function reproduced the absolute binding free energies of a test set of 50 protein-ligand complexes with a standard error of 8.31 kJ/mol. As a byproduct, a conformation-dependent log P calculation algorithm named ASPLOGP was also implemented. The predictive results of ASPLOGP for a test set of 138 compounds were r = 0.968, s = 0.344 for the all-atom model and r = 0.962, s = 0.367 for the united model, which were better than previous conformation-dependent approaches and comparable to fragmental and atom-based methods. ASPLOGP also gave good predictive results for small peptides. The score function based on the ASP model can be applied widely in protein-ligand interaction studies and structure-based drug design.     

Ligand binding to the voltage-gated Kv1.5 potassium channel in the open state--docking and computer simulations of a homology model

The binding of blockers to the human voltage-gated Kv1.5 potassium ion channel is investigated using a three-step procedure consisting of homology modeling, automated docking, and binding free energy calculations from molecular dynamics simulations, in combination with the linear interaction energy method. A reliable homology model of Kv1.5 is constructed using the recently published crystal structure of the Kv1.2 channel as a template. This model is expected to be significantly more accurate than earlier ones based on less similar templates. Using the three-dimensional homology model, a series of blockers with known affinities are docked into the cavity of the ion channel and their free energies of binding are calculated. The predicted binding free energies are in very good agreement with experimental data and the binding is predicted to be mainly achieved through nonpolar interactions, whereas the relatively small differences in the polar contribution determine the specificity. Apart from confirming the importance of residues V505, I508, V512, and V516 for ligand binding in the cavity, the results also show that A509 and P513 contribute significantly to the nonpolar binding interactions. Furthermore, we find that pharmacophore models based only on optimized free ligand conformations may not necessarily capture the geometric features of ligands bound to the channel cavity. The calculations herein give a detailed structural and energetic picture of blocker binding to Kv1.5 and this model should thus be useful for further ligand design efforts.     

Protein chemistry at membrane interfaces: non-additivity of electrostatic and hydrophobic interactions

Non-specific binding of proteins and peptides to charged membrane interfaces depends upon the combined contributions of hydrophobic (DeltaG(HPhi)) and electrostatic (DeltaG(ES)) free energies. If these are simply additive, then the observed free energy of binding (DeltaG(obs)) will be given by DeltaG(obs)=DeltaG(HPhi)+DeltaG(ES), where DeltaG(HPhi)=-sigma(NP)A(NP) and DeltaG(ES)=zFphi. In these expressions, A(NP) is the non-polar accessible area, sigma(NP) the non-polar solvation parameter, z the formal peptide valence, F the Faraday constant, and phi the membrane surface potential. But several lines of evidence suggest that hydrophobic and electrostatic binding free energies of proteins at membrane interfaces, such as those associated with cell signaling, are not simply additive. In order to explore this issue systematically, we have determined the interfacial partitioning free energies of variants of indolicidin, a cationic proline-rich antimicrobial peptide. The synthesized variants of the 13 residue peptide covered a wide range of hydrophobic free energies, which allowed us to examine the effect of hydrophobicity on electrostatic binding to membranes formed from mixtures of neutral and anionic lipids. Although DeltaG(obs) was always a linear function of DeltaG(HPhi), the slope depended upon anionic lipid content: the slope was 1.0 for pure, zwitterionic phosphocholine bilayers and 0.3 for pure phosphoglycerol membranes. DeltaG(obs) also varied linearly with surface potential, but the slope was smaller than the expected value, zF. As observed by others, this suggests an effective peptide valence z(eff) that is smaller than the formal valence z. Because of our systematic approach, we were able to establish a useful rule-of-thumb: z(eff) is reduced relative to z by about 20 % for each 3 kcal mol(-1) (1 kcal=4.184 kJ) favorable increase in DeltaG(HPhi). For neutral phosphocholine interfaces, we found that DeltaG(obs) could be predicted with remarkable accuracy using the Wimley-White experiment-based interfacial hydrophobicity scale.     

Potential of mean force for protein-protein interaction studies.

Calculating protein-protein interaction energies is crucial for understanding protein-protein associations. On the basis of the methodology of mean-field potential, we have developed an empirical approach to estimate binding free energy for protein-protein interactions. This knowledge-based approach has been used to derive distance-dependent free energies of protein complexes from a nonredundant training set in the Protein Data Bank (PDB), with a careful treatment of homology. We calculate atom pair potentials for 16 pair interactions, which can reflect the importance of hydrophobic interactions and specific hydrogen-bonding interactions. The derived potentials for hydrogen-bonding interactions show a valley of favorable interactions at a distance of approximately 3 A, corresponding to that of an established hydrogen bond. For the test set of 28 protein complexes, the calculated energies have a correlation coefficient of 0.75 compared with experimental binding free energies. The performance of the method in ranking the binding energies of different protein-protein complexes shows that the energy estimation can be applied to value binding free energies for protein-protein associations.     

Analysis of individual-site binding data.

Individual-site isotherms add experimental data which may allow for a more detailed definition of the parameters in a system with interacting binding sites. Individual-site isotherms accomplish the following: (A) In general, they define little more than the total or combined isotherm except to reveal the existence of different sites. (B) Under the limiting conditions of symmetrical interactions in two site systems they define: (1) the ratio of the unperturbed or intrinsic binding constants rather than their actual values, (2) the unperturbed shape of the total isotherm, that is, the shape of the total isotherm if there were no ligand dependent interactions between the sites, and (3) the perturbation of the shape of the total isotherm derived from interactions between the sites. (C) They do not define the nature of the interactions; that is, they do not resolve the free energies of the interactions between the sites. (D) When some assumptions about the nature of the interactions are made they may aid in defining some free energies of interaction between the sites.     

Beauty Is in the Eye of the Beholder: Proteins Can Recognize Binding Sites of Homologous Proteins in More than One Way

Understanding the mechanisms of protein–protein interaction is a fundamental problem with many practical applications. The fact that different proteins can bind similar partners suggests that convergently evolved binding interfaces are reused in different complexes. A set of protein complexes composed of non-homologous domains interacting with homologous partners at equivalent binding sites was collected in 2006, offering an opportunity to investigate this point. We considered 433 pairs of protein–protein complexes from the ABAC database (AB and AC binary protein complexes sharing a homologous partner A) and analyzed the extent of physico-chemical similarity at the atomic and residue level at the protein–protein interface. Homologous partners of the complexes were superimposed using Multiprot, and similar atoms at the interface were quantified using a five class grouping scheme and a distance cut-off. We found that the number of interfacial atoms with similar properties is systematically lower in the non-homologous proteins than in the homologous ones. We assessed the significance of the similarity by bootstrapping the atomic properties at the interfaces. We found that the similarity of binding sites is very significant between homologous proteins, as expected, but generally insignificant between the non-homologous proteins that bind to homologous partners. Furthermore, evolutionarily conserved residues are not colocalized within the binding sites of non-homologous proteins. We could only identify a limited number of cases of structural mimicry at the interface, suggesting that this property is less generic than previously thought. Our results support the hypothesis that different proteins can interact with similar partners using alternate strategies, but do not support convergent evolution.     

Magnesium-cationic dummy atom molecules enhance representation of DNA polymerase beta in molecular dynamics simulations: improved accuracy in studies of structural features and mutational effects

Human DNA polymerase beta (pol beta) fills gaps in DNA as part of base excision DNA repair. Due to its small size it is a convenient model enzyme for other DNA polymerases. Its active site contains two Mg(2+) ions, of which one binds an incoming dNTP and one catalyzes its condensation with the DNA primer strand. Simulating such binuclear metalloenzymes accurately but computationally efficiently is a challenging task. Here, we present a magnesium-cationic dummy atom approach that can easily be implemented in molecular mechanical force fields such as the ENZYMIX or the AMBER force fields. All properties investigated here, namely, structure and energetics of both Michaelis complexes and transition state (TS) complexes were represented more accurately using the magnesium-cationic dummy atom model than using the traditional one-atom representation for Mg(2+) ions. The improved agreement between calculated free energies of binding of TS models to different pol beta variants and the experimentally determined activation free energies indicates that this model will be useful in studying mutational effects on catalytic efficiency and fidelity of DNA polymerases. The model should also have broad applicability to the modeling of other magnesium-containing proteins.     

Molecular dynamics simulation reveals sequence-intrinsic and protein-induced geometrical features of the OL1 DNA operator

We have carried out molecular dynamics simulation of the lambda OL1 DNA operator on the free and the protein-bound forms. Our results lead us to conclude that the binding of the repressor actually makes the N-7 atom of Gua8' more solvent exposed, thereby enhancing its reactivity to chemical methylation. This increase in solvent accessibility surface area occurs simultaneously with the formation of hydrogen bonds between Lys-4 of the nonconsensus flexible N-terminal arm and Gua6' of the nonconsensus half-site operator DNA. Calculations of protein--DNA interaction energies reveal that among the residues of the arm, Lys-4 contributes the most favorably to the interaction energies. This result is consistent with mutagenesis studies that established that lysine at position 4 is absolutely required for tight binding. We find that the nonconsensus arm and the nonconsensus monomer interacts less favorably with DNA than do their respective counterparts of the consensus monomer. Moreover, the six-residue flexible arm accounts for at least half the total protein--DNA interactions energy. These results are in agreement with previous experimental studies. In accord with the diffuse electron density map observed in crystallographic studies of the nonconsensus flexible arm, we find that our model built for this region is more flexible and exhibits more conformations than its consensus counterpart. The simulation also reveals that DNA bending observed near the outer edge of the operator site is an intrinsic sequence-dependent property. By contrast, the DNA-bending features observed toward the center of the operator are induced by the protein. On the whole, stepwise protein-induced bending is more pronounced in the consensus half-site operator. We also find that the unusually large helical twist (49 degrees ) observed in the protein-bound form near the center of the operator results from the binding of the protein at a base step with some propensity for high twists.     

Contribution of a single hydroxyl group to transition-state discrimination by adenosine deaminase: evidence for an "entropy trap" mechanism

Adenosine deaminase was found to bind 6-hydroxy-1,6-dihydropurine ribonucleoside (II), formed by reversible addition of water to purine ribonucleoside (I) in a reaction analogous to formation of a tetrahedral intermediate in substrate deamination, with an apparent Ki value of 3 x 10(-13) M at 20 degrees C. 1,6-Dihydropurine ribonucleoside (IV), synthesized by photolysis of purine ribonucleoside in the presence of NaBH4, exhibited a Ki value of 5.4 x 10-6 M. After correction for differences between the relative free energies of solvation of II and IV, the 6-hydroxyl group of II was estimated to contribute more than 16 kcal to the free energy of binding, approaching the enthalapy of formation of a single hydrogen bond to charged group in the vapor phase. The relatively weak binding of IV and of substrate water suggests that entropic effects, arising from the cooperative action of binding determinants contained within these separate molecules, contribute more than 10 kcal/mol to the free energy of binding of II in which these binding determinants are contained within a single molecule. In free solution, the entropy of reversible hydration of I was evaluated by measuring the temperature dependence of equilibria of protonation of I and of pseudobase formation from I-methylpurinium ribonucleoside as -35 eu, comparable with the entropy of activation for the uncatalyzed hydrolysis of adenosine. In the active site of adenosine deaminase, this thermodynamic obstacle is evidently climbed spontaneously as a result of attractive interactions between the active site and the critical hydroxyl group at the 6-position.(ABSTRACT TRUNCATED AT 250 WORDS)     

A preference-based free-energy parameterization of enzyme-inhibitor binding. Applications to HIV-1-protease inhibitor design.

The interface between protein receptor-ligand complexes has been studied with respect to their binary interatomic interactions. Crystal structure data have been used to catalogue surfaces buried by atoms from each member of a bound complex and determine a statistical preference for pairs of amino-acid atoms. A simple free energy model of the receptor-ligand system is constructed from these atom-atom preferences and used to assess the energetic importance of interfacial interactions. The free energy approximation of binding strength in this model has a reliability of about +/- 1.5 kcal/mol, despite limited knowledge of the unbound states. The main utility of such a scheme lies in the identification of important stabilizing atomic interactions across the receptor-ligand interface. Thus, apart from an overall hydrophobic attraction (Young L, Jernigan RL, Covell DG, 1994, Protein Sci 3:717-729), a rich variety of specific interactions is observed. An analysis of 10 HIV-1 protease inhibitor complexes is presented that reveals a common binding motif comprised of energetically important contacts with a rather limited set of atoms. Design improvements to existing HIV-1 protease inhibitors are explored based on a detailed analysis of this binding motif.     

Interfacial free energies of intact and reconstituted erythrocyte surfaces: Implications for biological adhesion

Model cell surfaces consisting of phospholipids or phospholipids and the erythrocyte membrane glycoprotein glycophorin have been formed at an oil/water interface. Interfacial free energies have been estimated from surface wetting by both hydrophobic and hydrophilic test droplets on both the model surfaces and on intact erythrocytes. The use of a dense fluorocarbon oil to form the oil/water interface facilitates analysis by minimising surface deformation by the test drop. Hydrophobic test droplets (polar hydrocarbon oils) show increasing contact angles (decreasing wetting) with increasing hydrophilicity (decreasing interfacial free energy) of the model interface. Hydrophilic test droplets (phase separated aqueous polymer systems) show the opposite behaviour, spreading more as the interfacial free energy is decreased. Both systems give similar estimates of the interfacial free energy. Glycophorin reproduces the wetting properties of intact cell surfaces by reducing the lipid-water interfacial free energy from 5·10^?3 J·m^?2 to 1·10^?6 J·m^?2. From molecular considerations it is concluded that ‘cell surface free energy’ is an ambiguous term; its magnitude depends on the location of the interface in question. Thus, in a thermodynamic analysis of interactions at biosurfaces (such as cellular adhesion, chemotaxis or membrane fusion), the interfacial free energies may vary by more than three orders of magnitude depending on the location of the particular interface.     

Thermodynamic, spectroscopic, and equilibrium binding studies of DNA sequence context effects in six 22-base pair deoxyoligonucleotides.

Effects of different end sequences on stability, circular dichroism spectra (CD), and enzyme binding properties were investigated for six 22-base pair, non-self-complementary duplex DNA oligomers. The center sequences of these deoxyoligonucleotides have 8-14 base pairs in common and are flanked on both sides by sequences differing in context and A-T content. Temperature-induced melting transitions monitored by differential scanning calorimetry (DSC) and ultraviolet absorbance were measured for the six duplexes in buffered 115 mM Na(+) solutions. Values of the melting transition enthalpy, DeltaH(cal), and entropy, DeltaS(cal), were obtained directly from DSC experiments. Melting transition parameters, DeltaH(vH) and DeltaS(vH), were also estimated from van't Hoff analysis of optical melting curves collected as a function of DNA concentration, assuming a two-state melting transition. Melting free energies (20 degrees C) of the six DNAs evaluated from DSC experiments ranged from -18.7 to -32.7 kcal/mol. van't Hoff estimates of the free energies ranged from -18.5 to -48.0 kcal/mol. With either method, the trends in free energy as a function of sequence were identical. Equilibrium binding by BamHI restriction endonuclease to the 22-base pair DNAs was also investigated. The central eight base pairs of all six molecules, 5'-A-GGATCC-A-3', contained a BamHI recognition sequence bounded by A-T base pairs. Magnesium free binding assays were performed by titering BamHI against a constant concentration of each of the deoxyoligonucleotide substrates and analyzing reaction products by gel retardation. Binding isotherms of the total amount of bound DNA versus protein concentration were constructed which provided semiquantitative estimates of the equilibrium dissociation constants for dissociation of BamHI from the six DNA oligomers. Dissociation constants ranged from 0.5 x 10(-)(9) to 12.0 x 10(-)(9) M with corresponding binding free energies of -12.5 to -10.6 (+/-0. 1) kcal/mol. An inverse relationship is found when binding and stability are compared.     

Consistency in structural energetics of protein folding and peptide recognition.

We report a new free energy decomposition that includes structure-derived atomic contact energies for the desolvation component, and show that it applies equally well to the analysis of single-domain protein folding and to the binding of flexible peptides to proteins. Specifically, we selected the 17 single-domain proteins for which the three-dimensional structures and thermodynamic unfolding free energies are available. By calculating all terms except the backbone conformational entropy change and comparing the result to the experimentally measured free energy, we estimated that the mean entropy gain by the backbone chain upon unfolding (delta Sbb) is 5.3 cal/K per mole of residue, and that the average backbone entropy for glycine is 6.7 cal/K. Both numbers are in close agreement with recent estimates made by entirely different methods, suggesting a promising degree of consistency between data obtained from disparate sources. In addition, a quantitative analysis of the folding free energy indicates that the unfavorable backbone entropy for each of the proteins is balanced predominantly by favorable backbone interactions. Finally, because the binding of flexible peptides to receptors is physically similar to folding, the free energy function should, in principle, be equally applicable to flexible docking. By combining atomic contact energies, electrostatics, and sequence-dependent backbone entropy, we calculated a priori the free energy changes associated with the binding of four different peptides to HLA-A2, 1 MHC molecule and found agreement with experiment to within 10% without parameter adjustment.