Parameterization of an effective potential for protein–ligand binding from host–guest affinity data

Force field accuracy is still one of the “stalemates” in biomolecular modeling. Model systems with high quality experimental data are valuable instruments for the validation and improvement of effective potentials. With respect to protein–ligand binding, organic host–guest complexes have long served as models for both experimental and computational studies because of the abundance of binding affinity data available for such systems. Binding affinity data collected for cyclodextrin (CD) inclusion complexes, a popular model for molecular recognition, is potentially a more reliable resource for tuning energy parameters than hydration free energy measurements. Convergence of binding free energy calculations on CD host–guest systems can also be obtained rapidly, thus offering the opportunity to assess the robustness of these parameters. In this work, we demonstrate how implicit solvent parameters can be developed using binding affinity experimental data and the binding energy distribution analysis method (BEDAM) and validated using the Grid Inhomogeneous Solvation Theory analysis. These new solvation parameters were used to study protein–ligand binding in two drug targets against the HIV‐1 virus and improved the agreement between the calculated and the experimental binding affinities. This work illustrates how benchmark sets of high quality experimental binding affinity data and physics‐based binding free energy models can be used to evaluate and optimize force fields for protein–ligand systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Stability of Ligand-induced Protein Conformation Influences Affinity in Maltose-binding Protein

Our understanding of what determines ligand affinity of proteins is poor, even with high-resolution structures available. Both the non-covalent ligand–protein interactions and the relative free energies of available conformations contribute to the affinity of a protein for a ligand. Distant, non-binding site residues can influence the ligand affinity by altering the free energy difference between a ligand-free and ligand-bound conformation. Our hypothesis is that when different ligands induce distinct ligand-bound conformations, it should be possible to tweak their affinities by changing the free energies of the available conformations. We tested this idea for the maltose-binding protein (MBP) from Escherichia coli. We used single-molecule Förster resonance energy transfer (smFRET) to distinguish several unique ligand-bound conformations of MBP. We engineered mutations, distant from the binding site, to affect the stabilities of different ligand-bound conformations. We show that ligand affinity can indeed be altered in a conformation-dependent manner. Our studies provide a framework for the tuning of ligand affinity, apart from modifying binding site residues.     

蛋白质与极性配体复合物的绝对结合自由能计算

介绍了用分子动力学模拟与热力学积分法相结合,模拟蛋白质与配体的绝对结合自由能的方法.通过分子转换法,使蛋白质分子（包括水分子）与配体小分子之间的相互作用逐渐减弱 （或增强）至完全消失（或完全出现）. 运用体约束方法,计算了配体与受体结合后平动、转动自由度的丧失即熵效应所引起的自由能变化.以胰蛋白酶双突变体（D189G/G226D）与极性配体苯甲脒为例,研究了蛋白质活性部位与极性配体的相互作用对结合自由能的影响,该复合物绝对结合自由能的模拟结果(－15.5 kJ/mol)与实验值(－10.5 kJ/mol)相近.     

Multiple functions of aromatic-carbohydrate interactions in a processive cellulase examined with molecular simulation

Proteins employ aromatic residues for carbohydrate binding in a wide range of biological functions. Glycoside hydrolases, which are ubiquitous in nature, typically exhibit tunnels, clefts, or pockets lined with aromatic residues for processing carbohydrates. Mutation of these aromatic residues often results in significant activity differences on insoluble and soluble substrates. However, the thermodynamic basis and molecular level role of these aromatic residues remain unknown. Here, we calculate the relative ligand binding free energy by mutating tryptophans in the Trichoderma reesei family 6 cellulase (Cel6A) to alanine. Removal of aromatic residues near the catalytic site has little impact on the ligand binding free energy, suggesting that aromatic residues immediately upstream of the active site are not directly involved in binding, but play a role in the glucopyranose ring distortion necessary for catalysis. Removal of aromatic residues at the entrance and exit of the Cel6A tunnel, however, dramatically impacts the binding affinity, suggesting that these residues play a role in chain acquisition and product stabilization, respectively. The roles suggested from differences in binding affinity are confirmed by molecular dynamics and normal mode analysis. Surprisingly, our results illustrate that aromatic-carbohydrate interactions vary dramatically depending on the position in the enzyme tunnel. As aromatic-carbohydrate interactions are present in all carbohydrate-active enzymes, these results have implications for understanding protein structure-function relationships in carbohydrate metabolism and recognition, carbon turnover in nature, and protein engineering strategies for biomass utilization. Generally, these results suggest that nature employs aromatic-carbohydrate interactions with a wide range of binding affinities for diverse functions.     

Affinity and specificity of protein U1A-RNA complex formation based on an additive component free energy model

An MM-GBSA computational protocol was used to investigate wild-type U1A-RNA and F56 U1A mutant experimental binding free energies. The trend in mutant binding free energies compared to wild-type is well-reproduced. Following application of a linear-response-like equation to scale the various energy components, the binding free energies agree quantitatively with observed experimental values. Conformational adaptation contributes to the binding free energy for both the protein and the RNA in these systems. Small differences in DeltaGs are the result of different and sometimes quite large relative contributions from various energetic components. Residual free energy decomposition indicates differences not only at the site of mutation, but throughout the entire protein. MM-GBSA and ab initio calculations performed on model systems suggest that stacking interactions may nearly, but not completely, account for observed differences in mutant binding affinities. This study indicates that there may be different underlying causes of ostensibly similar experimentally observed binding affinities of different mutants, and thus recommends caution in the interpretation of binding affinities and specificities purely by inspection.     

Monte Carlo simulations of the peptide recognition at the consensus binding site of the constant fragment of human immunoglobulin G: the energy landscape analysis of a hot spot at the intermolecular interface

Monte Carlo simulations of molecular recognition at the consensus binding site of the constant fragment (Fc) of human immunoglobulin G (Ig) protein have been performed to analyze structural and thermodynamic aspects of binding for the 13-residue cyclic peptide DCAWHLGELVWCT. The energy landscape analysis of a hot spot at the intermolecular interface using alanine scanning and equilibrium-simulated tempering dynamics with the simplified, knowledge-based energy function has enabled the role of the protein hot spot residues in providing the thermodynamic stability of the native structure to be determined. We have found that hydrophobic interactions between the peptide and the Met-252, Ile-253, His-433, and His-435 protein residues are critical to guarantee the thermodynamic stability of the crystallographic binding mode of the complex. Binding free energy calculations, using a molecular mechanics force field and a solvation energy model, combined with alanine scanning have been conducted to determine the energetic contribution of the protein hot spot residues in binding affinity. The conserved Asn-434, Ser-254, and Tyr-436 protein residues contribute significantly to the binding affinity of the peptide-protein complex, serving as an energetic hot spot at the intermolecular interface. The results suggest that evolutionary conserved hot spot protein residues at the intermolecular interface may be partitioned in fulfilling thermodynamic stability of the native binding mode and contributing to the binding affinity of the complex.     

An efficient computational method for calculating ligand binding affinities

Virtual compound screening using molecular docking is widely used in the discovery of new lead compounds for drug design. However, the docking scores are not sufficiently precise to represent the protein-ligand binding affinity. Here, we developed an efficient computational method for calculating protein-ligand binding affinity, which is based on molecular mechanics generalized Born/surface area (MM-GBSA) calculations and Jarzynski identity. Jarzynski identity is an exact relation between free energy differences and the work done through non-equilibrium process, and MM-GBSA is a semimacroscopic approach to calculate the potential energy. To calculate the work distribution when a ligand is pulled out of its binding site, multiple protein-ligand conformations are randomly generated as an alternative to performing an explicit single-molecule pulling simulation. We assessed the new method, multiple random conformation/MM-GBSA (MRC-MMGBSA), by evaluating ligand-binding affinities (scores) for four target proteins, and comparing these scores with experimental data. The calculated scores were qualitatively in good agreement with the experimental binding affinities, and the optimal docking structure could be determined by ranking the scores of the multiple docking poses obtained by the molecular docking process. Furthermore, the scores showed a strong linear response to experimental binding free energies, so that the free energy difference of the ligand binding (ΔΔG) could be calculated by linear scaling of the scores. The error of calculated ΔΔG was within ≈±1.5 kcal•mol⁻¹ of the experimental values. Particularly, in the case of flexible target proteins, the MRC-MMGBSA scores were more effective in ranking ligands than those generated by the MM-GBSA method using a single protein-ligand conformation. The results suggest that, owing to its lower computational costs and greater accuracy, the MRC-MMGBSA offers efficient means to rank the ligands, in the post-docking process, according to their binding affinities, and to compare these directly with the experimental values.     

Hydration energy landscape of the active site cavity in cytochrome P450cam

Hydration of protein cavities influences protein stability, dynamics, and function. Protein active sites usually contain water molecules that, upon ligand binding, are either displaced into bulk solvent or retained to mediate protein–ligand interactions. The contribution of water molecules to ligand binding must be accounted for to compute accurate values of binding affinities. This requires estimation of the extent of hydration of the binding site. However, it is often difficult to identify the water molecules involved in the binding process when ligands bind on the surface of a protein. Cytochrome P450cam is, therefore, an ideal model system because its substrate binds in a buried active site, displacing partially disordered solvent, and the protein is well characterized experimentally. We calculated the free energy differences for having five to eight water molecules in the active site cavity of the unliganded enzyme from molecular dynamics simulations by thermodynamic integration employing a three-stage perturbation scheme. The computed free energy differences between the hydration states are small (within 12 kJ mol⁻¹) but distinct. Consistent with the crystallographic determination and studies employing hydrostatic pressure, we calculated that, although ten water molecules could in principle occupy the volume of the active site, occupation by five to six water molecules is thermodynamically most favorable. Proteins 32:381–396, 1998. © 1998 Wiley-Liss, Inc.     

DFT study of the V(IV)/V(V) oxidation mechanism in the presence of N-hydroxyacetamide

The oxidation mechanism of V(IV)/V(V) in the presence of N-hydroxyacetamide (acetohydroxamic acid, HL) in aqueous solution has been investigated using density functional theory (DFT) calculations aiming to contribute to the understanding of this process at a molecular level. The mechanism proposed involves formation of the *OH, *OOH, H2O2 radicals and complexes formed from the interaction of these species with VOL2 complex. The Gibbs free energy of each step of the mechanism has been evaluated. The solvation energy has been estimated by means of united atoms Hartree-Fock/polarizable continuum method (UAHF/PCM). The Gibbs free energy of the global reaction of the V(IV)/V(V) oxidation has been estimated and compared with the available experimental equilibrium constant. The difference between the calculated and experimental estimates for the reaction energy of the global equation is about 1.5 kcal mol(-1). The thermodynamic profile of the reaction mechanism has been provided and discussed in terms of the possible intermediates. The influence of the ligand and the reaction rate in terms of the steady-state approximation has been briefly discussed.     

Comparative thermodynamic analysis of cyclic nucleotide binding to protein kinase A

We have investigated the thermodynamic parameters and binding of a regulatory subunit of cAMP-dependent protein kinase (PKA) to its natural low-molecular-weight ligand, cAMP, and analogues thereof. For analysis of this model system, we compared side-by-side isothermal titration calorimetry (ITC) with surface plasmon resonance (SPR). Both ITC and SPR analyses revealed that binding of the protein to cAMP or its analogues was enthalpically driven and characterised by similar free energy values (DeltaG=-9.4 to -10.7 kcal mol-1) for all interactions. Despite the similar affinities, binding of the cyclic nucleotides used here was characterised by significant differences in the contribution of entropy (-TDeltaS) and enthalpy (DeltaH) to DeltaG. The comparison of ITC and SPR data for one cAMP analogue further revealed deviations caused by the method. These equilibrium parameters could be complemented by thermodynamic data of the transition state (DeltaHnot equal, DeltaGnot equal, DeltaSnot equal) for both association and dissociation measured by SPR. This direct comparison of ITC and SPR highlights method-specific advantages and drawbacks for thermodynamic analyses of protein/ligand interactions.     

Relative binding free energy calculations of inhibitors to two mutants (Glu46----Ala/Gln) of ribonuclease T1 using molecular dynamics/free energy perturbation approaches.

We present free energy perturbation calculations on the complexes of Glu46----Ala46 (E46A) and Glu46----Gln46 (E46Q) mutants of ribonuclease T1 (RNaseT1) with inhibitors 2'-guanosine monophosphate (GMP) and 2'-adenosine monophosphate (AMP) by a thermodynamic perturbation method implemented with molecular dynamics (MD). Using the available crystal structure of the RNaseT1-GMP complex, the structures of E46A-GMP and E46Q-GMP were model built and equilibrated with MD simulations. The structures of E46A-AMP and E46Q-AMP were obtained as a final structure of the GMP----AMP perturbation calculation respectively. The calculated difference in the free energy of binding (delta delta Gbind) was 0.31 kcal/mol for the E46A system and -1.04 kcal/mol for the E46Q system. The resultant free energies are much smaller than the experimental and calculated value of approximately 3 kcal/mol for the native RNaseT1, which suggests that both mutants have greater relative adenine affinities than native RNaseT1. Especially E46Q is calculated to have a larger affinity for adenine than guanine, as we suggested previously from the calculation on the native RNaseT1. Thus, the molecular dynamics/free energy perturbation method may be helpful in protein engineering, directed toward increasing or changing the substrate specificity of enzymes.     

Molecular Determinants of Epidermal Growth Factor Binding: A Molecular Dynamics Study

The epidermal growth factor receptor (EGFR) is a member of the receptor tyrosine kinase family that plays a role in multiple cellular processes. Activation of EGFR requires binding of a ligand on the extracellular domain to promote conformational changes leading to dimerization and transphosphorylation of intracellular kinase domains. Seven ligands are known to bind EGFR with affinities ranging from sub-nanomolar to near micromolar dissociation constants. In the case of EGFR, distinct conformational states assumed upon binding a ligand is thought to be a determining factor in activation of a downstream signaling network. Previous biochemical studies suggest the existence of both low affinity and high affinity EGFR ligands. While these studies have identified functional effects of ligand binding, high-resolution structural data are lacking. To gain a better understanding of the molecular basis of EGFR binding affinities, we docked each EGFR ligand to the putative active state extracellular domain dimer and 25.0 ns molecular dynamics simulations were performed. MM-PBSA/GBSA are efficient computational approaches to approximate free energies of protein-protein interactions and decompose the free energy at the amino acid level. We applied these methods to the last 6.0 ns of each ligand-receptor simulation. MM-PBSA calculations were able to successfully rank all seven of the EGFR ligands based on the two affinity classes: EGF>HB-EGF>TGF-α>BTC>EPR>EPG>AR. Results from energy decomposition identified several interactions that are common among binding ligands. These findings reveal that while several residues are conserved among the EGFR ligand family, no single set of residues determines the affinity class. Instead we found heterogeneous sets of interactions that were driven primarily by electrostatic and Van der Waals forces. These results not only illustrate the complexity of EGFR dynamics but also pave the way for structure-based design of therapeutics targeting EGF ligands or the receptor itself.     

Interplay between binding affinity and kinetics in protein–protein interactions

To clarify the interplay between the binding affinity and kinetics of protein–protein interactions, and the possible role of intrinsically disordered proteins in such interactions, molecular simulations were carried out on 20 protein complexes. With bias potential and reweighting techniques, the free energy profiles were obtained under physiological affinities, which showed that the bound‐state valley is deep with a barrier height of 12 ? 33 RT. From the dependence of the affinity on interface interactions, the entropic contribution to the binding affinity is approximated to be proportional to the interface area. The extracted dissociation rates based on the Arrhenius law correlate reasonably well with the experimental values (Pearson correlation coefficient R = 0.79). For each protein complex, a linear free energy relationship between binding affinity and the dissociation rate was confirmed, but the distribution of the slopes for intrinsically disordered proteins showed no essential difference with that observed for ordered proteins. A comparison with protein folding was also performed. Proteins 2016; 84:920–933. © 2016 Wiley Periodicals, Inc.     

Accounting for Ligand Conformational Restriction in Calculations of Protein-Ligand Binding Affinities

The conformation adopted by a ligand on binding to a receptor may differ from its lowest-energy conformation in solution. In addition, the bound ligand is more conformationally restricted, which is associated with a configurational entropy loss. The free energy change due to these effects is often neglected or treated crudely in current models for predicting binding affinity. We present a method for estimating this contribution, based on perturbation theory using the quasi-harmonic model of Karplus and Kushick as a reference system. The consistency of the method is checked for small model systems. Subsequently we use the method, along with an estimate for the enthalpic contribution due to ligand-receptor interactions, to calculate relative binding affinities. The AMBER force field and generalized Born implicit solvent model is used. Binding affinities were estimated for a test set of 233 protein-ligand complexes for which crystal structures and measured binding affinities are available. In most cases, the ligand conformation in the bound state was significantly different from the most favorable conformation in solution. In general, the correlation between measured and calculated ligand binding affinities including the free energy change due to ligand conformational change is comparable to or slightly better than that obtained by using an empirically-trained docking score. Both entropic and enthalpic contributions to this free energy change are significant.     

Thermodynamic analysis of ligand-induced changes in protein thermal unfolding applied to high-throughput determination of ligand affinities with extrinsic fluorescent dyes

The quantification of protein-ligand interactions is essential for systems biology, drug discovery, and bioengineering. Ligand-induced changes in protein thermal stability provide a general, quantifiable signature of binding and may be monitored with dyes such as Sypro Orange (SO), which increase their fluorescence emission intensities upon interaction with the unfolded protein. This method is an experimentally straightforward, economical, and high-throughput approach for observing thermal melts using commonly available real-time polymerase chain reaction instrumentation. However, quantitative analysis requires careful consideration of the dye-mediated reporting mechanism and the underlying thermodynamic model. We determine affinity constants by analysis of ligand-mediated shifts in melting-temperature midpoint values. Ligand affinity is determined in a ligand titration series from shifts in free energies of stability at a common reference temperature. Thermodynamic parameters are obtained by fitting the inverse first derivative of the experimental signal reporting on thermal denaturation with equations that incorporate linear or nonlinear baseline models. We apply these methods to fit protein melts monitored with SO that exhibit prominent nonlinear post-transition baselines. SO can perturb the equilibria on which it is reporting. We analyze cases in which the ligand binds to both the native and denatured state or to the native state only and cases in which protein:ligand stoichiometry needs to treated explicitly.     

Predicting the elution behavior of proteins in affinity chromatography on non-porous particles.

Affinity chromatography on non-porous particles of microsize is particularly useful for the rapid analysis and micropreparative separation of proteins. The elution behavior of proteins in an affinity column packed with non-porous copolymerized particles of styrene, methyl methacrylate and glycidyl methacrylate was investigated both theoretically and experimentally, using the lysozyme-Cibacron Blue 3G-A affinity system. Equations used to predict the elution profiles, resulting from the elution by increasing the ionic strength (NaCl concentration) in the mobile phase, were obtained. The maximum adsorbate concentration, desorption rate constant and equilibrium constant under elution conditions were determined by matching experimental data with predicted elution profiles. Based on the parameters determined at a flow-rate of 0.5 ml/min and with 1 M NaCl in the elution buffer, the model equations could predict the elution profiles for other experimental runs, where different flow-rates and sodium chloride concentrations were used. Both the experimental and predicted results revealed that the affinity interaction kinetics are not significantly influenced by the flow-rate and, hence, the film mass transfer. To elute bound lysozyme from immobilized dye ligand, a higher value of the ionic strength leads to a faster elution and a sharper elution peak. The influence of elution conditions on the kinetic and thermodynamic parameters and, consequently, on the elution peak profiles was evaluated. The model equations can also predict the behavior of protein elution from an affinity column by changing the pH of the mobile phase, according to a previous study.     

An all atom energy based computational protocol for predicting binding affinities of protein-ligand complexes

We report here a computationally fast protocol for predicting binding affinities of non-metallo protein-ligand complexes. The protocol builds in an all atom energy based empirical scoring function comprising electrostatics, van der Waals, hydrophobicity and loss of conformational entropy of protein side chains upon ligand binding. The method is designed to ensure transferability across diverse systems and has been validated on a heterogenous dataset of 161 complexes consisting of 55 unique protein targets. The scoring function trained on a dataset of 61 complexes yielded a correlation of r=0.92 for the predicted binding free energies against the experimental binding affinities. Model validation and parameter analysis studies ensure the predictive ability of the scoring function. When tested on the remaining 100 protein-ligand complexes a correlation of r=0.92 was recovered. The high correlation obtained underscores the potential applicability of the methodology in drug design endeavors. The scoring function has been web enabled at as binding affinity prediction of protein-ligand (BAPPL) server.     

Binding free energy calculations between bovine β‐lactoglobulin and four fatty acids using the MMGBSA method

The bovine dairy protein β‐lactoglobulin (βlg) is a promiscuous protein that has the ability to bind several hydrophobic ligands. In this study, based on known experimental data, the dynamic interaction mechanism between bovine βlg and four fatty acids was investigated by a protocol combining molecular dynamics (MD) simulations and molecular mechanics generalized Born surface area (MMGBSA) binding free energy calculations. Energetic analyses revealed binding free energy trends that corroborated known experimental findings; larger ligand size corresponded to greater binding affinity. Finally, binding free energy decomposition provided detailed information about the key residues stabilizing the complex. © 2014 Wiley Periodicals, Inc. Biopolymers 101: 1010–1018, 2014.