Contributions to the binding free energy of ligands to avidin and streptavidin

The free energy of binding of a ligand to a macromolecule is here formally decomposed into the (effective) energy of interaction, reorganization energy of the ligand and the macromolecule, conformational entropy change of the ligand and the macromolecule, and translational and rotational entropy loss of the ligand. Molecular dynamics simulations with implicit solvation are used to evaluate these contributions in the binding of biotin, biotin analogs, and two peptides to avidin and streptavidin. We find that the largest contribution opposing binding is the protein reorganization energy, which is calculated to be from 10 to 30 kcal/mol for the ligands considered here. The ligand reorganization energy is also significant for flexible ligands. The translational/rotational entropy is 4.5-6 kcal/mol at 1 M standard state and room temperature. The calculated binding free energies are in the correct range, but the large statistical uncertainty in the protein reorganization energy precludes precise predictions. For some complexes, the simulations show multiple binding modes, different from the one observed in the crystal structure. This finding is probably due to deficiencies in the force field but may also reflect considerable ligand flexibility.     

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.     

Quantitative predictions of binding free energy changes in drug-resistant influenza neuraminidase

Quantitatively predicting changes in drug sensitivity associated with residue mutations is a major challenge in structural biology. By expanding the limits of free energy calculations, we successfully identified mutations in influenza neuraminidase (NA) that confer drug resistance to two antiviral drugs, zanamivir and oseltamivir. We augmented molecular dynamics (MD) with Hamiltonian Replica Exchange and calculated binding free energy changes for H274Y, N294S, and Y252H mutants. Based on experimental data, our calculations achieved high accuracy and precision compared with results from established computational methods. Analysis of 15 μs of aggregated MD trajectories provided insights into the molecular mechanisms underlying drug resistance that are at odds with current interpretations of the crystallographic data. Contrary to the notion that resistance is caused by mutant-induced changes in hydrophobicity of the binding pocket, our simulations showed that drug resistance mutations in NA led to subtle rearrangements in the protein structure and its dynamics that together alter the active-site electrostatic environment and modulate inhibitor binding. Importantly, different mutations confer resistance through different conformational changes, suggesting that a generalized mechanism for NA drug resistance is unlikely.     

Accounting for conformational entropy in predicting binding free energies of protein-protein interactions

Protein-protein interactions are governed by the change in free energy upon binding, ΔG = ΔH - TΔS. These interactions are often marginally stable, so one must examine the balance between the change in enthalpy, ΔH, and the change in entropy, ΔS, when investigating known complexes, characterizing the effects of mutations, or designing optimized variants. To perform a large-scale study into the contribution of conformational entropy to binding free energy, we developed a technique called GOBLIN (Graphical mOdel for BiomoLecular INteractions) that performs physics-based free energy calculations for protein-protein complexes under both side-chain and backbone flexibility. Goblin uses a probabilistic graphical model that exploits conditional independencies in the Boltzmann distribution and employs variational inference techniques that approximate the free energy of binding in only a few minutes. We examined the role of conformational entropy on a benchmark set of more than 700 mutants in eight large, well-studied complexes. Our findings suggest that conformational entropy is important in protein-protein interactions--the root mean square error (RMSE) between calculated and experimentally measured ΔΔGs decreases by 12% when explicit entropic contributions were incorporated. GOBLIN models all atoms of the protein complex and detects changes to the binding entropy along the interface as well as positions distal to the binding interface. Our results also suggest that a variational approach to entropy calculations may be quantitatively more accurate than the knowledge-based approaches used by the well-known programs FOLDX and Rosetta--GOBLIN's RMSEs are 10 and 36% lower than these programs, respectively.     

Protein free energy landscapes remodeled by ligand binding

Glucose/galactose binding protein (GGBP) functions in two different larger systems of proteins used by enteric bacteria for molecular recognition and signaling. Here we report on the thermodynamics of conformational equilibrium distributions of GGBP. Three fluorescence components appear at zero glucose concentration and systematically transition to three components at high glucose concentration. Fluorescence anisotropy correlations, fluorescent lifetimes, thermodynamics, computational structure minimization, and literature work were used to assign the three components as open, closed, and twisted conformations of the protein. The existence of three states at all glucose concentrations indicates that the protein continuously fluctuates about its conformational state space via thermally driven state transitions; glucose biases the populations by reorganizing the free energy profile. These results and their implications are discussed in terms of the two types of specific and nonspecific interactions GGBP has with cytoplasmic membrane proteins.     

Empirical calculation of the relative free energies of peptide binding to the molecular chaperone DnaK

We describe a methodology to calculate the relative free energies of protein-peptide complex formation. The interaction energy was decomposed into nonpolar, electrostatic and entropic contributions. A free energy-surface area relationship served to calculate the nonpolar free energy term. The electrostatic free energy was calculated with the finite difference Poisson-Boltzmann method and the entropic contribution was estimated from the loss in the conformational entropy of the peptide side chains. We applied this methodology to a series of DnaK*peptide complexes. On the basis of the single known crystal structure of the peptide-binding domain of DnaK with a bound heptapeptide, we modeled ten other DnaK*heptapeptide complexes with experimentally measured K(d) values from 0.06 microM to 11 microM, using molecular dynamics to refine the structures of the complexes. Molecular dynamic trajectories, after equilibration, were used for calculating the energies with greater accuracy. The calculated relative binding free energies were compared with the experimentally determined free energies. Linear scaling of the calculated terms was applied to fit them to the experimental values. The calculated binding free energies were between -7.1 kcal/mol and - 9.4 kcal/mol with a correlation coefficient of 0.86. The calculated nonpolar contributions are mainly due to the central hydrophobic binding pocket of DnaK for three amino acid residues. Negative electrostatic fields generated by the protein increase the binding affinity for basic residues flanking the hydrophobic core of the peptide ligand. Analysis of the individual energy contributions indicated that the nonpolar contributions are predominant compared to the other energy terms even for peptides with low affinity and that inclusion of the change in conformational entropy of the peptide side chains does not improve the discriminative power of the calculation. The method seems to be useful for predicting relative binding energies of peptide ligands of DnaK and might be applicable to other protein-peptide systems, particularly if only the structure of one protein-ligand complex is available.     

Impact of calcium on N1 influenza neuraminidase dynamics and binding free energy

The highly pathogenic influenza strains H5N1 and H1N1 are currently treated with inhibitors of the viral surface protein neuraminidase (N1). Crystal structures of N1 indicate a conserved, high affinity calcium binding site located near the active site. The specific role of this calcium in the enzyme mechanism is unknown, though it has been shown to be important for enzymatic activity and thermostability. We report molecular dynamics (MD) simulations of calcium‐bound and calcium‐free N1 complexes with the inhibitor oseltamivir (marketed as the drug Tamiflu), independently using both the AMBER FF99SB and GROMOS96 force fields, to give structural insight into calcium stabilization of key framework residues. Y347, which demonstrates similar sampling patterns in the simulations of both force fields, is implicated as an important N1 residue that can “clamp” the ligand into a favorable binding pose. Free energy perturbation and thermodynamic integration calculations, using two different force fields, support the importance of Y347 and indicate a +3 to +5 kcal/mol change in the binding free energy of oseltamivir in the absence of calcium. With the important role of structure‐based drug design for neuraminidase inhibitors and the growing literature on emerging strains and subtypes, inclusion of this calcium for active site stability is particularly crucial for computational efforts such as homology modeling, virtual screening, and free energy methods. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Free energy calculations for the relative binding affinity between DNA and lambda-repressor

The change in the binding free energy between DNA and lambda-repressor resulting from a base substitution, thymine (T)-->deoxyuracil (abbreviated as U), was evaluated by the free energy perturbation method on the basis of molecular dynamics simulations for the DNA-lambda-repressor complex in water with all degrees of freedom and including long-range Coulomb interactions. The binding free energy change that we calculated (1.47 +/- 0.40 kcal/mol) was in good agreement with an experimental value (1.8 kcal/mol). We clarified why the small difference between T and U (CH(3) in T is replaced with H in U) caused such a significant change in the binding free energy: The substitution of CH(3) in T with H in U lowered the dissociated-state free energy level due to the gain of the hydration free energy. Furthermore, the T-->U substitution raised the free energy level in the associated state due to the loss of the favored van der Waals (vdW) interactions with the lambda-repressor amino acid residues. In other words, the amino acid residues of lambda-repressor can recognize the CH(3) in T through the vdW interactions with the CH(3). This recognition is enhanced in a water environment, because the hydrophobic CH(3) prefers the amino acid residues of lambda-repressor to water molecules.     

Compromise in competition between free energy and binding effect of intrinsically disordered protein p53 C-terminal domain

The C-terminal domain (CTD) of tumour suppressor p53 is an intrinsically disordered protein which has been shown to be able to bind multiple partner proteins and exercise diverse physiological functions in the cell. In this study, we performed molecular dynamics simulations on the isolated p53 CTD, as well as three regulatory binding complexes to investigate the conformational ensemble of isolated p53 CTD and its dynamic structures when different binding partner present. The results demonstrate that the isolated p53 CTD resembles a molten globule rather than extended structure. It mainly adopts random coil conformations with some tendency to form helical structures, which is consistent with experimental observations. For isolated p53 CTD, the dynamics is exclusively dominated by the intrinsic free energy and the p53 CTD could not folded spontaneously to each binding competent state which is located in high free energy region. However, when the binding partners present, the dynamics of p53 CTD are dominated by two mechanisms, the p53 CTD tending to adopt the structure with minimum free energy as isolate existed and the binding energy from partner protein tending to minimum. Each of them has an extreme tendency and corresponds to a possible characteristic state, the random coil state and each binding competent state. The compromise in competition between these two mechanisms results in alternate realisation of different characteristic states, while the relative strength of each mechanism determines the sampling frequency of each characteristic state.     

Prediction of protein-protein binding free energies

We present an energy function for predicting binding free energies of protein-protein complexes, using the three-dimensional structures of the complex and unbound proteins as input. Our function is a linear combination of nine terms and achieves a correlation coefficient of 0.63 with experimental measurements when tested on a benchmark of 144 complexes using leave-one-out cross validation. Although we systematically tested both atomic and residue-based scoring functions, the selected function is dominated by residue-based terms. Our function is stable for subsets of the benchmark stratified by experimental pH and extent of conformational change upon complex formation, with correlation coefficients ranging from 0.61 to 0.66.     

Role of tyrosine hot‐spot residues at the interface of colicin E9 and immunity protein 9: A comparative free energy simulation study

The endonuclease activity of the bacterial colicin 9 enzyme is controlled by the specific and high‐affinity binding of immunity protein 9 (Im9). Molecular dynamics simulation studies in explicit solvent were used to investigate the free energy change associated with the mutation of two hot‐spot interface residues [tyrosine (Tyr): Tyr54 and Tyr55] of Im9 to Ala. In addition, the effect of several other mutations (Leu33Ala, Leu52Ala, Val34Ala, Val37Ala, Ser48Ala, and Ile53Ala) with smaller influence on binding affinity was also studied. Good qualitative agreement of calculated free energy changes and experimental data on binding affinity of the mutations was observed. The simulation studies can help to elucidate the molecular details on how the mutations influence protein–protein binding affinity. The role of solvent and conformational flexibility of the partner proteins was studied by comparing the results in the presence or absence of solvent and with or without positional restraints. Restriction of the conformational mobility of protein partners resulted in significant changes of the calculated free energies but of similar magnitude for isolated Im9 and for the complex and therefore in only modest changes of binding free energy differences. Although the overall binding free energy change was similar for the two Tyr–Ala mutations, the physical origin appeared to be different with solvation changes contributing significantly to the Tyr55Ala mutation and to a loss of direct protein–protein interactions dominating the free energy change due to the Tyr54Ala mutation. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Conformational flexibility,binding energy,role of salt bridge and alanine-mutagenesis for c-Abl kinase complex

Abl kinase plays a decisive role in the mechanism of the most fatal human pathogen chronic mylogenous leukemia (CML). Here, we have carried out a comprehensive study about the conformational flexibility, role of salt bridge and the protein- ligand interaction for this kinase with its well-known inhibitor, Imatinib. We have performed molecular dynamics simulations for conformational behavior, investigated the salt bridges and calculated the binding free energy of Imatinib with MM-PB/SA method for Abl kinase complex. We also explored the role of salt-bridge in the kinase complex and its effect on binding activity of inhibitors. Furthermore, to investigate the importance of those residues which form salt bridges, we mutated them by Alanine with the help of Alanine scanning program. We noticed significant variations in total free energy of Imatinib in all possible mutations. The binding free energy of ligand for kinase receptor was analyzed by molecular mechanics Poission Boltzmann surface area (MM-PB/SA) method. These results suggest that conserved glutamic acid and lysine are necessary for stability of complex.     

Relative free energy of binding between antimicrobial peptides and SDS or DPC micelles

We present relative binding free energy calculations for six antimicrobial peptide-micelle systems, three peptides interacting with two types of micelles. The peptides are the scorpion derived antimicrobial peptide (AMP), IsCT and two of its analogues. The micelles are dodecylphosphatidylcholine (DPC) and sodium dodecylsulphate (SDS) micelles. The interfacial electrostatic properties of DPC and SDS micelles are assumed to be similar to those of zwitterionic mammalian and anionic bacterial membrane interfaces, respectively. We test the hypothesis that the binding strength between peptides and the anionic micelle SDS can provide information on peptide antimicrobial activity, since it is widely accepted that AMPs function by binding to and disrupting the predominantly anionic lipid bilayer of the bacterial cytoplasmic membrane. We also test the hypothesis that the binding strength between peptides and the zwitterionic micelle DPC can provide information on peptide haemolytic activities, since it is accepted that they also bind to and disrupt the zwitterionic membrane of mammalian cells. Equilibrium structures of the peptides, micelles and peptide-micelle complexes are obtained from more than 300 ns of molecular dynamics simulations. A thermodynamic cycle is introduced to compute the binding free energy from electrostatic, non-electrostatic and entropic contributions. We find relative binding free energy strengths between peptides and SDS to correlate with the experimentally measured rankings for peptide antimicrobial activities, and relative free energy binding strengths between peptides and DPC to correlate with the observed rankings for peptide haemolytic toxicities. These findings point to the importance of peptide-membrane binding strength for antimicrobial activity and haemolytic activity.     

Non-Boltzmann thermodynamic integration (NBTI) for macromolecular systems: relative free energy of binding of trypsin to benzamidine and benzylamine

The relative free energies of binding of trypsin to two amine inhibitors, benzamidine (BZD) and benzylamine (BZA), were calculated using non-Boltzmann thermodynamic integration (NBTI). Comparison of the simulations with the crystal structures of both complexes, trypsin-BZD and trypsin-BZA, shows that NBTI simulations better sample conformational space relative to thermodynamic integration (TI) simulations. The relative binding free energy calculated using NBTI was much closer to the experimentally determined value than that obtained using TI. The error in the TI simulation was found to be primarily due to incorrect sampling of BZA's conformation in the binding pocket. In contrast, NBTI produces a smooth mutation from BZD to BZA using a surrogate potential, resulting in a much closer agreement between the inhibitors' conformations and the omit electron density maps. This superior agreement between experiment and simulation, of both relative binding free energy differences and conformational sampling, demonstrates NBTI's usefulness for free energy calculations in macromolecular simulations.     

Investigating the disorder–order transition of calmodulin binding domain upon binding calmodulin using molecular dynamics simulation

We have studied the conformational transition of the calmodulin binding domains (CBD) in several calmodulin‐binding kinases, in which CBD changes from the disordered state to the ordered state when binding with calmodulin (CaM). Targeted molecular dynamics simulation was used to investigate the binding process of CaM and CBD of CaM‐dependent kinase I (CaMKI–CBD). The results show that CaMKI–CBD began to form an α‐helix and the interaction free energy between CaM and CaMKI–CBD increased once CaM fully encompassed CaMKI–CBD. Two series of CaM/CBD complex systems, including the complexes of CaM with the initially disordered and the final ordered CBD, were constructed to study the interaction using molecular dynamics simulations. Our analyses suggest that the VDW interaction plays a dominant role in CaM/CBD binding and is a key factor in the disorder–order transition of CBD. Additionally, the entropy effect is not in favor of the formation of the CaM/CBD complex, which is consistent with the experimental evidence. Based on the results, it appears that the CBD conformational change from a non‐compact extended structure to compact α‐helix is critical in gaining a favorable VDW interaction and interaction free energy. Copyright © 2009 John Wiley & Sons, Ltd.     

Activation of the edema factor of Bacillus anthracis by calmodulin: evidence of an interplay between the EF-calmodulin interaction and calcium binding

Calmodulin (CaM) is a remarkably flexible protein which can bind multiple targets in response to changes in intracellular calcium concentration. It contains four calcium-binding sites, arranged in two globular domains. The calcium affinity of CaM N-terminal domain (N-CaM) is dramatically reduced when the complex with the edema factor (EF) of Bacillus anthracis is formed. Here, an atomic explanation for this reduced affinity is proposed through molecular dynamics simulations and free energy perturbation calculations of the EF-CaM complex starting from different crystallographic models. The simulations show that electrostatic interactions between CaM and EF disfavor the opening of N-CaM domains usually induced by calcium binding. Relative calcium affinities of the N-CaM binding sites are probed by free energy perturbation, and dissociation probabilities are evaluated with locally enhanced sampling simulations. We show that EF impairs calcium binding on N-CaM through a direct conformational restraint on Site 1, by an indirect destabilization of Site 2, and by reducing the cooperativity between the two sites.     

Minimum free energy path of ligand-induced transition in adenylate kinase

Large-scale conformational changes in proteins involve barrier-crossing transitions on the complex free energy surfaces of high-dimensional space. Such rare events cannot be efficiently captured by conventional molecular dynamics simulations. Here we show that, by combining the on-the-fly string method and the multi-state Bennett acceptance ratio (MBAR) method, the free energy profile of a conformational transition pathway in Escherichia coli adenylate kinase can be characterized in a high-dimensional space. The minimum free energy paths of the conformational transitions in adenylate kinase were explored by the on-the-fly string method in 20-dimensional space spanned by the 20 largest-amplitude principal modes, and the free energy and various kinds of average physical quantities along the pathways were successfully evaluated by the MBAR method. The influence of ligand binding on the pathways was characterized in terms of rigid-body motions of the lid-shaped ATP-binding domain (LID) and the AMP-binding (AMPbd) domains. It was found that the LID domain was able to partially close without the ligand, while the closure of the AMPbd domain required the ligand binding. The transition state ensemble of the ligand bound form was identified as those structures characterized by highly specific binding of the ligand to the AMPbd domain, and was validated by unrestrained MD simulations. It was also found that complete closure of the LID domain required the dehydration of solvents around the P-loop. These findings suggest that the interplay of the two different types of domain motion is an essential feature in the conformational transition of the enzyme.     

Conformational selection in protein binding and function

Protein binding and function often involves conformational changes. Advanced nuclear magnetic resonance (NMR) experiments indicate that these conformational changes can occur in the absence of ligand molecules (or with bound ligands), and that the ligands may “select” protein conformations for binding (or unbinding). In this review, we argue that this conformational selection requires transition times for ligand binding and unbinding that are small compared to the dwell times of proteins in different conformations, which is plausible for small ligand molecules. Such a separation of timescales leads to a decoupling and temporal ordering of binding/unbinding events and conformational changes. We propose that conformational‐selection and induced‐change processes (such as induced fit) are two sides of the same coin, because the temporal ordering is reversed in binding and unbinding direction. Conformational‐selection processes can be characterized by a conformational excitation that occurs prior to a binding or unbinding event, while induced‐change processes exhibit a characteristic conformational relaxation that occurs after a binding or unbinding event. We discuss how the ordering of events can be determined from relaxation rates and effective on‐ and off‐rates determined in mixing experiments, and from the conformational exchange rates measured in advanced NMR or single‐molecule fluorescence resonance energy transfer experiments. For larger ligand molecules such as peptides, conformational changes and binding events can be intricately coupled and exhibit aspects of conformational‐selection and induced‐change processes in both binding and unbinding direction.     

The binding mechanism of a novel nicotinamide isostere inhibiting with TNKSs: a molecular dynamic simulation and binding free energy calculation

Tankyrases (TNKSs), a member of human poly (ADP-ribose) polymerase (PARP) protein superfamily, plays a key role in regulation of cell proliferation. Among the representative proteins of the PARPs family, it is found that the inhibitors have high selectivity for Tankyrase1 (TNKS1). The specific binding modes are investigated between the TNKS1 protein and nicotinamide isostere (ISX) which functions as an inhibitor of TNKS1. The stabilities of ISX-TNKS1 and AVA939-TNKS1 complexes are estimated by molecular dynamics (MD) simulations and free energy calculations; a good agreement with experimental results is reached. On the basis of the calculated results of MD simulations, we found that the inhibitors influence the conformational flexibility of TNKS1 and the XAV939 binding drive the peptide Ile1228-Gly1229-Gly1230 to form a helical structure while the ISX binding drive the peptide to form a turn structure. Moreover, the formed important hydrogen bonds of Tyr1203 residue with XVA939 and WAT1551 with ISX enhance stabilities of the complexes, and the electrostatic interactions in XAV939-TNKS1 and van der Waals interactions in ISX-TNKS1 system are main driving forces for affinity. According to the results of the decomposition of binding free energy, it is obvious that the residues Try1224 and Lys1220 make the most favorable contributions to the binding in, respectively, ISX and XAV939 complexes. Taken together, the obtained results are useful for studying the binding mechanisms of TNKSs and inhibitors and for designing potent inhibitors.     

Molecular dynamics and free energy analysis of neuraminidase-ligand interactions

We report molecular dynamics calculations of neuraminidase in complex with an inhibitor, 4-amino-2-deoxy-2,3-didehydro-N-acetylneuraminic acid (N-DANA), with subsequent free energy analysis of binding by using a combined molecular mechanics/continuum solvent model approach. A dynamical model of the complex containing an ionized Glu119 amino acid residue is found to be consistent with experimental data. Computational analysis indicates a major van der Waals component to the inhibitor-neuraminidase binding free energy. Based on the N-DANA/neuraminidase molecular dynamics trajectory, a perturbation methodology was used to predict the binding affinity of related neuraminidase inhibitors by using a force field/Poisson-Boltzmann potential. This approach, incorporating conformational search/local minimization schemes with distance-dependent dielectric or generalized Born solvent models, correctly identifies the most potent neuraminidase inhibitor. Mutation of the key ligand four-substituent to a hydrogen atom indicates no favorable binding free energy contribution of a hydroxyl group; conversely, cationic substituents form favorable electrostatic interactions with neuraminidase. Prospects for further development of the method as an analysis and rational design tool are discussed.