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.     

Validation of an automated procedure for the prediction of relative free energies of binding on a set of aldose reductase inhibitors

Among the available methods for predicting free energies of binding of ligands to a protein, the molecular mechanics Poisson–Boltzmann surface area (MM-PBSA) and molecular mechanics generalized Born surface area (MM-GBSA) approaches have been validated for a relatively limited number of targets and compounds in the training set. Here, we report the results of an extensive study on a series of 28 inhibitors of aldose reductase with experimentally determined crystal structures and inhibitory activities, in which we evaluate the ability of MM-PBSA and MM-GBSA methods in predicting binding free energies using a number of different simulation conditions. While none of the methods proved able to predict absolute free energies of binding in quantitative agreement with the experimental values, calculated and experimental free energies of binding were significantly correlated. Comparing the predicted and experimental ΔG of binding, MM-PBSA proved to perform better than MM-GBSA, and within the MM-PBSA methods, the PBSA of Amber performed similarly to Delphi. In particular, significant relationships between experimental and computed free energies of binding were obtained using Amber PBSA and structures minimized with a distance-dependent dielectric function. Importantly, while free energy predictions are usually made on large collections of equilibrated structures sampled during molecular dynamics in water, we have found that a single minimized structure is a reasonable approximation if relative free energies of binding are to be calculated. This finding is particularly relevant, considering that the generation of equilibrated MD ensembles and the subsequent free energy analysis on multiple snapshots is computationally intensive, while the generation and analysis of a single minimized structure of a protein–ligand complex is relatively fast, and therefore suited for high-throughput virtual screening studies. At this aim, we have developed an automated workflow that integrates all the necessary steps required to generate structures and calculate free energies of binding. The procedure is relatively fast and able to screen automatically and iteratively molecules contained in databases and libraries of compounds. Taken altogether, our results suggest that the workflow can be a valuable tool for ligand identification and optimization, being able to automatically and efficiently refine docking poses, which sometimes may not be accurate, and rank the compounds based on more accurate scoring functions.     

Development and validation of an empirical free energy function for calculating protein–protein binding free energy surfaces

In a previous paper, we described a novel empirical free energy function that was used to accurately predict experimental binding free energies for a diverse test set of 31 protein–protein complexes to within ≈ 1.0 kcal. Here, we extend that work and show that an updated version of the function can be used to (1) accurately predict native binding free energies and (2) rank crystallographic, native-like and non-native binding modes in a physically realistic manner. The modified function includes terms designed to capture some of the unfavorable interactions that characterize non-native interfaces. The function was used to calculate one-dimensional binding free energy surfaces for 21 protein complexes. In roughly 90% of the cases tested, the function was used to place native-like and crystallographic binding modes in global free energy minima. Our analysis further suggests that buried hydrogen bonds might provide the key to distinguishing native from non-native interactions. To the best of our knowledge our function is the only one of its kind, a single expression that can be used to accurately calculate native and non-native binding free energies for a large number of proteins. Given the encouraging results presented in this paper, future work will focus on improving the function and applying it to the protein–protein docking problem.     

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.     

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.     

A simple model for predicting the free energy of binding between anthracycline antibiotics and DNA

A theoretical model for predicting the free energy of binding between anthracycline antibiotics and DNA was developed using the electron density functional (DFT) and molecular mechanics (MM) methods. Partial DFT-ESP charges were used in calculating the MM binding energies for complexes formed between anthracycline antibiotics and oligodeoxynucleotides. These energies were then compared with experimental binding free energies. The good correlation between the experimental and theoretical energies allowed us to propose a model for predicting the binding free energy for derivatives of anthracycline antibiotics and for quickly screening new anthracycline derivatives.     

Molecular Modeling for a Comparative Analysis of Interactions Between 2LTRZFP and 2-LTR-Circle Junctions

In eukaryotes, one of the most often noticed DNA-binding motifs are Cys2His2 zinc finger proteins which have been extensively utilized as a framework for designing novel DNA-binding proteins. In this study, the conformational change, and binding stability, affinity and interactions of the 2LTRZFP–HIV-1 2-LTR-circle junction complexes were successfully reproduced with MD simulations, MM-PBSA/GBSA and binding mode analyses. The binding free energies were obtained, and it was found that the calculated binding free energy of Zif1 is lower than Zif2 and together with pharmacophore modeling, these binding results indicate strong affinity of 2LTRZFP for the DNA. Mutants of 2LTRZFP were analyzed. The computed energies provided proof for a relationship between the binding free energy and total electrostatic interaction energy. The mutation in a key amino acid (Glu81Tyr) of the finger 3 in position 6 showed increased binding energy to the DNA. The result agrees with our previous study which showed that the HIV-1 IN may be hindered by the 2LTRZFP. The obtained results may assist in the design of ZFPs depended on the 2-LTR-circle junctions inhibition mechanism.

     

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.     

Quantum and molecular dynamics study for binding of macrocyclic inhibitors to human alpha-thrombin

Molecular dynamics simulations followed by quantum mechanical calculation and Molecular Mechanics Poisson-Boltzmann Surface Area (MM-PBSA) analysis have been carried out to study binding of proline- and pyrazinone-based macrocyclic inhibitors (L86 and T76) to human alpha-thrombin. Detailed binding interaction energies between these inhibitors and individual protein fragments are calculated using DFT method based on a new quantum mechanical approach for computing protein-ligand interaction energy. The analysis of detailed interaction energies provides insight on the protein-ligand binding mechanism. Study shows that T76 and L86 bind to thrombin in a very similar "inhibition mode" except that T76 has relatively weaker binding interaction with Glu(217). The analysis from quantum calculation of binding interaction is consistent with the MM-PBSA calculation of binding free energy, and the calculated free energies for L86/T76-thrombin binding agree well with the experimental data.     

Zinc finger protein binding to DNA: an energy perspective using molecular dynamics simulation and free energy calculations on mutants of both zinc finger domains and their specific DNA bases

Energy calculations based on MM-GBSA were employed to study various zinc finger protein (ZF) motifs binding to DNA. Mutants of both the DNA bound to their specific amino acids were studied. Calculated energies gave evidence for a relationship between binding energy and affinity of ZF motifs to their sites on DNA. ΔG values were ?15.82(12), ?3.66(12), and ?12.14(11.6) kcal/mol for finger one, finger two, and finger three, respectively. The mutations in the DNA bases reduced the value of the negative energies of binding (maximum value for ΔΔG = 42Kcal/mol for F1 when GCG mutated to GGG, and ΔΔG = 22 kcal/mol for F2, the loss in total energy of binding originated in the loss in electrostatic energies upon mutation (r = .98). The mutations in key amino acids in the ZF motif in positions-1, 2, 3, and 6 showed reduced binding energies to DNA with correlation coefficients between total free energy and electrostatic was .99 and with Van der Waal was .93. Results agree with experimentally found selectivity which showed that Arginine in position-1 is specific to G, while Aspartic acid (D) in position 2 plays a complicated role in binding. There is a correlation between the MD calculated free energies of binding and those obtained experimentally for prepared ZF motifs bound to triplet bases in other reports (), our results may help in the design of ZF motifs based on the established recognition codes based on energies and contributing energies to the total energy.     

Molecular docking study and development of an empirical binding free energy model for phosphodiesterase 4 inhibitors

In the present work, several computational methodologies were combined to develop a model for the prediction of PDE4B inhibitors' activity. The adequacy of applying the ligand docking approach, keeping the enzyme rigid, to the study of a series of PDE4 inhibitors was confirmed by a previous molecular dynamics analysis of the complete enzyme. An exhaustive docking procedure was performed to identify the most probable binding modes of the ligands to the enzyme, including the active site metal ions and the surrounding structural water molecules. The enzyme-inhibitor interaction enthalpies, refined by using the semiempirical molecular orbital approach, were combined with calculated solvation free energies and entropy considerations in an empirical free energy model that enabled the calculation of binding free energies that correlated very well with experimentally derived binding free energies. Our results indicate that both the inclusion of the structural water molecules close to the ions in the binding site and the use of a free energy model with a quadratic dependency on the ligand free energy of solvation are important aspects to be considered for molecular docking investigations involving the PDE4 enzyme family.     

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.     

FastContact: rapid estimate of contact and binding free energies

Interaction free energies are crucial for analyzing binding propensities in proteins. Although the problem of computing binding free energies remains open, approximate estimates have become very useful for filtering potential binding complexes. We report on the implementation of a fast computational estimate of the binding free energy based on a statistically determined desolvation contact potential and Coulomb electrostatics with a distance-dependent dielectric constant, and validated in the Critical Assessment of PRotein Interactions experiment. The application also reports residue contact free energies that rapidly highlight the hotspots of the interaction. AVAILABILITY: The program was written in Fortran. The executable and full documentation is freely available at http://structure.pitt.edu/software/FastContact     

Predicting the binding affinities of misacylated tRNAs for Thermus thermophilus EF-Tu.GTP

The free energies for the binding of 20 different unmodified Escherichia coli elongator aminoacyl-tRNAs to Thermus thermophilus elongation factor Tu (EF-Tu) were determined. When combined with the binding free energies for the same tRNA bodies misacylated with either valine or phenylalanine determined previously [Asahara, H., and Uhlenbeck, O. C. (2002) Proc. Natl. Acad. Sci. U.S.A. 99, 3499-3504], these data permit the calculation of the contribution of each esterified amino acid to the total free energy of binding of the complex. The two data sets can also be used to calculate the free energy of binding of EF-Tu to any misacylated E. coli tRNA, and the values agree well with previously published experimental values. In addition, a survey of active misacylated suppressor tRNAs suggests that a minimal threshold of binding free energy for EF-Tu is required for suppression to occur.     

Predicting Ligand Binding Affinity with Alchemical Free Energy Methods in a Polar Model Binding Site

We present a combined experimental and modeling study of organic ligand molecules binding to a slightly polar engineered cavity site in T4 lysozyme (L99A/M102Q). For modeling, we computed alchemical absolute binding free energies. These were blind tests performed prospectively on 13 diverse, previously untested candidate ligand molecules. We predicted that eight compounds would bind to the cavity and five would not; 11 of 13 predictions were correct at this level. The RMS error to the measurable absolute binding energies was 1.8 kcal/mol. In addition, we computed “relative” binding free energies for six phenol derivatives starting from two known ligands: phenol and catechol. The average RMS error in the relative free energy prediction was 2.5 kcal/mol (phenol) and 1.1 kcal/mol (catechol). To understand these results at atomic resolution, we obtained x-ray co-complex structures for nine of the diverse ligands and for all six phenol analogs. The average RMSD of the predicted pose to the experiment was 2.0 Å (diverse set), 1.8 Å (phenol-derived predictions), and 1.2 Å (catechol-derived predictions). We found that predicting accurate affinities and rank-orderings required near-native starting orientations of the ligand in the binding site. Unanticipated binding modes, multiple ligand binding, and protein conformational change all proved challenging for the free energy methods. We believe that these results can help guide future improvements in physics-based absolute binding free energy methods.     

A Statistical Thermodynamic Model for Investigating the Stability of DNA Sequences from Oligonucleotides to Genomes

We describe the development and testing of a simple statistical mechanics methodology for duplex DNA applicable to sequences of any composition and extensible to genomes. The microstates of a DNA sequence are modeled in terms of blocks of basepairs that are assumed to be fully closed (paired) or open. This approach generates an ensemble of bubblelike microstates that are used to calculate the corresponding partition function. The energies of the microstates are calculated as additive contributions from hydrogen bonding, basepair stacking, and solvation terms parameterized from a comprehensive series of molecular dynamics simulations including solvent and ions. Thermodynamic properties and nucleotide stability constants for DNA sequences follow directly from the partition function. The methodology was tested by comparing computed free energies per basepair with the experimental melting temperatures of 60 oligonucleotides, yielding a correlation coefficient of −0.96. The thermodynamic stability of genic/nongenic regions was tested in terms of nucleotide stability constants versus sequence for the Escherichia coli K-12 genome. It showed clear differentiation of the genes from promoters and captures genic regions with a sensitivity of 0.94. The statistical thermodynamic model presented here provides a seemingly new handle on the challenging problem of interpreting genomic sequences.     

A Statistical Thermodynamic Model for Investigating the Stability of DNA Sequences from Oligonucleotides to Genomes

We describe the development and testing of a simple statistical mechanics methodology for duplex DNA applicable to sequences of any composition and extensible to genomes. The microstates of a DNA sequence are modeled in terms of blocks of basepairs that are assumed to be fully closed (paired) or open. This approach generates an ensemble of bubblelike microstates that are used to calculate the corresponding partition function. The energies of the microstates are calculated as additive contributions from hydrogen bonding, basepair stacking, and solvation terms parameterized from a comprehensive series of molecular dynamics simulations including solvent and ions. Thermodynamic properties and nucleotide stability constants for DNA sequences follow directly from the partition function. The methodology was tested by comparing computed free energies per basepair with the experimental melting temperatures of 60 oligonucleotides, yielding a correlation coefficient of −0.96. The thermodynamic stability of genic/nongenic regions was tested in terms of nucleotide stability constants versus sequence for the Escherichia coli K-12 genome. It showed clear differentiation of the genes from promoters and captures genic regions with a sensitivity of 0.94. The statistical thermodynamic model presented here provides a seemingly new handle on the challenging problem of interpreting genomic sequences.     

Effects of base substitutions in an RNA hairpin from molecular dynamics and free energy simulations

Contributions of individual interactions in the GGCGCAAGCC hairpin containing a GCAA tetraloop were studied by computer simulations using base substitutions. The G in the first tetraloop position was replaced by inosine (I) or adenosine (A), and the G in the C-G basepair closing the tetraloop was replaced by I. These substitutions eliminate particular hydrogen bonds proposed in the nuclear magnetic resonance model of the GCAA tetraloop. Molecular dynamics simulations of the GCAA tetraloop in aqueous solvent displayed a well-defined hydrogen pattern between the first and last loop nucleotides (G and A) stabilized by a bridging water molecule. Substitution of G-->I in the basepair closing the tetraloop did not significantly influence the loop structure and dynamics. The ICAA loop maintained the overall structure, but displayed variation in the hydrogen-bond network within the tetraloop itself. Molecular dynamics simulations of the ACAA loop led to conformational heterogeneity of the resulting structures. Changes of hairpin formation free energy associated with substitutions of individual bases were calculated by the free energy perturbation method. The calculated decrease of the hairpin stability upon G-->I substitution in the C-G basepair closing the tetraloop was in good agreement with experimental thermodynamic data. Our theoretical estimates for G-->I and G-->A mutations located in the tetraloop suggest larger loop destabilization than corresponding experimental results. The extent of conformational sampling of the structures resulting from base substitutions and its impact on the calculated free energy was discussed.