An accurate free energy estimator: based on MM/PBSA combined with interaction entropy for protein-ligand binding affinity.

The molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) method is constantly used to calculate the binding free energy of protein-ligand complexes, and has been shown to effectively balance computational cost against accuracy. The relative binding affinities obtained by the MM/PBSA approach are acceptable, while it usually overestimates the absolute binding free energy. This paper proposes four free energy estimators based on the MM/PBSA for enthalpy change combined with interaction entropy (IE) for entropy change using different weights for individual energy terms. The ΔGPBSA_IE method is determined to be an optimal estimator based on its performance in terms of the correlation between experimental and theoretical values and error estimations. This approach is optimized using high-quality experimental values from a training set containing 84 protein-ligand systems, and the coefficients for the sum of electrostatic energy and polar solvation free energy, van der Waals (vdW) energy, non-polar solvation energy and entropy change are obtained by multivariate linear fitting to the corresponding experimental values. A comparison between the traditional MM/PBSA method and this method shows that the correlation coefficient is improved from 0.46 to 0.72 and the slope of the regression line increases from 0.10 to 1.00. More importantly, the mean absolute error (MAE) is significantly reduced from 22.52 to 1.59 kcal mol-1. Furthermore, the numerical stability of this method is validated on a test set with a similar correlation coefficient, slope and MAE to those of the training set. Based on the above advantages, the ΔGPBSA_IE method can be a powerful tool for a reliable and accurate estimation of binding free energy and plays a significant role in a detailed energetic investigation of protein-ligand interaction.

Entropic effect and residue specific entropic contribution to the cooperativity in streptavidin-biotin binding.

Molecular dynamics (MD) simulations were performed employing the polarized protein-specific charge (PPC) to explore the origin of the cooperativity in streptavidin-biotin systems (wild type, two single mutations and one double-mutation). The results of the experiment found that the existence of cooperativity is mainly the result of the entropic effect. In this study, the entropic contribution to the binding free energy was calculated using the recently developed interaction entropy (IE) method, and computational results are in excellent agreement with the experimental observations and are further verified by the calculation of the thermodynamic integration. Comparison of different force fields in terms of predicted binding strength ordering, cooperativity of energy and the stability of hydrogen bonding suggests that the PPC force field combined IE method is a suitable choice. In addition, the IE method enables us to obtain the residue-specific entropic contributions to the streptavidin-biotin binding affinity and identify ten hot-spot residues providing the dominant contribution to the cooperative binding. Importantly, the overall cooperativity obtained from the ten residues also comes mainly from the entropic effect in our study. The calculation of the potential of mean force shows that the unbinding of streptavidin-biotin is a multi-step process, and each step corresponds to the formation and rupture of the hydrogen bond network. And S45A mutation may increase the rigidity of the linker region, making the flap region relatively difficult to open. The present study provides significant molecular insight into the binding cooperativity of the streptavidin-biotin complex.

Improving the performance of the MM/PBSA and MM/GBSA methods in recognizing the native structure of the Bcl-2 family using the interaction entropy method.

In the research and development of new drugs, theoretical and computational studies play an increasingly important role in discriminating native and decoy structures by their binding free energies. Predicting the binding free energy using the molecular mechanics/Poisson-Boltzmann (Generalized Born) surface area (MM/PB(GB)SA) methods to identify the native structure as the lowest-energy conformation is more theoretically rigorous than most scoring functions, but the main challenge of this method is the calculation of the entropic contribution. In this study, we add the entropic contribution to the MM/PBSA and two MM/GBSA (GBHCT and GBOBC1) models using the interaction entropy (IE) method. We then systemically evaluate the performance of these methods in recognizing the native structures by predicting the binding affinities of 176 protein-ligand and protein-protein systems of the Bcl-2 family. By calculating a series of statistical metrics, sensitivity, specificity, accuracy, Matthews correlation coefficient, the G-mean, and the receiver operating characteristic (ROC) curve, we find that the ability to discern the native structure from a decoy ensemble is improved significantly by the modification of the binding free energy using the IE method in both protein-ligand and protein-protein systems. Furthermore, the maximum area under the ROC curve (AUC) was 0.97, which was obtained by the GBHCT model combined with the IE method, indicating that this method has the best performance. The largest improvement occurs in the PB method, with a change in the AUC of 0.32. The modification of the energy is more obvious for protein-protein interactions than for protein-ligand interactions. This study indicates the effectiveness of the IE method in successfully recognizing the native structure, which is critical in rational drug design.

Drug-resistance mechanisms of three mutations in anaplastic lymphoma kinase against two inhibitors based on MM/PBSA combined with interaction entropy.

As a promising drug target in the treatment of lung cancer, anaplastic lymphoma kinase (ALK) and its mutations have been studied widely through the development of multiple generations of inhibitors. Experiments have found that compared with the wild-type, the L1198F and C1156Y/L1198F mutations resulted in resistance to 5P8 inhibitors, and the C1156Y mutation resulted in resistance to VGH inhibitors. In this study, the newly developed interaction entropy (IE) method combined with the polarized protein-specific charge (PPC) force field was utilized to explore the origin of the resistance mechanism of the ALK mutant system. The calculated binding free energy was consistent with the experimental results. Per-residue binding free energy decomposition showed that the predicted hot-spot residues (LEU1122, LEU/PHE1198, MET1199, GLY1202 and LEU1256) were almost identical across systems. Especially, the GLU1197 residue played an important role in inducing drug-resistance for both inhibitors. The electrostatic interaction of GLU1197, PHE1198 and MET1199 mainly resulted in the resistances of the L1198F and C1156Y/L1198F mutations to 5P8. And the van der Waals interaction energy of LEU1256 residue, and electrostatic energy and entropy change of GLU1197 resulted in the resistances of the C1156Y mutations to VGH. The indicated origins of the drug-resistance in the ALK systems provide a theoretical foundation for the design of potent inhibitors.

Binding Mechanism of Thrombin-Ligand Systems Investigated by a Polarized Protein-Specific Charge Force Field and Interaction Entropy Method.

In this study, 2 groups of 10 modified ligand systems with modified P3 and P2 side chains are used to study the binding mechanism with thrombin. Experimental results show that the binding affinity is enhanced by complex ligand side chains. The binding free energy obtained from the polarized protein-specific charge (PPC) force field combined with the newly developed interaction entropy (IE) method is consistent with the experimental values with a high correlation coefficient. On the contrary, poor correlation is obtained using the traditional normal mode (Nmode) method for calculating the entropy change. Furthermore, the binding free energy and hot-spot residue energy are decomposed, and the common hot-spot residues in the two groups of systems are Trp50, Leu96, Ile179, Asp199, Cyx201, Ser226, Trp227, Gly228, and Gly230. The electrostatic and van der Waals interaction energies were found to be the main contributors in the binding energy difference. CH-π and CH-CH interactions of Leu96 ligands are significantly related to the energy change due to the modified side chain, and the hydrogen bond between Asp199 and the ligand provides a strong electrostatic interaction, contributing to the binding free energy. Investigating the B-factor, principal component, and binding pocket also explains the change in the binding affinity caused by the modified side chains in ligands from the viewpoint of conformational change. This study demonstrates that the new IE method is superior to the Nmode method in the predicting binding free energy and emphasizes the importance of electronic polarization in molecular dynamics simulation. Moreover, from the viewpoint of energy and structure analysis, this study reveals the origin of the change in binding free energy in modified ligands with different binding sites.

Insight Into the Binding Mechanism of p53/pDIQ-MDMX/MDM2 With the Interaction Entropy Method.

The study of the p53-MDMX/MDM2 binding sites is a research hotspot for tumor drug design. The inhibition of p53-targeted MDMX/MDM2 has become an effective approach in anti-tumor drug development. In this paper, a theoretically rigorous and computationally accurate method, namely, the interaction entropy (IE) method, combined with the polarized protein-specific charge (PPC) force field, is used to explore the difference in the binding mechanism between p53-MDMX and p53-MDM2. The interaction of a 12mer peptide inhibitor (pDIQ), which is similar to p53 in structure, with MDMX/MDM2 is also studied. The results demonstrate that p53/pDIQ with MDM2 generates a stronger interaction than with MDMX. Compared to p53, pDIQ has larger binding free energies with MDMX and MDM2. According to the calculated binding free energies, the differences in the binding free energy among the four complexes that are obtained from the combination of PPC and IE are more consistent with the experimental values than with the results from the combination of the non-polarizable AMBER force field and IE. In addition, according to the decomposition of the binding free energy, the van der Waals (vdW) interactions are the main driving force for the binding of the four complexes. They are also the main source of the weaker binding affinity of p53/pDIQ-MDMX relative to p53/pDIQ-MDM2. Compared with p53-MDMX/MDM2, according to the analysis of the residue decomposition, the predicated total residue contributions are higher in pDIQ-MDMX/MDM2 than in p53-MDMX/MDM2, which explains why pDIQ has higher binding affinity than p53 with MDMX/MDM2. The current study provides theoretical guidance for understanding the binding mechanisms and designing a potent dual inhibitor that is targeted to MDMX/MDM2.

Exploring the Reasons for Decrease in Binding Affinity of HIV-2 Against HIV-1 Protease Complex Using Interaction Entropy Under Polarized Force Field.

In this study, the differences of binding patterns between two type HIV (HIV-1 and HIV-2) protease and two inhibitors (darunavir and amprenavir) are analyzed and compared using the newly developed interaction entropy (IE) method for the entropy change calculation combined with the polarized force field. The functional role of protonation states in the two HIV-2 complexes is investigated and our study finds that the protonated OD1 atom of Asp25' in B chain is the optimal choice. Those calculated binding free energies obtained from the polarized force field combined with IE method are significantly consistent with the experimental observed. The bridging water W301 is favorable to the binding of HIV-1 complexes; however, it is unfavorable to the HIV-2 complexes in current study. The volume of pocket, B-factor of Cα atoms and the distance of flap tip in HIV-2 complexes are smaller than that of HIV-1 consistently. These changes may cause localized rearrangement of residues lining their surface and finally result in the different binding mode for the two types HIV. Predicated hot-spot residues (Ala28/Ala28', Ile50/Ile50', and Ile84/Ile84') are nearly same in the four systems. However, the contribution to the free energy of Asp30 residue is more favorable in HIV-1 system than in HIV-2 system. Current study, to some extent, reveals the origin for the decrease in binding affinity of inhibitors against HIV-2 compared with HIV-1 and will provides theoretical guidance for future design of potent dual inhibitors targeting two type HIV protease.

The impact of interior dielectric constant and entropic change on HIV-1 complex binding free energy prediction.

At present, the calculated binding free energy obtained using the molecular mechanics/Poisson-Boltzmann (Generalized-Born) surface area (MM/PB(GB)SA) method is overestimated due to the lack of knowledge of suitable interior dielectric constants in the simulation on the interaction of Human Immunodeficiency Virus (HIV-1) protease systems with inhibitors. Therefore, the impact of different values of the interior dielectric constant and the entropic contribution when using the MM/PB(GB)SA method to calculate the binding free energy was systemically evaluated. Our results show that the use of higher interior dielectric constants (1.4-2.0) can clearly improve the predictive accuracy of the MM/PBSA and MM/GBSA methods, and computational errors are significantly reduced by including the effects of electronic polarization and using a new highly efficient interaction entropy (IE) method to calculate the entropic contribution. The suitable range for the interior dielectric constant is 1.4-1.6 for the MM/PBSA method; within this range, the correlation coefficient fluctuates around 0.84, and the mean absolute error fluctuates around 2 kcal/mol. Similarly, an interior dielectric constant of 1.8-2.0 produces a correlation coefficient of approximately 0.76 when using the MM/GBSA method. In addition, the entropic contribution of each individual residue was further calculated using the IE method to predict hot-spot residues, and the detailed binding mechanisms underlying the interactions of the HIV-1 protease, its inhibitors, and bridging water molecules were investigated. In this study, the use of a higher interior dielectric constant and the IE method can improve the calculation accuracy of the HIV-1 system.