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Predicting the mutation effects of protein–ligand interactions via end-point binding free energy calculations: strategies and analyses

Abstract

Protein mutations occur frequently in biological systems, which may impact, for example, the binding of drugs to their targets through impairing the critical H-bonds, changing the hydrophobic interactions, etc. Thus, accurately predicting the effects of mutations on biological systems is of great interests to various fields. Unfortunately, it is still unavailable to conduct large-scale wet-lab mutation experiments because of the unaffordable experimental time and financial costs. Alternatively, in silico computation can serve as a pioneer to guide the experiments. In fact, numerous pioneering works have been conducted from computationally cheaper machine-learning (ML) methods to the more expensive alchemical methods with the purpose to accurately predict the mutation effects. However, these methods usually either cannot result in a physically understandable model (ML-based methods) or work with huge computational resources (alchemical methods). Thus, compromised methods with good physical characteristics and high computational efficiency are expected. Therefore, here, we conducted a comprehensive investigation on the mutation issues of biological systems with the famous end-point binding free energy calculation methods represented by MM/GBSA and MM/PBSA. Different computational strategies considering different length of MD simulations, different value of dielectric constants and whether to incorporate entropy effects to the predicted total binding affinities were investigated to provide a more accurate way for predicting the energetic change upon protein mutations. Overall, our result shows that a relatively long MD simulation (e.g. 100 ns) benefits the prediction accuracy for both MM/GBSA and MM/PBSA (with the best Pearson correlation coefficient between the predicted ∆∆G and the experimental data of ~ 0.44 for a challenging dataset). Further analyses shows that systems involving large perturbations (e.g. multiple mutations and large number of atoms change in the mutation site) are much easier to be accurately predicted since the algorithm works more sensitively to the large change of the systems. Besides, system-specific investigation reveals that conformational adjustment is needed to refine the micro-environment of the manually mutated systems and thus lead one to understand why longer MD simulation is necessary to improve the predicting result. The proposed strategy is expected to be applied in large-scale mutation effects investigation with interpretation.

Graphical Abstract

Introduction

Chemical thermodynamics and kinetics play foundational roles in regulating biological processes [1,2,3,4], such as the processes of protein–protein interactions [5], protein-metabolite recognitions [6] and protein-nucleic acids interactions [7, 8], where binding free energy between the systems controls the tendency of the spontaneous reactions. However, these spontaneous reactions may be broken by perturbations occurring in the systems, such as mutations in the protein, which may seriously affect the binding affinities of i.e. drugs to their targets (namely drug resistance), protein–protein interactions (PPI), through impairing the critical H-bonds and/or changing the hydrophobic interactions. Thus, accurately predicting the binding energy change of the perturbed (mutated) systems has always been an essential question in various biological issues. Unfortunately, it is still unavailable to conduct large-scale wet-lab mutation experiments because of the unaffordable experimental time and financial costs. Alternatively, with the development of the computational hardware (i.e. GPU acceleration) and advanced algorithms (i.e. artificial intelligence) in recent years, in silico computation can serve as a pioneer to guide the experiments.

Actually, numerous pioneering theoretical works have been conducted on the mutated systems to predict the change of the free energy for issues such as drug resistance [9,10,11], protein–protein interactions [12, 13]. Generally, the predicting approaches can be divided into two categories, namely the statistics-based methods using machine learning (ML) and the structure-based methods using physical models (such as those applying force fields). Although the ML-based methods usually exhibit higher computational efficiency and accuracy compared with the physics-based approaches [14, 15], these methods may usually suffer from the problems of difficulty for mechanism explanation. And the ML-based methods tend to show a limited scope of application due to the biased or limited training set. On the other hand, structure-based methods such as force field guided free energy calculations exhibit more advantages in the issues of model generalizability and interpretability, and can be used in various types of predictions due to the shared physical foundation [13, 16,17,18,19]. In these algorithms, alchemical methods represented by free energy perturbation (FEP) and thermodynamics integration (TI) may be the most theoretically rigorous and precise ones with an average error of ~ 1 kcal/mol against the experimental data (i.e. FEP+ [20]). However, these approaches may be fall into the other extreme of requiring huge computational resources and convergence issues, and are usually hard to be applied in large-scale drug design campaigns.

Nevertheless, between these two extremes (ML-based models and alchemical methods), there also exist compromised methods that are able to provide not only reasonable accuracy with good generalizability, but also relatively fast computational efficiency with great interpretability. End-point binding free energy calculation methods represented by MM/GB(PB)SA (molecular mechanics [MM] with generalized Born [GB]/Poisson-Boltzmann [PB] and surface area [SA]) [21] are one of the most famous methods in this area, which calculate the binding free energy of the systems using only the initial (i.e. conformations of the receptor and ligand) and the final states (conformation of the complex), the so-called two-end-state methods. The physics-based algorithm offers a more reliable physical reality than ML-based approaches and exhibits a much faster computational efficiency compared with the alchemical methods, thus making these methods successfully used in various situations, such as drug resistance/selectivity mechanism analyses [22, 23].

Numerous mutation associated studies have been conducted with the end-point binding free energy calculation methods for various purposes, such as understanding the drug resistance mechanisms for specific targets [19, 23,24,25,26,27,28], identifying hot-spot residues responsible for protein–protein interactions [13, 29,30,31,32], or protein stabilities [33]. For instance, Ikemura et al. have conducted MM/GBSA and MM/PBSA calculations to predict the drug sensitivity of several EGFR inhibitors upon rare mutations [24], and they successfully predicted the diverse sensitivities of exon 20 insertion mutants with very high correlation against the experimental data (r2 = 0.72, n = 9). Using MD simulation and MM/PBSA calculation, Fulle et al. revealed that the drug resistance of linezolid in the large ribosomal subunit is caused by the long-range propagated mutation effects (with the drug-mutation distance > 10 Å) [25], demonstrating that MD simulation is capable of capturing long-range mutation effects. Zhang et al. have investigated the dynamic effects of the mutations in the SARS-CoV-2 spike protein with MD simulation and MM/PBSA calculation, and they demonstrated that several mutations on the spike protein (V367F and N354D/D364Y) may enhance its binding to hACE2. Moreover, Schrodinger Inc. has conducted two comprehensive analyses with FEP and end-point binding free energy calculations on massive mutations for PPI hot-spot identification [13], and protein-stability investigation [33], and reasonable accuracies are shown of the two studies (rp = 0.45 ~ 0.6). Although significant correlations are usually shown of these works against the experimental data, most of the studies have been conducted on individual systems and, up to now, there is no comprehensive study to propose a general rule for accurately predicting the mutation effects on protein–ligand systems. Therefore, in this study, we have systematically assessed the performance of MM/GBSA and MM/PBSA approaches on the mutated systems with the consideration of different MD simulation times, dielectric constants and entropy effects. A dataset containing 89 single/multiple mutations within 13 diverse proteins and 20 ligands was used for this study (Table S1 in Additional file 1). The result shows that the MD simulation time can significantly affect the performance of the calculated binding free energies for both MM/GBSA and MM/PBSA. Further investigation shows that systems suffering from large perturbations (e.g. multiple mutations or large number of atoms change in the mutation site) are much easier to be accurately predicted because the algorithm usually works sensitively to the large change of the systems. Moreover, to understand the detailed mechanism of the MD simulation time on the mutated systems, a representative system was used to intuitively reveal how the MD simulation time explicitly affects the prediction result.

Methods

Dataset preparation

Consisting of 13 proteins and 20 ligands, a dataset containing 89 single/multiple mutations from Aldeghi’s work (Platinum database) was used for this study [34, 35]. It should be noted that ligands containing the phosphate group were excluded from the original dataset since unreasonable large atomic charges were usually assigned by the atomic charge fitting algorithm. Besides, one more thing needs to be noted that a part of the mutation sites were wrongly recorded in the supporting material of the original database (the amino acid of the wild-type and the mutants were reversely recorded), thus we have corrected these mutations and the full mutations were listed in Additional file 1: Table S1.

In the preparation of the systems, all the mutants without a crystal structure were manually mutated from the corresponding protein–ligand structure. In detail, the mutations were introduced with the “Build and Edit Protein” module in Discovery Studio 2019 (Accelrys Inc., http://www.accelrys.com), followed by the geometry refinement and CHARMm force field optimization for the purpose of cleaning the structural bumps between the manually introduced mutations and the surroundings.

The resulted systems were prepared with antechamber and tleap modules in AMBER/20 simulation package [36, 37]. Considering the comparable performance in the binding free energy calculation and much lower computational cost compared with the RESP charges [38], AM1-BCC atomic charges [39] were employed for all ligands for the subsequent calculations. The small molecules were parameterized with the general amber force field (gaff, version 1.81) [40], while amber ff14SB force field [41] was used for the simulation of the proteins. To balance the redundant charges, counterions of Na+ and Cl were added to the ligand–protein systems. Each ligand–protein complex was immersed in a cubic TIP3P water box with a 10 Å boundary [42].

Molecular mechanics (MM) minimization

For MM minimization, the real-space cutoff distance (including the van der Waals and short-range electrostatic interactions) was set to 10 Å, while the PME algorithm (particle mesh Ewald) [43] was used to treat the long-range electrostatic interactions [44]. All the systems were optimized with four steps of minimizations. Note that the manually introduced mutations may impact the conformation of the surrounding residues. Here, different optimization strategies were conducted for the full-crystal systems and the in silico-mutation-containing systems in the first step of the minimization, in which all the hydrogen atoms were released with others atoms constrained for the full-crystal systems, whereas all the hydrogen atoms and the heavy atoms within 5 Å of the mutations (including the heavy atoms in amino acids, ligand, solvent and the mutation itself) were optimized with other atoms constrained for the in silico-mutation-containing systems; next, heavy atom (oxygen atom) in water and counterions (Na+/Cl−) were released; then, the sidechains in residues were additionally set free for optimization; and finally, all the atoms were released for full minimization. In each step, 5000 steps of minimization, including 1000 circles of steepest descent and 4000 cycles of conjugate gradient minimizations, were conducted with an elastic constant of 5 kcal/mol Å2 of the constraint on the systems.

Molecular dynamics (MD) simulation

In the process of MD simulation, three steps of MD simulation were conducted for each system. First, the temperature of the system was heated from 0 to 300 K during a period of 50 ps in the NVT ensemble, in which heavy atoms in the protein backbone were constrained with an elastic constant of 2 kcal/mol∙Å2. Then, a 50 ps of density equilibration was carried out in the NTP ensemble (T = 300 K and P = 1 atm) with the same constraint on the heavy atoms of the protein backbone as that of the heating process. Finally, a 100 ns MD simulation was performed in the NPT ensemble without any restraint. In all the MD simulations, the time step was set to 2 fs with the SHAKE algorithm [45] constraining the covalent bonds between the hydrogen atoms and the connected heavy atoms. The coordinates (the MD trajectory) were collected with an interval of 5 ps (25,000 steps), thus a total of 2000 frames were collected for each system.

Moreover, to fully investigate the sampling effect of MD based on one single long trajectory (100 ns), four short MD simulations (25 ns) were additionally conducted using random seeds with the same parameters/process as that of the 100 ns MD simulation for each system. All the MD simulations were performed with the pmemd.cuda module in AMBER/20.

End-point binding free energy calculations with MM/GBSA and MM/PBSA

The four 25 ns and one 100 ns MD trajectories of each system were used for the MM/GBSA and MM/PBSA calculations. In the MM/PBSA and MM/GBSA approaches, the free energy for binding of a ligand to the receptor (Eq. 1) can be decomposed into different energetic contributions as expressed below [46]:

$$\Delta {G}_{bind}={G}_{complex}-\left({G}_{receptor}-{G}_{ligand}\right)$$
(1)
$${\Delta G}_{bind}={\Delta E}_{MM}+{\Delta G}_{sol}-T\Delta S$$
(2)
$$\Delta {E}_{MM}={\Delta E}_{bond}+{\Delta E}_{angle}+{\Delta E}_{dihedral}{+{\Delta E}_{ele}+\Delta E}_{vdW}$$
(3)
$$\Delta {G}_{sol}={\Delta G}_{PB/GB}+{\Delta G}_{SA}$$
(4)
$$\Delta {G}_{SA}=\gamma *SASA+b$$
(5)

where ΔEMM, ΔGsol, and -TΔS represent the energy contributions of the molecular mechanics energy, the solvation free energy and the entropy upon ligand binding, respectively (Eq. 2), in which ΔEMM consists of five energetic terms, namely the bond (ΔEbond), the angle (ΔEangle), the dihedral (ΔEdihedral), the electrostatic (ΔEele) and the van der Waals (ΔEvdW) energies (Eq. 3). Here, we applied the single MD trajectory protocol for the end-point binding free energy calculation for the reasons to derive stable results. Therefore, ΔEbond, ΔEangle and ΔEdihedral can be well canceled out in the following calculations, leaving ΔEMM being the sum of ΔEvdW and ΔEele. ΔGsol is composed of the polar (ΔGPB/GB) and the nonpolar (ΔGSA) contributions to the solvation energy (Eq. 4), where the polar part of the solvation energy can be calculated by either GB or PB model and the nonpolar part of the solvation energy can be calculated with the solvent accessible surface area (SASA) using LCPO algorithm (Eq. 5) [47]. Here, the modified GB model developed by Onufriev (GBOBC1) [48] and the PB model parameterized by Tan and Luo (PBpbsa) [49] were employed for the polar solvation energy calculations (ΔGPB/GB) [38, 50]. Since the interior dielectric constant (εin) can significantly affect the electrostatic parts (ΔEele and ΔGPB/GB) of the resulted binding free energy as shown in previous studies [51, 52], herein we tested εin taking 1, 2 and 4 for a comprehensive comparison. The outer dielectric constant was set to 80 to mimic the high dielectric effect of the water environment. The parameters of γ and b were set to 0.0072 and 0, respectively, for the calculation of ΔGSA (Eq. 5). All the MM/GBSA and MM/PBSA calculations were performed with the MMPBSA.py module [53] in AMBER simulation package.

Conformational entropy estimated by NMA

Normal mode analysis (NMA) was used to estimate the conformational entropy of the system upon ligand binding (termed as normal mode entropy, NME). To save the computational cost, the structure-truncation strategy [54] was employed to speed up the NME calculations, where a cutoff of 9 Å was set to truncate the protein around the ligand as the reasonable performance in our previous work [52]. In the truncation of the protein structure, if any heavy atoms of a residue drop into the cutoff sphere, the whole residue is taken into the truncated structure. All the discontinuous residues were treated with charged terminals (COO and NH3+) as the better performance in our previous work [52]. For each system, 50 and 12 frames were collected from the 100 ns and each 25 ns MD trajectories, respectively, for the entropy calculation (with equal interval of 2 ns/frame). The maximum optimizing step was set to 10,000, and the convergence condition was set to 1 × 10–4. All the NME calculations were conducted by the nmode module in MMPBSA.py [53].

Analysis

In this study, the binding free energy difference between the mutated and the wild-type systems was reported (∆∆G = ∆GMT-∆GWT). Pearson correlation coefficient was employed to compare the results resulted from different computational strategies, and the standard deviation of the Pearson correlation coefficient was estimated by randomly selecting 80% data for 100 times. All the results can be found in GitHub (https://github.com/yuyangniuer/MUTATION).

Hardware and computational cost

We performed MD simulations and MM/PB(GB)SA calculations on a 384 GB-memory Linux Cluster (Centos7 operating system) with 12 NVIDIA GeForce RTX 2080Ti graphics cards and Intel Xeon Gold 5120 processors (2.2 GHz, a total of 168 CPU cores). Typically, for a system containing ~ 40,000 atoms (~ 300 residues), the computational cost for a 100 ns MD simulation and 2000 frames of MM/PB(GB)SA calculation is about 8 ~ 10 h on one GPU card and 14 CPU cores.

Results and discussion

Overall features of the investigated systems

Herein, 13 targets belonging to different protein families with 20 small molecular ligands were employed for the investigation (Fig. 1), which construct a total of 89 systems containing one or multiple mutations with Isothermal Titration Calorimetry (ITC) determined binding free energy difference upon mutations (Additional file 1: Table S1). In the dataset, 71 of them contain single mutation. A further investigation shows that 85% of the mutations (60 systems) locates within 5 Å of the co-crystallized ligand, which usually exhibits direct interactions with the ligands and may be intuitively thought to lead serious impact on drugs binding. Nevertheless, as shown in Additional file 1: Fig. S1, there is no obvious correlation between the drug-mutation distance (measured by the nearest two atoms located in the ligand and the mutation site) and the binding free energy change of the ligand upon mutations (rp = 0.001), implying that the simple observation or traditional experience is not usually valid and more rational investigation should be considered for accurately evaluating the mutation effects on drugs binding. Therefore, MD simulation in conjunction with various protocols of end-point binding free energy calculations was conducted with the purpose to accurately characterize the mutation effects on drugs binding.

Fig. 1
figure 1

Structural illustration of the 13 investigated targets and the corresponding mutation sites (red) and ligands (cyan)

End-point binding free energy calculations based on various simulation protocols

In this section, we systemically investigated the performance of the MM/GBSA and MM/PBSA approaches on the mutated systems, in which the effects of the MD simulation time (including the minimized structures), the dielectric constants and the entropy effects were taken into consideration. Different from the previous studies where the absolute binding free energy was employed for the comparison, here, the comparison was carried out on the binding free energy difference between the mutated and the wild-type systems (∆∆G = ∆GMT − ∆GWT). The Pearson correlation coefficient between the predicted binding affinity and the experimental data was used as the metric for various comparisons.

Performance of the minimized structures

Our previous work concluded that end-point binding free energy (MM/GBSA and MM/PBSA) estimated based on the minimized structures can give a better predicting accuracy compared with those calculated based on the MD trajectories for the absolute binding free energy ranking [52]. However, it is not clear for the estimation of the relative binding free energy between the mutated and the wild-type systems since the mutated residue may affect the binding free energy of the drug through different orientations or conformations. Thus, herein we performed the MM/GBSA and MM/PBSA calculations with the minimized structures to give a comparison. As shown in the last line of the left panel in Fig. 2, MM/PBSA with the minimized structure using εin = 2 exhibits the best accuracy (rp = 0.201), which is much better than the results of MM/GBSA (rp = 0.075 ~ 0.155). Nevertheless, even for the best case, the performance of the end-point calculation based on the minimized structures is still worse (rp = 0.201), indicating that structural adjustment should be taken into consideration since the manually introduced mutations may impair the microenvironment of the surrounding residues. Encouragingly, significant improvement is shown of the result when carrying out MD simulations for the binding free energy calculations, in which the best rps of MM/GBSA and MM/PBSA achieve 0.431 and 0.439, respectively, and are significantly better than the corresponding result based on the minimized structures, implying that MD simulation is a valid approach for the adjustment of the mutation sites to derive a more accurate result.

Fig. 2
figure 2

Impacts of MD simulation time, dielectric constant and entropy on the performance of MM/GBSA and MM/PBSA. The Pearson correlation between the predicted binding free energy and the experimental data are colored from blue to red. The left panel shows the accuracy based on the effective binding free energy (enthalpy), while the right panel illustrates the results based on the total binding free energy (enthalpy + entropy). The label min corresponds to the result based on the minimized structures. For clear reading, Pearson correlation coefficient less than 0.06 was colored in blue

Impact of the MD simulation time

As discussed above, a minimized structure may be unable to sample a favorable conformation of the mutated residue to appropriately adjust the binding free energy. Thus, MD simulation is apparently necessary to derive a more reasonable result. Nevertheless, the introduction of MD simulation to end-point binding free energy calculation leads to a new question that how long a MD simulation should be performed to derive a reasonable result. To answer this question, here, different MD simulation time were compared (from 20 to 100 ns or four 25 ns MD trajectories) to give an advisable strategy. As shown in the left panel of Fig. 2, for MM/GBSA at εin = 1, with the extension of the MD simulation time, the Pearson correlation coefficient gradually increases from 0.075 of the minimized structure to 0.401 of the 100 ns MD simulation. A similar tendency is shown of the result based on higher dielectric constants (εin = 2 or 4) of MM/GBSA, where no matter how to adjust the dielectric constant, the accuracy increases with the MD simulation time. Moreover, a similar result is shown of the MM/PBSA result, where the results based on 50 ~ 100 ns MD simulations are much better than those based on the corresponding minimized structures. Nevertheless, comparable best accuracies are shown of MM/GBSA and MM/PBSA at 100 ns MD simulation (0.431 and 0.439 for MM/GBSA and MM/PBSA, respectively, at εin = 2). Moreover, to investigate the performance of MM/GB(PB)SA on the converged part of the MD trajectories, we calculated the standard binding free energy (enthalpy) based on the last 50 ns trajectory for each system. As shown in Additional file 1: Fig. S2, the best accuracy of MM/GBSA and MM/PBSA are 0.428 and 0.421 (εin = 2), respectively, which is comparable with or a bit lower than the corresponding result based on the full 100 ns MD trajectories (0.431 and 0.439 for MM/GBSA and MM/PBSA, respectively, at εin = 2), indicating that the whole conformational ensemble of a MD trajectory contributes to the final energetic change of the ligand upon mutations, and therefore no additional attention needs to be taken to exclude the so-called unconverged samples for binding free energy calculation. Nevertheless, all the production runs (100 ns or the following 4 × 25 ns) were conducted after a heating and an equilibrium stage of MD simulation, which may, to a large degree, mitigate the unfavorable interactions arising from the manually introduced mutations in the initial structures.

Besides, compared with the result based on one single long MD trajectory (100 ns), both MM/GBSA and MM/PBSA exhibit much lower accuracy based on the four short MD trajectories (25 ns for each with the aggregated MD simulation time of 100 ns for each system, the row of “4 × 25 ns” in Fig. 2) with the result reasonably consistent with the first 20 ns result using one single long MD trajectory (namely better than the result based on the minimized structures but worse than the 50 ns MD result), implying that long MD simulation is necessary to be used to adjust the manually introduced mutations to improve the prediction result since the mutations may need long MD time to propagate their effects. Indeed, the analysis of the six distant-mutation-containing systems (with the drug-mutation distance > 8 Å, Additional file 1: Fig. S1) verifies the speculation. As shown in Fig. 3, a short MD simulation (20 ns) may be hard to propagate the mutation effect from a distant mutation to the binding site, thus resulting in a very bad result (rp = − 0.57 for MM/GBSA at εin = 2, left panel of Fig. 3), whereas a longer MD simulation (100 ns) is capable of propagating the mutation effect from a distant mutation to the binding pocket, thus substantially improves the prediction result (rp = 0.64 for MM/GBSA at εin = 2, right panel of Fig. 3). Moreover, the mechanism of how MD simulation time influences the performance of the predicted binding affinity has been analyzed on a representative system in the last part of this section, which may facilitate one to understand how the mutation effect propagated with the extension of MD simulation time.

Fig. 3
figure 3

Impact of the MD simulation time on the distant-mutation-containing systems, where the Pearson correlation coefficient can be substantially improved with the extension of the MD simulation time for the MM/GBSA calculation (enthalpy at εin = 2)

Impact of the dielectric constant

How to choose an appropriate dielectric constant is usually a vital issue in the end-point binding free energy calculations since it may significantly affect the prediction accuracy. Notably, different types of systems may exhibit different tendencies to the employed dielectric constant [38, 50,51,52, 55,56,57,58,59,60,61,62], such as a higher dielectric constant (i.e. εin = 4) may be a good choice for the protein–ligand systems [51, 52, 63,64,65], while a medium dielectric constant (i.e. εin = 2) may be more suitable for the protein-peptide [60] and protein-RNA/DNA systems [56], whereas a low dielectric constant (εin = 1) is better for the protein–protein systems [57]. Therefore, to find the suitable dielectric constant for the manually mutated systems, we also used the dielectric constants of 1, 2 and 4 for the MM/GB(PB)SA calculations. As shown in the left panel of Fig. 2, MM/GBSA and MM/PBSA exhibit different preferences: For MM/GBSA, although choosing a medium dielectric constant (εin = 2) may achieve a better result, not much difference is evident from the results based on different dielectric constant (rp = 0.401 ~ 0.431 for 100 ns MD result). On the other hand, for MM/PBSA, a relatively higher dielectric constant (εin = 2 and 4) can generate a better accuracy (rp = 0.439 under the 100 ns MD simulations with εin = 2). Nevertheless, comparable accuracies are demonstrated for the standard MM/GB(PB)SA calculations (without considering the entropy, left panel in Fig. 2) when using any dielectric constant (εin = 1 ~ 4) for MM/GBSA calculations and a relatively higher dielectric constant (εin = 2 and 4) for MM/PBSA calculations. This result indicates that, different from the absolute binding free energy calculation, where the predicted binding free energy may be significantly affected by the use of different dielectric constants [51], the relative binding free energy calculation between e.g. the mutants and the wild-type system (∆∆G) may largely cancel out the difference of the electrostatic effects at different dielectric constants, making the systems insensitive to the dielectric constant.

Impact of the conformational entropy

Another important issue for the end-point binding free energy calculation is whether it is necessary to incorporate the entropy term for the standard MM/GB(PB)SA calculations (the so called effective binding free energy or enthalpy) since the incorporation of entropy may not be able to improve the correlation between the predicted binding free energies and the experimental data in most cases [50]. However, different voices arise in various system-specific studies, where incorporating entropy into the standard MM/GB(PB)SA calculations helps not only to reveal the binding mechanisms, such as drug resistance [23], but also to reproduce the absolute binding free energy against the experimental data. Therefore, here the entropy effect has also been taken into consideration for the accuracy investigation. The structure-truncation strategy was employed for the entropy calculation since the too high computational cost of the normal mode entropy (NME) calculation. As shown in the right panel of Fig. 2, unfortunately, incorporating entropy into the standard MM/GB(PB)SA calculations seriously impairs the prediction accuracy, where no obvious rules can be summarized from the result. Nevertheless, since the characterization of the mutation effect usually involves the relative binding free energy calculation (∆∆G between the mutated and the wild-type systems), where the entropy contributions can be largely canceled out between systems, there is no necessary to incorporate the entropy term into the predicted binding free energies.

Impact of the mutation properties and target specificity on the predicting accuracy

To further investigate the impacting factors on the performance of the predicted binding free energies upon mutations, the difference of the mutated and the original residues is analyzed based on MM/GBSA under the condition of εin = 2 and 100 ns MD simulation. As shown in Fig. 4, here, three main impacting factors were investigated, including the number of mutations in the targets (single or multiple mutation(s), Fig. 4A), the number of heavy atoms change between the mutated and the original residues (Fig. 4B), and the change of charge state of the mutation (Fig. 4C). The distribution of each property on the investigated targets can be found in Additional file 1: Figs. S3–S5.

Fig. 4
figure 4

Impact of mutation properties on the predicting accuracy. A Single or multiple mutation(s), B the number of heavy atoms change in mutations, and C the change of charge state of the mutation on the predicting accuracy. All the investigation were performed based on MM/GBSA at εin = 2 and 100 ns MD simulation

For the investigation of the number of mutations in a system (Fig. 4A), it shows that systems involving multiple mutations exhibit higher predicting accuracy (rp = 0.517) compared with those involving only one mutation (rp = 0.400). It is easy to understand that systems involving multiple mutations may generate larger impact on the binding of a ligand to its receptor compared with the original system, and thus can be more accurately predicted. Moreover, the further investigation on the number of heavy atoms change between the mutated and the original systems also shows a same tendency (Fig. 4B), where the predicting accuracy improves with the increased change of the heavy atom count between the mutated and the original residues (with the rp of 0.335 for 0 ~ 1 heavy atom change, 0.393 for 2 ~ 4 heavy atom change, and 0.511 for > 5 heavy atom change), implying that the impact of large change between the mutated and the original residues is much easier to be predicted (e.g. systems with multiple mutations or with > 5 heavy atoms change) than those with tiny difference between the mutated and the wild-type residues (e.g. systems with single mutation or with 0 ~ 1 heavy atom change). Besides, the impact of charge-state change of the mutations is also investigated, where if one residue (before or after mutation) involves charged residue (ASP, GLU, LYS and ARG), the system is assigned to the charged group, otherwise, it will be assigned to the neutral group. As shown in Fig. 4C, comparable result is shown of the neutral (rp = 0.458) and the changed groups (rp = 0.478), suggesting that the change of charge state of the mutated residue(s) may not affect the accuracy of the predictions so much because of the well parameterized protein force field.

Furthermore, we also investigated the system dependency of MM/GBSA on characterizing the mutation effect for specific proteins, where systems with ≥ 6 individuals were plotted based on εin = 2 and 100 ns MD simulation. As shown in Fig. 5, the Pearson correlation coefficient is higher than 0.8 in the systems of Esterase-LipA, Steptavidin and D7R4-tryptamine, whereas lower than or around 0 in the systems of HSP82 and HIV-1 protease. Although one may concern that too few samples were incorporated in each protein group, the predicted result of some systems (e.g. HIV-1 protease) is consistent with the existing result reported by previous studies on the same system, such as the previous investigation on 220 HIV-1 protease systems shows the best Pearson correlation coefficient of 0.165 for the absolute binding free energy calculation using MM/GBSA [51], which is consistent with the current observed low accuracy of the HIV-1 protease group on the relative binding free energy calculation. The deeper reason may attribute to complicated chemical structures of the HIV1-protease inhibitors (usually containing > 100 atoms and > 10 rotatable bonds), and thus is hard to be accurately predicted by the classical force field. Therefore, we emphasize that caution should always be minded when using a computational method.

Fig. 5
figure 5

Performance of MM/GBSA on specific targets based on εin = 2 and 100 ns MD simulation

Insights into the impact of MD simulation time on the mutated system

As shown in the preceding section, the length of MD simulation time is of crucial importance in regulating the performance of the end-point binding free energy in the mutated systems, where it can be concluded that longer MD simulation (e.g. 100 ns) benefits the relative binding free energy calculation (∆∆G) for both MM/GBSA and MM/PBSA. To better understand the role of MD simulation time on the mutated systems, here a case analysis is performed on the system of D7R4-tryptamine (including 10 mutants).

As shown in Fig. 6A, the Pearson correlation coefficient of the standard binding free energy predicted by MM/GBSA (enthalpy at εin = 1) improves with the extension of MD simulation time from 0.45 to 0.58 in the 20 ns and 100 ns results, respectively, where 5 systems in 10 show correct tendency (consistent sign with the experimental binding free energy difference) of the predicted relative binding free energy against the experimental data in 20 ns MD simulation, whereas 7 out of the 10 systems exhibit correct result in the 100 ns MD simulation. In the two additionally correctly adjusted systems (D111L and Y94L mutants, Fig. 6A), the relative binding free energy of the D111L mutant changes remarkably (with > 4 kcal/mol binding free energy difference between the 100 ns and the 20 ns results), thus we investigated this mutant to reveal how the extension of the MD simulation time ameliorates the result.

Fig. 6
figure 6

Correlation between the predicted binding free energy difference and the experimental data of the D7R4-tryptamine systems in different MD simulation time, where the standard MM/GBSA results based on 20 and 100 ns MD simulation (εin = 1) are shown in panel A. The energetic difference of the vital residues between the D111L mutant and the wild-type system is shown in panel B with the corresponding most populated conformations illustrated in panel C, in which structures derived from 20 and 100 ns MD simulations are colored in blue and orange, respectively, with the mutation site colored in red

As shown in Table 1, since the relative binding free energy calculation incorporates two systems (namely, the wild-type and the mutated systems), we illustrated the MM/GBSA binding free energy for both systems in each reference time point (20, 50 and 100 ns) to give a comparison. It can be found that the calculated binding free energy of the wild-type system is very stable across the whole 100 ns MD simulation with the energetic difference between the 20 and 100 ns results < 1 kcal/mol (∆∆GWT_100ns-20ns = − 0.56 kcal/mol), whereas large energetic difference is shown of the D111L-mutated system (∆∆GMT_100ns-20ns = 4.25 kcal/mol). The reason why so large energetic difference happens in the mutated system may be attributed to the manually introduced mutation that may probably perturb the surrounding residues of the protein. Therefore, we further decomposed the total binding free energy into residue level to reveal a more detailed picture. Figure 6B illustrates the most energetic difference contributed residues, where TYR25 exhibits the most significant energetic change between the mutated and the wide-type systems. Further superimposition of the most populated conformations of the wild-type and the mutated systems shows that, although the conformation of TYR25 does not change dramatically during the 100 ns MD simulation, the sidechain of the ligand exhibits an obvious conformational shift (Fig. 6C) that does not occur at the beginning of MD simulation, but gradually shifts with the extension of the MD simulation and finally results in remarkably attenuated interaction to TYR25 (− 3.39 versus − 2.24 kcal/mol in the 20 and 100 ns MD results, respectively), implying that long time MD simulation is capable of re-adjusting the distribution of the micro-environment of the protein around the mutation site, thus leading to more reasonable energetic result against the experimental data.

Table 1 Energetic difference of the D7R4-tryptamine systems in the 20, 50 and 100 ns MD simulations based on MM/GBSA (kcal/mol, εin = 1)

Conclusion

In this study, comprehensive analyses were performed to investigate the mutation effects on the performance of end-point binding free energy calculations. Compared with the alchemical methods, end-point binding free energy calculations represented by MM/GBSA and MM/PBSA are much computationally cheaper with reasonable accuracy (with the best rp ~ 0.44 on a challenging dataset), thus are useful for application in large-scale mutation associated studies.

Specifically, the current result shows that a relatively long MD simulation (e.g. 100 ns) usually benefits the prediction accuracy in both MM/GBSA and MM/PBSA, in which MM/GBSA is insensitive to the dielectric constant, while MM/PBSA prefers a relatively higher dielectric constant (εin = 2 or 4). Overall, MM/GBSA and MM/PBSA give a comparable best accuracy in the MD-based calculations (with the Pearson correlation coefficients of 0.431 and 0.439 for MM/GBSA and MM/PBSA, respectively), while MM/PBSA performs remarkably better than MM/GBSA in the minimized structures though the best Pearson correlation coefficient is very low (rp = 0.201).

Moreover, analyses of the mutation properties to the prediction accuracy show that systems suffering from large perturbations (e.g. multiple mutations or large number of heavy atoms change in the mutation site) are much easier to be accurately predicted due to the significant change of the systems. Besides, a system of D7R4-tryptamine was employed as an example to reveal the impact of MD simulation time on the mutation effect, where conformational change of the ligand caused by the manually introduced mutation is found responsible for the adjustment of the binding free energy difference along the MD trajectory, indicating that manually modeled structures should be well adjusted by strategies such as MD simulation to match the micro-environment of the protein.

Availability of data and materials

All the initial structures, resulting data and scripts for AMBER simulations (including the four stages of minimization, three stages of MD simulation and MM/PB(GB)SA/NMA calculation) were made available in GitHub (https://github.com/yuyangniuer/MUTATION).

References

  1. Limongelli V (2020) Ligand binding free energy and kinetics calculation in 2020. Wiley Interdiscip Rev Comput Mol Sci 10:e1455

    CAS  Article  Google Scholar 

  2. Bernetti M, Masetti M, Rocchia W et al (2019) Kinetics of drug binding and residence time. Annu Rev Phys Chem 70:143–171

    CAS  PubMed  Article  Google Scholar 

  3. Ijzerman AP, Guo D (2019) Drug-target association kinetics in drug discovery. Trends Biochem Sci 44:861–871

    CAS  PubMed  Article  Google Scholar 

  4. Du B, Zielinski DC, Palsson BO (2018) Estimating metabolic equilibrium constants: progress and future challenges. Trends Biochem Sci 43:960–969

    CAS  PubMed  Article  Google Scholar 

  5. Siebenmorgen T, Zacharias M (2020) Computational prediction of protein–protein binding affinities. Wiley Interdiscip Rev Comput Mol Sci 10:e1448

    CAS  Article  Google Scholar 

  6. Calhoun S, Korczynska M, Wichelecki DJ et al (2018) Prediction of enzymatic pathways by integrative pathway mapping. Elife 7:e31097

    PubMed  PubMed Central  Article  Google Scholar 

  7. Kappel K, Jarmoskaite I, Vaidyanathan PP et al (2019) Blind tests of RNA–protein binding affinity prediction. Proc Natl Acad Sci USA 116:8336–8341

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  8. Blanco JD, Radusky LG, Cianferoni D et al (2019) Protein-assisted RNA fragment docking (RnaX) for modeling RNA–protein interactions using ModelX. Proc Natl Acad Sci USA 116:24568–24573

    CAS  Article  Google Scholar 

  9. Aldeghi M, Gapsys V, de Groot BL (2019) Predicting kinase inhibitor resistance: physics-based and data-driven approaches. ACS Cent Sci 5:1468–1474

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  10. Bhati AP, Wan S, Coveney PV (2018) Ensemble-based replica exchange alchemical free energy methods: the effect of protein mutations on inhibitor binding. J Chem Theory Comput 15:1265–1277

    PubMed Central  Article  CAS  Google Scholar 

  11. Koohi-Moghadam M, Wang H, Wang Y et al (2019) Predicting disease-associated mutation of metal-binding sites in proteins using a deep learning approach. Nat Mach Intell 1:561–567

    Article  Google Scholar 

  12. Rodrigues CH, Pires DE, Ascher DB (2021) mmCSM-PPI: predicting the effects of multiple point mutations on protein–protein interactions. Nucleic Acids Res 9(W1):W417–W424

    Article  CAS  Google Scholar 

  13. Clark AJ, Negron C, Hauser K et al (2019) Relative binding affinity prediction of charge-changing sequence mutations with FEP in protein–protein interfaces. J Mol Biol 431:1481–1493

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  14. Iqbal S, Li F, Akutsu T et al (2021) Assessing the performance of computational predictors for estimating protein stability changes upon missense mutations. Brief Bioinform 22(6):bbab184

    PubMed  Article  CAS  Google Scholar 

  15. Li B, Yang YT, Capra JA et al (2020) Predicting changes in protein thermodynamic stability upon point mutation with deep 3D convolutional neural networks. PLoS Comput Biol 16:e1008291

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  16. Gapsys V, Pérez-Benito L, Aldeghi M et al (2020) Large scale relative protein ligand binding affinities using non-equilibrium alchemy. Chem Sci 11:1140–1152

    CAS  Article  Google Scholar 

  17. Jespers W, Isaksen GV, Andberg TA et al (2019) QresFEP: an automated protocol for free energy calculations of protein mutations in Q. J Chem Theory Comput 15:5461–5473

    CAS  PubMed  Article  Google Scholar 

  18. Li Z, Huang Y, Wu Y et al (2019) Absolute binding free energy calculation and design of a subnanomolar inhibitor of phosphodiesterase-10. J Med Chem 62:2099–2111

    CAS  PubMed  Article  Google Scholar 

  19. Chen J, Wang X, Pang L et al (2019) Effect of mutations on binding of ligands to guanine riboswitch probed by free energy perturbation and molecular dynamics simulations. Nucleic Acids Res 47:6618–6631

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  20. Wang L, Wu Y, Deng Y et al (2015) Accurate and reliable prediction of relative ligand binding potency in prospective drug discovery by way of a modern free-energy calculation protocol and force field. J Am Chem SOC 137:2695–2703

    CAS  PubMed  Article  Google Scholar 

  21. Kollman PA, Massova I, Reyes C et al (2000) Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models. Acc Chem Res 33:889–897

    CAS  PubMed  Article  Google Scholar 

  22. Kong X, Sun H, Pan P et al (2016) Molecular principle of the cyclin-dependent kinase selectivity of 4-(thiazol-5-yl)-2-(phenylamino) pyrimidine-5-carbonitrile derivatives revealed by molecular modeling studies. Phys Chem Chem Phys 18:2034–2046

    CAS  PubMed  Article  Google Scholar 

  23. Sun H, Li Y, Li D et al (2013) Insight into crizotinib resistance mechanisms caused by three mutations in ALK tyrosine kinase using free energy calculation approaches. J Chem Inf Model 53:2376–2389

    CAS  PubMed  Article  Google Scholar 

  24. Ikemura S, Yasuda H, Matsumoto S et al (2019) Molecular dynamics simulation-guided drug sensitivity prediction for lung cancer with rare EGFR mutations. Proc Natl Acad Sci USA 116:10025–10030

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  25. Fulle S, Saini JS, Homeyer N et al (2015) Complex long-distance effects of mutations that confer linezolid resistance in the large ribosomal subunit. Nucleic Acids Res 43:7731–7743

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  26. Kim P, Li H, Wang J et al (2021) Landscape of drug-resistance mutations in kinase regulatory hotspots. Brief Bioinform 22:bbaa108

    PubMed  Article  CAS  Google Scholar 

  27. Guan Y, Sun H, Pan P et al (2015) Exploring resistance mechanisms of HCV NS3/4A protease mutations to MK5172: insight from molecular dynamics simulations and free energy calculations. Mol BioSyst 11:2568–2578

    CAS  PubMed  Article  Google Scholar 

  28. Sun HY, Ji FQ (2012) A molecular dynamics investigation on the crizotinib resistance mechanism of C1156Y mutation in ALK. Biochem Biophys Res Commun 423:319–324

    CAS  PubMed  Article  Google Scholar 

  29. Simões IC, Costa IP, Coimbra JT et al (2017) New parameters for higher accuracy in the computation of binding free energy differences upon alanine scanning mutagenesis on protein–protein interfaces. J Chem Inf Model 57:60–72

    PubMed  Article  CAS  Google Scholar 

  30. Li M, Petukh M, Alexov E et al (2014) Predicting the impact of missense mutations on protein–protein binding affinity. J Chem Theory Comput 10:1770–1780

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  31. Petukh M, Li M, Alexov E (2015) Predicting binding free energy change caused by point mutations with knowledge-modified MM/PBSA method. PLoS Comput Biol 11:e1004276

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  32. Zhang Y, He X, Zhai J et al (2021) In silico binding profile characterization of SARS-CoV-2 spike protein and its mutants bound to human ACE2 receptor. Brief Bioinform. https://doi.org/10.1093/bib/bbab1188

    Article  PubMed  PubMed Central  Google Scholar 

  33. Steinbrecher T, Zhu C, Wang L et al (2017) Predicting the effect of amino acid single-point mutations on protein stability—large-scale validation of MD-based relative free energy calculations. J Mol Biol 429:948–963

    CAS  PubMed  Article  Google Scholar 

  34. Aldeghi M, Gapsys V, de Groot BL (2018) Accurate estimation of ligand binding affinity changes upon protein mutation. ACS Cent Sci 4:1708–1718

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  35. Pires DEV, Blundell TL, Ascher DB (2015) Platinum: a database of experimentally measured effects of mutations on structurally defined protein–ligand complexes. Nucleic Acids Res 43:D387–D391

    CAS  PubMed  Article  Google Scholar 

  36. Wang J, Wang W, Kollman PA et al (2006) Automatic atom type and bond type perception in molecular mechanical calculations. J Mol Graph Model 25:247–260

    PubMed  Article  CAS  Google Scholar 

  37. Case DA, Cheatham TE 3rd, Darden T et al (2005) The Amber biomolecular simulation programs. J Comput Chem 26:1668–1688

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  38. Xu L, Sun H, Li Y et al (2013) Assessing the performance of MM/PBSA and MM/GBSA methods. 3. The impact of force fields and ligand charge models. J Phys Chem B 117:8408–8421

    CAS  PubMed  Article  Google Scholar 

  39. Jakalian A, Jack DB, Bayly CI (2002) Fast, efficient generation of high-quality atomic charges. AM1-BCC model: II. Parameterization and validation. J Comput Chem 23:1623–1641

    CAS  PubMed  Article  Google Scholar 

  40. Wang JM, Wolf RM, Caldwell JW et al (2004) Development and testing of a general amber force field. J Comput Chem 25:1157–1174

    CAS  PubMed  Article  Google Scholar 

  41. Maier JA, Martinez C, Kasavajhala K et al (2015) ff14SB: improving the accuracy of protein side chain and backbone parameters from ff99SB. J Chem Theory Comput 11:3696–3713

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  42. Jorgensen WL, Chandrasekhar J, Madura JD et al (1983) Comparison of simple potential functions for simulating liquid water. J Chem Phys 79:926–935

    CAS  Article  Google Scholar 

  43. Darden T, York D, Pedersen L (1993) Particle mesh Ewald: AnNlog(N) method for Ewald sums in large systems. J Chem Phys 98:10089–10092

    CAS  Article  Google Scholar 

  44. York DM, Darden TA, Pedersen LG (1993) The effect of long-range electrostatic interactions in simulations of macromolecular crystals: a comparison of the Ewald and truncated list methods. J Chem Phys 99:8345–8348

    CAS  Article  Google Scholar 

  45. Ryckaert JP, Ciccotti G, Berendsen HJC (1977) Numerical integration of the Cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes. J Comput Phys 23:327–341

    CAS  Article  Google Scholar 

  46. Wang E, Sun H, Wang J et al (2019) End-point binding free energy calculation with MM/PBSA and MM/GBSA: strategies and applications in drug design. Chem Rev 119:9478–9508

    CAS  PubMed  Article  Google Scholar 

  47. Weiser J, Shenkin PS, Still WC (1999) Approximate atomic surfaces from linear combinations of pairwise overlaps (LCPO). J Comput Chem 20:217–230

    CAS  Article  Google Scholar 

  48. Onufriev A, Bashford D, Case DA (2004) Exploring protein native states and large-scale conformational changes with a modified generalized born model. Proteins Struct Funct Bioinf 55:383–394

    CAS  Article  Google Scholar 

  49. Tan C, Yang L, Luo R (2006) How well does Poisson-Boltzmann implicit solvent agree with explicit solvent? A quantitative analysis. J Phys Chem B 110:18680–18687

    CAS  PubMed  Article  Google Scholar 

  50. Hou T, Wang J, Li Y et al (2011) Assessing the performance of the MM/PBSA and MM/GBSA methods: I. The accuracy of binding free energy calculations based on molecular dynamics simulations. J Chem Inf Model 51:69–82

    CAS  PubMed  Article  Google Scholar 

  51. Sun H, Li Y, Tian S et al (2014) Assessing the performance of MM/PBSA and MM/GBSA methods. 4. Accuracies of MM/PBSA and MM/GBSA methodologies evaluated by various simulation protocols using PDBbind data set. Phys Chem Chem Phys 16:16719–16729

    CAS  PubMed  Article  Google Scholar 

  52. Sun H, Duan L, Chen F et al (2018) Assessing the performance of MM/PBSA and MM/GBSA methods. 7. Entropy effects on the performance of end-point binding free energy calculation approaches. Phys Chem Chem Phys 20:14450–14460

    CAS  PubMed  Article  Google Scholar 

  53. Miller BR III, McGee TD, Swails JM et al (2012) MMPBSApy: an efficient program for end-state free energy calculations. J Chem Theory Comput 8:3314–3321

    CAS  PubMed  Article  Google Scholar 

  54. Genheden S, Kuhn O, Mikulskis P et al (2012) The normal-mode entropy in the MM/GBSA method: effect of system truncation, buffer region, and dielectric constant. J Chem Inf Model 52:2079–2088

    CAS  PubMed  Article  Google Scholar 

  55. Sun H, Li Y, Shen M et al (2014) Assessing the performance of MM/PBSA and MM/GBSA methods. 5. Improved docking performance using high solute dielectric constant MM/GBSA and MM/PBSA rescoring. Phys Chem Chem Phys 16:22035–22045

    CAS  PubMed  Article  Google Scholar 

  56. Chen F, Sun H, Wang J et al. Assessing the performance of MM/PBSA and MM/GBSA methods. 8. Predicting binding free energies and poses of protein-RNA complexes, RNA 2018:rna. 065896.065118.

  57. Chen F, Liu H, Sun H et al (2016) Assessing the performance of the MM/PBSA and MM/GBSA methods. 6. Capability to predict protein-protein binding free energies and re-rank binding poses generated by protein-protein docking. Phys Chem Chem Phys 18:22129–22139

    CAS  PubMed  Article  Google Scholar 

  58. Hou T, Wang J, Li Y et al (2011) Assessing the performance of the molecular mechanics/Poisson Boltzmann surface area and molecular mechanics/generalized Born surface area methods. II. The accuracy of ranking poses generated from docking. J Comput Chem 32:866–877

    CAS  PubMed  Article  Google Scholar 

  59. Wang E, Weng G, Sun H et al (2019) Assessing the performance of the MM/PBSA and MM/GBSA methods. 10. Impacts of enhanced sampling and variable dielectric model on protein–protein Interactions. Phys Chem Chem Phys 21:18958–18969

    CAS  PubMed  Article  Google Scholar 

  60. Weng G, Wang E, Chen F et al (2019) Assessing the performance of MM/PBSA and MM/GBSA methods. 9. Prediction reliability of binding affinities and binding poses for protein–peptide complexes. Phys Chem Chem Phys 21:10135–10145

    CAS  PubMed  Article  Google Scholar 

  61. Wang E, Liu H, Wang J et al (2020) Development and evaluation of MM/GBSA based on a variable dielectric GB model for predicting protein-ligand binding affinities. J Chem Inf Model 60:5353–5365

    CAS  PubMed  Article  Google Scholar 

  62. Wang E, Fu W, Jiang D et al (2021) VAD-MM/GBSA: a variable atomic dielectric MM/GBSA model for improved accuracy in protein-ligand binding free energy calculations. J Chem Inf Model. https://doi.org/10.1021/acs.jcim.1021c00091

    Article  PubMed  PubMed Central  Google Scholar 

  63. Pa¨r So¨derhjelm JK, Ulf Ryde. Ligand Affinities Estimated by Quantum Chemical Calculations, J. Chem. Theory Comput. 2010;6:1726–1737.

  64. Genheden S, Ryde U (2015) The MM/PBSA and MM/GBSA methods to estimate ligand-binding affinities. Expert Opin Drug Discov 10:449–461

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  65. Yang T, Wu JC, Yan C et al (2011) Virtual screening using molecular simulations. Proteins 79:1940–1951

    CAS  PubMed  PubMed Central  Article  Google Scholar 

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Funding

This work was supported by the National Natural Science Foundation of China (Grant 81603031), Natural Science Foundation of Zhejiang Province (LQ21H300007), and the Young Elite Scientists Sponsorship Program by CPU (Nos. 131810011 and 1132010013).

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YY, ZW and HS collected the data, performed the calculations and analyzed the data; LW and ST evaluated and interpreted the results; HS and TH conceived, supervised the project and wrote the manuscript. All authors read and approved the final manuscript.

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Correspondence to Tingjun Hou or Huiyong Sun.

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Yu, Y., Wang, Z., Wang, L. et al. Predicting the mutation effects of protein–ligand interactions via end-point binding free energy calculations: strategies and analyses. J Cheminform 14, 56 (2022). https://doi.org/10.1186/s13321-022-00639-y

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