Absolute binding free energy calculations using molecular dynamics simulations with restraining potentials

The absolute (standard) binding free energy of eight FK506-related ligands to FKBP12 is calculated using free energy perturbation molecular dynamics (FEP/MD) simulations with explicit solvent. A number of features are implemented to improve the accuracy and enhance the convergence of the calculations. First, the absolute binding free energy is decomposed into sequential steps during which the ligand-surrounding interactions as well as various biasing potentials restraining the translation, orientation, and conformation of the ligand are turned "on" and "off." Second, sampling of the ligand conformation is enforced by a restraining potential based on the root mean-square deviation relative to the bound state conformation. The effect of all the restraining potentials is rigorously unbiased, and it is shown explicitly that the final results are independent of all artificial restraints. Third, the repulsive and dispersive free energy contribution arising from the Lennard-Jones interactions of the ligand with its surrounding (protein and solvent) is calculated using the Weeks-Chandler-Andersen separation. This separation also improves convergence of the FEP/MD calculations. Fourth, to decrease the computational cost, only a small number of atoms in the vicinity of the binding site are simulated explicitly, while all the influence of the remaining atoms is incorporated implicitly using the generalized solvent boundary potential (GSBP) method. With GSBP, the size of the simulated FKBP12/ligand systems is significantly reduced, from approximately 25,000 to 2500. The computations are very efficient and the statistical error is small ( approximately 1 kcal/mol). The calculated binding free energies are generally in good agreement with available experimental data and previous calculations (within approximately 2 kcal/mol). The present results indicate that a strategy based on FEP/MD simulations of a reduced GSBP atomic model sampled with conformational, translational, and orientational restraining potentials can be computationally inexpensive and accurate.     

Structure and folding of disulfide-rich miniproteins: insights from molecular dynamics simulations and MM-PBSA free energy calculations

The fold of small disulfide-rich proteins largely relies on two or more disulfide bridges that are main components of the hydrophobic core. Because of the small size of these proteins and their high cystine content, the cysteine connectivity has been difficult to ascertain in some cases, leading to uncertainties and debates in the literature. Here, we use molecular dynamics simulations and MM-PBSA free energy calculations to compare similar folds with different disulfide pairings in two disulfide-rich miniprotein families, namely the knottins and the short-chain scorpion toxins, for which the connectivity has been discussed. We first show that the MM-PBSA approach is able to discriminate the correct knotted topology of knottins from the laddered one. Interestingly, a comparison of the free energy components for kalata B1 and MCoTI-II suggests that cyclotides and squash inhibitors, although sharing the same scaffold, are stabilized through different interactions. Application to short-chain scorpion toxins suggests that the conventional cysteine pairing found in many homologous toxins is significantly more stable than the unconventional pairing reported for maurotoxin and for spinoxin. This would mean that native maurotoxin and spinoxin are not at the lowest free energy minimum and might result from kinetically rather than thermodynamically driven oxidative folding processes. For both knottins and toxins, the correct or conventional disulfide connectivities provide lower flexibilities and smaller deviations from the initial conformations. Overall, our work suggests that molecular dynamics simulations and the MM-PBSA approach to estimate free energies are useful tools to analyze and compare disulfide bridge connectivities in miniproteins.     

Insight into binding mechanisms of EGFR allosteric inhibitors using molecular dynamics simulations and free energy calculations

Abstract

Lung cancer is the leading cause of cancer death, and epidermal growth factor receptor (EGFR) kinase domain mutations are a common cause of non-small-cell lung cancer (NSCLC), a major subtype of lung cancers. Patients harboring most of these mutations respond well to the EGFR inhibitors Gefitinib and Erlotinib initially, but soon develop resistance to them due to the emergence of the gatekeeper mutation T790M. The new-generation inhibitors such as AZD9291, HM61713, CO-1686 and WZ4002 can overcome T790M through covalent binding to Cys 797, but ultimately lose their efficacy upon the emergence of the C797S mutation that abolishes the covalent bonding. Allosteric inhibitors EAI001 and EAI045 are a new type of EGFR inhibitors that bind to EGFR away from the ATP-binding site and not relying on Cys 797. In this study, molecular dynamics simulations and free energy calculations were carried out on EAI001 and EAI045 in complex with EGFR, revealing the detailed inhibitory mechanism of EAI001 and EAI045 as EGFR allosteric inhibitor, which was expected to provide a basis for rational drug design of the EGFR allosteric inhibitors.

Communicated by Ramaswamy H. Sarma     

Computational investigation of the HIV-1 Rev multimerization using molecular dynamics simulations and binding free energy calculations

The HIV Rev protein mediates the nuclear export of viral mRNA, and is thereby essential for the production of late viral proteins in the replication cycle. Rev forms a large organized multimeric protein-protein complex for proper functioning. Recently, the three-dimensional structures of a Rev dimer and tetramer have been resolved and provide the basis for a thorough structural analysis of the binding interaction. Here, molecular dynamics (MD) and binding free energy calculations were performed to elucidate the forces thriving dimerization and higher order multimerization of the Rev protein. It is found that despite the structural differences between each crystal structure, both display a similar behavior according to our calculations. Our analysis based on a molecular mechanics-generalized Born surface area (MM/GBSA) and a configurational entropy approach demonstrates that the higher order multimerization site is much weaker than the dimerization site. In addition, a quantitative hot spot analysis combined with a mutational analysis reveals the most contributing amino acid residues for protein interactions in agreement with experimental results. Additional residues were found in each interface, which are important for the protein interaction. The investigation of the thermodynamics of the Rev multimerization interactions performed here could be a further step in the development of novel antiretrovirals using structure based drug design. Moreover, the variability of the angle between each Rev monomer as measured during the MD simulations suggests a role of the Rev protein in allowing flexibility of the arginine rich domain (ARM) to accommodate RNA binding.     

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

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

Exploring the energy landscape of protein folding using replica-exchange and conventional molecular dynamics simulations

Two independent replica-exchange molecular dynamics (REMD) simulations with an explicit water model were performed of the Trp-cage mini-protein. In the first REMD simulation, the replicas started from the native conformation, while in the second they started from a nonnative conformation. Initially, the first simulation yielded results qualitatively similar to those of two previously published REMD simulations: the protein appeared to be over-stabilized, with the predicted melting temperature 50-150K higher than the experimental value of 315K. However, as the first REMD simulation progressed, the protein unfolded at all temperatures. In our second REMD simulation, which starts from a nonnative conformation, there was no evidence of significant folding. Transitions from the unfolded to the folded state did not occur on the timescale of these simulations, despite the expected improvement in sampling of REMD over conventional molecular dynamics (MD) simulations. The combined 1.42 micros of simulation time was insufficient for REMD simulations with different starting structures to converge. Conventional MD simulations at a range of temperatures were also performed. In contrast to REMD, the conventional MD simulations provide an estimate of Tm in good agreement with experiment. Furthermore, the conventional MD is a fraction of the cost of REMD and continuous, realistic pathways of the unfolding process at atomic resolution are obtained.     

Assignment of side-chain conformation using adiabatic energy mapping, free energy perturbation, and molecular dynamic simulations

NMR spectroscopic analysis of the C-terminal Kunitz domain fragment (alpha3(VI)) from the human alpha3-chain of type VI collagen has revealed that the side chain of Trp21 exists in two unequally populated conformations. The major conformation (M) is identical to the conformation observed in the X-ray crystallographic structure, while the minor conformation (m) cannot structurally be resolved in detail by NMR due to insufficient NOE data. In the present study, we have applied: (1) rigid and adiabatic mapping, (2) free energy simulations, and (3) molecular dynamic simulations to elucidate the structure of the m conformer and to provide a possible pathway of the Trp21 side chain between the two conformers. Adiabatic energy mapping of conformations of the Trp21 side chain obtained by energy minimization identified two energy minima: One corresponding to the conformation of Trp21 observed in the X-ray crystallographic structure and solution structure of alpha3(VI) (the M conformation) and the second corresponding to the m conformation predicted by NMR spectroscopy. A transition pathway between the M and m conformation is suggested. The free-energy difference between the two conformers obtained by the thermodynamic integration method is calculated to 1.77+/-0.7 kcal/mol in favor of the M form, which is in good agreement with NMR results. Structural and dynamic properties of the major and minor conformers of the alpha3(VI) molecule were investigated by molecular dynamic. Essential dynamics analysis of the two resulting 800 ps trajectories reveals that when going from the M to the m conformation only small, localized changes in the protein structure are induced. However, notable differences are observed in the mobility of the binding loop (residues Thr13-Ile18), which is more flexible in the m conformation than in the M conformation. This suggests that the reorientation of Trp2 might influence the inhibitory activity against trypsin, despite the relative large distance between the binding loop and Trp21.     

Insight into the dynamic interaction between different flavonoids and bovine serum albumin using molecular dynamics simulations and free energy calculations

In this study, the binding of Bovine serum albumin (BSA) with three flavonoids, kaempferol-3-O-a-L-rhamnopyranosyl-(1–3)-a-L-rhamnopyranosyl-(1–6)-b-D-galacto- pyranoside (drug 1),kaempfol-7-O-rhamnosyl-3-O-rutinoside (drug 2)andkaempferide-7-O-(4”-O-acetylrhamnosyl)-3-O-ruti- noside (drug 3) is investigated by molecular docking, molecular dynamics (MD) simulation, and binding free energy calculation. The free energies are consistent with available experimental results and suggest that the binding site of BSA-drug1 is more stable than those of BSA-drug2 and BSA-drug3. The energy decomposition analysis is performed and reveals that the electrostatic interactions play an important role in the stabilization of the binding site of BSA-drug1 while the van der Waals interactions contribute largely to stabilization of the binding site of BSA-drug2 and BSA-drug3. The key residues stabilizing the binding sites of BSA-drug1, BSA-drug2 and BSA-drug3 are identified based on the residue decomposition analysis.     

Molecular dynamics simulations and free energy calculations of base flipping in dsRNA

The family of adenosine deaminases acting on RNA (ADARs) targets adenosines in RNA that is mainly double stranded. Some substrates are promiscuously deaminated whereas others, such as the mammalian glutamate receptor B (gluR-B) pre-mRNA, are more selectively deaminated. Many DNA/RNA-base modification enzymes use a base flipping mechanism to be able to reach their target base and it is believed that ADARs function in a similar way. In this study we used molecular dynamics (MD) simulations to describe two sites on the gluR-B pre-mRNA, the selectively targeted R/G site and the nontargeted 46 site, in an attempt to explain the substrate specificity. We used regular MD and also a forced base flipping method with umbrella sampling to calculate the free energy of base opening. Spontaneous opening of the mismatched adenosine was observed for the R/G site but not for the 46 site.     

Sensitivity of the folding/unfolding transition state ensemble of chymotrypsin inhibitor 2 to changes in temperature and solvent

To better characterize the transition state for folding/unfolding and its sensitivity to environmental changes, we have run multiple molecular dynamics simulations of chymotrypsin inhibitor 2 (CI2) under varying solvent conditions and temperature. The transition state structures agree well with experiment, and are similar under all of the conditions investigated here. Increasing the temperature leads to some movement in the position of the transition state along several reaction coordinates, as measured by changes in properties of the transition state structures. These structural changes are in the direction of a more native-like transition state as denaturation conditions become more severe, as expected for a Hammond effect. These structural changes are not, however, reflected in the global structure as measured by the total number of contacts or the average S-values. These results suggest that the small changes in average Phi-values with temperature seen by experiment may be due to an increase in the sensitivity of the transition state to mutation rather than a change in the average structure of the transition state. A simple analysis of the rates of unfolding indicates that the free energy barrier to unfolding decreases with increasing temperature, but even in our very high temperature simulations there is a small free energy barrier.     

Insights into the functional role of protonation states in the HIV-1 protease-BEA369 complex: molecular dynamics simulations and free energy calculations

The molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) method combined with molecular dynamics (MD) simulations were used to investigate the functional role of protonation in human immunodeficiency virus type 1 (HIV-1) protease complexed with the inhibitor BEA369. Our results demonstrate that protonation of two aspartic acids (Asp25/Asp25′) has a strong influence on the dynamics behavior of the complex, the binding free energy of BEA369, and inhibitor–residue interactions. Relative binding free energies calculated using the MM-PBSA method show that protonation of Asp25 results in the strongest binding of BEA369 to HIV-1 protease. Inhibitor–residue interactions computed by the theory of free energy decomposition also indicate that protonation of Asp25 has the most favorable effect on binding of BEA369. In addition, hydrogen-bond analysis based on the trajectories of the MD simulations shows that protonation of Asp25 strongly influences the water-mediated link of a conserved water molecule, Wat301. We expect that the results of this study will contribute significantly to binding calculations for BEA369, and to the design of high affinity inhibitors.     

CXC and CC chemokines form mixed heterodimers: association free energies from molecular dynamics simulations and experimental correlations

CXC and CC chemokines are involved in numerous biological processes, and their function in situ may be significantly influenced by heterodimer formation, as was recently reported, for example, for CXC chemokines CXCL4/PF4 and CXCL8/IL8 that interact to form heterodimers that modulate chemotactic and cell proliferation activities. Here we used molecular dynamics simulations to determine relative association free energies (overall average and per residue) for homo- and heterodimer pairs of CXC (CXCL4/PF4, CXCL8/IL8, CXCL1/Gro-alpha, and CXCL7/NAP-2) and CC (CCL5/RANTES, CCL2/MCP-1, and CCL8/MCP-2) chemokines. Even though structural homology among monomer folds of all CXC and CC chemokines permits heterodimer assembly, our calculated association free energies depend upon the particular pair of chemokines in terms of the net electrostatic and nonelectrostatic forces involved, as well as (for CC/CXC mixed chemokines) the selection of dimer type (CC or CXC). These relative free energies indicate that association of some pairs of chemokines is more favorable than others. Our approach is validated by correlation of calculated and experimentally determined free energies. Results are discussed in terms of CXC and CC chemokine function and have significant biological implications.     

Insight into the key active sites of afChiA1 based on molecular dynamics simulations and free energy calculations

In this study, the binding of the enzyme chitinase A1 (afChiA1) from the plant-type Aspergillus fumigatus with four potent inhibitors, allosamidin (ASM), acetazolamide (AZM), 8-chloro-theophylline (CTP) and kinetin (KIT) is investigated by molecular docking, molecular dynamics simulation and binding free energy calculation. The results reveal that the electrostatic interactions play an important role in the stabilisation of the binding of afChiA1 with inhibitors. Based on the binding energy of afChiA1-ligands, the key residues (Gln37 and Trp312) in the active binding pocket of the complex systems are confirmed by molecular mechanics/Poisson–Boltzmann surface area method, and the active inhibitors, ASM and AZM, both could form strong interaction with Gln37 and Trp312, and the non-active ligands, CTP and KIT, could not interact with these two residues, which is consistent with the result of experimental report. Then, it is identified that Gln37 and Trp312 should be one of the important active site residues of afChiA1.     

Binding free energies and free energy components from molecular dynamics and Poisson-Boltzmann calculations. Application to amino acid recognition by aspartyl-tRNA synthetase

Specific amino acid binding by aminoacyl-tRNA synthetases (aaRS) is necessary for correct translation of the genetic code. Engineering a modified specificity into aminoacyl-tRNA synthetases has been proposed as a means to incorporate artificial amino acid residues into proteins in vivo. In a previous paper, the binding to aspartyl-tRNA synthetase of the substrate Asp and the analogue Asn were compared by molecular dynamics free energy simulations. Molecular dynamics combined with Poisson-Boltzmann free energy calculations represent a less expensive approach, suitable for examining multiple active site mutations in an engineering effort. Here, Poisson-Boltzmann free energy calculations for aspartyl-tRNA synthetase are first validated by their ability to reproduce selected molecular dynamics binding free energy differences, then used to examine the possibility of Asn binding to native and mutant aspartyl-tRNA synthetase. A component analysis of the Poisson-Boltzmann free energies is employed to identify specific interactions that determine the binding affinities. The combined use of molecular dynamics free energy simulations to study one binding process thoroughly, followed by molecular dynamics and Poisson-Boltzmann free energy calculations to study a series of related ligands or mutations is proposed as a paradigm for protein or ligand design.The binding of Asn in an alternate, "head-to-tail" orientation observed in the homologous asparagine synthetase is analyzed, and found to be more stable than the "Asp-like" orientation studied earlier. The new orientation is probably unsuitable for catalysis. A conserved active site lysine (Lys198 in Escherichia coli) that recognizes the Asp side-chain is changed to a leucine residue, found at the corresponding position in asparaginyl-tRNA synthetase. It is interesting that the binding of Asp is calculated to increase slightly (rather than to decrease), while that of Asn is calculated, as expected, to increase strongly, to the same level as Asp binding. Insight into the origin of these changes is provided by the component analyses. The double mutation (K198L,D233E) has a similar effect, while the triple mutation (K198L,Q199E,D233E) reduces Asp binding strongly. No binding measurements are available, but the three mutants are known to have no ability to adenylate Asn, despite the "Asp-like" binding affinities calculated here. In molecular dynamics simulations of all three mutants, the Asn ligand backbone shifts by 1-2 A compared to the experimental Asp:AspRS complex, and significant side-chain rearrangements occur around the pocket. These could reduce the ATP binding constant and/or the adenylation reaction rate, explaining the lack of catalytic activity in these complexes. Finally, Asn binding to AspRS with neutral K198 or charged H449 is considered, and shown to be less favorable than with the charged K198 and neutral H449 used in the analysis.     

Exploring binding modes of the selected inhibitors to phosphodiesterase delta by all-atom molecular dynamics simulations and free energy calculations

It’s favorable to alter KRas mutation’s location to endomembrane by interfering the binding of PDEδ (the prenyl-binding protein phosphodiesterase delta) to KRas. In the present work, the binding of four inhibitors (Deltarasin, allyl analogue, pyrazolopyridazinone derivative, and Deltazinone 1) to PDEδ is investigated with all-atom Molecular Dynamic (MD) simulations. The binding free energy calculation results reveal that van der Waals (VDW) energy provides the major force for affinity binding. Moreover, the binding energy decomposition indicates that residues R61 and I129 provide important contributions to binding energies in all systems. The conserved hydrogen bonds play crucial roles in anchoring the inhibitors to the exact site for binding. The results for conformational analysis of PDEδ/free and PDEδ/inhibitors systems show that the structures are more stable after the inhibitors’ binding to the PDEδ. It is also found that the most unstable system among four complexes is PDEδ/pyrazolopyridazinone derivative system whose α3-helix formed by the residues P113-Q116 disappears. This study may provide valuable information for the design of high potency PDEδ inhibitors.

Communicated by Ramaswamy H. Sarma     

Prediction of zanamivir efficiency over the possible 2009 Influenza A (H1N1) mutants by multiple molecular dynamics simulations and free energy calculations

As one of the most important antiviral drugs against 2009 influenza A (H1N1), will zanamivir be effective for the possible drug resistant mutants? To answer this question, we combined multiple molecular dynamics simulations and molecular mechanics generalized Born surface area (MM-GBSA) calculations to study the efficiency of zanamivir over the most frequent drug-resistant strains of neuraminidase including R293K, R152K, E119A/D and H275Y mutants. The calculated results indicate that the modeled mutants of the 2009-H1N1 strains except H275Y will be significantly resistant to zanamivir. The resistance to zanamivir is mainly caused by the loss of polar interactions. The identified potential resistance sites in this study will be useful for the development of new effective anti-influenza drugs and to avoid the occurrence of the state without effective drugs to new mutant influenza strains.

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Figure The studied mutations of neuraminidase and their influence to zanamivir binding

     

Efficiency of a second-generation HIV-1 protease inhibitor studied by molecular dynamics and absolute binding free energy calculations

A subnanomolar inhibitor of human immunodeficiency virus type 1 (HIV-1) protease, designated QF34, potently inhibits the wild-type and drug-resistant enzyme. To explain its broad activity, the binding of QF34 to the wild-type HIV-1 protease is investigated by molecular dynamics simulations and compared to the binding of two inhibitors that are used clinically, saquinavir (SQV) and indinavir (IDV). Analysis of the flexibility of protease residues and inhibitor segments in the complex reveals that segments of QF34 were more mobile during the dynamics studies than the segments of SQV and IDV. The dynamics of hydrogen bonding show that QF34 forms a larger number of stable hydrogen bonds than the two inhibitors that are used clinically. Absolute binding free energies were calculated with molecular mechanics-generalized Born surface area (MM-GBSA) methodology using three protocols. The most consistent results were obtained using the single-trajectory approach, due to cancellation of errors and inadequate sampling in the separate-trajectory protocols. For all three inhibitors, energy components in favor of binding include van der Waals and electrostatic terms, whereas polar solvation and entropy terms oppose binding. Decomposition of binding energies reveals that more protease residues contribute significantly to the binding of QF34 than to the binding of SQV and IDV. Moreover, contributions from protease main chains and side chains are balanced in the case of QF34 (52:48 ratio, respectively), whereas side chain contributions prevail in both SQV and IDV (main-chain:side-chain ratios of 41:59 and 45:55, respectively). The presented results help explain the ability of QF34 to inhibit multiple resistant mutants and should be considered in the design of broad-specificity second-generation HIV-1 protease inhibitors.     

An efficient protocol for obtaining accurate hydration free energies using quantum chemistry and reweighting from molecular dynamics simulations

The non-Boltzmann Bennett (NBB) free energy estimator method is applied to 21 molecules from the blind subset of the SAMPL4 challenge. When NBB is applied with the SMD implicit solvent model, and the OLYP/DZP level of quantum chemistry, highly accurate hydration free energy calculations are obtained with respect to experiment (RMSD = 0.89 kcal·mol⁻¹). Other quantum chemical methods are also tested, and the effects of solvent model, density functional, basis set are explored in this benchmarking study, providing a framework for improvements in calculating hydration free energies. We provide a practical guide for using the best QM-NBB protocols that are consistently more accurate than either pure QM or pure MM alone. In situations where high accuracy hydration free energy predictions are needed, the QM-NBB method with SMD implicit solvent should be the first choice of quantum chemists.