Folding of a helix at room temperature is critically aided by electrostatic polarization of intraprotein hydrogen bonds

Building polarization into protein-inhibitor binding dynamics in rational drug design for rheumatoid arthritis

Standard force field-based simulations to accomplish structure-based evaluations of lead molecules is a powerful tool. Combining protein fragmentation into tractable sub-systems with continuum solvation method is envisaged to enable quantum mechanics-based electronic structure calculations of macromolecules in their realistic environment. This along with incorporation of many-body polarization effect in molecular dynamics simulations may augment an accurate description of electrostatics of protein-inhibitor systems for effective drug design. Rheumatoid arthritis (RA) is a complex autoimmune disorder plagued by the ceiling effect of current targeted therapies, encouraging identification of new druggable targets and corresponding drug design to tackle the refractory form of disease. In this study, polarization-inclusive force field approach has been used to model protein solvation and ligand binding for 'Mitogen-activated protein kinase' (MAP3K8), a regulatory node of notable pharmacological relevance in RA synovial biology. For MAP3K8 inhibitors belonging to different scaffold series, the calculations illustrated differential electrostatic contribution to their relative binding affinities and successfully explained examples from available structure-activity relationship studies. Results from this study exemplified i) the advantage of this approach in reliably ranking inhibitors having close nanomolar range activities for the same target; and ii) its prospective application in lead molecule identification aiding drug discovery efforts in RA.Communicated by Ramaswamy H. Sarma.

A study of ab initio folding of chignolins using replica-exchange molecular dynamics simulations

More and more studies have confirmed the importance of polarization effects in hydrogen bonding interactions in protein folding simulations. In this paper, a recently developed charge update scheme termed polarized structure-specific backbone charge (PSBC) model was applied to the folding of 10-residue chignolin. A comparison between simulations performed using PSBC and a nonpolarizable (AMBER99SB) force field demonstrably showed the importance of the electrostatic polarization effect in the folding of the short β-hairpin peptide by a series of analyses such as DSSP, free-energy landscape, hydrogen bond occupancy, and melting curve. The PSBC model was further validated by folding two other chignolin variants.

A fast-slow method to treat solute dynamics in explicit solvent

Aiming to reduce the computational cost in the current explicit solvent molecular dynamics (MD) simulation, this paper proposes a fast-slow method for the fast MD simulation of biomolecules in explicit solvent. This fast-slow method divides the entire system into two parts: a core layer (typically solute or biomolecule) and a peripheral layer (typically solvent molecules). The core layer is treated using standard MD method but the peripheral layer is treated by a slower dynamics method to reduce the computational cost. We compared four different simulation models in testing calculations for several small proteins. These include gas-phase, implicit solvent, fast-slow explicit solvent and standard explicit solvent MD simulations. Our study shows that gas-phase and implicit solvent models do not provide a realistic solvent environment and fail to correctly produce reliable dynamic structures of proteins. On the other hand, the fast-slow method can essentially reproduce the same solvent effect as the standard explicit solvent model while gaining an order of magnitude in efficiency. This fast-slow method thus provides an efficient approach for accelerating the MD simulation of biomolecules in explicit solvent.

The molecular docking and molecular dynamics study of flavonol synthase and flavonoid 3'-monooxygenase enzymes involved for the enrichment of kaempferol

Kaempferol is a natural flavonol that shows many pharmacological properties including anti-inflammatory, antioxidant, anticancer, antidiabetic activities etc. It has been reported in many vegetables, fruits, herbs and medicinal plants. The enzyme flavonol synthase (FLS, EC 1.14.20.6) catalyses the conversion of dihydroflavonols to flavonols. Whereas flavonoid 3'-monooxygenase (F3'H, EC 1.14.14.82) catalyses the hydroxylation of dihydroflavonol, and flavonol. FLS is involved in the synthesis of the kaempferol whereas F3'H causes degradation of kaempferol. The present study aimed to analyse the binding affinity, stability and activating activity of enzyme FLS as well as inhibitory activity of enzyme F3'H involved in the enrichment of the kaempferol using the in-silico approaches. Computational study for physico-chemical properties, conserved domain identification, 3-D structure prediction and its validation, conservation analysis, molecular docking followed by molecular dynamics analysis of FLS and F3'H, protein-activator (FLS-LIG Complex) and protein-inhibitor (F3'H-LIG Complex) complexes have been performed. Other structural analyses like root mean square fluctuation (RMSF), root mean square deviation (RMSD), surface area solvent accessibility (SASA), radius of gyration (Rg), hydrogen bond analysis, principal component analysis (PCA), Poisson-Boltzmann analysis (MM_PBSA) and the dynamic cross correlation map (DCCM) analysis to explore the structural, functional and thermodynamic stability of the proteins and the complexes were also studied. The molecular docking result showed that FLS binds strongly with the activator ascorbate (CID _54670067) while F3'H binds with the inhibitor ketoconazole (CID_456201). The most powerful inhibitor (ketoconazole for F3'H) and activator (ascorbate for FLS) is determined by computing the thermodynamic binding free energy through MM_PBSA analysis. The current work provides wide-ranging structural and functional information about FLS and F3'H enzymes showing detailed molecular mechanism of kaempferol biosynthesis and its degradation and hence kaempferol enrichment. Finding of the present work opens up new possibilities for future research towards enrichment of kaempferol by using activator (ascorbate) for FLS and inhibitor (ketoconazole) for F3'H as well as for its large-scale production using in vitro approaches.Communicated by Ramaswamy H. Sarma.

A Versatile Method for the End-Functionalization of Polycarbenes

End-functionalization is an effective strategy for constructing functional materials. A method for chain-end functionalization of helical polycarbenes is herein developed that relied on Sonogashira coupling reaction. In this work, a family of helical polycarbenes with controlled molecular mass (M_n ) and low polydispersity (M_w /M_n ) is readily prepared using Pd(II) and the Wei-Phos ligand as initiator. The Pd(II) complex is confirmed to remain at the chain end of polycarbene. Subsequently, a series of terminal alkyne derivatives with interesting functional groups, including the F atom, aldehyde, or anthracene groups, are synthesized. They could be installed at the chain end of polycarbene through Sonogashira coupling reaction catalyzed by the Pd(II) complex at the chain end. Moreover, a couple of hybrid block copolymers are easily obtained by installing terminal alkynes modified by another type of polymer. The structures of the isolated polymers are confirmed by ¹ H nuclear magnetic resonance (¹ H NMR), ¹⁹ F nuclear magnetic resonance (¹⁹ F NMR), ³¹ P nuclear magnetic resonance (³¹ P NMR), and Fourier transform infrared spectroscopy (FT-IR), respectively. The self-assembly properties of the hybrid block copolymers are also investigated by atomic force spectroscopy analysis. By the hereby developed method, various functional groups can be introduced at the chain end of helical polycarbenes for constructing functional polymer materials, moreover, the transition metal residues at the end of polymer chains can be easily removed.

A fixed multi-site interaction charge model for an accurate prediction of the QM/MM interactions

A fixed multi-site interaction charge (FMIC) model was proposed for the accurate prediction of intermolecular electrostatic interactions based on the quantum mechanical linear response of a molecule to an external electric field. In such a model, some additional off-center interaction sites were added for capturing multipole interactions for a given molecule. By multivariate least-square fitting analysis of the calculated QM/MM interactions of a given molecule with the electrostatic environment and the electrostatic potentials of the environment at the pre-defined distributed interaction sites, the FMIC of the molecule was obtained. The model system of CO in myoglobin (Mb) was utilized to demonstrate the derivation of the FMIC. The accuracy of FMIC in predicting the electrostatic interactions between CO and the Mb environment was investigated using 10 000 different Mb-CO configurations generated from the 400 ps QM/MM MD simulation. In comparison to the QM/MM calculations at the B3LYP/aug-cc-pVTZ/ff99SB level, the mean unsigned error (MUE) of the results based on the FMIC model was merely 0.10 kcal mol^-1, and the root mean square error (RMSE) was only 0.13 kcal mol^-1, which are significantly lower than the results predicted by the ESP charge model (MUE = 1.45 kcal mol^-1, and RMSE = 1.7 kcal mol^-1, respectively). The transferability of FMIC was tested by applying the obtained FMIC in the wild type Mb-CO system to the mutants of V68F and H64L Mb-CO systems. The MUEs of the obtained results for 10 000 different configurations are both smaller than 0.2 kcal mol^-1 for the V68F and H64L Mb-CO systems in comparison to the B3LYP/aug-cc-pVTZ/ff99SB calculations, and the RMSEs are also lower than 0.2 kcal mol^-1 for both mutants. The applications of FMIC were extended to model the electrostatic interactions between a hydrogen fluoride molecule and 492 waters in a truncated octahedron box; our study showed that the FMIC could give satisfactory results with a MUE of 0.12 kcal mol^-1 and a RMSE of 0.16 kcal mol^-1 in comparison to the B3LYP/aug-cc-pVDZ/TIP3P calculations for 10 000 different configurations generated using the 10 ns classical MD simulation. Therefore, the FMIC method provides an accurate and efficient tool for predicting intermolecular electrostatic interactions, which can be utilized in the future development of molecular force fields.

An electrostatic energy-based charge model for molecular dynamics simulation

The interactions of the polar chemical bonds such as C=O and N-H with an external electric field were investigated, and a linear relationship between the QM/MM interaction energies and the electric field along the chemical bond is established in the range of weak to intermediate electrical fields. The linear relationship indicates that the electrostatic interactions of a polar group with its surroundings can be described by a simple model of a dipole with constant moment under the action of an electric field. This relationship is employed to develop a general approach to generating an electrostatic energy-based charge (EEC) model for molecules containing single or multiple polar chemical bonds. Benchmark test studies of this model were carried out for (CH₃)₂-CO and N-methyl acetamide in explicit water, and the result shows that the EEC model gives more accurate electrostatic energies than those given by the widely used charge model based on fitting to the electrostatic potential (ESP) in direct comparison to the energies computed by the QM/MM method. The MD simulations of the electric field at the active site of ketosteroid isomerase based on EEC demonstrated that EEC gave a better representation of the electrostatic interaction in the hydrogen-bonding environment than the Amber14SB force field by comparison with experiment. The current study suggests that EEC should be better suited for molecular dynamics study of molecular systems with polar chemical bonds such as biomolecules than the widely used ESP or RESP (restrained ESP) charge models.

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.

QM Implementation in Drug Design: Does It Really Help?

Computational chemistry allows one to characterize the structure, dynamics, and energetics of protein-ligand interactions, which makes it a valuable tool in drug discovery in both academic research and pharmaceutical industry. Molecular mechanics (MM)-based approaches are widely utilized to assist the discovery of new drug candidates. However, the complexity of protein-ligand interactions challenges the accuracy and efficiency of the commonly used empirical methods. Aiming to provide better accuracy in the description of protein-ligand interactions, quantum mechanics (QM)-based approaches are becoming increasingly explored. In principle, QM calculation includes all contributions to the energy, accounting for terms usually missing in empirical force fields, and provides a greater degree of transferability. The usefulness of QM in drug design cannot be overemphasized. In this chapter, we present recent developments and applications of fragment-based QM method in studying the protein-ligand and protein-protein interactions. We critically discuss the performance of the fragment-based QM method at different ab initio levels while trying to answer a critical question: do QM-based methods really help in drug design?

Incorporating Polarizability of Backbone Hydrogen Bonds Improved Folding of Short α-Helical Peptides

Reliability of force fields is an essential aspect of protein-folding simulation. In this work, we introduced a newly developed on-the-fly charge-updating scheme called the polarized structure-specific backbone charge (PSBC) model. The PSBC model was designed with the purpose of building the polarizability of backbone hydrogen bonds into the force field by updating the partial charges of backbone hydrogen-bond donor and acceptor atoms during folding simulation. This implementation was intended to mimic the heterogeneity of the protein surrounding during folding. Multiple single-trajectory molecular dynamics simulations were performed to fold a polyalanine peptide, namely ER (Ac-A(EAAAR)₃A-NH₂), using both polarizable (PSBC) and nonpolarizable (Amber03) force fields. Through the PSBC model, ER was folded into a helical peptide with helix content that agrees well with experiments. Comparison between simulations performed using the aforementioned force fields demonstrably showed the importance of electrostatic polarization effect in the folding of the short α-helical peptide. The PSBC model was further validated by folding two other short peptides with different helicities.

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.

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. This work explored the origin of the resistance mechanism of the ALK mutants again two inhibitors.

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.

An Ab Initio QM/MM Study of the Electrostatic Contribution to Catalysis in the Active Site of Ketosteroid Isomerase

The electric field in the hydrogen-bond network of the active site of ketosteroid isomerase (KSI) has been experimentally measured using vibrational Stark effect (VSE) spectroscopy, and utilized to study the electrostatic contribution to catalysis. A large gap was found in the electric field between the computational simulation based on the Amber force field and the experimental measurement. In this work, quantum mechanical (QM) calculations of the electric field were performed using an ab initio QM/MM molecular dynamics (MD) simulation and electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method. Our results demonstrate that the QM-derived electric field based on the snapshots from QM/MM MD simulation could give quantitative agreement with the experiment. The accurate calculation of the electric field inside the protein requires both the rigorous sampling of configurations, and a QM description of the electrostatic field. Based on the direct QM calculation of the electric field, we theoretically confirmed that there is a linear correlation relationship between the activation free energy and the electric field in the active site of wild-type KSI and its mutants (namely, D103N, Y16S, and D103L). Our study presents a computational protocol for the accurate simulation of the electric field in the active site of the protein, and provides a theoretical foundation that supports the link between electric fields and enzyme catalysis.

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.

A Force Balanced Fragmentation Method for ab Initio Molecular Dynamic Simulation of Protein

A force balanced generalized molecular fractionation with conjugate caps (FB-GMFCC) method is proposed for ab initio molecular dynamic simulation of proteins. In this approach, the energy of the protein is computed by a linear combination of the QM energies of individual residues and molecular fragments that account for the two-body interaction of hydrogen bond between backbone peptides. The atomic forces on the caped H atoms were corrected to conserve the total force of the protein. Using this approach, ab initio molecular dynamic simulation of an Ace-(ALA)₉-NME linear peptide showed the conservation of the total energy of the system throughout the simulation. Further a more robust 110 ps ab initio molecular dynamic simulation was performed for a protein with 56 residues and 862 atoms in explicit water. Compared with the classical force field, the ab initio molecular dynamic simulations gave better description of the geometry of peptide bonds. Although further development is still needed, the current approach is highly efficient, trivially parallel, and can be applied to ab initio molecular dynamic simulation study of large proteins.

A quantum mechanical computational method for modeling electrostatic and solvation effects of protein

An efficient computational approach for modeling protein electrostatic is developed according to static point-charge model distributions based on the linear-scaling EE-GMFCC (electrostatically embedded generalized molecular fractionation with conjugate caps) quantum mechanical (QM) method. In this approach, the Electrostatic-Potential atomic charges are obtained from ab initio calculation of protein, both polarization and charge transfer effect are taken into consideration. This approach shows a significant improvement in the description of electrostatic potential and solvation energy of proteins comparing with current popular molecular mechanics (MM) force fields. Therefore, it has gorgeous prospect in many applications, including accurate calculations of electric field or vibrational Stark spectroscopy in proteins and predicting protein-ligand binding affinity. It can also be applied in QM/MM calculations or electronic embedding method of ONIOM to provide a better electrostatic environment.

Zinc ion-induced conformational changes in new Delphi metallo-β-lactamase 1 probed by molecular dynamics simulations and umbrella sampling

The hydrolysis of a β-lactam core ring caused by new Delphi metallo-β-lactamase 1 (NDM-1) with the help of two zinc cofactors induces significant resistance toward β-lactam antibiotics. Molecular dynamics (MD) simulations and the umbrella sampling method are integrated to study the conformational change mechanism of NDM-1 mediated by zinc ion binding. The statistical analyses of interaction contacts of the antibiotic ampicillin (AMP) with residues based on MD trajectories suggest that two Zn ions are essential for maintaining the binding of AMP with NDM-1. Umbrella sampling simulations further reveal that double-Zn coordination exerts strong restriction on the motions of loop L10 relative to loops L3 and L4. Principal component (PC) analysis also demonstrates that zinc ion binding totally inhibits the motion extent of NDM-1 and changes internal motion modes in NDM-1. We expect that the current study can provide significant dynamical information involving conformational changes of NDM-1 for the development of efficient inhibitors to decrease drug resistance of NDM-1 toward antibiotics.

Computational Study of PCSK9-EGFA Complex with Effective Polarizable Bond Force Field

Inhibiting of Proprotein Convertase Subtilisin/Kexin-type 9 (PCSK9) and Low Density Lipoprotein Receptor (LDLR) binding is an effective way for reducing Low Density Lipoprotein cholesterol (LDL-C). Understanding the interaction between PCSK9 and LDLR is useful for PCSK9 inhibitor design. In this work, MD simulations with the standard (non-polarizable) AMBER force field and effective polarizable bond (EPB) force field were performed for wild type and four mutants of PCSK9 and EGFA (Epidermal Growth Factor-like repeat A) domain of LDLR complexes. These four mutants are gain-of-function mutants. The analysis of hydrogen bond dynamics and the relative binding free energy indicates that EPB is more reliable in simulating protein dynamics and predicting relative binding affinity. Structures sampled from MD simulations with the standard AMBER force field deviate too far away from crystal structures. Many important interaction components between of PCSK9 and EGFA no longer exist in the simulation with the Amber force field. For comparison, simulation using EPB force field gives more stable structures as shown by hydrogen bond analysis and produced relative binding free energies that are consistent with experimental results. Our study suggests that inclusion of polarization effects in MD simulation is important for studying the protein-protein interaction.

Validation of Molecular Dynamics Simulations for Prediction of Three-Dimensional Structures of Small Proteins

Although various higher-order protein structure prediction methods have been developed, almost all of them were developed based on the three-dimensional (3D) structure information of known proteins. Here we predicted the short protein structures by molecular dynamics (MD) simulations in which only Newton’s equations of motion were used and 3D structural information of known proteins was not required. To evaluate the ability of MD simulationto predict protein structures, we calculated seven short test protein (10–46 residues) in the denatured state and compared their predicted and experimental structures. The predicted structure for Trp-cage (20 residues) was close to the experimental structure by 200-ns MD simulation. For proteins shorter or longer than Trp-cage, root-mean square deviation values were larger than those for Trp-cage. However, secondary structures could be reproduced by MD simulations for proteins with 10–34 residues. Simulations by replica exchange MD were performed, but the results were similar to those from normal MD simulations. These results suggest that normal MD simulations can roughly predict short protein structures and 200-ns simulations are frequently sufficient for estimating the secondary structures of protein (approximately 20 residues). Structural prediction method using only fundamental physical laws are useful for investigating non-natural proteins, such as primitive proteins and artificial proteins for peptide-based drug delivery systems.

Significantly Improved Protein Folding Thermodynamics Using a Dispersion-Corrected Water Model and a New Residue-Specific Force Field

An accurate potential energy model is crucial for biomolecular simulations. Despite many recent improvements of classical protein force fields, there are remaining key issues: much weaker temperature dependence of folding/unfolding equilibrium and overly collapsed unfolded or disordered states. For the latter problem, a new water model (TIP4P-D) has been proposed to correct the significantly underestimated water dispersion interactions. Here, using TIP4P-D, we reveal problems in current force fields through failures in folding model systems (a polyalanine peptide, Trp-cage, and the GB1 hairpin). By using residue-specific parameters to achieve better match between amino acid sequences and native structures and adding a small H-bond correction to partially compensate the missing many-body effects in α-helix formation, the new RSFF2+ force field with the TIP4P-D water model can excellently reproduce experimental melting curves of both α-helical and β-hairpin systems. The RSFF2+/TIP4P-D method also gives less collapsed unfolded structures and describes well folded proteins simultaneously.

Effect of polarization on HIV-1protease and fluoro-substituted inhibitors binding energies by large scale molecular dynamics simulations

Molecular dynamics simulations in explicit water are carried out to study the binding of six inhibitors to HIV-1 protease (PR) for up to 700 ns using the standard AMBER force field and polarized protein-specific charge (PPC). PPC is derived from quantum mechanical calculation for protein in solution and therefore it includes electronic polarization effect. Our results show that in all six systems, the bridging water W301 drifts away from the binding pocket in AMBER simulation. However, it is very stable in all six complexes systems using PPC. Especially, intra-protease, protease-inhibitor hydrogen bonds are dynamic stabilized in MD simulation. The computed binding free energies of six complexes have a significantly linear correlation with those experiment values and the correlation coefficient is found to be 0.91 in PPC simulation. However, the result from AMBER simulation shows a weaker correlation with the correlation coefficient of −0.51 due to the lack of polarization effect. Detailed binding interactions of W301, inhibitors with PR are further analyzed and discussed. The present study provides important information to quantitative understanding the interaction mechanism of PR-inhibitor and PR-W301 and these data also emphasizes the importance of both the electronic polarization and the bridging water molecule in predicting precisely binding affinities.

Direct folding simulation of helical proteins using an effective polarizable bond force field

Snapshots of the intermediate conformation of Trp-cage at various simulation times using AMBER03, EPB03, AMBER12SB, and EPB12SB. Here, the N terminal is always on the top.

Effect of electrostatic polarization and bridging water on CDK2–ligand binding affinities calculated using a highly efficient interaction entropy method

A new highly efficient interaction entropy (IE) method combined with the polarized protein-specific charge (PPC) force field is employed to investigate the interaction mechanism of CDK2–ligand binding and the effect of the bridging water.

Mechanism of Phosphorylation-Induced Folding of 4E-BP2 Revealed by Molecular Dynamics Simulations

Site-specific phosphorylation of an intrinsically disordered protein, eIF4E-binding protein isoform 2 (4E-BP2), can suppress its native function by folding it into a four-stranded β-sheet, but the mechanism of this phosphorylation-induced folding is unclear. In this work, we use all-atom molecular dynamics simulations to investigate both the folded and unfolded states of 4E-BP2 under different phosphorylation states of T37 and T46. The results show that the phosphorylated forms of both T37 and T46 play important roles in stabilizing the folded structure, especially for the β-turns and the sequestered binding motif. The phosphorylated residues not only guide the folding of the protein through several intermediate states but also affect the conformational distribution of the unfolded ensemble. Significantly, the phosphorylated residues can function as nucleation sites for the folding of the protein by forming certain local structures that are stabilized by hydrogen bonding involving the phosphate group. The region around phosphorylated T46 appears to fold before that around phosphorylated T37. These findings provide new insight into the intricate effects of protein phosphorylation.

Large-scale molecular dynamics simulation: Effect of polarization on thrombin-ligand binding energy

Molecular dynamics (MD) simulations lasting 500 ns were performed in explicit water to investigate the effect of polarization on the binding of ligands to human α-thrombin based on the standard nonpolarizable AMBER force field and the quantum-derived polarized protein-specific charge (PPC). The PPC includes the electronic polarization effect of the thrombin-ligand complex, which is absent in the standard force field. A detailed analysis and comparison of the results of the MD simulation with experimental data provided strong evidence that intra-protein, protein-ligand hydrogen bonds and the root-mean-square deviation of backbone atoms were significantly stabilized through electronic polarization. Specifically, two critical hydrogen bonds between thrombin and the ligand were broken at approximately 190 ns when AMBER force field was used and the number of intra-protein backbone hydrogen bonds was higher under PPC than under AMBER. The thrombin-ligand binding energy was computed using the molecular mechanics Poisson-Boltzmann surface area (MM/PBSA) method, and the results were consistent with the experimental value obtained using PPC. Because hydrogen bonds were unstable, it was failed to predict the binding affinity under the AMBER force field. Furthermore, the results of the present study revealed that differences in the binding free energy between AMBER and PPC almost comes from the electrostatic interaction. Thus, this study provides evidence that protein polarization is critical to accurately describe protein-ligand binding.

Folding Simulations of an α-Helical Hairpin Motif αtα with Residue-Specific Force Fields

α-Helical hairpin (two-helix bundle) is a structure motif composed of two interacting helices connected by a turn or a short loop. It is an important model for protein folding studies, filling the gap between isolated α-helix and larger all-α domains. Here, we present, for the first time, successful folding simulations of an α-helical hairpin. Our RSFF1 and RSFF2 force fields give very similar predicted structures of this αtα peptide, which is in good agreement with its NMR structure. Our simulations also give site-specific stability of α-helix formation in good agreement with amide hydrogen exchange experiments. Combining the folding free energy landscapes and analyses of structures sampled in five different ranges of the fraction of native contacts (Q), a folding mechanism of αtα is proposed. The most stable sites of Q9-E15 in helix-1 and E24-A30 in helix-2 close to the loop region act as the folding initiation sites. The formation of interhelix side-chain contacts also initiates near the loop region, but some residues in the central parts of the two helices also form contacts quite early. The two termini fold at a final stage, and the loop region remains flexible during the whole folding process. This mechanism is similar to the "zipping out" pathway of β-hairpin folding.

A new algorithm for construction of coarse-grained sites of large biomolecules

The development of coarse-grained (CG) models for large biomolecules remains a challenge in multiscale simulations, including a rigorous definition of CG representations for them. In this work, we proposed a new stepwise optimization imposed with the boundary-constraint (SOBC) algorithm to construct the CG sites of large biomolecules, based on the s cheme of essential dynamics CG. By means of SOBC, we can rigorously derive the CG representations of biomolecules with less computational cost. The SOBC is particularly efficient for the CG definition of large systems with thousands of residues. The resulted CG sites can be parameterized as a CG model using the normal mode analysis based fluctuation matching method. Through normal mode analysis, the obtained modes of CG model can accurately reflect the functionally related slow motions of biomolecules. The SOBC algorithm can be used for the construction of CG sites of large biomolecules such as F-actin and for the study of mechanical properties of biomaterials.

Probing Origin of Binding Difference of inhibitors to MDM2 and MDMX by Polarizable Molecular Dynamics Simulation and QM/MM-GBSA Calculation

Binding abilities of current inhibitors to MDMX are weaker than to MDM2. Polarizable molecular dynamics simulations (MD) followed by Quantum mechanics/molecular mechanics generalized Born surface area (QM//MM-GBSA) calculations were performed to investigate the binding difference of inhibitors to MDM2 and MDMX. The predicted binding free energies not only agree well with the experimental results, but also show that the decrease in van der Walls interactions of inhibitors with MDMX relative to MDM2 is a main factor of weaker bindings of inhibitors to MDMX. The analyses of dihedral angles based on MD trajectories suggest that the closed conformation formed by the residues M53 and Y99 in MDMX leads to a potential steric clash with inhibitors and prevents inhibitors from arriving in the deep of MDMX binding cleft, which reduces the van der Waals contacts of inhibitors with M53, V92, P95 and L98. The calculated results using the residue-based free energy decomposition method further prove that the interaction strength of inhibitors with M53, V92, P95 and L98 from MDMX are obviously reduced compared to MDM2. We expect that this study can provide significant theoretical guidance for designs of potent dual inhibitors to block the p53-MDM2/MDMX interactions.

Quantum Fragment Based ab Initio Molecular Dynamics for Proteins

Developing ab initio molecular dynamics (AIMD) methods for practical application in protein dynamics is of significant interest. Due to the large size of biomolecules, applying standard quantum chemical methods to compute energies for dynamic simulation is computationally prohibitive. In this work, a fragment based ab initio molecular dynamics approach is presented for practical application in protein dynamics study. In this approach, the energy and forces of the protein are calculated by a recently developed electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method. For simulation in explicit solvent, mechanical embedding is introduced to treat protein interaction with explicit water molecules. This AIMD approach has been applied to MD simulations of a small benchmark protein Trpcage (with 20 residues and 304 atoms) in both the gas phase and in solution. Comparison to the simulation result using the AMBER force field shows that the AIMD gives a more stable protein structure in the simulation, indicating that quantum chemical energy is more reliable. Importantly, the present fragment-based AIMD simulation captures quantum effects including electrostatic polarization and charge transfer that are missing in standard classical MD simulations. The current approach is linear-scaling, trivially parallel, and applicable to performing the AIMD simulation of proteins with a large size.

Correct folding of an α-helix and a β-hairpin using a polarized 2D torsional potential

A new modification to the AMBER force field that incorporates the coupled two-dimensional main chain torsion energy has been evaluated for the balanced representation of secondary structures. In this modified AMBER force field (AMBER03(2D)), the main chain torsion energy is represented by 2-dimensional Fourier expansions with parameters fitted to the potential energy surface generated by high-level quantum mechanical calculations of small peptides in solution. Molecular dynamics simulations are performed to study the folding of two model peptides adopting either α-helix or β-hairpin structures. Both peptides are successfully folded into their native structures using an AMBER03(2D) force field with the implementation of a polarization scheme (AMBER03(2D)p). For comparison, simulations using a standard AMBER03 force field with and without polarization, as well as AMBER03(2D) without polarization, fail to fold both peptides successfully. The correction to secondary structure propensity in the AMBER03 force field and the polarization effect are critical to folding Trpzip2; without these factors, a helical structure is obtained. This study strongly suggests that this new force field is capable of providing a more balanced preference for helical and extended conformations. The electrostatic polarization effect is shown to be indispensable to the growth of secondary structures.

Numerical study on the partitioning of the molecular polarizability into fluctuating charge and induced atomic dipole contributions

In order to carry out a detailed analysis of the molecular static polarizability, which is the response of the molecule to a uniform external electric field, the molecular polarizability was computed using the finite-difference method for 21 small molecules, using density functional theory. Within nine charge population schemes (Löwdin, Mulliken, Becke, Hirshfeld, CM5, Hirshfeld-I, NPA, CHELPG, MK-ESP) in common use, the charge fluctuation contribution is found to dominate the molecular polarizability, with its ratio ranging from 59.9% with the Hirshfeld or CM5 scheme to 96.2% with the Mulliken scheme. The Hirshfeld-I scheme is also used to compute the other contribution to the molecular polarizability coming from the induced atomic dipoles, and the atomic polarizabilities in eight small molecules and water pentamer are found to be highly anisotropic for most atoms. Overall, the results suggest that (a) more emphasis probably should be placed on the charge fluctuation terms in future polarizable force field development and (b) an anisotropic polarizability might be more suitable than an isotropic one in polarizable force fields based entirely or partially on the induced atomic dipoles.

Intermediate electrostatic field for the generalized elongation method

An intermediate electrostatic field is introduced to improve the accuracy of fragment-based quantum-chemical computational methods by including long-range polarizations of biomolecules. The point charge distribution of the intermediate field is generated by a charge sensitivity analysis that is parameterized for five different population analyses, namely, atoms-in-molecules, Hirshfeld, Mulliken, natural orbital, and Voronoi population analysis. Two model systems are chosen to demonstrate the performance of the generalized elongation method (ELG) combined with the intermediate electrostatic field. The calculations are performed for the STO-3G, 6-31G, and 6-31G(d) basis sets and compared with reference Hartree-Fock calculations. It is shown that the error in the total energy is reduced by one order of magnitude, independently of the population analyses used. This demonstrates the importance of long-range polarization in electronic-structure calculations by fragmentation techniques.

A comparative study of trypsin specificity based on QM/MM molecular dynamics simulation and QM/MM GBSA calculation

Hydrogen bonding and polar interactions play a key role in identification of protein-inhibitor binding specificity. Quantum mechanics/molecular mechanics molecular dynamics (QM/MM MD) simulations combined with DFT and semi-empirical Hamiltonian (AM1d, RM1, PM3, and PM6) methods were performed to study the hydrogen bonding and polar interactions of two inhibitors BEN and BEN1 with trypsin. The results show that the accuracy of treating the hydrogen bonding and polar interactions using QM/MM MD simulation of PM6 can reach the one obtained by the DFT QM/MM MD simulation. Quantum mechanics/molecular mechanics generalized Born surface area (QM/MM-GBSA) method was applied to calculate binding affinities of inhibitors to trypsin and the results suggest that the accuracy of binding affinity prediction can be significantly affected by the accurate treatment of the hydrogen bonding and polar interactions. In addition, the calculated results also reveal the binding specificity of trypsin: (1) the amidinium groups of two inhibitors generate favorable salt bridge interaction with Asp189 and form hydrogen bonding interactions with Ser190 and Gly214, (2) the phenyl of inhibitors can produce favorable van der Waals interactions with the residues His58, Cys191, Gln192, Trp211, Gly212, and Cys215. This systematic and comparative study can provide guidance for the choice of QM/MM MD methods and the designs of new potent inhibitors targeting trypsin.