Polarized Protein-specific Charge Research Articles

Fragment Quantum Mechanical Method for Excited States of Proteins: Development and Application to the Green Fluorescent Protein.

Understanding the excited-state properties of luminescent biomolecules is of central importance to their biophysical applications. In this study, we develop the Electrostatically Embedded Generalized Molecular Fractionation with Conjugate Caps (EE-GMFCC) method for quantitatively characterizing properties of covalently bonded systems with localized excitations (i.e., involving a single chromophore), such as fluorescent proteins. The excitation energy, transition dipole moment, and oscillator strength of wild-type Green Fluorescent Protein (wt-GFP) calculated by EE-GMFCC are found to be in excellent agreement with full system time-dependent density functional theory results. We also applied the Polarized Protein-Specific Charge model to wt-GFP, and found that electronic polarization of the protein is critical in stabilizing hydrogen bonding interactions in wt-GFP, which influences its absorption spectrum. The predicted absorption spectra of wt-GFP in the A and B states qualitatively agree with experiment. The fragmentation approach further allows a straightforward per residue decomposition of the excitation which reveals the influence of the protein environment on the absorption spectra of wt-GFP A and B states. Our results demonstrate that the EE-GMFCC method is both accurate and efficient for excited-state property calculations on proteins.

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.

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

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

Influence of the Protein Environment on the Electronic Excitation of Chromophores in the Phycoerythrin 545 Light-Harvesting Complex: A Combined MD-QM/MM Method with Polarized Protein-Specific Charge Scheme.

To gain better insight into how the fluctuating protein environment influences the site energy ordering of the chromophores in PE545 light-harvesting antenna system, we carried out quantum mechanics/molecular mechanics (QM/MM) calculations along the molecular dynamics (MD) trajectory. The Polarized Protein-Specific Charge (PPC) scheme was adopted in both the MD simulation and the QM/MM calculations for a more realistic description of the protein environment. The deduced site energy ladder calculated using ZINDO/S-CIS agrees well with the best model extracted from experiments by a simultaneous fit of the steady-state spectra and transient absorption spectra. Three combinations of charge schemes were compared to elucidate how the protein environment modulates the site energy of chromophores. The result indicates that the multiroles that the protein environment is playing, for instance, by fine-tuning of the conformation of chromophores or by specific pigment-protein interactions, are both crucial for site energy arrangement. Furthermore, we investigated the effects of individual environments and found that the polar residues and water molecules contribute most to the energy shifts.

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.

Trypsin-Ligand binding affinities calculated using an effective interaction entropy method under polarized force field

Molecular dynamics (MD) simulation in the explicit water is performed to study the interaction mechanism of trypsin-ligand binding under the AMBER force field and polarized protein-specific charge (PPC) force field combined the new developed highly efficient interaction entropy (IE) method for calculation of entropy change. And the detailed analysis and comparison of the results of MD simulation for two trypsin-ligand systems show that the root-mean-square deviation (RMSD) of backbone atoms, B-factor, intra-protein and protein-ligand hydrogen bonds are more stable under PPC force field than AMBER force field. Our results demonstrate that the IE method is superior than the traditional normal mode (Nmode) method in the calculation of entropy change and the calculated binding free energy under the PPC force field combined with the IE method is more close to the experimental value than other three combinations (AMBER-Nmode, AMBER-IE and PPC-Nmode). And three critical hydrogen bonds between trypsin and ligand are broken under AMBER force field. However, they are well preserved under PPC force field. Detailed binding interactions of ligands with trypsin are further analyzed. The present work demonstrates that the polarized force field combined the highly efficient IE method is critical in MD simulation and free energy calculation.

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.

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. Our result shows that the computed binding free energies for five CDK2-ligand complexes using the IE method have a significantly linear correlation with the experimentally measured values with a correlation coefficient of 0.98 in consideration of the bridging water under the PPC force field. And the correlation coefficient is found to be slightly weaker with a value of 0.95 using the traditional normal mode (Nmode) method for calculation of entropy change. Importantly, the rank of the predicted binding free energies is significantly consistent with the experimental rank based on the IE method calculated entropy change using the PPC force field. However, without including the bridging water under PPC simulation, the correlation coefficient is below 0.83. For comparison, the result obtained from the simulation using the nonpolarized AMBER force field gives a much weaker correlation with the correlation coefficients of 0.44 and 0.45 using the Nmode method and IE method, due to the lack of electrostatic polarization. Furthermore, hydrogen bond analysis indicates that the bridging water makes a significant contribution to mediating the hydrogen bond network of protein-ligand binding and stabilizing the complex structure. The current study demonstrates that the new IE method is superior to the standard Nmode method in computing the binding free energy. And our results also emphasize the importance of electronic polarization and bridging water in MD simulations and free energy calculations.

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.

Hybrid QM/MM study of FMO complex with polarized protein-specific charge.

The Fenna-Matthews-Olson (FMO) light-harvesting complex is now one of the primary model systems for the study of excitation energy transfer (EET). However, the mechanism of the EET in this system is still controversial. In this work, molecular dynamics simulations and the electrostatic-embedding quantum-mechanics/molecular-mechanics single-point calculations have been employed to predict the energy transfer pathways utilizing the polarized protein-specific charge (PPC), which provides a more realistic description of Coulomb interaction potential in the protein than conventional mean-field charge scheme. The recently discovered eighth pigment has also been included in this study. Comparing with the conventional mean-field charges, more stable structures of FMO complex were found under PPC scheme during molecular dynamic simulation. Based on the electronic structure calculations, an exciton model was constructed to consider the couplings during excitation. The results show that pigments 3 and 4 dominate the lowest exciton levels whereas the highest exciton level are mainly constituted of pigments 1 and 6. This observation agrees well with the assumption based on the spatial distribution of the pigments. Moreover, the obtained spectral density in this study gives a reliable description of the diverse local environment embedding each pigment.

Molecular Dynamics Simulation of Protein Crystal with Polarized Protein-Specific Charge

The polarized force field model is indispensable in the simulation of protein crystal due to the particular electrostatic environment which is different from water solution or membrane. The polarized protein-specific charge (PPC) is fitted from in situ linear scaling quantum mechanical calculations of protein. The atomic charge for each residue is determined by its conformation and its location in the protein. Therefore, it gives a more accurate delineation of charge distribution in protein than the mean-field charge schemes in pairwise force fields do. Two 250 ns molecular simulations are carried out to study the structure and dynamics of crystal toxin protein II from the scorpion Androctonus australis Hector employing PPC, as well as the standard AMBER99SB force field, to investigate the effect of electrostatic polarization on the simulated crystal stability. Results show that PPC provides more reliable description of the monomers in the unit cell as well as the lattice in supercell with much smaller RMSDs and more realistic lattice atomic fluctuations. Most of the interactions at the interfaces among the protein units in the X-ray structure are well preserved, underscoring the important effect of polarization on maintaining the crystal stability.

Molecular dynamics simulation of protein crystal with polarized protein-specific force field.

Two 250 ns molecular simulations have been carried out to study the structure and dynamics of crystal toxin protein II from the scorpion Androctonus australis Hector employing the polarized protein-specific charge (PPC), as well as the standard AMBER99SB force field, to investigate the electrostatic polarization on the simulated crystal stability. Results show that under PPC, the monomers in unit cell as well as the lattice in supercell are more stable with smaller root-mean-square deviations and more accurate lattice atomic fluctuations compared with the crystallographic B-factors than under AMBER99SB force field. Most of the interactions at interfaces in the X-ray structure are quite well-preserved, underscoring the important effect of polarization on maintaining the crystal stability. However, the results also show that the hydrogen bond between Asp53 and Gln37 and the cation-π interaction between Arg56 and His64 are not stable, indicating that further optimization of force field, especially the van der Waals interaction parameters, is desired.

Correction of erroneously packed protein's side chains in the NMR structure based on ab initio chemical shift calculations.

In this work, protein side chain (1)H chemical shifts are used as probes to detect and correct side-chain packing errors in protein's NMR structures through structural refinement. By applying the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) method for ab initio calculation of chemical shifts, incorrect side chain packing was detected in the NMR structures of the Pin1 WW domain. The NMR structure is then refined by using molecular dynamics simulation and the polarized protein-specific charge (PPC) model. The computationally refined structure of the Pin1 WW domain is in excellent agreement with the corresponding X-ray structure. In particular, the use of the PPC model yields a more accurate structure than that using the standard (nonpolarizable) force field. For comparison, some of the widely used empirical models for chemical shift calculations are unable to correctly describe the relationship between the particular proton chemical shift and protein structures. The AF-QM/MM method can be used as a powerful tool for protein NMR structure validation and structural flaw detection.

Some Practical Approaches to Treating Electrostatic Polarization of Proteins

Conspectus Electrostatic interaction plays a significant role in determining many properties of biomolecules, which exist and function in aqueous solution, a highly polar environment. For example, proteins are composed of amino acids with charged, polar, and nonpolar side chains and their specific electrostatic properties are fundamental to the structure and function of proteins. An important issue that arises in computational study of biomolecular interaction and dynamics based on classical force field is lack of polarization. Polarization is a phenomenon in which the charge distribution of an isolated molecule will be distorted when interacting with another molecule or presented in an external electric field. The distortion of charge distribution is intended to lower the overall energy of the molecular system, which is counter balanced by the increased internal energy of individual molecules due to the distorted charge distributions. The amount of the charge redistribution, which characterizes the polarizability of a molecule, is determined by the level of the charge distortion. Polarization is inherently quantum mechanical, and therefore classical force fields with fixed atomic charges are incapable of capturing this important effect. As a result, simulation studies based on popular force fields, AMBER, CHARMM, etc., lack the polarization effect, which is a widely known deficiency in most computational studies of biomolecules today. Many efforts have been devoted to remedy this deficiency, such as adding additional movable charge on the atom, allowing atomic charges to fluctuate, or including induced multipoles. Although various successes have been achieved and progress at various levels has been reported over the past decades, the issue of lacking polarization in force field based simulations is far from over. For example, some of these methods do not always give converged results, and other methods require huge computational cost. This Account reviews recent work on developing polarized and polarizable force fields based on fragment quantum mechanical calculations for proteins. The methods described here are based on quantum mechanical calculations of proteins in solution, but with a different level of rigor and different computational efficiency for the molecular dynamics applications. In the general approach, a fragment quantum mechanical calculation for protein with implicit solvation is carried out to derive a polarized protein-specific charge (PPC) for any given protein structure. The PPC correctly reflects the polarization state of the protein in a given conformation, and it can also be dynamically changed as the protein changes conformation in dynamics simulations. Another approach that is computationally more efficient is the effective polarizable bond method in which only polar bonds or groups can be polarized and their polarizabilities are predetermined from quantum mechanical calculations of these groups in external electric fields. Both methods can be employed for applications in various situations by taking advantage of their unique features.

Importance of polarization effect in the study of metalloproteins: application of polarized protein specific charge scheme in predicting the reduction potential of azurin.

Molecular dynamics (MD) simulation is commonly used in the study of protein dynamics, and in recent years, the extension of MD simulation to the study of metalloproteins is gaining much interest. Choice of force field is crucial in MD studies, and the inclusion of metal centers complicates the process of accurately describing the electrostatic environment that surrounds the redox centre. Herein, we would like to explore the importance of including electrostatic contribution from both protein and solvent in the study of metalloproteins. MD simulations with the implementation of thermodynamic integration will be conducted to model the reduction process of azurin from Pseudomonas aeruginosa. Three charge schemes will be used to derive the partial charges of azurin. These charge schemes differ in terms of the amount of immediate environment, respective to copper, considered during charge fitting, which ranges from the inclusion of copper and residues in the first coordination sphere during density functional theory charge fitting to the comprehensive inclusion of protein and solvent effect surrounding the metal centre using polarized protein-specific charge scheme. From the simulations conducted, the relative reduction potential of the mutated azurins respective to that of wild-type azurin (ΔEcal) were calculated and compared with experimental values. The ΔEcal approached experimental value with increasing consideration of environmental effect hence substantiating the importance of polarization effect in the study of metalloproteins. This study also attests the practicality of polarized protein-specific charge as a computational tool capable of incorporating both protein environment and solvent effect into MD simulations.

Effect of Electronic Polarization to Human α-Thrombin

The polarized protein-specific charges (PPC) of human α-thrombin (thrombin) and its inhibitor (L86) are made possible by employing the recently developed molecular fractionation with conjugate caps approach incorporated the Poisson—Boltzmann model. Molecular dynamics (MD) simulations of thrombin have been carried out to investigate the dynamics and stability of the thrombin-inhibitor using PPC and AMBER charges respectively. Detailed analysis and comparison of MD results show that the PPC can correctly describe the polarized state of the thrombin and L86. Especially, the root-mean-square deviation of backbone atoms and the hydrogen bonds using PPC are more stable than the AMBER charge. The present results indicate that protein polarization plays critical roles in maintaining the compact structure of thrombin.

Accessing the applicability of polarized protein‐specific charge in linear interaction energy analysis

The reliability of the linear interaction energy (LIE) depends on the atomic charge model used to delineate the Coulomb interaction between the ligand and its environment. In this work, the polarized protein-specific charge (PPC) implementing a recently proposed fitting scheme has been examined in the LIE calculations of the binding affinities for avidin and β-secretase binding complexes. This charge fitting scheme, termed delta restrained electrostatic potential, bypasses the prevalent numerical difficulty of rank deficiency in electrostatic-potential-based charge fitting methods via a dual-step fitting strategy. A remarkable consistency between the predicted binding affinities and the experimental measurement has been observed. This work serves as a direct evidence of PPC's applicability in rational drug design.

Polarized Protein-Specific Charges from Atoms-in-Molecule Electron Density Partitioning

Atomic partial charges for use in traditional force fields for biomolecular simulation are often fit to the electrostatic potentials of small molecules and, hence, neglect large-scale electronic polarization. On the other hand, recent advances in atoms-in-molecule charge derivation schemes show promise for use in flexible force fields but are limited in size by the underlying quantum mechanical calculation of the electron density. Here, we implement the density derived electrostatic and chemical charges method in the linear-scaling density functional theory code ONETEP. Our implementation allows the straightforward derivation of partial atomic charges for systems comprising thousands of atoms, including entire proteins. We demonstrate that the derived charges are chemically intuitive, reproduce ab initio electrostatic potentials of proteins and are transferable between closely related systems. Simulated NMR data derived from molecular dynamics of three proteins using force fields based on the ONETEP charges are in good agreement with experiment.

Predicting Mutation-Induced Stark Shifts in the Active Site of a Protein with a Polarized Force Field

The electric field inside a protein has a significant effect on the protein structure, function, and dynamics. Recent experimental developments have offered a direct approach to measure the electric field by utilizing a nitrile-containing inhibitor as a probe that can deliver a unique vibration to the specific site of interest in the protein. The observed frequency shift of the nitrile stretching vibration exhibits a linear dependence on the electric field at the nitrile site, thus providing a direct measurement of the relative electric field. In the present work, molecular dynamics simulations were carried out to compute the electric field shift in human aldose reductase (hALR2) using a polarized protein-specific charge (PPC) model derived from fragment-based quantum-chemistry calculations in implicit solvent. Calculated changes of electric field in the active site of hALR2 between the wild type and mutants were directly compared with measured vibrational frequency shifts (Stark shifts). Our study demonstrates that the Stark shifts calculated using the PPC model are in much better agreement with the experimental data than widely used nonpolarizable force fields, indicating that the electronic polarization effect is important for the accurate prediction of changes in the electric field inside proteins.

Adsorption and folding dynamics of MPER of HIV-1 gp41 in the presence of dpc micelle

Membrane-proximal ectodomain region (MPER) of HIV-1 gp41 is known to have several epitopes of monoclonal antibodies. It also plays an important role in the membrane fusion process that is well-evidenced, though not well-elucidated. There are also disputes over the true structure of MPER. In this study, MPER NMR structure in the presence of dodecylphosphatidylcholine micelle is used in the molecular dynamic simulation to elucidate structural dynamics and adsorption to model MPER interaction in a membrane environment. Polarized protein-specific charge derived from its NMR structure is found to better preserve the helical structure found in the NMR structure compared to AMBER03 calculation. The preserved helical structure also adsorb to the micelle using the hydrophobic side-chains, consistent to the NMR structure. Ab initio folding of MPER predicts a structure quite in well agreement with the NMR structure (RMSd 3.9 Å) and shows that the micelle plays a role in the folding process.