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

Revealing origin of decrease in potency of darunavir and amprenavir against HIV-2 relative to HIV-1 protease by molecular dynamics simulations

Clinical inhibitors Darunavir (DRV) and Amprenavir (APV) are less effective on HIV-2 protease (PR2) than on HIV-1 protease (PR1). To identify molecular basis associated with the lower inhibition, molecular dynamics (MD) simulations and molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) calculations were performed to investigate the effectiveness of the PR1 inhibitors DRV and APV against PR1/PR2. The rank of predicted binding free energies agrees with the experimental determined one. Moreover, our results show that two inhibitors bind less strongly to PR2 than to PR1, again in agreement with the experimental findings. The decrease in binding free energies for PR2 relative to PR1 is found to arise from the reduction of the van der Waals interactions induced by the structural adjustment of the triple mutant V32I, I47V and V82I. This result is further supported by the difference between the van der Waals interactions of inhibitors with each residue in PR2 and in PR1. The results from the principle component analysis suggest that inhibitor binding tends to make the flaps of PR2 close and the one of PR1 open. We expect that this study can theoretically provide significant guidance and dynamics information for the design of potent dual inhibitors targeting PR1/PR2.

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.

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.

Density functional tight binding: values of semi-empirical methods in an ab initio era

Semi-empirical (SE) methods are derived from Hartree-Fock (HF) or Density Functional Theory (DFT) by neglect and approximation of electronic integrals. Thereby, parameters are introduced which have to be determined from reference calculations and/or by fitting to available experimental data. This leads to computational methods that are about 2-3 orders of magnitude faster than the standard HF/DFT methods using medium sized basis sets while being about 3 orders of magnitude slower than empirical force field methods (Molecular Mechanics: MM). Therefore, SE methods are most appropriate for a specific range of applications. These include the study of systems that contain a large number of atoms and therefore being too large for ab initio or DFT methods and also problems where dynamic or entropic effects are particularly important. In the latter case, the errors made by considering a very limited number of molecular structures or neglecting entropic contributions can be much larger than the accuracy lost due to the use of SE methods. Another area where SE methods are attractive concerns the analysis of systems for which reliable MM models are not readily available. Therefore, even in an era when rapid progress is being made in ab initio methods, there is considerable interest in further developing SE methods. We illustrate this point by focusing on the discussion of recent development and application of the Density Functional Tight Binding method.

Protein's native structure is dynamically stabilized by electronic polarization

In this paper, molecular dynamics (MD) simulations were performed for a number of benchmark proteins using both the standard assisted model building with energy refinement (AMBER) charge and the dynamically adjusted polarized protein-specific charge (DPPC) from quantum fragment calculations to provide accurate electrostatic interactions. Our result shows that proteins' dynamic structures drifted away from the native structures in simulations under standard (nonpolarizable) AMBER force field. For comparison, proteins' native structures were dynamically stable after a long time simulation under DPPC. The free energy landscape reveals that the native structure is the lowest energy conformation under DPPC, while it is not under standard AMBER charge. To further investigate the polarization effect on the stability of native structures of proteins, we restarted from some decoy structures generated from simulations using standard AMBER charges and then carried out further MD simulation using DPPC to refine those structures. Our study shows that the native structures from these decoy structures can be mostly recovered using DPPC and that the dynamic structures with the highest population in cluster analysis are in close agreement with the corresponding native structures. The current study demonstrates the importance of electronic polarization of protein in stabilizing the native structure.

Design and application of implicit solvent models in biomolecular simulations

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Implicit solvent replaces explicit water by a potential of mean force.

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Popular models are SASA, VOL and Generalized Born.

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Implicit solvent is used in MD, protein modelling, folding, design, prediction and drug screening.

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Large-scale simulations allow for parametrisation via force matching.

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Application to nucleic acids and membranes is challenging.

We review implicit solvent models and their parametrisation by introducing the concepts and recent devlopments of the most popular models with a focus on parametrisation via force matching. An overview of recent applications of the solvation energy term in protein dynamics, modelling, design and prediction is given to illustrate the usability and versatility of implicit solvation in reproducing the physical behaviour of biomolecular systems. Limitations of implicit modes are discussed through the example of more challenging systems like nucleic acids and membranes.

Electronic polarization stabilizes tertiary structure prediction of HP-36

Molecular dynamic (MD) simulations with both implicit and explicit solvent models have been carried out to study the folding dynamics of HP-36 protein. Starting from the extended conformation, the secondary structure of all three helices in HP-36 was formed in about 50 ns and remained stable in the remaining simulation. However, the formation of the tertiary structure was difficult. Although some intermediates were close to the native structure, the overall conformation was not stable. Further analysis revealed that the large structure fluctuation of loop and hydrophobic core regions was devoted mostly to the instability of the structure during MD simulation. The backbone root-mean-square deviation (RMSD) of the loop and hydrophobic core regions showed strong correlation with the backbone RMSD of the whole protein. The free energy landscape indicated that the distribution of main chain torsions in loop and turn regions was far away from the native state. Starting from an intermediate structure extracted from the initial AMBER simulation, HP-36 was found to generally fold to the native state under the dynamically adjusted polarized protein-specific charge (DPPC) simulation, while the peptide did not fold into the native structure when AMBER force filed was used. The two best folded structures were extracted and taken into further simulations in water employing AMBER03 charge and DPPC for 25 ns. Result showed that introducing polarization effect into interacting potential could stabilize the near-native protein structure.

Structure and dynamics of the N-terminal domain of the Cu(I) binding protein CusB

CusCFBA is one of the metal efflux systems in Escherichia coli that is highly specific for its substrates, Cu(I) and Ag(I). It serves to protect the bacteria in environments that have lethal concentrations of these metals. The membrane fusion protein CusB is the periplasmic piece of CusCFBA, which has not been fully characterized by crystallography because of its extremely disordered N-terminal region. This region has both structural and functional importance because it has been experimentally proven to transfer the metal by itself from the metallochaperone CusF and to induce a structural change in the rest of CusB to increase Cu(I)/Ag(I) resistance. Understanding metal uptake from the periplasm is critical to gain insight into the mechanism of the whole CusCFBA pump, which makes resolving a structure for the N-terminal region necessary because it contains the metal binding site. We ran extensive molecular dynamics simulations to reveal the structural and dynamic properties of both the apo and Cu(I)-bound versions of the CusB N-terminal region. In contrast to its functional companion CusF, Cu(I) binding to the N-terminus of CusB causes only a slight, local stabilization around the metal site. The trajectories were analyzed in detail, revealing extensive structural disorder in both the apo and holo forms of the protein. CusB was further analyzed by breaking the protein up into three subdomains according to the extent of the observed disorder: the N- and C-terminal tails, the central beta strand motif, and the M21-M36 loop connecting the two metal-coordinating methionine residues. Most of the observed disorder was traced back to the tail regions, leading us to hypothesize that the latter two subdomains (residues 13-45) may form a functionally competent metal-binding domain because the tail regions appear to play no role in metal binding.

The F130L mutation in streptavidin reduces its binding affinity to biotin through electronic polarization effect

Recently, Baugh et al. discovered that a distal point mutation (F130L) in streptavidin causes no distinct variation to the structure of the binding pocket but a 1000-fold reduction in biotin binding affinity. In this work, we carry out molecular dynamics simulations and apply an end-state free energy method to calculate the binding free energies of biotin to wild type streptavidin and its F130L mutant. The absolute binding affinities based on AMBER charge are repulsive, and the mutation induced binding loss is underestimated. When using the polarized protein-specific charge, the absolute binding affinities are significantly enhanced. In particular, both the absolute and relative binding affinities are in line with the experimental measurements. Further investigation indicates that polarization effect is indispensable in both the generation of structural ensembles and the calculation of interaction energies. This work verifies Baugh's conjecture that electrostatic polarization effect plays an essential role in modulating the binding affinity of biotin to the streptavidin through F130L mutation.

The critical effect of polarization on the dynamical structure of guanine quadruplex DNA

Guanine quadruplex DNA (G-DNA), found in eukaryotic telomeres and recently in non-telomeric genomic DNA, plays important biological roles and their structures are being explored as potential targets for therapeutic intervention. Since the quadruplex structure of G-DNA is stabilized by cations, electrostatic interaction is expected to play important roles in the dynamical structure of G-DNA. In current work, MD simulation was carried out to study the dynamical structure of a special G-DNA (with sequence d(G(4)T(4)G(4))) complexed with five K(+) ions. In order to properly include polarization in MD simulation, a new set of polarized nucleic acid specific charge based on fragment quantum chemistry calculation was developed for G-DNA. Our study showed that polarization of the nucleobases by K(+) enhanced electrostatic attraction between the base and ions. This increased attractive interaction is critical to stabilizing the stem-loop junction ions in G-DNA. Without this polarization effect, as in MD simulation using a standard (nonpolarizable) force field, the top and bottom cations escaped into the solvent within just a few nanoseconds. Furthermore, an incorrect bifurcated bonding geometry of G-DNA, found in previous MD simulation study under a standard force field but not observed in experiments, disappeared in the present stimulation using the new polarized force field. The current study bridged an important gap between the simulation study and experimental observation on the dynamical structure of G-DNA.

Ab initio folding of extended α-helix: a theoretical study about the role of electrostatic polarization in the folding of helical structures

In this work, we report the ab initio folding of three different extended helical peptides namely 2khk, N36, and C34 through conventional molecular dynamics simulation at room temperature using implicit solvation model. Employing adaptive hydrogen bond specific charge (AHBC) scheme to account for the polarization effect of hydrogen bonds established during the simulation, the effective folding of the three extended helices were observed with best backbone RMSDs in comparison to the experimental structures over the helical region determined to be 1.30 Å for 2khk, 0.73 Å for N36 and 0.72 Å for C34. In this study, 2khk will be used as a benchmark case serving as a means to compare the ability of polarized (AHBC) and nonpolarized force field in the folding of an extended helix. Analyses conducted revealed the ability of the AHBC scheme in effectively folding the extended helix by promoting helix growth through the stabilization of backbone hydrogen bonds upon formation during the folding process. Similar observations were also noted when AHBC scheme was employed during the folding of C34 and N36. However, under Amber03 force field, helical structures formed during the folding of 2khk was not accompanied by stabilization thus highlighting the importance of electrostatic polarization in the folding of helical structures.

Solvent effect on the folding dynamics and structure of E6-associated protein characterized from ab initio protein folding simulations

Solvent effect on protein conformation and folding mechanism of E6-associated protein (E6ap) peptide are investigated using a recently developed charge update scheme termed as adaptive hydrogen bond-specific charge (AHBC). On the basis of the close agreement between the calculated helix contents from AHBC simulations and experimental results, we observed based on the presented simulations that the two ends of the peptide may simultaneously take part in the formation of the helical structure at the early stage of folding and finally merge to form a helix with lowest backbone RMSD of about 0.9 Å in 40% 2,2,2-trifluoroethanol solution. However, in pure water, the folding may start at the center of the peptide sequence instead of at the two opposite ends. The analysis of the free energy landscape indicates that the solvent may determine the folding clusters of E6ap, which subsequently leads to the different final folded structure. The current study demonstrates new insight to the role of solvent in the determination of protein structure and folding dynamics.

Fragment-based quantum mechanical methods for periodic systems with Ewald summation and mean image charge convention for long-range electrostatic interactions

We describe an Ewald-summation method to incorporate long-range electrostatic interactions into fragment-based electronic structure methods for periodic systems. The present method is an extension of the particle-mesh Ewald technique for combined quantum mechanical and molecular mechanical (QM/MM) calculations, and it has been implemented into the explicit polarization (X-Pol) potential to illustrate the computational details. As in the QM/MM-Ewald method, the X-Pol-Ewald approach is a linear-scaling electrostatic method, in which the short-range electrostatic interactions are determined explicitly in real space and the long-range Ewald pair potential is incorporated into the Fock matrix as a correction. To avoid the time-consuming Fock matrix update during the self-consistent field procedure, a mean image charge (MIC) approximation is introduced, in which the running average with a user-chosen correlation time is used to represent the long-range electrostatic correction as an average effect. Test simulations on liquid water show that the present X-Pol-Ewald method takes about 25% more CPU time than the usual X-Pol method using spherical cutoff, whereas the use of the MIC approximation reduces the extra costs for long-range electrostatic interactions by 15%. The present X-Pol-Ewald method provides a general procedure for incorporating long-range electrostatic effects into fragment-based electronic structure methods for treating biomolecular and condensed-phase systems under periodic boundary conditions.

Electrostatic polarization is critical for the strong binding in streptavidin-biotin system

The origin of strong affinity of biotin and its analogs binding to (strept)avidin is still the subject of an ongoing controversy. In this work, thermodynamic integration is carried out to study of the difference of binding free energies between biotin and iminobiotin to streptavidin. Three atomic charge schemes are implemented and compared. One is the traditional AMBER charge, and the other two, termed the polarized protein-specific charge, are based on a linear scaling quantum mechanical method and a continuous solvation model and have polarization effect partially or fully included. The result indicates that when nonpolarized AMBER force field is applied, the result is much underestimated. When electronic polarization is gradually included, the difference of binding affinity increases along with it. Using the linear-response approximation to eliminate the error in self-charging process, the corrected binding affinity agrees well with the experimental observation. This study is direct evidence indicating that polarization effect is critical for the strong binding in streptavidin-biotin system.

Multilevel X-Pol: a fragment-based method with mixed quantum mechanical representations of different fragments

The explicit polarization (X-Pol) method is a fragment-based quantum mechanical model, in which a macromolecular system or other large or complex system in solution is partitioned into monomeric fragments. The present study extends the original X-Pol method, where all fragments are treated using the same electronic structure theory, to multilevel representations, called multilevel X-Pol, in which different electronic structure methods are used to describe different fragments. The multilevel X-Pol method has been implemented into a locally modified version of Gaussian 09. A key ingredient that is used to couple interfragment electrostatic interactions at different levels of theory is the use of the response density for the post-self-consistent-field energy. (The response density is also called the generalized density.) The method is useful for treating fragments in a small region of the system such as a solute molecule or the substrate and amino acids in the active site of an enzyme with a high-level theory, and the fragments in the rest of the system by a lower-level and computationally more efficient method. Multilevel X-Pol is illustrated here by applications to hydrogen bonding complexes in which one fragment is treated with the hybrid M06 density functional, Møller-Plesset perturbation theory, or coupled cluster theory, and the other fragments are treated by Hartree-Fock theory or the B3LYP or M06 hybrid density functionals.

Optimization of the explicit polarization (X-Pol) potential using a hybrid density functional

The explicit polarization (X-Pol) method is a self-consistent fragment-based electronic structure theory in which molecular orbitals are block-localized within fragments of a cluster, macromolecule, or condensed-phase system. To account for short-range exchange repulsion and long-range dispersion interactions, we have incorporated a pairwise, empirical potential, in the form of Lennard-Jones terms, into the X-Pol effective Hamiltonian. In the present study, the X-Pol potential is constructed using the B3LYP hybrid density functional with the 6-31G(d) basis set to treat interacting fragments, and the Lennard-Jones parameters have been optimized on a dataset consisting of 105 bimolecular complexes. It is shown that the X-Pol potential can be optimized to provide a good description of hydrogen bonding interactions; the root mean square deviation of the computed binding energies from full (i.e., nonfragmental) CCSD(T)/aug-cc-pVDZ results is 0.8 kcal/mol, and the calculated hydrogen bond distances have an average deviation of about 0.1 Å from those obtained by full B3LYP/aug-cc-pVDZ optimizations.

Folding of a helix is critically stabilized by polarization of backbone hydrogen bonds: study in explicit water

Multiple single-trajectory molecular dynamics (MD) simulation at room temperature (300 K) in explicit water was carried out to study the folding dynamics of an α-helix (PDB 2I9M ) using a polarized charge scheme that includes electronic polarization of backbone hydrogen bonds. Starting from an extended conformation, the 17-residue peptide was successfully folded into the native structure (α-helix) between 80 and 130 ns with a root-mean-square deviation of ~1.0 Å. Analysis of the time-dependent trajectories revealed that helix formation of the peptide started at the terminals and progressed toward the center of the peptide. For comparison, MD trajectories generated under various versions of standard AMBER force fields failed to show any significant or stable helix formation in our simulation. Our result shows clear evidence that the electronic polarization of backbone hydrogen bonds energetically stabilizes the helix formation and is critical to the stable folding of the short helix structure.

Polarization of intraprotein hydrogen bond is critical to thermal stability of short helix

Simulation result for protein folding/unfolding is highly dependent on the accuracy of the force field employed. Even for the simplest structure of protein such as a short helix, simulations using the existing force fields often fail to produce the correct structural/thermodynamic properties of the protein. Recent research indicated that lack of polarization is at least partially responsible for the failure to successfully fold a short helix. In this work, we develop a simple formula-based atomic charge polarization model for intraprotein (backbone) hydrogen bonding based on the existing AMBER force field to study the thermal stability of a short helix (2I9M) by replica exchange molecular dynamics simulation. By comparison of the simulation results with those obtained by employing the standard AMBER03 force field, the formula-based atomic charge polarization model gave the helix melting curve in close agreement with the NMR experiment. However, in simulations using the standard AMBER force field, the helix was thermally unstable at the temperature of the NMR experiment, with a melting temperature almost below the freezing point. The difference in observed thermal stability from these two simulations is the effect of backbone intraprotein polarization, which was included in the formula-based atomic charge polarization model. The polarization of backbone hydrogen bonding thus plays a critical role in the thermal stability of helix or more general protein structures.