Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations

Computational studies of proteins based on empirical force fields represent a powerful tool to obtain structure-function relationships at an atomic level, and are central in current efforts to solve the protein folding problem. The results from studies applying these tools are, however, dependent on the quality of the force fields used. In particular, accurate treatment of the peptide backbone is crucial to achieve representative conformational distributions in simulation studies. To improve the treatment of the peptide backbone, quantum mechanical (QM) and molecular mechanical (MM) calculations were undertaken on the alanine, glycine, and proline dipeptides, and the results from these calculations were combined with molecular dynamics (MD) simulations of proteins in crystal and aqueous environments. QM potential energy maps of the alanine and glycine dipeptides at the LMP2/cc-pVxZ//MP2/6-31G* levels, where x = D, T, and Q, were determined, and are compared to available QM studies on these molecules. The LMP2/cc-pVQZ//MP2/6-31G* energy surfaces for all three dipeptides were then used to improve the MM treatment of the dipeptides. These improvements included additional parameter optimization via Monte Carlo simulated annealing and extension of the potential energy function to contain peptide backbone phi, psi dihedral crossterms or a phi, psi grid-based energy correction term. Simultaneously, MD simulations of up to seven proteins in their crystalline environments were used to validate the force field enhancements. Comparison with QM and crystallographic data showed that an additional optimization of the phi, psi dihedral parameters along with the grid-based energy correction were required to yield significant improvements over the CHARMM22 force field. However, systematic deviations in the treatment of phi and psi in the helical and sheet regions were evident. Accordingly, empirical adjustments were made to the grid-based energy correction for alanine and glycine to account for these systematic differences. These adjustments lead to greater deviations from QM data for the two dipeptides but also yielded improved agreement with experimental crystallographic data. These improvements enhance the quality of the CHARMM force field in treating proteins. This extension of the potential energy function is anticipated to facilitate improved treatment of biological macromolecules via MM approaches in general.     

New-generation amber united-atom force field

We have developed a new-generation Amber united-atom force field for simulations involving highly demanding conformational sampling such as protein folding and protein-protein binding. In the new united-atom force field, all hydrogens on aliphatic carbons in all amino acids are united with carbons except those on Calpha. Our choice of explicit representation of all protein backbone atoms aims at minimizing perturbation to protein backbone conformational distributions and to simplify development of backbone torsion terms. Tests with dipeptides and solvated proteins show that our goal is achieved quite successfully. The new united-atom force field uses the same new RESP charging scheme based on B3LYP/cc-pVTZ//HF/6-31g** quantum mechanical calculations in the PCM continuum solvent as that in the Duan et al. force field. van der Waals parameters are empirically refitted starting from published values with respect to experimental solvation free energies of amino acid side-chain analogues. The suitability of mixing new point charges and van der Waals parameters with existing Amber covalent terms is tested on alanine dipeptide and is found to be reasonable. Parameters for all new torsion terms are refitted based on the new point charges and the van der Waals parameters. Molecular dynamics simulations of three small globular proteins in the explicit TIP3P solvent are performed to test the overall stability and accuracy of the new united-atom force field. Good agreements between the united-atom force field and the Duan et al. all-atom force field for both backbone and side-chain conformations are observed. In addition, the per-step efficiency of the new united-atom force field is demonstrated for simulations in the implicit generalized Born solvent. A speedup around two is observed over the Duan et al. all-atom force field for the three tested small proteins. Finally, the efficiency gain of the new united-atom force field in conformational sampling is further demonstrated with a well-known toy protein folding system, an 18 residue polyalanine in distance-dependent dielectric. The new united-atom force field is at least a factor of 200 more efficient than the Duan et al. all-atom force field for ab initio folding of the tested peptide.     

Development of a polarizable force field for proteins via ab initio quantum chemistry: first generation model and gas phase tests

We present results of developing a methodology suitable for producing molecular mechanics force fields with explicit treatment of electrostatic polarization for proteins and other molecular system of biological interest. The technique allows simulation of realistic-size systems. Employing high-level ab initio data as a target for fitting allows us to avoid the problem of the lack of detailed experimental data. Using the fast and reliable quantum mechanical methods supplies robust fitting data for the resulting parameter sets. As a result, gas-phase many-body effects for dipeptides are captured within the average RMSD of 0.22 kcal/mol from their ab initio values, and conformational energies for the di- and tetrapeptides are reproduced within the average RMSD of 0.43 kcal/mol from their quantum mechanical counterparts. The latter is achieved in part because of application of a novel torsional fitting technique recently developed in our group, which has already been used to greatly improve accuracy of the peptide conformational equilibrium prediction with the OPLS-AA force field.1 Finally, we have employed the newly developed first-generation model in computing gas-phase conformations of real proteins, as well as in molecular dynamics studies of the systems. The results show that, although the overall accuracy is no better than what can be achieved with a fixed-charges model, the methodology produces robust results, permits reasonably low computational cost, and avoids other computational problems typical for polarizable force fields. It can be considered as a solid basis for building a more accurate and complete second-generation model.     

How Cations Change Peptide Structure

Specific interactions between cations and proteins have a strong impact on peptide and protein structure. Herein, we shed light on the nature of the underlying interactions, especially regarding effects on the polyamide backbone structure. This was done by comparing the conformational ensembles of model peptides in isolation and in the presence of either Li⁺ or Na⁺ by using state‐of‐the‐art density‐functional theory (including van der Waals effects) and gas‐phase infrared spectroscopy. These monovalent cations have a drastic effect on the local backbone conformation of turn‐forming peptides, by disruption of the hydrogen‐bonding networks, thus resulting in severe distortion of the backbone conformations. In fact, Li⁺ and Na⁺ can even have different conformational effects on the same peptide. We also assess the predictive power of current approximate density functionals for peptide–cation systems and compare to results with those of established protein force fields as well as high‐level quantum chemistry calculations (CCSD(T)).     

Polarizable Simulations with Second order Interaction Model (POSSIM) force field: Developing parameters for alanine peptides and protein backbone

A previously introduced POSSIM (POlarizable Simulations with Second order Interaction Model) force field has been extended to include parameters for alanine peptides and protein backbones. New features were introduced into the fitting protocol, as compared to the previous generation of the polarizable force field for proteins. A reduced amount of quantum mechanical data was employed in fitting the electrostatic parameters. Transferability of the electrostatics between our recently developed NMA model and the protein backbone was confirmed. Binding energy and geometry for complexes of alanine dipeptide with a water molecule were estimated and found in a good agreement with high-level quantum mechanical results (for example, the intermolecular distances agreeing within ca. 0.06?). Following the previously devised procedure, we calculated average errors in alanine di- and tetra-peptide conformational energies and backbone angles and found the agreement to be adequate (for example, the alanine tetrapeptide extended-globular conformational energy gap was calculated to be 3.09 kcal/mol quantim mechanically and 3.14 kcal/mol with the POSSIM force field). However, we have now also included simulation of a simple alpha-helix in both gas-phase and water as the ultimate test of the backbone conformational behavior. The resulting alanine and protein backbone force field is currently being employed in further development of the POSSIM fast polarizable force field for proteins.     

Calculation of Host-Guest Binding Affinities Using a Quantum-Mechanical Energy Model

The prediction of protein-ligand binding affinities is of central interest in computer-aided drug discovery, but it is still difficult to achieve a high degree of accuracy. Recent studies suggesting that available force fields may be a key source of error motivate the present study, which reports the first mining minima (M2) binding affinity calculations based on a quantum mechanical energy model, rather than an empirical force field. We apply a semi-empirical quantum-mechanical energy function, PM6-DH+, coupled with the COSMO solvation model, to 29 host-guest systems with a wide range of measured binding affinities. After correction for a systematic error, which appears to derive from the treatment of polar solvation, the computed absolute binding affinities agree well with experimental measurements, with a mean error 1.6 kcal/mol and a correlation coefficient of 0.91. These calculations also delineate the contributions of various energy components, including solute energy, configurational entropy, and solvation free energy, to the binding free energies of these host-guest complexes. Comparison with our previous calculations, which used empirical force fields, point to significant differences in both the energetic and entropic components of the binding free energy. The present study demonstrates successful combination of a quantum mechanical Hamiltonian with the M2 affinity method.     

Development of modified force field for cation–amino acid interactions: Ab initio-derived empirical correction terms with comments on cation–π interactions

The modeling of voltage-gated ion-channel proteins is a continuing challenge for force-field calculations because of the diverse range of interactions involved. In particular, current force fields are not parameterized for either ion–amino acid or amino acid–electric field interactions. To address the parameterization of ion–amino acid interactions, we have tested the use of empirical correction terms, derived from ab initio calculations of single amino acids (representing the peptide backbone) interacting with K⁺ ions. Having demonstrated the utility of such an approach, we then extended the application to the amino acid side chains. The calculation of the interaction of K⁺ with serine, cysteine, methionine, lysine, arginine, aspartate, histidine (uncharged), tyrosine, tryptophan, and phenylalanine, both completes the parameterization of the molecular environments contained in the amino acids, and allows specific comment on these ion–functional group interactions. The cation–π interactions were of particular interest, given recent proposals in the literature and the fear that force fields would not be able to treat such interactions. We present a comprehensive comparison of the ab initio (DFT [BLYP], 6-311 G**) and force field (CHARMm22.0) assessments of these interactions. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1515–1525, 1998     

Intrinsically stable secondary structure elements of proteins: a comprehensive study of folding units of proteins by computation and by analysis of data determined by X-ray crystallography

Different protein architectures show strong similarities regardless of their amino acid composition: the backbone folds of the different secondary structural elements exhibit nearly identical geometries. To investigate the principles of folding and stability properties, oligopeptide models (that is, HCO-(NH-L-CHR-CO)(n)-NH(2)) have been studied. Previously, ab initio structure determinations have provided a small amount of information on the conformational building units of di- and tripeptides. A maximum of nine differently folded backbone types is available for any natural alpha-amino acid residue, with the exception of proline. All of these conformers have different relative energies. The present study compiles an ab inito database of optimized HCO-(L-Xxx)(n)-NH(2) structures, where 1相似文献   

Study of peptide conformation in terms of the ABEEM/MM method

The ABEEM/MM model (atom-bond electronegativity equalization method fused into molecular mechanics) is applied to study of the polypeptide conformations. The Lennard-Jones and torsional parameters were optimized to be consistent with the ABEEM/MM fluctuating charge electrostatic potential. The hydrogen bond was specially treated with an electrostatic fitting function. Molecular dipole moments, dimerization energies, and hydrogen bond lengths of complexes are reasonably achieved by our model, compared to ab initio results. The ABEEM/MM fluctuating charge model reproduces both the peptide conformational energies and structures with satisfactory accuracy with low computer cost. The transferability is tested by applying the parameters of our model to the tetrapeptide of alanine and another four dipeptides. The overall RMS deviations in conformational energies and key dihedral angles for four di- or tetrapeptide, is 0.39 kcal/mol and 7.7 degrees . The current results agree well with those by the accurate ab initio method, and are comparable to those from the best existing force fields. The results make us believe that our fluctuating charge model can obtain more promising results in protein and macromolecular modeling with good accuracy but less computer cost.     

原子-键电负性均衡方法融合进分子力场(ABEEM/MM)应用于蛋白质分子(Crambin)模拟

建立应用于多肽和蛋白质模拟的ABEEM/MM浮动电荷力场.利用该模型和参数,对实际蛋白质分子Crambin(植物种子中的一种小的蛋白质)进行模拟,得到了满意的结果,为其更广泛的应用开辟了道路.     

Empirical force-field assessment: The interplay between backbone torsions and noncovalent term scaling

The kinetic and thermodynamic aspects of the helix-coil transition in polyalanine-based peptides have been studied at the ensemble level using a distributed computing network. This study builds on a previous report, which critically assessed the performance of several contemporary force fields in reproducing experimental measurements and elucidated the complex nature of helix-coil systems. Here we consider the effects of modifying backbone torsions and the scaling of noncovalent interactions. Although these elements determine the potential of mean force between atoms separated by three covalent bonds (and thus largely determine the local conformational distributions observed in simulation), we demonstrate that the interplay between these factors is both complex and force field dependent. We quantitatively assess the heliophilicity of several helix-stabilizing potentials as well as the changes in heliophilicity resulting from such modifications, which can "make or break" the accuracy of a given force field, and our findings suggests that future force field development may need to better consider effect that vary with peptide length. This report also serves as an example of the utility of distributed computing in analyzing and improving upon contemporary force fields at the level of absolute ensemble equilibrium, the next step in force field development.     

Double-hybrid density functionals with long-range dispersion corrections: higher accuracy and extended applicability

The objective of this work is the further systematic improvement of the accuracy of Double-Hybrid Density Functionals (DHDF) that add non-local electron correlation effects to a standard hybrid functional by second-order perturbation theory (S. Grimme, J. Chem. Phys., 2006, 124, 034108). The only known shortcoming of these generally highly accurate functionals is an underestimation of the long-range dispersion (van der Waals) interactions. To correct this deficiency, we add a previously developed empirical dispersion term (DFT-D) to the energy expression but leave the electronic part of the functional untouched. Results are presented for the S22 set of non-covalent interaction energies, the G3/99 set of heat of formations and conformational energies of a phenylalanyl-glycyl-glycine peptide model. We furthermore propose seven hydrocarbon reactions with strong intramolecular dispersion contributions as a benchmark set for newly developed density functionals. In general, the proposed composite approach is for many chemically relevant properties of similar quality as high-level coupled-cluster treatments. A significant increase of the accuracy for non-covalent interactions is obtained and the corrected B2PLYP DHDF provides one of the lowest ever obtained Mean Absolute Deviations (MAD) for the S22 set (0.2-0.3 kcal mol(-1)). Unprecedented high accuracy is also obtained for the relative energies of peptide conformations that turn out to be very difficult. The significant improvements found for the G3/99 set (reduction of the MAD from 2.4 to 1.7 kcal mol(-1)) underline the importance of intramolecular dispersion effects in large molecules. In all tested cases the results from the standard B3LYP approach are also significantly improved, and we recommend the general use of dispersion corrections in DFT treatments.     

Molecular mechanics force-field development for amino acid zwitterions

Understanding the conformational flexibility of amino acid zwitterions (ZWs) and their associated conformational energies is crucial for predicting their interactions in biological systems. Gas-phase ab initio calculations of ZWs are intractable. Molecular mechanics (MM), on the other hand, is able to handle large systems but lacks the necessary force field parameters to model ZWs. To develop force field parameters that are able to correctly model ZW geometries and energetics we used a novel combinatorial approach: amino acid ZWs were broken down structurally into key functional components, which were parameterized separately. M?ller-Plesset second-order perturbation calculations on small carboxylates, on the glycine cation, and on novel hydrogen bonded systems, coupled with available experimental data, were used to generate MM3(2000) ZW parameters (Allinger N. L.; Yuh, Y. H.; Lii, J.-H. J Am Chem Soc 1989, 111, 8551). The MM3 results from this combinatorial approach gave geometries that are in good agreement with neutron diffraction experiments, plus their frequencies and energies appear to be reasonably modeled. Current limitations and future development of MM force fields are discussed briefly.     

Simulation of multiphase systems utilizing independent force fields to control intraphase and interphase behavior

Fixed‐charge empirical force fields have been developed and widely used over the past three decades for all‐atom molecular simulations. Most simulation programs providing these methods enable only one set of force field parameters to be used for the entire system. Whereas this is generally suitable for single‐phase systems, the molecular environment at the interface between two phases may be sufficiently different from the individual phases to require a different set of parameters to be used to accurately represent the system. Recently published simulations of peptide adsorption to material surfaces using the CHARMM force field have clearly demonstrated this issue by revealing that calculated values of adsorption free energy substantially differ from experimental results. Whereas nonbonded parameters could be adjusted to correct this problem, this cannot be done without also altering the conformational behavior of the peptide in solution, for which CHARMM has been carefully tuned. We have developed a dual‐force‐field approach (Dual‐FF) to address this problem and implemented it in the CHARMM simulation package. This Dual‐FF method provides the capability to use two separate sets of nonbonded force field parameters within the same simulation: one set to represent intraphase interactions and a separate set to represent interphase interactions. Using this approach, we show that interfacial parameters can be adjusted to correct errors in peptide adsorption free energy without altering peptide conformational behavior in solution. This program thus provides the capability to enable both intraphase and interphase molecular behavior to be accurately and efficiently modeled in the same simulation. © 2012 Wiley Periodicals, Inc.     

A CGenFF-based force field for simulations of peptoids with both cis and trans peptide bonds

Peptoids, or poly-n-substituted glycines, are peptide-like polymers composed of a flexible backbone decorated with diverse chemical side chains. Peptoids can form a variety of self-assembling structures based on the type and sequence of the side chains attached to their backbones. All-atom molecular dynamics simulations have been useful in predicting the conformational structures of proteins and will be valuable tools for identifying combinations of peptoid side chains that may form interesting folded structures. However, peptoid models must address a major degree of freedom not common in proteins – the cis/trans isomerization of the peptide bond. This work presents CHARMM general force field (CGenFF) parameters developed to accurately represent peptoid conformational behavior, with an emphasis on a correct representation of both the cis and trans isomers of the peptoid backbone. These parameters are validated against experimental and quantum mechanics data and used to simulate three peptoid side chains in explicitly solvated systems. © 2019 Wiley Periodicals, Inc.     

Theoretical study of alkali cation-benzene complexes: potential energy surfaces and binding energies with improved results for rubidium and cesium

High level ab initio quantum chemical calculations have been carried out on the binding of alkali metal to benzene with special attention to heavier metals for which the agreement between the most recent theoretical investigations and the experimental bond dissociation energies (BDEs) is not very good. We performed BSSE-corrected geometry optimizations employing the MP2 level of theory with large basis sets and a modified Stuttgart RSC 1997 basis set for rubidium and cesium and carried out single point energy calculations at the MP4 level, obtaining, also for the latter metals, BDE values in good agreement with the experimental results. Furthermore, in view of the development of empirical correction terms to force fields to describe cation-pi interactions, we evaluated the potential energy surface along the benzene symmetry axis and discussed the role of the BSSE correction on the accuracy of our results.     

Prediction of Protein Loop Conformations using the AGBNP Implicit Solvent Model and Torsion Angle Sampling

The OPLS-AA all-atom force field and the Analytical Generalized Born plus Non-Polar (AGBNP) implicit solvent model, in conjunction with torsion angle conformational search protocols based on the Protein Local Optimization Program (PLOP), are shown to be effective in predicting the native conformations of 57 9-residue and 35 13-residue loops of a diverse series of proteins with low sequence identity. The novel nonpolar solvation free energy estimator implemented in AGBNP augmented by correction terms aimed at reducing the occurrence of ion pairing are important to achieve the best prediction accuracy. Extended versions of the previously developed PLOP-based conformational search schemes based on calculations in the crystal environment are reported that are suitable for application to loop homology modeling without the crystal environment. Our results suggest that in general the loop backbone conformation is not strongly influenced by crystal packing. The application of the temperature Replica Exchange Molecular Dynamics (T-REMD) sampling method for a few examples where PLOP sampling is insufficient are also reported. The results reported indicate that the OPLS-AA/AGBNP effective potential is suitable for high-resolution modeling of proteins in the final stages of homology modeling and/or protein crystallographic refinement.     

Cluster expansion models for flexible‐backbone protein energetics

Protein structure prediction and design often involve discrete modeling of side‐chain conformations on structural templates. Introducing backbone flexibility into such models has proven important in many different applications. Backbone flexibility improves model accuracy and provides access to larger sequence spaces in computational design, although at a cost in complexity and time. Here, we show that the influence of backbone flexibility on protein conformational energetics can be treated implicitly, at the level of sequence, using the technique of cluster expansion. Cluster expansion provides a way to convert structure‐based energies into functions of sequence alone. It leads to dramatic speed‐ups in energy evaluation and provides a convenient functional form for the analysis and optimization of sequence‐structure relationships. We show that it can be applied effectively to flexible‐backbone structural models using four proteins: α‐helical coiled‐coil dimers and trimers, zinc fingers, and Bcl‐x_L/peptide complexes. For each of these, low errors for the sequence‐based models when compared with structure‐based evaluations show that this new way of treating backbone flexibility has considerable promise, particularly for protein design. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009