Improved side‐chain torsion potentials for the Amber ff99SB protein force field

Recent advances in hardware and software have enabled increasingly long molecular dynamics (MD) simulations of biomolecules, exposing certain limitations in the accuracy of the force fields used for such simulations and spurring efforts to refine these force fields. Recent modifications to the Amber and CHARMM protein force fields, for example, have improved the backbone torsion potentials, remedying deficiencies in earlier versions. Here, we further advance simulation accuracy by improving the amino acid side‐chain torsion potentials of the Amber ff99SB force field. First, we used simulations of model alpha‐helical systems to identify the four residue types whose rotamer distribution differed the most from expectations based on Protein Data Bank statistics. Second, we optimized the side‐chain torsion potentials of these residues to match new, high‐level quantum‐mechanical calculations. Finally, we used microsecond‐timescale MD simulations in explicit solvent to validate the resulting force field against a large set of experimental NMR measurements that directly probe side‐chain conformations. The new force field, which we have termed Amber ff99SB‐ILDN, exhibits considerably better agreement with the NMR data. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

On contribution of known atomic partial charges of protein backbone in electrostatic potential density maps

Partial charges of atoms in a molecule and electrostatic potential (ESP) density for that molecule are known to bear a strong correlation. In order to generate a set of point‐field force field parameters for molecular dynamics, Kollman and coworkers have extracted atomic partial charges for each of all 20 amino acids using restrained partial charge‐fitting procedures from theoretical ESP density obtained from condensed‐state quantum mechanics. The magnitude of atomic partial charges for neutral peptide backbone they have obtained is similar to that of partial atomic charges for ionized carboxylate side chain atoms. In this study, the effect of these known atomic partial charges on ESP is examined using computer simulations and compared with the experimental ESP density recently obtained for proteins using electron microscopy. It is found that the observed ESP density maps are most consistent with the simulations that include atomic partial charges of protein backbone. Therefore, atomic partial charges are integral part of atomic properties in protein molecules and should be included in model refinement.     

Hydration effects on the electrostatic potential around tuftsin

The electrostatic potential and component dielectric constants from molecular dynamics (MD) trajectories of tuftsin, a tetrapeptide with the amino acid sequence Thr–Lys–Pro–Arg in water and in saline solution are presented. The results obtained from the analysis of the MD trajectories for the total electrostatic potential at points on a grid using the Ewald technique are compared with the solution to the Poisson–Boltzmann (PB) equation. The latter was solved using several sets of dielectric constant parameters. The effects of structural averaging on the PB results were also considered. Solute conformational mobility in simulations gives rise to an electrostatic potential map around the solute dominated by the solute monopole (or lowest order multipole). The detailed spatial variation of the electrostatic potential on the molecular surface brought about by the compounded effects of the distribution of water and ions close to the peptide, solvent mobility, and solute conformational mobility are not qualitatively reproducible from a reparametrization of the input solute and solvent dielectric constants to the PB equation for a single structure or for structurally averaged PB calculations. Nevertheless, by fitting the PB to the MD electrostatic potential surfaces with the dielectric constants as fitting parameters, we found that the values that give the best fit are the values calculated from the MD trajectories. Implications of using such field calculations on the design of tuftsin peptide analogues are discussed. © 1999 John Wiley & Sons, Inc. Biopoly 50: 133–143, 1999     

Residue-specific α-helix propensities from molecular simulation

Formation of α-helices is a fundamental process in protein folding and assembly. By studying helix formation in molecular simulations of a series of alanine-based peptides, we obtain the temperature-dependent α-helix propensities of all 20 naturally occurring residues with two recent additive force fields, Amber ff03w and Amber ff99SB¹. Encouragingly, we find that the overall helix propensity of many residues is captured well by both energy functions, with Amber ff99SB¹ being more accurate. Nonetheless, there are some residues that deviate considerably from experiment, which can be attributed to two aspects of the energy function: i), variations of the charge model used to determine the atomic partial charges, with residues whose backbone charges differ most from alanine tending to have the largest error; ii), side-chain torsion potentials, as illustrated by the effect of modifications to the torsion angles of I, L, D, N. We find that constrained refitting of residue charges for charged residues in Amber ff99SB¹ significantly improves their helix propensity. The resulting parameters should more faithfully reproduce helix propensities in simulations of protein folding and disordered proteins.     

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 (ΔE_cal) were calculated and compared with experimental values. The ΔE_cal 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. Proteins 2014; 82:2209–2219. © 2014 Wiley Periodicals, Inc.     

On the ability of molecular dynamics force fields to recapitulate NMR derived protein side chain order parameters

Molecular dynamics (MD) simulations have become a central tool for investigating various biophysical questions with atomistic detail. While many different proxies are used to qualify MD force fields, most are based on largely structural parameters such as the root mean square deviation from experimental coordinates or nuclear magnetic resonance (NMR) chemical shifts and residual dipolar couplings. NMR derived Lipari–Szabo squared generalized order parameter (O²) values of amide N? H bond vectors of the polypeptide chain were also often employed for refinement and validation. However, with a few exceptions, side chain methyl symmetry axis order parameters have not been incorporated into experimental reference sets. Using a test set of five diverse proteins, the performance of several force fields implemented in the NAMDD simulation package was examined. It was found that simulations employing explicit water implemented using the TIP3 model generally performed significantly better than those using implicit water in reproducing experimental methyl symmetry axis O² values. Overall the CHARMM27 force field performs nominally better than two implementations of the Amber force field. It appeared that recent quantum mechanics modifications to side chain torsional angles of leucine and isoleucine in the Amber force field have significantly hindered proper motional modeling for these residues. There remained significant room for improvement as even the best correlations of experimental and simulated methyl group Lipari–Szabo generalized order parameters fall below an R² of 0.8.     

Elastic, electrostatic and electrokinetic forces influencing membrane curvature

Many cellular and intracellular processes critically depend on membrane shape, but the shape generating mechanisms are still to be fully understood. In this study we evaluate how electrostatic/electrokinetic forces contribute to membrane curvature. Membrane bilayer had finite thickness and was either elastically anisotropic or anisotropic overall, but isotropic per sections (heads and tails). The physics of the situation was evaluated using a coupled system of elastic and electrostatic/electrokinetic (Poisson-Nernst-Planck) equations. The fixed charges present only on the upper membrane surface lead to the accumulation of counter-ions and depletion of co-ions that decay spatially very rapidly (Debye length<1nm), as does the potential and electric field. Spatially uneven electric field and the permittivity mismatch also induce charges at the membrane-solution interface, which are not fixed but influence the electrostatics nevertheless. Membrane bends due to - Coulomb force (caused by fixed membrane charges in the electric field) and the dielectric force (due to the non-uniform electric field and the permittivity mismatch between the membrane and the solution). Both act as membrane surface forces, and both depend supra-linearly on the fixed charge density. Regardless of sign of the fixed charges, the membrane bends toward the charged (upper) surface owing to the action of the Coulomb force, but this is opposed by the smaller dielectric force. The spontaneous membrane curvature becomes very pronounced at high fixed charge densities, leading to very small spontaneous radii (<50nm). In conclusion the electrostatic/electrokinetic forces contribute significantly to the membrane curvature.     

Patterns in ionizable side chain interactions in protein structures

In a selected set of 44 high-resolution, non-homologous protein structures, the intramolecular hydrogen bonds or salt bridges formed by ionizable amino acid side chains were identified and analyzed. The analysis was based on the investigation of several properties of the involved residues such as their solvent exposure, their belonging to a certain secondary structural element, and their position relative to the N- and C-termini of their respective structural element. It was observed that two-thirds of the interactions made by basic or acidic side chains are hydrogen bonds to polar uncharged groups. In particular, the majority (78%) of the hydrogen bonds between ionizable side chains and main chain polar groups (sch:mch bonds) involved at least one buried atom, and in 42% of the cases both interacting atoms were buried. In α-helices, the sch:mch bonds observed in the proximity of the C- and N-termini show a clear preference for acidic and basic side chains, respectively. This appears to be due to the partial charges of peptide group atoms at the termini of α-helices, which establish energetically favorable electrostatic interactions with side chain carrying opposite charge, at distances even greater than 4.5 Å. The sch:mch interactions involving ionizable side chains that belong either to β-strands or to the central part of α-helices are based almost exclusively on basic residues. This results from the presence of main chain carbonyl oxygen atoms in the protein core which have unsatisfied hydrogen bonding capabilities.     

Molecular dynamics studies on the NMR structures of rabbit prion protein wild type and mutants: surface electrostatic charge distributions

Prion diseases are invariably fatal and highly infectious neurodegenerative diseases that affect a wide variety of mammalian species such as sheep and goats, cattle, deer and elk, and humans. But for rabbits, studies have shown that they have a low susceptibility to be infected by prion diseases. This paper does molecular dynamics (MD) studies of rabbit NMR structures (of the wild type and its two mutants of two surface residues), in order to understand the specific mechanism of rabbit prion proteins (RaPrP^C). Protein surface electrostatic charge distributions are specially focused to analyze the MD trajectories. This paper can conclude that surface electrostatic charge distributions indeed contribute to the structural stability of wild-type RaPrP^C; this may be useful for the medicinal treatment of prion diseases.     

Derivation of original RESP atomic partial charges for MD simulations of the LDAO surfactant with AMBER: applications to a model of micelle and a fragment of the lipid kinase PI4KA

In this paper, we describe the derivation and the validation of original RESP atomic partial charges for the N, N-dimethyl-dodecylamine oxide (LDAO) surfactant. These charges, designed to be fully compatible with all the AMBER force fields, are at first tested against molecular dynamics simulations of pure LDAO micelles and with a fragment of the lipid kinase PIK4A (DI) modeled with the QUARK molecular modeling server. To model the micelle, we used two distinct AMBER force fields (i.e. Amber99SB and Lipid14) and a variety of starting conditions. We find that the micelle structural properties (such as the shape, size, the LDAO headgroup hydration, and alkyl chain conformation) slightly depend on the force field but not on the starting conditions and more importantly are in good agreement with experiments and previous simulations. We also show that the Lipid14 force field should be used instead of the Amber99SB one to better reproduce the C(sp3)C(sp3)C(sp3)C(sp3) conformation in the surfactant alkyl chain. Concerning the simulations with LDAO-DI protein, we carried out different runs at two NaCl concentrations (i.e. 0 and 300 mM) to mimic, in the latter case, the experimental conditions. We notice a small dependence of the simulation results with the LDAO parameters and the salt concentration. However, we find that in the simulations, three out of four tryptophans of the DI protein are not accessible to water in agreement with our fluorescence spectroscopy experiments reported in the paper.     

New Multicentre Point Charge Models for Molecular Electrostatic Potentials from Semiempirical M0-Calculations

Two quasi-multipole electrostatic models for molecular charge distributions are presented. They assign arrays of point charges to nonhydrogen atoms on the basis of hybrid orbitals or localised molecular orbitals. When used with common semiempirical MO-techniques, they reproduce natural atomic orbital derived point charge (NAO-PC) and ab initio molecular potentials well. The localised orbital technique (LMO-PC) is intuitively more attractive than the hybrid orbital-point charge (HO-PC) method, although the former is more CPU-intensive.Electronic Supplementary Material available.     

Dynamics and Binding Modes of Free cdk2 and its Two Complexes with Inhibitors Studied by Computer Simulations

Abstract

This article presents a molecular dynamics (MD) study of the cdk2 enzyme and its two complexes with the inhibitors isopentenyladenine and roscovitine using the Cornell et al. force field from the AMBER software package. The results show that inserting an inhibitor into the enzyme active site does not considerably change enzyme structure but it seemingly changes the distribution of internal motions. The inhibitor causes differences in the domain motions in free cdk2 and in its complexes. It was found out that repulsion of roscovitine N9 substituent causes conformational change on Lys 33 side chain. Isopentenyladenine forms with Lys 33 side chain terminal amino group a hydrogen bond. It implies that the cavity, where N9 substituent of roscovitine is buried, can adopt larger substituent due to Lys 33 side chain flexibility. The composition of electrostatic and van der Waals interactions between the inhibitor and the enzyme were also calculated along both cdk2/inhibitor MD trajectories together with MM-PB/GBSA analysis. These results show that isopentenyladenine-like inhibitors could be more effective after modifications leading to an increase in their van der Waals contact with the enzyme. We suggest that a way leading to better inhibitors occupying isopentenyladenine binding mode could be: to keep N9 and N7 purine positions free, to keep 3,3-dimethylallylamino group at C6 position, and to add, e.g., benzylamino group at C2 position. The results support the idea that the isopentenyladenine binding mode can be used for cdk2 inhibitors design and that all possibilities to improve this binding mode were not uncovered yet.     

Hybridization-displaced charges for amino-acids: a new model using two point charges per atom along with bond-center charges

A new charge distribution is proposed for the amino acids where each atom is associated with two point charges while each bond center is associated with one point charge. Centroids of charges arising due to atomic orbital hybridization called hybridization-displaced charges (HDC) and those located at the atomic sites and bond centers obtained by a modified form of the Mulliken scheme were combined. The density matrix calculations required for this analysis were performed at the B3LYP/6-31G** level of density functional theory. The combination of HDC centroids with the modified Mulliken charges was found to yield dipole moments and surface molecular electrostatic potentials (MEP) of the amino acids in good agreement with those obtained by rigorous DFT calculations or those obtained using the MEP-fitted CHelpG charges. This study shows that the combination of HDC centroids with the modified Mulliken charges is significantly superior to the conventional Mulliken charges.     

The electrostatic potential for the phosphodiester group determined from X-ray diffraction.

The charge density distribution in the crystal structure of ammonium dimethylphosphate at 123 K has been determined from x-ray diffraction data (MoK alpha) using 8437 reflections with sin theta/lambda less than 1.33 A-1 [NH4+.(CH3)2PO4-, M(r) = 143.08, monoclinic, P2(1)/c, a = 10.007(1), b = 6.926(1), c = 9.599(2) A, beta = 105.40(1) degrees, V = 641.4(3) A3, Z = 4, F000 = 304, Dx = 1.4815 g.cm-3, mu = 3.726 cm-1]. Least-squares structure refinement assuming Stewart's rigid pseudoatom model (variables including Slater-type radial exponents and electron populations for multipole terms extending to octapoles for C, N, O, and P, and dipoles for H) gave R(F2) = 0.039 for all reflections. The dimethylphosphate anion is in the gauche-gauche conformation and has approximate twofold symmetry. One phosphoryl O atom forms three hydrogen bonds and the other forms one. Neither of the ester O atoms is hydrogen bonded. For the dimethylphosphate anion isolated from the crystal structure, a map of the electrostatic potential obtained using the pseudoatom charge parameters shows that the phosphoryl O atoms are considerably more electronegative than the ester O atoms. The electrostatic potential distribution obtained in this way has been fitted by least squares to a system of atom-centered point charges. The potential calculated from these point charges agrees with the experimental result. It also agrees reasonably well with potentials obtained from three other systems of point charges that are widely used as part of the semiempirical force field for molecular mechanics and molecular dynamics calculations involving nucleic acids.     

Effects of cation charges on the binding of stabilizers with human telomere and TERRA G-quadruplexes

Both telomere and telomeric repeat-containing RNAs (TERRA) can fold into G-quadruplexes (G4) in eukaryotic cells. Given their key roles in the regulation of telomere length and translation, telomere and TERRA G4 are interesting targets of novel drug development strategies. It is known that the cation charge of a stabilizer is crucial to the binding of G4 and stabilizer. However, the quantitative relationship between the cation charge of a stabilizer and the binding strengths with telomere and TERRA G4 remain unclear. In the current study, by substituting positive charged TMPyP4 with neutral and negative charged groups, the effects of cation charges on the binding conformation and binding strength of porphyrin stabilizers are investigated via molecular docking and molecular dynamic (MD) simulations. The results show that all TMPyP4 analogs form stable binding complexes with telomere and TERRA G4 and that, stabilizer charges have limited effects on binding conformation and can hardly lead to any special conformational alternations of G4. Our hydrogen bond analysis shows that all stabilizers can hardly form stable intermolecular hydrogen bonds with G4. Regarding binding strength levels, a linear correlation is found between the binding free energies and cation charges of stabilizers in all G4?stabilizer complexes, revealing the pivotal role of electrostatic interactions. The present work is the first to reveal a quantitative correlation between the charges and binding strengths of stabilizers in their binding with human telomere and TERRA G4, which will prove pivotal for G4 targeted drug design and development.     

Kinetics of nanochain formation in a simplified model of amelogenin biomacromolecules

We show that the kinetics of nanochain formation of amelogenin molecules is well described by a combination of translational and rotational diffusion of a simplified anisotropic bipolar model consisting of hydrophobic spherical colloid particles and a point charge located on each particle surface. The colloid particles interact via a standard depletion attraction whereas the point charges interact through a screened Coulomb repulsion. We study the kinetics via a Brownian dynamics simulation of both translational and rotational motions and show that the anisotropy brought in by the charge dramatically affects the kinetic pathway of cluster formation and our simple model captures the main features of the experimental observations.     

Polycations as prostaglandin sythesis inducers. II. structure-activity relationships

Moderately high molecular weight polycations stimulate arachidonic acid release with concomitant synthesis and release of prostaglandins in cultured 3T3 mouse fibroblasts. We have examined a series of synthetic polycations for prostaglandin synthesis-inducing activity as an approach to defining the structural features required for activity. Extensive (>80%) acetylation of poly(vinylamine) was tolerated without loss of activity, indicating that a uniform high density of charges is not required. However, complete acetylation of poly(vinylamine) abolished activity, indicating that some positive charges are required for activity. Full activity was observed for charge densities in the range of one per two to one per six atoms of polymer backbone. Branched and linear polycations activated equally well. Location of the charge with respect to the polymer backbone did not affect activity in polymers bearing charges located up to seven atoms away from the backbone. Polycations lacking primary or secondary amino groups exhibited full activity, indicating that Schiff base formation is not required for activity. These results are consistent with a model in which activation involves electrostatic interactions with discrete anionic sites on the target cell.     

Polycations as prostaglandin synthesis inducers. II. Structure-activity relationships

Moderately high molecular weight polycations stimulate arachidonic acid release with concomitant synthesis and release of prostaglandins in cultured 3T3 mouse fibroblasts. We have examined a series of synthetic polycations for prostaglandin synthesis-inducing activity as an approach to defining the structural features required for activity. Extensive (greater than 80%) acetylation of poly(vinylamine) was tolerated without loss of activity, indicating that a uniform high density of charges is not required. However, complete acetylation of poly(vinylamine) abolished activity, indicating that some positive charges are required for activity. full activity was observed for charge densities in the range of one per two to one per six atoms of polymer backbone. Branched and linear polycations activated equally well. Location of the charge with respect to the polymer backbone did not affect activity in polymers bearing charges located up to seven atoms away from the backbone. Polycations lacking primary or secondary amino groups exhibited full activity, indicating that Schiff base formation is not required for activity. These results are consistent with a model in which activation involves electrostatic interactions with discrete anionic sites on the target cell.     

Building proteins from C alpha coordinates using the dihedral probability grid Monte Carlo method.

Dihedral probability grid Monte Carlo (DPG-MC) is a general-purpose method of conformational sampling that can be applied to many problems in peptide and protein modeling. Here we present the DPG-MC method and apply it to predicting complete protein structures from C alpha coordinates. This is useful in such endeavors as homology modeling, protein structure prediction from lattice simulations, or fitting protein structures to X-ray crystallographic data. It also serves as an example of how DPG-MC can be applied to systems with geometric constraints. The conformational propensities for individual residues are used to guide conformational searches as the protein is built from the amino-terminus to the carboxyl-terminus. Results for a number of proteins show that both the backbone and side chain can be accurately modeled using DPG-MC. Backbone atoms are generally predicted with RMS errors of about 0.5 A (compared to X-ray crystal structure coordinates) and all atoms are predicted to an RMS error of 1.7 A or better.