Molecular Dynamics Simulations of a DMPC Bilayer Using Nonadditive Interaction Models

We present a polarizable force field based on the charge-equilibration formalism for molecular dynamics simulations of phospholipid bilayers. We discuss refinement of headgroup dihedral potential parameters to reproduce ab initio conformational energies of dimethylphosphate calculated at the MP2/cc-pVTZ level of theory. We also address the refinement of electrostatic and Lennard-Jones (van der Waals) parameters to reproduce ab initio polarizabilities and water interaction energies of dimethylphosphate and tetramethylammonium. We present results of molecular dynamics simulations of a solvated dimyristoylphosphatidylcholine bilayer using this polarizable force field as well as the nonpolarizable, fixed-charge CHARMM27 and CHARMM27r force fields for comparison. Calculated atomic and electron-density profiles, deuterium order parameters, and headgroup orientations are found to be consistent with previous simulations and with experiment. Polarizable interaction models for solvent and lipid exhibit greater water penetration into the lipid interior; this is due to the variation of water molecular dipole moment from a bulk value of 2.6 Debye to a value of 1.9 Debye in the membrane interior. The reduction in the electrostatic component of the desolvation free-energy penalty allows for greater water density. The surface dipole potential predicted by the polarizable model is 0.95 V compared to the value of 0.8 V based on nonpolarizable force-field calculations. Effects of inclusion of explicit polarization are discussed in relation to water dipole moment and varying charge distributions. Dielectric permittivity profiles for polarizable and nonpolarizable interactions exhibit subtle differences arising from the nature of the individual component parameterizations; for the polarizable force field, we obtain a bulk dielectric permittivity of 79, whereas the nonpolarizable force field plateaus at 97 (the value for pure TIP3P water). In the membrane interior, both models predict unit permittivities, with the polarizable models contributing from one to two more units due to the optical dielectric (high-frequency dipole fluctuations). This contribution is a step toward the continuing development of a CHARMM (Chemistry at Harvard Molecular Mechanics) polarizable force field for simulations of biomacromolecular systems.     

Reparameterization of all-atom dipalmitoylphosphatidylcholine lipid parameters enables simulation of fluid bilayers at zero tension

Molecular dynamics simulations of dipalmitoylphosphatidylcholine (DPPC) lipid bilayers using the CHARMM27 force field in the tensionless isothermal-isobaric (NPT) ensemble give highly ordered, gel-like bilayers with an area per lipid of approximately 48 A(2). To obtain fluid (L(alpha)) phase properties of DPPC bilayers represented by the CHARMM energy function in this ensemble, we reparameterized the atomic partial charges in the lipid headgroup and upper parts of the acyl chains. The new charges were determined from the electron structure using both the Mulliken method and the restricted electrostatic potential fitting method. We tested the derived charges in molecular dynamics simulations of a fully hydrated DPPC bilayer. Only the simulation with the new restricted electrostatic potential charges shows significant improvements compared with simulations using the original CHARMM27 force field resulting in an area per lipid of 60.4 +/- 0.1 A(2). Compared to the 48 A(2), the new value of 60.4 A(2) is in fair agreement with the experimental value of 64 A(2). In addition, the simulated order parameter profile and electron density profile are in satisfactory agreement with experimental data. Thus, the biologically more interesting fluid phase of DPPC bilayers can now be simulated in all-atom simulations in the NPT ensemble by employing our modified CHARMM27 force field.     

Substrate polarization in enzyme catalysis: QM/MM analysis of the effect of oxaloacetate polarization on acetyl-CoA enolization in citrate synthase

Citrate synthase is an archetypal carbon-carbon bond forming enzyme. It promotes the conversion of oxaloacetate (OAA) to citrate by catalyzing the deprotonation (enolization) of acetyl-CoA, followed by nucleophilic attack of the enolate form of this substrate on OAA to form a citryl-CoA intermediate and subsequent hydrolysis. OAA is strongly bound to the active site and its alpha-carbonyl group is polarized. This polarization has been demonstrated spectroscopically, [(Kurz et al., Biochemistry 1985;24:452-457; Kurz and Drysdale, Biochemistry 1987;26:2623-2627)] and has been suggested to be an important catalytic strategy. Substrate polarization is believed to be important in many enzymes. The first step, formation of the acetyl-CoA enolate intermediate, is thought to be rate-limiting in the mesophilic (pig/chicken) enzyme. We have examined the effects of substrate polarization on this key step using quantum mechanical/molecular mechanical (QM/MM) methods. Free energy profiles have been calculated by AM1/CHARMM27 umbrella sampling molecular dynamics (MD) simulations, together with potential energy profiles. To study the influence of OAA polarization, profiles were calculated with different polarization of the OAA alpha-carbonyl group. The results indicate that OAA polarization influences catalysis only marginally but has a larger effect on intermediate stabilization. Different levels of treatment of OAA are compared (MM or QM), and its polarization in the protein and in water analyzed at the B3LYP/6-31+G(d)/CHARMM27 level. Analysis of stabilization by individual residues shows that the enzyme mainly stabilizes the enolate intermediate (not the transition state) through electrostatic (including hydrogen bond) interactions: these contribute much more than polarization of OAA.     

Quantum chemical analysis explains hemagglutinin peptide-MHC Class II molecule HLA-DRbeta1*0101 interactions

We present a new method to explore interactions between peptides and major histocompatibility complex (MHC) molecules using the resultant vector of the three principal multipole terms of the electrostatic field expansion. Being that molecular interactions are driven by electrostatic interactions, we applied quantum chemistry methods to better understand variations in the electrostatic field of the MHC Class II HLA-DRbeta1*0101-HA complex. Multipole terms were studied, finding strong alterations of the field in Pocket 1 of this MHC molecule, and weak variations in other pockets, with Pocket 1>Pocket 4>Pocket 9 approximately Pocket 7>Pocket 6. Variations produced by "ideal" amino acids and by other occupying amino acids were compared. Two types of interactions were found in all pockets: a strong unspecific one (global interaction) and a weak specific interaction (differential interaction). Interactions in Pocket 1, the dominant pocket for this allele, are driven mainly by the quadrupole term, confirming the idea that aromatic rings are important in these interactions. Multipolar analysis is in agreement with experimental results, suggesting quantum chemistry methods as an adequate methodology to understand these interactions.     

Polarizability rescaling and atom-based Thole scaling in the CHARMM Drude polarizable force field for ethers

Within the CHARMM polarizable force field based on the classical Drude oscillator, atomic polarizabilities are derived via fitting to ab initio calculated data on isolated gas phase molecules, with an empirical scaling factor applied to account for differences between the gas and condensed phases. In the development of polarizable models for the ethers, a polarizability scaling factor of 0.7 was previously applied [Vorobyov et al. J Comput Chem 3:1120–1133, 2007]. While the resulting force field models gave good agreement with a variety of experimental data, they systematically underestimated the liquid phase dielectric constants. Here, a new CHARMM polarizable model is developed for the ethers, employing a polarizability scaling factor of 0.85 and including atom-based Thole scale factors recently introduced into the CHARMM Drude polarizable force field [Harder et al. J Phys Chem B 112:3509-3521, 2008]. The new model offers a significant improvement in the reproduction of liquid phase dielectric constants, while maintaining the good agreement of the previous model with all other experimental and quantum mechanical data, highlighting the sensitivity of liquid phase properties to the choice of atomic polarizability parameters.     

Force field comparisons of the heat capacity of carbon nanotubes

The force fields Tersoff, CHARMM, COMPASS, CVFF and PCFF are compared using molecular calculations and simulations of SWNT thermal properties. The heat capacity results from the force fields vary significantly in the low (room) temperature range. The COMPASS force field best reproduces the phonon frequencies calculated from density functional theory and is consistent with the Raman scattering results. The temperature dependent behavior of SWNT heat capacity is investigated using harmonic and quasi-harmonic dynamics theories. The impact of quasi-harmonic analysis is not significant in the low and intermediate temperature range (below 500 K). Thus, force field comparisons based on the harmonic approximation are valid in that temperature range. Above 500 K, heat capacity results based on the Tersoff force field using a quasi-harmonic approximation are further investigated.     

工业酶研究中的计算化学方法

文中介绍用于工业酶研究特别是用于指导酶工程的主要计算化学方法,包括分子力学力场和分子动力学模拟、量子力学以及量子力学/分子力学结合模型、连续介质静电模型以及分子对接等。文中从以下两个角度分别概要地介绍这些方法:一是方法本身的基本概念、原始计算结果、适用条件和优缺点等;二是通过计算得到有价值的信息,指导突变体和突变库设计。     

Experimental validation of molecular dynamics simulations of lipid bilayers: a new approach

A novel protocol has been developed for comparing the structural properties of lipid bilayers determined by simulation with those determined by diffraction experiments, which makes it possible to test critically the ability of molecular dynamics simulations to reproduce experimental data. This model-independent method consists of analyzing data from molecular dynamics bilayer simulations in the same way as experimental data by determining the structure factors of the system and, via Fourier reconstruction, the overall transbilayer scattering-density profiles. Multi-nanosecond molecular dynamics simulations of a dioleoylphosphatidylcholine bilayer at 66% RH (5.4 waters/lipid) were performed in the constant pressure and temperature ensemble using the united-atom GROMACS and the all-atom CHARMM22/27 force fields with the GROMACS and NAMD software packages, respectively. The quality of the simulated bilayer structures was evaluated by comparing simulation with experimental results for bilayer thickness, area/lipid, individual molecular-component distributions, continuous and discrete structure factors, and overall scattering-density profiles. Neither the GROMACS nor the CHARMM22/27 simulations reproduced experimental data within experimental error. The widths of the simulated terminal methyl distributions showed a particularly strong disagreement with the experimentally observed distributions. A comparison of the older CHARMM22 with the newer CHARMM27 force fields shows that significant progress is being made in the development of atomic force fields for describing lipid bilayer systems empirically.     

Effects of force fields on the conformational and dynamic properties of amyloid β(1‐40) dimer explored by replica exchange molecular dynamics simulations

The conformational space and structural ensembles of amyloid beta (Aβ) peptides and their oligomers in solution are inherently disordered and proven to be challenging to study. Optimum force field selection for molecular dynamics (MD) simulations and the biophysical relevance of results are still unknown. We compared the conformational space of the Aβ(1‐40) dimers by 300 ns replica exchange MD simulations at physiological temperature (310 K) using: the AMBER‐ff99sb‐ILDN, AMBER‐ff99sb*‐ILDN, AMBER‐ff99sb‐NMR, and CHARMM22* force fields. Statistical comparisons of simulation results to experimental data and previously published simulations utilizing the CHARMM22* and CHARMM36 force fields were performed. All force fields yield sampled ensembles of conformations with collision cross sectional areas for the dimer that are statistically significantly larger than experimental results. All force fields, with the exception of AMBER‐ff99sb‐ILDN (8.8 ± 6.4%) and CHARMM36 (2.7 ± 4.2%), tend to overestimate the α‐helical content compared to experimental CD (5.3 ± 5.2%). Using the AMBER‐ff99sb‐NMR force field resulted in the greatest degree of variance (41.3 ± 12.9%). Except for the AMBER‐ff99sb‐NMR force field, the others tended to under estimate the expected amount of β‐sheet and over estimate the amount of turn/bend/random coil conformations. All force fields, with the exception AMBER‐ff99sb‐NMR, reproduce a theoretically expected β‐sheet‐turn‐β‐sheet conformational motif, however, only the CHARMM22* and CHARMM36 force fields yield results compatible with collapse of the central and C‐terminal hydrophobic cores from residues 17‐21 and 30‐36. Although analyses of essential subspace sampling showed only minor variations between force fields, secondary structures of lowest energy conformers are different.     

Solution conformational study of nociceptin an(d its 1-13 and 1-11 fragments using circular dichroism and two-dimensional NMR in conjunction with theoretical conformational analysis.

Conformational studies of nociceptin (NC-NH2), its fully active fragment, NC(1-13)-NH2, and two significantly less potent fragments, NC(1-13)-OH and NC(1-11)-OH, were conducted in water and TFE solutions by the employment of circular dichroism, and in DMSO-d6 by 2DNMR spectroscopy in conjunction with theoretical conformational analysis. The conformations of all thepeptides studied were calculated taking two approaches. The first assumes multiconformational equilibrium of the peptide studied, which is characterized by a set of conformations (and their statistical weight values)obtained from a global conformational analysis using three methods: the electrostatically driven Monte-Carlo (EDMC) with the ECEPP/3 force field, the simulated annealing (SA) protocols in the AMBER and CHARMM force fields. The second approach incorporates the interproton distance and dihedral angle constraints into the starting conformation. Calculations were performed using the distance geometry and SA protocol in the CHARMM force field implemented in the X-PLOR program. The CD experiments indicated that for the active peptides, hydrophobic solvents induced a significantly higher (compared with those remaining)content order, probably a helical structure. Unfortunately, as a result of the conformational flexibility of thepeptides, the analysis of conformations obtained with both approaches and different force fields did not alllow the selection of any structural elements of the NC peptides that might be connected with their bioactivity. The only common element found in most conformations of the active peptides was a helical character of fragment 8-13, which allowed the side chains of basic amino acid residues to be exposed to the outside of the molecule and probably to interact with the ORL1 receptor.     

Thermodynamics calculation of protein–ligand interactions by QM/MM polarizable charge parameters

The calculation of protein–ligand binding free energy (ΔG) is of great importance for virtual screening and drug design. Molecular dynamics (MD) simulation has been an attractive tool to investigate this scientific problem. However, the reliability of such approach is affected by many factors including electrostatic interaction calculation. Here, we present a practical protocol using quantum mechanics/molecular mechanics (QM/MM) calculations to generate polarizable QM protein charge (QMPC). The calculated QMPC of some atoms in binding pockets was obviously different from that calculated by AMBER ff03, which might significantly affect the calculated ΔG. To evaluate the effect, the MD simulations and MM/GBSA calculation with QMPC for 10 protein–ligand complexes, and the simulation results were then compared to those with the AMBER ff03 force field and experimental results. The correlation coefficient between the calculated ΔΔG using MM/GBSA under QMPC and the experimental data is .92, while that with AMBER ff03 force field is .47 for the complexes formed by streptavidin or its mutants and biotin. Moreover, the calculated ΔΔG with QMPC for the complexes formed by ERβ and five ligands is positively related to experimental result with correlation coefficient of .61, while that with AMBER ff03 charge is negatively related to experimental data with correlation coefficient of .42. The detailed analysis shows that the electrostatic polarization introduced by QMPC affects the electrostatic contribution to the binding affinity and thus, leads to better correlation with experimental data. Therefore, this approach should be useful to virtual screening and drug design.     

On Calculation of the Electrostatic Potential of a Phosphatidylinositol Phosphate-Containing Phosphatidylcholine Lipid Membrane Accounting for Membrane Dynamics

Many signaling events require the binding of cytoplasmic proteins to cell membranes by recognition of specific charged lipids, such as phosphoinositol-phosphates. As a model for a protein-membrane binding site, we consider one charged phosphoinositol phosphate (PtdIns(3)P) embedded in a phosphatidylcholine bilayer. As the protein-membrane binding is driven by electrostatic interactions, continuum solvent models require an accurate representation of the electrostatic potential of the phosphoinositol phosphate-containing membrane. We computed and analyzed the electrostatic potentials of snapshots taken at regular intervals from molecular dynamics simulations of the bilayer. We observe considerable variation in the electrostatic potential of the bilayer both along a single simulation and between simulations performed with the GAFF or CHARMM c36 force fields. However, we find that the choice of GAFF or CHARMM c36 parameters has little effect on the electrostatic potential of a given configuration of the bilayer with a PtdIns(3)P embedded in it. From our results, we propose a remedian averaging method for calculating the electrostatic potential of a membrane system that is suitable for simulations of protein-membrane binding with a continuum solvent model.     

Development and current status of the CHARMM force field for nucleic acids.

The CHARMM27 all-atom force field for nucleic acids represents a highly optimized model for investigations of nucleic acids via empirical force field calculations. The force field satisfactorily treats the A, B, and Z forms of DNA as well as RNA, and it also useful for nucleosides and nucleotides. In addition, it is compatible with the CHARMM force fields for proteins and lipids, allowing for simulation studies of heterogeneous systems.     

Effect of membrane tension on the electric field and dipole potential of lipid bilayer membrane

The dipole potential of lipid bilayer membrane controls the difference in permeability of the membrane to oppositely charged ions. We have combined molecular dynamics (MD) simulations and experimental studies to determine changes in electric field and electrostatic potential of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer in response to applied membrane tension. MD simulations based on CHARMM36 force field showed that electrostatic potential of DOPC bilayer decreases by ~45mV in the physiologically relevant range of membrane tension values (0 to 15dyn/cm). The electrostatic field exhibits a peak (~0.8×10(9)V/m) near the water/lipid interface which shifts by 0.9? towards the bilayer center at 15dyn/cm. Maximum membrane tension of 15dyn/cm caused 6.4% increase in area per lipid, 4.7% decrease in bilayer thickness and 1.4% increase in the volume of the bilayer. Dipole-potential sensitive fluorescent probes were used to detect membrane tension induced changes in DOPC vesicles exposed to osmotic stress. Experiments confirmed that dipole potential of DOPC bilayer decreases at higher membrane tensions. These results are suggestive of a potentially new mechanosensing mechanism by which mechanically induced structural changes in the lipid bilayer membrane could modulate the function of membrane proteins by altering electrostatic interactions and energetics of protein conformational states.     

Conformational solution studies of neuropeptide gamma using CD and NMR spectroscopy.

Neuropeptide gamma is one of the largest members of the tachykinin family of peptides, exhibiting strong agonistic activity towards the NK-2 tachykinin receptor. This peptide was synthesized by the solid-phase method using the Fmoc chemistry. Circular-dichroism spectroscopy (CD) investigations of this peptide were performed in phosphate buffer, in the presence of sodium dodecylsulphate (SDS) micelles and trifluoroethanol (TFE) solutions and in DMSO-d6 using the 2D NMR technique in conjunction with two different theoretical approaches. The first assumes multiconformational equilibrium of the peptide studied characterized by the values of statistical weights of low-energy conformations. These calculations were performed using three different force fields ECEPP/3, AMBER4.1 and CHARMM (implemented in the X-PLOR program). The second method incorporates interproton distance and dihedral angle constraints into the starting conformation using the Simulated Annealing algorithm (X-PLOR program). The CD experiments revealed that although the peptide studied is flexible in polar solvents, a tendency to adopt a helical structure was observed in the hydrophobic environment. The NMR data (NOE effects) indicate a helical or reverse structure in the Ile7-His12 fragment of the peptide studied in DMSO-d6 solution. The results obtained cannot be interpreted in terms of a single conformation. Most of the conformations obtained with the ECEPP/3 force field possess a high content of a helical structure. None of the conformers, obtained with the AMBER4.1 and CHARMM force fields, can be considered as the dominant one. In all conformations several beta-turns were detected and in some cases gamma-turns were also found. But in fact, it is rather difficult to select the position of the secondary element(s) present in the structure of NPgamma in solution. All conformers calculated with the X-PLOR program (with using NMR derived distance and torsion angle constraints) are stabilized by several beta-turns. Common structural motives are a type IV beta-turn in the Gln6-His12 fragment. All conformations obtained using two approaches adopt very similar turn shapes in the middle region of molecule and a random structure on the N- and C-terminal fragments.     

Structural equilibrium of DNA represented with different force fields.

We have recently indicated preliminary evidence of different equilibrium average structures with the CHARMM and AMBER force fields in explicit solvent molecular dynamics simulations on the DNA duplex d(C5T5) . d(A5G5) (Feig, M. and B.M. Pettitt, 1997, Experiment vs. Force Fields: DNA conformation from molecular dynamics simulations. J. Phys. Chem. B. (101:7361-7363). This paper presents a detailed comparison of DNA structure and dynamics for both force fields from extended simulation times of 10 ns each. Average structures display an A-DNA base geometry with the CHARMM force field and a base geometry that is intermediate between A- and B-DNA with the AMBER force field. The backbone assumes B form on both strands with the AMBER force field, while the CHARMM force field produces heterogeneous structures with the purine strand in A form and the pyrimidine strand in dynamical equilibrium between A and B conformations. The results compare well with experimental data for the cytosine/guanine part but fail to fully reproduce an overall B conformation in the thymine/adenine tract expected from crystallographic data, particularly with the CHARMM force field. Fluctuations between A and B conformations are observed on the nanosecond time scale in both simulations, particularly with the AMBER force field. Different dynamical behavior during the first 4 ns indicates that convergence times of several nanoseconds are necessary to fully establish a dynamical equilibrium in all structural quantities on the time scale of the simulations presented here.     

Gramicidin A channel as a test ground for molecular dynamics force fields

We use the well-known structural and functional properties of the gramicidin A channel to test the appropriateness of force fields commonly used in molecular dynamics (MD) simulations of ion channels. For this purpose, the high-resolution structure of the gramicidin A dimer is embedded in a dimyristoylphosphatidylcholine bilayer, and the potential of mean force of a K(+) ion is calculated along the channel axis using the umbrella sampling method. Calculations are performed using two of the most common force fields in MD simulations: CHARMM and GROMACS. Both force fields lead to large central barriers for K(+) ion permeation, that are substantially higher than those deduced from the physiological data by inverse methods. In long MD simulations lasting over 60 ns, several ions are observed to enter the binding site but none of them crossed the channel despite the presence of a large driving field. The present results, taken together with many earlier studies, highlights the shortcomings of the standard force fields used in MD simulations of ion channels and calls for construction of more appropriate force fields for this purpose.