A comparison of the potential energy parameters of aliphatic alkanes: molecular dynamics simulations of triacylglycerols in the alpha phase

A comparison of six GROMOS parameter sets for aliphatic alkanes is presented using simulations of a triglyceride, trioctanoin, in the gel or alpha phase. It is found that the parameter set 43A2 results in a system that is rigid and close packed, forcing a collective tilt of the molecules, known experimentally to be disallowed. The parameter set 45A3-45 results in an expanded system where the molecules undergo a conformational change from the chair to tuning-fork form. The lamellae are fragmented, with the fragments shifted in the direction parallel to the layer normal. The newest parameter set 45A3, when used with either of two sets of partial charges for the glycerol ester group, retains the characteristics of the gel phase. The last parameter set tested, 45A3-45x12, also performs well when combined with either set of partial charges, although the system expands in the plane of the bilayer.     

On the use of one-step perturbation to investigate the dependence of NOE-derived atom–atom distance bound violations of peptides upon a variation of force-field parameters

The method of one-step perturbation can be used to predict from a single molecular dynamics simulation the values of observable quantities as functions of variations in the parameters of the Hamiltonian or biomolecular force field used in the simulation. The method is used to predict violations of nuclear overhauser effect (NOE) distance bounds measured in nuclear magnetic resonance (NMR) experiments by atom–atom distances of the NOE atom pairs when varying force-field parameters. Predictions of NOE distance bound violations between different versions of the GROMOS force field for a hexa-β-peptide in solution show that the technique works for rather large force-field parameter changes as well as for very different NOE bound violation patterns. The effect of changing individual force-field parameters on the NOE distance bound violations of the β-peptide and an α-peptide was investigated too. One-step perturbation, which in this case is equivalent to reweighting configurations, constitutes an efficient technique to predict many values of different quantities from a single conformational ensemble for a particular system, which makes it a powerful force-field development technique that easily reduces the number of required separate simulations by an order of magnitude.     

Molecular dynamics simulation of human interleukin-4: comparison with NMR data and effect of pH,counterions and force field on tertiary structure stability

The human protein interleukin-4 (IL-4) has been simulated at two different pH values 2 and 6, with different amounts of counterions present in the aqueous solution, and with two different force-field parameter sets using molecular dynamics simulation with the aim of validation of force field and simulation set-up by comparison to experimental nuclear magnetic resonance data, such as proton–proton nuclear Overhauser effect (NOE) distance bounds, ³ J(HN,HC_α) coupling constants and backbone N–H order parameters. Thirteen simulations varying in the length from 3 to 7 ns are compared.

At pH 6 both force-field parameter sets used do largely reproduce the NOE's and order parameters, the GROMOS 45A3 set slightly better than the GROMOS 53A6 set. ³ J values predicted from the simulation agree less well with experimental values. At pH 2 the protein unfolds, unless counterions are explicitly present in the system, but even then the agreement with experiment is worse than at pH 6. When simulating a highly charged protein, such as IL-4 at pH 2, the inclusion of counterions in the simulation seems mandatory.     

Lipidbook: A Public Repository for Force-Field Parameters Used in Membrane Simulations

Lipidbook is a public database for force-field parameters with a special emphasis on lipids, detergents and similar molecules that are of interest when simulating biological membrane systems. It stores parameter files that are supplied by the community. Topologies, parameters and lipid or whole bilayer structures can be deposited in any format for any simulation code, preferably under a license that promotes “open knowledge.” A number of mechanisms are implemented to aid a user in judging the appropriateness of a given parameter set for a project. For instance, parameter sets are versioned, linked to the primary citation via PubMed identifier and digital object identifier (DOI), and users can publicly comment on deposited parameters. Licensing and, hence, the conditions for use and dissemination of academically generated data are often unclear. In those cases it is also possible to provide a link instead of uploading a file. A snapshot of the linked file is then archived using the WebCite^® service without further involvement of the user or Lipidbook, thus ensuring a transparent and permanent history of the parameter set. Lipidbook can be accessed freely online at http://lipidbook.bioch.ox.ac.uk. Deposition of data requires online registration.     

Validation of the 53A6 GROMOS force field

The quality of biomolecular dynamics simulations relies critically on the force field that is used to describe the interactions between particles in the system. Force fields, which are generally parameterized using experimental data on small molecules, can only prove themselves in realistic simulations of relevant biomolecular systems. In this work, we begin the validation of the new 53A6 GROMOS parameter set by examining three test cases. Simulations of the well-studied 129 residue protein hen egg-white lysozyme, of the DNA dodecamer d(CGCGAATTCGCG)₂, and a proteinogenic ³-dodecapeptide were performed and analysed. It was found that the new parameter set performs as well as the previous parameter sets in terms of protein (45A3) and DNA (45A4) stability and that it is better at describing the folding–unfolding balance of the peptide. The latter is a property that is directly associated with the free enthalpy of hydration, to which the 53A6 parameter set was parameterized.     

Temperature and urea induced denaturation of the TRP‐cage mini protein TC5b: A simulation study consistent with experimental observations

The effects of temperature and urea denaturation (6M urea) on the dominant structures of the 20‐residue Trp‐cage mini‐protein TC5b are investigated by molecular dynamics simulations of the protein at different temperatures in aqueous and in 6M urea solution using explicit solvent degrees of freedom and the GROMOS force‐field parameter set 45A3. In aqueous solution at 278 K, TC5b is stable throughout the 20 ns of MD simulation and the trajectory structures largely agree with the NMR‐NOE atom–atom distance data available. Raising the temperature to 360 K and to 400 K, the protein denatures within 22 ns and 3 ns, showing that the denaturation temperature is well below 360 K using the GROMOS force field. This is 40–90 K lower than the denaturation temperatures observed in simulations using other much used protein force fields. As the experimental denaturation temperature is about 315 K, the GROMOS force field appears not to overstabilize TC5b, as other force fields and the use of continuum solvation models seem to do. This feature may directly stem from the GROMOS force‐field parameter calibration protocol, which primarily involves reproduction of condensed phase thermodynamic quantities such as energies, densities, and solvation free energies of small compounds representative for protein fragments. By adding 6M urea to the solution, the onset of denaturation is observed in the simulation, but is too slow to observe a particular side‐chain side‐chain contact (Trp6‐Ile4) that was experimentally observed to be characteristic for the denatured state. Interestingly, using temperature denaturation, the process is accelerated and the experimental data are reproduced.     

Validation of the GROMOS force-field parameter set 45A3 against nuclear magnetic resonance data of hen egg lysozyme

The quality of molecular dynamics (MD) simulations of proteins depends critically on the biomolecular force field that is used. Such force fields are defined by force-field parameter sets, which are generally determined and improved through calibration of properties of small molecules against experimental or theoretical data. By application to large molecules such as proteins, a new force-field parameter set can be validated. We report two 3.5 ns molecular dynamics simulations of hen egg white lysozyme in water applying the widely used GROMOS force-field parameter set 43A1 and a new set 45A3. The two MD ensembles are evaluated against NMR spectroscopic data NOE atom–atom distance bounds, ³J_NH and ³J coupling constants, and ¹5N relaxation data. It is shown that the two sets reproduce structural properties about equally well. The 45A3 ensemble fulfills the atom–atom distance bounds derived from NMR spectroscopy slightly less well than the 43A1 ensemble, with most of the NOE distance violations in both ensembles involving residues located in loops or flexible regions of the protein. Convergence patterns are very similar in both simulations atom-positional root-mean-square differences (RMSD) with respect to the X-ray and NMR model structures and NOE inter-proton distances converge within 1.0–1.5 ns while backbone ³J_HN-coupling constants and ¹H– ¹5N order parameters take slightly longer, 1.0–2.0 ns. As expected, side-chain ³J-coupling constants and ¹H– ¹5N order parameters do not reach full convergence for all residues in the time period simulated. This is particularly noticeable for side chains which display rare structural transitions. When comparing each simulation trajectory with an older and a newer set of experimental NOE data on lysozyme, it is found that the newer, larger, set of experimental data agrees as well with each of the simulations. In other words, the experimental data converged towards the theoretical result.     

Comparison of energy-minimized crystal structures of 2,3-dilauroyl-D-glycerol, 3-palmitoyl-DL-glycerol-1-phosphorylethanolamine and 1,2-dilauroyl-DL-phosphatidylethanolamine:acetic acid

Computational procedures have been developed by which the total energy of a lipid multibilayer can be calculated and minimized. The energy is expressed as a sum of non-bonded, electrostatic, hydrogen bonded and torsional energy terms and includes intramolecular and intermolecular components. Calculations were carried out on three lipid crystals for which structural data are available from X-ray diffraction analysis. For each crystal, the energy was minimized as a function of all bond rotations, molecular rotations and translations and the lattice constants. The minimized structures differed by only small amounts from the experimental structures, which confirms the validity of the current set of energy functions and parameters for use with lipids. The intermolecular energy of each crystal is analyzed in terms of lateral interactions, interactions between the two monolayers of the same bilayer and interactions between bilayers. The intermolecular non-bonded energy per CH2 or CH3 group in the acyl chains is also given.     

Molecular dynamics simulation of hen egg white lysozyme: a test of the GROMOS96 force field against nuclear magnetic resonance data

Biomolecular force fields for use in molecular dynamics (MD) simulations of proteins, DNA, or membranes are generally parametrized against ab initio quantum-chemical and experimental data for small molecules. The application of a force field in a simulation of a biomolecular system, such as a protein in solution, may then serve as a test of the quality and transferability of the force field. Here, we compare various properties obtained from two MD simulations of the protein hen egg white lysozyme (HEWL) in aqueous solution using the latest version, GROMOS96, of the GROMOS force field and an earlier version, GROMOS87+, with data derived from nuclear magnetic resonance (NMR) experiments: NOE atom-atom distance bounds, (3)J(HNalpha)-coupling constants, and backbone and side-chain order parameters. The convergence of these quantities over a 2-ns period is considered, and converged values are compared to experimental ones. The GROMOS96 simulation shows better agreement with the NMR data and also with the X-ray crystal structure of HEWL than the GROMOS87+ simulation, which was based on an earlier version of the GROMOS force field.     

Molecular dynamics study of the lauryl alcohol-laurate model bilayer

Molecular dynamics (MD) calculation of the fluid phase lauryl alcohol-laurate bilayer has been executed based on Berendsen's surface-constrained model. Structure and dynamics of the bilayer have been investigated by analyzing the trajectories of the chain configurations. Newly defined correlation functions as well as the conventional ones showed that the tilt and bend of the chain play an important role in the bilayer structure, including behavior of the order parameter. Interpenetration of the layers as well as formation of collectively ordered small domains was also found. The calculated lateral diffusion coefficient was in satisfactory agreement with the experimental one. Successive jumps of the head group, rather than the hydrodynamic continuous motion, were observed. Between the jumps, the molecule librated in a local site. Time-dependent autocorrelation functions showed evidence of several different modes of the chain motion, whose time constant ranged from a few tenths of picoseconds to several tens of picoseconds.     

Studying the structure of single-component ceramide bilayers with molecular dynamics simulations using different force fields

Molecular dynamics simulations are performed on a lipid bilayer that consists of ceramide NS 24:0 in an attempt to examine several structural and physicochemical properties of the specific system. The simulations are carried out with five different force fields (OPLS, GROMOS, BERGER, CHARMM and GAFF) in order to evaluate and compare their performance in modelling lipid systems that contain ceramides. The examined properties include bilayer thickness, chain tilt, density profiles, order parameters, chain conformation, area per lipid and (intermolecular or intramolecular) hydrogen bonding between the head groups. Special focus is given to the lateral lipid arrangement. To this purpose, a method is proposed that utilises the radial distribution functions of the alkyl chains to derive quantitative information about the lateral lipid packing. In most cases, all force fields lead to similar results. For a few properties (e.g. intramolecular hydrogen bonding), there is some discrepancy between the force fields but the lack of respective experimental data does not allow an unambiguous conclusion on which force field is the most reliable.     

Multiple binding modes for palmitate to barley lipid transfer protein facilitated by the presence of proline 12

Molecular dynamics simulations have been used to characterise the binding of the fatty acid ligand palmitate in the barley lipid transfer protein 1 (LTP) internal cavity. Two different palmitate binding modes (1 and 2), with similar protein–ligand interaction energies, have been identified using a variety of simulation strategies. These strategies include applying experimental protein–ligand atom–atom distance restraints during the simulation, or protonating the palmitate ligand, or using the vacuum GROMOS 54B7 force‐field parameter set for the ligand during the initial stages of the simulations. In both the binding modes identified the palmitate carboxylate head group hydrogen bonds with main chain amide groups in helix A, residues 4 to 19, of the protein. In binding mode 1 the hydrogen bonds are to Lys 11, Cys 13, and Leu 14 and in binding mode 2 to Thr 15, Tyr 16, Val 17, Ser 24 and also to the OH of Thr 15. In both cases palmitate binding exploits irregularity of the intrahelical hydrogen‐bonding pattern in helix A of barley LTP due to the presence of Pro 12. Simulations of two variants of barley LTP, namely the single mutant Pro12Val and the double mutant Pro12Val Pro70Val, show that Pro 12 is required for persistent palmitate binding in the LTP cavity. Overall, the work identifies key MD simulation approaches for characterizing the details of protein–ligand interactions in complexes where NMR data provide insufficient restraints.     

Protein molecular dynamics with electrostatic force entirely determined by a single Poisson-Boltzmann calculation

The electrostatic force including the intramolecular Coulombic interactions and the electrostatic contribution of solvation effect were entirely calculated by using the finite difference Poisson-Boltzmann method (FDPB), which was incorporated into the GROMOS96 force field to complete a new finite difference stochastic dynamics procedure (FDSD). Simulations were performed on an insulin dimer. Different relative dielectric constants were successively assigned to the protein interior; a value of 17 was selected as optimal for our system. The simulation data were analyzed and compared with those obtained from 500-ps molecular dynamics (MD) simulation with explicit water and a 500-ps conventional stochastic dynamics (SD) simulation without the mean solvent force. The results indicate that the FDSD method with GROMOS96 force field is suitable to study the dynamics and structure of proteins in solution if used with the optimal protein dielectric constant.     

How alcohol chain-length and concentration modulate hydrogen bond formation in a lipid bilayer

Molecular dynamics simulations are used to measure the change in properties of a hydrated dipalmitoylphosphatidylcholine bilayer when solvated with ethanol, propanol, and butanol solutions. There are eight oxygen atoms in dipalmitoylphosphatidylcholine that serve as hydrogen bond acceptors, and two of the oxygen atoms participate in hydrogen bonds that exist for significantly longer time spans than the hydrogen bonds at the other six oxygen atoms for the ethanol and propanol simulations. We conclude that this is caused by the lipid head group conformation, where the two favored hydrogen-bonding sites are partially protected between the head group choline and the sn-2 carbonyl oxygen. We find that the concentration of the alcohol in the ethanol and propanol simulations does not have a significant influence on the locations of the alcohol/lipid hydrogen bonds, whereas the concentration does impact the locations of the butanol/lipid hydrogen bonds. The concentration is important for all three alcohol types when the lipid chain order is examined, where, with the exception of the high-concentration butanol simulation, the alcohol molecules having the longest hydrogen-bonding relaxation times at the favored carbonyl oxygen acceptor sites also have the largest order in the upper chain region. The lipid behavior in the high-concentration butanol simulation differs significantly from that of the other alcohol concentrations in the order parameter, head group rotational relaxation time, and alcohol/lipid hydrogen-bonding location and relaxation time. This appears to be the result of the system being very near to a phase transition, and one occurrence of lipid flip-flop is seen at this concentration.     

A comparative study of the phase transitions of phospholipid bilayers and monolayers

Phase transitions in bilayers and monolayers of various synthetic phospholipids with different chain lengths as well as different polar head groups were studied by differential scanning calorimetry or with the film balance technique, respectively. With the film balance, area versus temperature curves (isobars) were recorded at different surface pressures. The monolayer phase transition from the fluid-condensed to the fluid-expanded phase is shifted towards higher temperature when the lateral pressure in the monolayer is increased. The temperature dependence of the equilibrium pressure as well as the magnitude of the area change at the transition depends only on the nature of the phospholipid head group and not on the chain length of the hydrocarbon chains of the lipid. Phospholipids with strong intermolecular attractive interactions between the head groups show low values for dpi/dTm and for the area change, deltaf, whereas phospholipids with negatively charged head groups without intermolecular attractive forces exhibit higher values for dpi/dTm and deltaf. The shift of the monolayer phase transition temperature when increasing the chain length of the lipid is almost identical to the shift in Tm observed for the bilayer system of the same phospholipids. A comparison of monolayer and bilayer systems on the basis of the absolute value of the molecular area of the phospholipid in the bilayer gel phase and the change in area at the bilayer and monolayer transition leads to the following conclusions. The behaviour of the bilayer system is very similar to that of the respective monolayer system at a lateral pressure of approx. 30 dyne/cm, because at this pressure the absolute area and the area change in both systems are the same. Further support for this conclusion comes from the experimental finding that a lateral pressure of 30 dyne/cm the shift in Tm due to the increase in charge when the methyl ester of phosphatidic acid is investigated is the same for the bilayer and the monolayer system.     

A comparison of DMPC- and DLPE-based lipid bilayers.

A 250 ps molecular dynamics simulation of the dimyristoylphosphatidylcholine (DMPC)-based lipid bilayer, including explicit water molecules, is reported. The solvent environment of the head groups and other structural properties of the bilayer have been analyzed and compared with experimental results as well as our previous simulation of the dilauroylphosphatidylethanolamine (DLPE)-based bilayer. From this comparison we find that the solvent structure around the DMPC head group (clathrate shell) is significantly different than that around the DLPE head group (typical hydrogen bonding interactions). We have modeled the probable relationship between the different solvent environments around the R-N(CH3)3+ (DMPC) and R-NH3+ (DLPE) head groups and the different interlammelar distances in these systems by performing potential of mean force (PMF) simulations on two N(CH3)4+ and NH4+ ions in water. From the PMF simulations it appears that the differences in the hydration of the DMPC and DLPE head groups is not responsible for the differences in the hydration force observed for these systems. We also find that the orientational polarization of DLPE and DMPC is similar, which suggests that solvent polarization is not responsible for the differences in the hydration repulsion behavior observed in these systems. We also examined the order parameters for DMPC and found them to be in reasonable agreement with experiment. Given the different characteristics of the DLPE and DMPC head groups, we suggest an explanation of the differences in the interlammellar spacings of bilayers composed of these like-charged lipids. From our DLPE simulations we find that the R-NH3+ head groups can interact with the nonesterified oxygens of the phosphate group in an intraleaflet or an interleaflet manner. For the latter a "cross link" between two leaflets can be formed, which causes a stabilization of the interlamellar spacings at fairly short distances. Moreover, due to the strong intraleaflet interaction we find that the DLPE interface is relatively "flat" (as opposed to DMPC-based bilayers), which results in a surface that has regions of positive and negative charge that reside in the same plane along the bilayer normal. Based on this we propose that the DLPE bilayer interface can correlate itself with another DLPE interface by alignment of the regions of positive (or negative) charge on one leaflet with the opposite charges on the opposing leaflet.     

Free energy of helical transmembrane peptide dimerization in OPLS-AA/Berger force field simulations: inaccuracy and implications for partner-specific Lennard-Jones parameters between peptides and lipids

Interactions between transmembrane (TM) peptides are important in biophysical chemistry, but there are few studies assessing atomistic simulation parameters concerning the energetics of interactions of TM helical peptides. Our potential of mean force analysis using OPLS-AA protein/Berger lipid force fields (FFs) shows that the dimerisation energy of (AALALAA)₃ helical peptides in the dioleoylphosphatidylcholine bilayer is ?4.4 kJ/mol, which was much smaller than the reported experimental value (?12.7 kJ/mol), thus calling for improvement of parameters of the combined FFs. As each of the FFs has been independently developed, we then tested the effects of downscaling the Lennard-Jones (LJ) energy terms between the OPLS-AA atoms and Berger lipid atoms, preserving the parameters within each FF. A 0.9-fold rescaling of the LJ energies was found to render the dimerisation energy close to the experimental value. Solvation of backbone atoms as well as side chain atoms in lipids is crucial for the TM helix interaction. In similar analyses, GROMOS 53A6 FF exhibited as weak dimerisation propensity (~?5.2 kJ/mol) as OPLS-AA/Berger, but CHARMM36 showed relatively accurate propensity (~?9.9 kJ/mol). Challenges and strategies in rendering the TM interaction energy realistic within the framework of current FFs are discussed.