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Download Hi-Res ImageDownload to MS-PowerPointCite This:J. Chem. Theory Comput. 2014, 10, 2, 865-879
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Lipid14: The Amber Lipid Force Field

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§ Department of Chemistry and Institute of Chemical Biology, Imperial College London, South Kensington SW7 2AZ, United Kingdom
‡ San Diego Supercomputer Center, University of California San Diego, 9500 Gilman Drive MC0505, La Jolla, California 92093-0505, United States
Department of Biomedicine, University of Bergen, N-5009 Bergen, Norway
± Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive MC0505, La Jolla, California 92093-0505, United States
*E-mail: [email protected]
*E-mail: [email protected]
Cite this: J. Chem. Theory Comput. 2014, 10, 2, 865–879
Publication Date (Web):January 30, 2014
https://doi.org/10.1021/ct4010307
Copyright © 2014 American Chemical Society
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Abstract

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The AMBER lipid force field has been updated to create Lipid14, allowing tensionless simulation of a number of lipid types with the AMBER MD package. The modular nature of this force field allows numerous combinations of head and tail groups to create different lipid types, enabling the easy insertion of new lipid species. The Lennard-Jones and torsion parameters of both the head and tail groups have been revised and updated partial charges calculated. The force field has been validated by simulating bilayers of six different lipid types for a total of 0.5 μs each without applying a surface tension; with favorable comparison to experiment for properties such as area per lipid, volume per lipid, bilayer thickness, NMR order parameters, scattering data, and lipid lateral diffusion. As the derivation of this force field is consistent with the AMBER development philosophy, Lipid14 is compatible with the AMBER protein, nucleic acid, carbohydrate, and small molecule force fields.

Introduction

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Membranes are integral components of the cell, separating intracellular compartments from the cytosol. Such membranes consist of a back-to-back arrangement of lipid molecules, driven into a bilayer structure by the hydrophobic effect, leaving the polar lipid head groups exposed to water, and bringing the nonpolar lipid tail groups together. The composition of cell membranes is complex, with constituent species including, but not limited to, saturated and unsaturated PC and PE lipids, sphingomyelin and cholesterol, which serve as a matrix in which membrane proteins may reside. (1) Cell membranes possess functions such as regulating transport in to and out of the cell and modulating the activity of membrane embedded ion channels and proteins. (2, 3)
In order to probe the many roles of membranes in the cell, membrane structures are studied experimentally using techniques such as X-ray and neutron scattering, IR/Raman, and NMR spectroscopy. (4, 5) To gain atomic-level resolution, however, membranes may also be simulated computationally using molecular dynamics (MD). The validity of results obtained using MD methods depends, to a large extent, on the potential energy function, or force field, that is used.
Membranes can be simulated using all-atom, united-atom, or coarse-grained models, (6-13) with the increasing simplicity of each representation allowing access to larger models and longer time scales, at the expense of atomic detail. All-atom models may be preferred for bilayer simulations due to their ability to reproduce NMR order parameters and easy combination with all-atom protein, nucleic acid, carbohydrate, and small molecule force fields. (14-16) One such MD software package that includes all-atom simulations is AMBER, (17, 18) which contains extensively validated protein, nucleic, carbohydrate, and small molecule force fields. The AMBER simulation code has also been ported to NVIDIA GPU cards, making simulation speeds in excess of 100 ns per day possible for systems of 25,000 to 50,000 atoms, with systems of up to 4 million atoms possible on the latest generation hardware. (19-21) Although the AMBER force field suite includes numerous different species of biological interest, parameters for the simulation of lipids have traditionally been lacking. Recently the Lipid11 framework was introduced, which is a modular lipid AMBER force field, allowing the simulation of a number of lipids via the combination of different head and tail groups. (22) Lipid11 used force field parameters predominantly taken directly from the General Amber Force Field (GAFF). (16) Although previous studies found some success in simulating lipid bilayers using GAFF parameters, (23-25) longer time scale simulations required a surface tension term in order to keep a bilayer in the correct phase at a given temperature. (22)
In this paper we draw inspiration from previous work (26) to update Lipid11 headgroup and tail group charges and parameters to enable proper tensionless simulation of lipid bilayers, thereby creating a modular AMBER lipid force field. Lennard-Jones and torsion parameters are revised, while charges are derived according to the standard AMBER convention, as was implemented in Lipid11 with minor improvements in sampling for Lipid14. As such, the resulting parameters are expected to be compatible with other force fields in the AMBER package.
We validate these parameters for a number of PC and PE lipids – six different lipid types are simulated for a total of 500 ns each, with resulting area per lipid, volume per lipid, isothermal compressibility, NMR order parameters, scattering form factors, and lipid lateral diffusion finding favorable comparison to experiment, particularly for PC lipids. We also assess the conformation of the lipid tails by examining the number of rotamers and rotamer sequences. To fully test the reproducibility of the results, a number of additional GPU and CPU runs were performed. We believe that these parameters will be transferable thus allowing the easy insertion of new lipid types into Lipid14 owing to the modular nature of the force field. The Lipid14 force field will be released with the upcoming AmberTools14. It is our intention to incorporate support for additional lipid types and other residues commonly found in bilayers, as part of the upcoming release. The derivation of these parameters will be described elsewhere.

Parameterization Strategy

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Generation of Lipid14 Parameters

Lipid14 aims to extend the Lipid11 (22) framework to allow accurate, tensionless simulation of numerous lipid types via a modular lipid force field. Bond, angle, torsion, and Lennard-Jones (LJ) parameters in Lipid11 were taken directly from the General Amber Force Field (GAFF). (16) Although bond and angle parameters should not require updating, it was expected that torsion and LJ parameters would need modification to realize this aim.
Previous work on lipid simulation with AMBER indicated that the Lennard-Jones and torsion parameters of the lipid aliphatic tails are intricately linked to the ability of the force field to reproduce experimentally observed bilayer properties. (26) Indeed, the majority of all-atom lipid force field parameterization has involved the modification of the LJ and torsion parameters used to model the aliphatic tail regions of the lipids. (7, 8, 10, 27)
Simulating a box of 144 pentadecane chains using the standard GAFF LJ and torsion parameters at constant pressure (1 atm) and temperature (298.15 K) causes the hydrocarbon chains to ‘freeze’ into a crystalline state in under 2 ns (see Figure 1). Such a scenario has previously been observed by Klauda et al. using a box of tetradecane molecules and the AMBER99 force field. (28) Consequently, the calculated density and heat of vaporization are much higher and the diffusion much lower than experiment.

Figure 1

Figure 1. A box of 144 pentadecane molecules simulated in the NPT ensemble at 298.15 K using the General Amber Force Field (16) to model the carbon chains.

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In light of this, LJ and torsion parameters were modified to reproduce the experimental density (ρ) and heat of vaporization (ΔHvap) of alkanes covering a range of chain lengths. Given that both the torsion and LJ parameters affected the simulated ρ and ΔHvap, these parameters were altered simultaneously, with the CH2–CH2–CH2–CH2 torsion being fitted to ab initio data using Paramfit. (17, 29) Satisfactory agreement was found by modifying only the LJ parameters of the hydrogen atom on the alkane chains.
The modified LJ and torsion parameters were tested by examining the density ρ, heat of vaporization ΔHvap, the diffusion D, the 13C NMR T1 relaxation times, and the trans/gauche conformer populations of a selection of hydrocarbon chains.
The parameters of the ester linkage region connecting headgroup and tail residues in the lipids were then examined using methyl acetate as a model compound. The density and heat of vaporization of methyl acetate were calculated and ΔHvap found to be in poor agreement with experiment. Hence the Lennard-Jones parameters of a number of atoms in this region were also adjusted until better agreement with experiment was achieved.
Once optimal hydrocarbon and glycerol parameters were identified, attention turned to the lipid partial charges. The Lipid11 force field used a capping procedure, separating the lipid head and tail groups into ‘residues’, thus creating a modular lipid force field. (22) The standard AMBER RESP protocol (30) was used to generate partial charges from quantum mechanical (QM) optimized structures, using six different orientations of a single conformation.
This methodology was kept for Lipid14. However, in line with other all-atom lipid force field parameterizations, (10, 31) a greater number of conformations were used per residue (twenty-five headgroup conformations, fifty tail conformations), with the partial charges calculated as an average over all conformations. The head and tail group starting structures were extracted from previous in-house bilayer simulations. This allows one to obtain Boltzmann weighted charges, introducing a temperature dependence. (10, 31) The electrostatic potential (ESP) was calculated directly from the conformations extracted from a bilayer simulation, with no QM optimization performed on those structures. Charges were derived using the standard AMBER RESP protocol (at the HF/6-31G* level in gas phase). (30)
Finally, on identification of appropriate LJ parameters and calculation of lipid partial charges, torsions involving the ester linkage in the glycerol region were fitted to QM scans performed on a capped lauroyl (LA) tail moiety.

Hydrocarbon Tail Parameters

The alkane CH2–CH2–CH2–CH2 torsion potential was refitted using torsion scans performed on hexane and octane molecules using an estimation of the CCSD(T)/cc-pVQZ level of theory via the HM-IE relation (32)where the small basis set (SBS) was cc-pVDZ and the large basis set (LBS) was cc-pVQZ. Consequently molecules were optimized at the MP2/cc-pVDZ level before single-point energy calculations were performed at the CCSD(T)/cc-pVDZ and MP2/cc-pVQZ levels. In order to obtain a representative torsion fit, it was ensured that torsion scans, conducted at increments of 15°, included local minima of hexane and octane. (10, 28, 33) The Paramfit program of AmberTools13 (17, 29) was used to perform a multiple molecule weighted torsion fit, with the tgt local minima of hexane and tgttt local minima of octane given a weighting of 10, all other local minima given a weighting of 4 and cis conformers given a weighting of 0.1; all other structures were assigned a weighting of 1. These weighting values have previously given good results for alkane torsion fitting. (33) Torsions were fitted using a genetic algorithm.
Lennard-Jones parameters were modified while simultaneously refitting the torsion parameters (see Table 1) until good agreement with experiment was achieved for heats of vaporization and densities for a range of alkane chains. These properties were monitored by performing liquid phase simulations of pentane, hexane, heptane, octane, decane, tridecane, and pentadecane. The alkane trajectories also enabled the calculation of a number of other properties for comparison to experiment.
Table 1. Modification of LJ and Torsion Parameters of Alkane Chains
 LJ parametersCH2–CH2–CH2–CH2 torsion
 atom typeradius R (Å)well-depth ε (kcal mol–1)force constant PK (kcal mol–1)periodicity PNphase (deg)
Lipid11cA1.90800.10940.201180
hA1.48700.01570.252180
0.1830
Lipid14cD1.90800.10940.31121180
hL1.46000.0100–0.12332180
0.114930
–0.219940
0.217050
Initial charges for each hydrocarbon chain were generated using the standard AMBER RESP protocol (optimization and calculation of the ESP at HF/6-31G* level in gas phase). A box of 288 (pentane, hexane and heptane) or 144 (octane, decane, tridecane, and pentadecane) molecules were then simulated in the liquid phase at 298.15 K for 10 ns using updated LJ and torsion parameters. From each liquid phase simulation, fifty different chains were extracted and used for the charge calculation, with the ESP calculated directly from each structure at the HF/6-31G* level, and partial charges derived using the RESP fitting procedure. Charges were taken as an average over all fifty RESP fits.
The heat of vaporization was calculated according to (34)(1)where Epot(g) is the average molecular potential energy in the gas phase, Epot(l) is the average molecular potential energy in the liquid phase, R is the gas constant, and T is temperature. In order to calculate the heat of vaporization, two simulations were performed in a similar manner to previous work. (26) A gas phase simulation consisting of a single alkane molecule was run for 10 ns equilibration and 50 ns production under the NPT ensemble, at a temperature of 298.15 K to obtain Epot(g). A liquid phase simulation consisting of a box of either 144 or 288 chains, run under the NPT ensemble with periodic boundary conditions using particle mesh Ewald to treat long-range electrostatics (35) and a real space cutoff of 10 Å, was also performed for 60 ns with the first 10 ns removed for equilibration to obtain Epot(l). The temperature was maintained at 298.15 K using Langevin dynamics and a collision frequency of 5 ps–1. Bonds involving hydrogen were constrained using the SHAKE algorithm. (36) Pressure regulation was achieved with isotropic position scaling, a Berendsen barostat, (37) and a pressure relaxation time of 1 ps. The system was heated from 0 to 298.15 K over 20 ps, with a force constant of 20 kcal/mol/Å2 restraining the chains. This restraint was gradually decreased to 10, 5 and finally 1 kcal/mol/Å2 and the system simulated for 20 ps at each value of the force constant. The heat of vaporization was then calculated using eq 1, with results reported as block averages ± standard deviation using five equal blocks of 10 ns.
By reducing the van der Waals radius (R) and well-depth (ε) of the alkane hydrogen atom type while simultaneously correcting the torsion fit, satisfactory agreement with experiment was achieved for ρ and ΔHvap for the alkane chains under study.
Three torsion scans about the C═C double bond were also performed on a cis-5-decene molecule using the MP2:CC extrapolation method – see Figure 2. When fitting the C═C double bond torsions, the LJ parameters of the alkene hydrogen atom (Lipid14 atom type hB) were scaled until satisfactory agreement with experiment was found for ρ and ΔHvap of cis-2-hexene, cis-5-decene, and cis-7-pentadecene. Reducing both the van der Waals radius (R) from 1.459 to 1.25 and the well-depth (ε) from 0.015 to 0.007 resulted in far better agreement for the density values (ρ); however, it proved difficult to correct the heat of vaporization (ΔHvap) of cis-5-decene to that of the experimental value by only modifying the LJ parameters. This is due to the high charge on the double bond atoms. A similar problem has previously been encountered by Chiu et al. (13) and Jämbeck et al. (10)

Figure 2

Figure 2. The energy profile for rotating about selected torsions of a cis-5-decene molecule. Energy evaluated using QM and the HM-IE method (filled triangle ▲), AMBER with standard GAFF parameters (dotted line), and AMBER with Lipid14 parameters (black line). Torsion fits from the top are as follows: CH2–CH–CH–CH2, CH–CH–CH2–CH2, and CH–CH2–CH2–CH2.

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The uncorrected diffusion DPBC was calculated for each alkane using the slope of a mean-square displacement (MSD) plot versus time for the centers of mass, averaged over the trajectories of each molecule via the Einstein relation(2)where nf is the number of dimensions (in this instance nf = 3), and Δr(t)2 is the distance that the molecule travels in time t. It is then possible to correct for the system size dependence of a diffusion coefficient calculated under periodic boundaries (DPBC) to yield the corrected diffusion coefficient Dcorr by adding the correction term derived by Yeh and Hummer (38)(3)where kB is Boltzmann’s constant, T is the temperature, ε = 2.837297, η is the viscosity, and L is the length of the simulation box.
The diffusion was calculated from 100 ns NVE ensemble simulations (extended from the 50 ns NPT runs). PME was used, along with a 10 Å cutoff, at a temperature of 298.15 K. In order to avoid energy and temperature drift, it was necessary to remove the center of mass motion every 500 steps (nscm = 500), make both the shake tolerance and Ewald direct sum tolerance more stringent, and reduce the time step to 1 fs. Diffusion values were then calculated by taking the slope of the linear 2–5 ns region of the MSD versus time curve and the correction calculated using experimental viscosity values. Diffusion results are reported with standard deviations calculated by block averaging, with each 100 ns run divided into five 20 ns blocks.
The trans, gauche, end gauche, double gauche, and kinked gtg′+gtg conformer populations were evaluated from the 50 ns NPT runs by classifying torsion angles as either gauche plus (g+) 0–120°, trans (t) 120–240°, or gauche minus (g–) 240–360°.
13C NMR T1 relaxation times were calculated from the NPT alkane simulations using the following formula for dipolar relaxation from the reorientation correlation functions of the CH vectors: (39)(4)
This assumes motional narrowing and an effective C–H bond length of 1.117 Å, (40) with N specifying the number of protons bonded to the carbon and μ̂ the CH vector. T1 relaxation times were calculated from simulations of alkanes of four different chain lengths. These simulations were repeated using the same NPT alkane protocol at the experimentally relevant temperature of 312 K and production runs extended to 200 ns to improve sampling.

Head Group Parameters

It was found that the heat of vaporization of methyl acetate, a model compound representing the ester linkage region connecting the lipid head and tail groups, was not sufficiently close to experiment using GAFF/Lipid11 parameters. In order to correct for this discrepancy with experiment, the Lennard-Jones well-depths of the carbonyl oxygen (oC), carbonyl carbon (cC), and ester oxygen (oS) atoms were scaled until better agreement with experiment was obtained (see Table 2). The ester oxygen parameters were also applied to oxygen atoms in the phosphate region.
Table 2. Thermodynamic Properties of Methyl Acetate Simulated with GAFF/Lipid11 and Lipid14 and Comparison to Experimenta
 LJ parameters  
 atom typeradius R (Å)well-depth ε (kcal mol–1)ΔHvap (kJ mol-1)ρ (kg m-3)
Lipid11oC1.66120.21039.11 ± 0.04928.38 ± 0.09
oS1.68370.170
cC1.90800.086
Lipid14oC1.65000.14033.0 ± 0.07925.8 ± 0.05
oS1.65000.120
cC1.90800.070
Expt   32.29 (41)934.2 (41)
a

All values at 298.15 K.

The density and heat of vaporization of methyl acetate were calculated using an identical procedure as for the hydrocarbon chains, with a box of 288 methyl acetate molecules applied for the liquid phase calculation. Simulations were run for 60 ns and the final 50 ns used for sampling. Results are reported as block averages (five blocks of 10 ns).

Partial Charges

RESP fitting was performed in exactly the same manner to Lipid11, (22) using the capping groups shown in Figure 3. However a greater number of conformations were used to calculate the average charges for each unit.
Twenty-five phosphatidylcholine (PC) and twenty-five phosphatidylethanolamine (PE) head groups were extracted from previous bilayer simulations of DOPC and POPE; while fifty lauroyl (LA), myristoyl (MY), palmitoyl (PA), and oleoyl (OL) tails were extracted from bilayer simulations of DLPC, DMPC, DPPC, and DOPC, respectively. Each headgroup was then capped with a methyl group and each tail capped with an acetate moiety (Figure 3), according to the Lipid11 charge derivation methodology. (22) For each conformation, the ESP was calculated directly from each structure at the HF/6-31G* level using Gaussian 09. (42) Charges were taken as an average over all conformations for each residue. Resulting charges for the PC and PE headgroup residues and the LA, MY, PA, and OL tail group residues are detailed in the Supporting Information.

Figure 3

Figure 3. Structure and charges of Lipid11/Lipid14 headgroup and tail group caps. (22)

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Head Group Torsion Fits

Two torsions involving the ester linkage region (see Figure 4) were fitted to QM data. The scans were performed on a capped lauroyl (LA) tail residue, at 15° increments using the HM-IE method with Gaussian 09. (42) These were then fitted using Paramfit (17, 29) for periodicity n = 1 to n = 5 using the genetic algorithm implemented in Paramfit.

Figure 4

Figure 4. A capped lauroyl tail group residue was used to fit the oS-cC-cD-cD and oC-cC-cD-cD torsions.

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Figure 5

Figure 5. The energy profiles for rotating about selected torsions of a capped lauroyl tail group residue. Energy evaluated using QM and the HM-IE method (filled triangle ▲), AMBER with standard GAFF/Lipid11 parameters (dotted line), and AMBER with Lipid14 parameters (black line). Torsion fits from the top are oC-cC-cD-cD and oS-cC-cD-cD.

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As can be seen from Figure 5 Paramfit brings the oS-cC-cD-cD and oC-cC-cD-cD torsions into substantially better agreement with the QM data.

Parameterization

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Hydrocarbon Parameters

Table 3. Thermodynamic and Dynamic Properties of a Selection of Alkane Chains Simulated Using the Updated Lipid14 Parameters and Comparison to Experimenta
 ΔHvap (kJ mol-1)ρ (kg m-3)DPBC (10-5 cm2 s-1)Dcorr (10-5 cm2 s-1)
Pentane
Lipid1423.03 ± 0.16592.45 ± 0.166.45 ± 0.567.1 ± 0.56
Expt26.43 (41)626.2 (41)5.45 (43)
Hexane
Lipid1428.54 ± 0.1636.3 ± 0.094.55 ± 0.295.02 ± 0.29
Expt31.56 (41)656, (44) 660.6 (41)4.21 (43)
Heptane
Lipid1433.37 ± 0.11667.31 ± 0.143.47 ± 0.233.85 ± 0.23
Expt36.57 (41)679.5 (41)3.12 (43)
Octane
Lipid1438.67 ± 0.31690.96 ± 0.102.11 ± 0.152.46 ± 0.15
Expt41.49 (41)698.6 (41)2.354 (45)
Decane
Lipid1449.34 ± 0.30724.47 ± 0.071.44 ± 0.151.65 ± 0.15
Expt51.42 (41)726.6 (41)1.39 (45)
Tridecane
Lipid1464.62 ± 0.27756.19 ± 0.240.48 ± 0.040.57 ± 0.04
Expt66.68 (41)756.4 (41)0.712 (45)
Pentadecane
Lipid1474.99 ± 0.39770.67 ± 0.250.30 ± 0.020.36 ± 0.02
Expt76.77 (41)768.5 (41)0.461 (45)
a

All values at 298.15 K.

The results for the alkane properties calculated using the updated torsion and LJ parameters are shown in Table 3. The heat of vaporization values increase with alkane chain length, following the experimental trend and converging with experiment as the number of carbon atoms in the chain increases. The simulation values match experiment with an RMS error of 7.67%. The simulated densities are reproduced somewhat better than ΔHvap, with an RMS error of 2.60% when compared to experiment. The diffusion values lie close to experiment and decrease with increasing chain length, following the experimental trend; however, the RMS error between simulation and experiment remains significant at 20.92%. As is also the case with the heat of vaporization results, the main source of this discrepancy is the result for the shorter alkane chains. The better agreement with experiment of these parameters at modeling longer hydrocarbon chains may arise from the use of a high number of octane structures during torsion fitting. Furthermore, this parameter set is intended for the simulation of membrane lipids, which typically contain aliphatic tails that are ten carbon atoms or greater in length.
Table 4. Thermodynamic Properties of a Selection of Alkene Chains Simulated Using the Updated Lipid14 Parameters and, Where Available, Comparison to Experiment
 ΔHvap (kJ mol-1)ρ (kg m-3)
cis-2-Hexene
Lipid1426.17 ± 0.21656.23 ± 0.13
Expt32.19 (41)683 (44)
cis-5-Decene
Lipid1445.27 ± 0.22739.19 ± 0.16
Expt42.9 (41)744.5 (41)
cis-7-Pentadecene
Lipid1469.5 ± 0.22781.44 ± 0.24
Expt775 (44)
Thermodynamic properties for a selection of alkenes calculated using the updated LJ and torsion parameters are shown in Table 4. As previously stated, properties of unsaturated chains are not as well reproduced as for alkanes due to the difficulty in tuning LJ parameters to achieve the experimental heat of vaporization, resulting in an RMS error of 13.80% for ΔHvap when compared to experiment. The density values are again better reproduced with an RMS error of 2.35%.
Table 5. Average Number of trans, gauche, End gauche (eg), Double gauche (gg), and gtg′+gtg Conformers Per Alkane Molecule and Comparison to Experiment
 transgauchet/g ratioeggggtg′+gtg
Pentane
Lipid141.200.801.490.800.13-
Hexane
Lipid141.831.171.570.830.220.14
Heptane
Lipid142.491.511.650.830.310.24
Octane
Lipid143.151.851.710.810.390.33
Decane
Lipid144.472.531.770.810.570.54
Tridecane
Lipid146.473.531.840.810.820.83
Expt (46)6.53.51.860.680.640.77
Pentadecane
Lipid147.804.201.860.811.001.02
The fractions of trans, gauche, end gauche, double gauche, and kinked gtg′+gtg conformers per molecule were computed for the selection of alkanes under study (see Table 5). Experimental data, estimated by FTIR, exists only for tridecane; (46) however, the updated Lipid14 parameters reproduce these results extremely well with an overestimation of the end gauche and double gauche conformations only. Furthermore, the population of gauche conformations per molecule falls close to the experimental value of 35% for all chains investigated (t/g ratio ∼1.86), meaning that the overpopulation of trans conformations which drives GAFF bilayer simulations into the gel phase is avoided.
The quality of the hydrocarbon parameters was further assessed by calculating the 13C NMR T1 relaxation times for heptane, decane, tridecane, and pentadecane. Similar to diffusion, this is a dynamic property; however, it depends on the rotation of the CH vector. Results are shown in Figure 6. In general the simulation values follow the same profile as the experimental data. Simulation values tend to converge with experiment upon moving further from the end carbon of the alkane chains. Although the result for pentadecane is slightly high, the overall comparison between simulation and experiment is reasonable.

Figure 6

Figure 6. Calculated 13C NMR T1 relaxation times for selected alkane chains and comparison to experiment. (47) Values at 312 K.

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Lipid Bilayer Simulation

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Initial Structures

Bilayers were constructed using the CHARMM Membrane Builder GUI (48) at the relevant experimental hydration level (see Table 6) and converted to Lipid14 PDB format using the charmmlipid2amber.x script. (17) All systems used the TIP3P water model (49) and had 0.15 M KCl salt concentration added to the water layer, modeled using suitable AMBER parameters. (50)
Table 6. System Size, Hydration, Temperature, and Simulation Time for the Lipid Bilayer Systems
 no. of lipidssimulation time (ns)temp (K)waters/lipid nW
DLPC1285 × 12530331.3
DMPC1285 × 12530325.6
DPPC1285 × 12532330.1
DOPC1285 × 12530332.8
POPC1285 × 12530331
POPE1285 × 12531032

Equilibration Procedure

The full system was minimized for 10000 steps, of which the first 5000 steps used the steepest descent method and the remaining steps used the conjugate gradient method. (51)
The system was then heated from 0 K to 100 K using Langevin dynamics (52) for 5 ps at constant volume, with weak restraints on the lipid (force constant 10 kcal mol–1 Å–2).
Following this, the volume was allowed to change freely and the temperature increased to a lipid dependent value (see Table 6) with a Langevin collision frequency of γ = 1.0 ps–1, and anisotropic Berendsen regulation (37) (1 atm) with a time constant of 2 ps for 100 ps. The same weak restraint of 10 kcal mol–1 Å–2 was maintained on the lipid molecules.

Production Runs

Constant pressure and constant temperature (NPT) runs were performed on the six bilayers using the AMBER 12 package. (17) The GPU implementation of the AMBER 12 code (bugfix 21) was used to run the simulations on NVIDIA GPU cards, achieving approximately 30 ns per day for the 128-lipid bilayer systems. (17, 19) Three dimensional periodic boundary conditions with the usual minimum image convention were employed. Bonds involving hydrogen were constrained using the SHAKE algorithm, (36) allowing a 2 fs time step. Structural data was recorded every 10 ps. PME was used to treat all electrostatic interactions with a real space cutoff of 10 Å. A long-range analytical dispersion correction was applied to the energy and pressure. All simulations were performed at constant pressure of 1 atm and constant target temperature (Table 6). Temperature was controlled by the Langevin thermostat, (52) with a collision frequency of γ = 1.0 ps–1, as this method was identified as the most suitable in previous work. (25) Pressure was regulated by the anisotropic Berendsen method (37) (1 atm) with a pressure relaxation time of 1.0 ps.
Each lipid type was simulated for 125 ns with five repeats. The first 25 ns of each run was removed for equilibration, resulting in a total of 500 ns of data per lipid system, an aggregate of 3 μs of data. Results are presented as block averages over the five repeats ± standard deviation. The majority of analysis in this paper used PTRAJ or CPPTRAJ analysis routines. (17, 53)
To check stability over time of the lipid bilayer systems, the simulations were extended from 125 ns to 250 ns. Additional GPU and CPU validations were also performed, and in all cases the GPU results were consistent with CPU results (see the Supporting Information).

Validation

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Bilayer Structural Properties

Table 7. Average Structural Properties over Five Repeats of the Six Lipid Systems Simulated with Lipid14 and Comparison to Experiment
lipid systemarea per lipid AL (Å2)volume per lipid VL (Å3)isothermal area compressibility modulus KA (mNm-1)bilayer thickness DHH (Å)bilayer Luzzati thickness DB (Å)ΔDB-H = (DB–DHH)/2 (Å)ratio r of terminal methyl to methylene volume
DLPC       
Lipid1463.0 ± 0.2948.9 ± 0.3281 ± 3730.4 ± 0.430.2 ± 0.1–0.1 ± 0.21.9
Expt63.2, (54)60.8 (55)991 (54)-30.8 (54)31.4 (54)0.8 (56)1.8–2.1 (57)
DMPC       
Lipid1459.7 ± 0.71050.2 ± 1.5264 ± 9034.7 ± 0.635.2 ± 0.40.3 ± 0.22.2
Expt60.6, (54)59.9 (55)1101 (4, 54)234 (58)34.4, (59) 35.3 (60)36.3, (54) 36.7, (55)0.8 (56)1.8–2.1 (57)
     36.9 (59)  
DPPC       
Lipid1462.0 ± 0.31177.3 ± 0.5244 ± 5037.9 ± 0.538.0 ± 0.20.1 ± 0.22.1
Expt63.1, (55)64.3 (61)1232 (4)231 (4)38, (62) 38.3 (4)39.0 (55, 62)0.8 (56)1.8–2.1 (57)
DOPC       
Lipid1469.0 ± 0.31249.6 ± 0.2338 ± 3137.0 ± 0.236.2 ± 0.2–0.4 ± 0.12.1
Expt67.4, (62) 72.5 (4)1303 (4)265, (58) 300, (63) 318 (64)35.3, (65) 36.7, (62, 66) 36.9, (4) 37.1 (67)35.9, (4) 36.1, (65, 67) 38.7 (62)1.0–1.7 (57)1.8–2.1 (57)
POPC       
Lipid1465.6 ± 0.51205.4 ± 0.4257 ± 4736.9 ± 0.636.8 ± 0.3–0.1 ± 0.21.9
Expt64.3, (55) 68.3 (68)1256 (68)180–330 (69)37 (68)36.8, (68) 39.1 (55)0.8 (56)1.8–2.1 (57)
POPE       
Lipid1455.5 ± 0.21138.7 ± 0.3350 ± 8142.4 ± 0.241.0 ± 0.1–0.7 ± 0.12.0
Expt56.6, (70) 59–60 (71)1180 (71)233 (70)39.5 (71)--1.8–2.1 (57)
Despite the degree of uncertainty in obtaining accurate experimental values, (72) the bilayer surface area each lipid occupies, or area per lipid, is easily calculated from membrane simulations and gives a quick indication of whether a bilayer is in the correct phase at a given temperature. The area per lipid for each system was calculated using the dimensions of the simulation box as per previous work. (22, 26) The AL for each lipid type is reported in Table 7, with all simulation values within 3% of experimental values, indicating that all the bilayers are in the correct Lα-phase. The result for POPE is closer to the older experimental AL value of 56.6 Å2 than the more recent AL value 59–60 Å2. Nevertheless, the AL should be but one of a number of properties calculated to validate a lipid force field. (73, 74)
Experimentally, the volume per lipid VL is more accurately measured and is thus a better comparison for simulation results than AL. The volume per lipid was calculated using the dimensions of the simulation box (26) and the volume of a water molecule as determined by simulating 1936 TIP3P waters in the NPT ensemble for 50 ns using an identical procedure to the bilayer simulations at the relevant temperature.
VL values for each lipid are reported in Table 7, which although systematically underestimated, are within 5% of experimental values. It is likely that the headgroup LJ parameters could be further tuned to remedy this discrepancy, as the thorough reparamaterization of the hydrocarbon chains makes it unlikely that the tail groups are causing this lack of agreement.
This intuition is confirmed when studying the lipid component volumes calculated with the SIMtoEXP software. (75) The headgroup volume of DOPC was found to be 305.41 Å3, which is below the experimental estimate of 319–331 Å3, while the hydrocarbon chain volume of 965.88 Å3 is closer to the experimental range of 972–984 Å3. (57)
The volume breakdown provided by SIMtoEXP was used to calculate the ratio r of terminal methyl to methylene volume. All lipid systems report a value of r = 1.85–2.17, within or very close to the experimental range of 1.8–2.1.
Isothermal area compressibility modulus, KA, was calculated from the fluctuation in the area per lipid. (26) In general, KA values fall close to experiment, with experimental values falling within the standard deviation of DMPC, DPPC, DOPC and POPC simulation results; however the POPE value comes out high and there is a large standard deviation in all values. Although the DOPC value is above the published experimental value of 300 mN m–1, (63) a personal communication with E. Evans revealed that this KA value has recently been revised upward to 318 mN m–1, (64) closer to the Lipid14 simulation result. This was not known prior to the lipid simulations.
In this work, the Berendsen method was used for pressure coupling, given that it is the only barostat currently available in the AMBER MD package. It has recently been shown that Berendsen pressure control is not ideal for simulations in which volume fluctuations are important, (76) thus by implementing other barostats into AMBER better KA results may potentially be achieved. This is a work in progress, the results of which will be shown elsewhere. Furthermore, larger system sizes and longer simulation times could also be investigated, as such changes have been shown to speed up the convergence of KA values. (74)
The membrane thickness was examined by calculating DHH, the peak-to-peak distance, from electron density profiles of the membranes. Again, satisfactory agreement with experiment is achieved for all lipids, though the POPE value is a little high, indicating that this system is slightly too ordered.
An alternative bilayer thickness, the Luzzati thickness DB, was calculated using the z-dimension of the simulation box and the integral of the probability distribution of the water density along the z-axis. (9, 10)DB values are found to lie close to experimental values, though the DB thicknesses for the saturated lipids are slightly underestimated. Given that DB is the distance between the points along the membrane normal at which the water density is half of its bulk value, this suggests that water is penetrating slightly too far into the hydrophobic region of the bilayer, thereby lowering the value of DB.

Ordering and Conformation of Lipid Acyl Chains

The ordering of the lipid acyl chains may be determined by calculation of the order parameter SCD. This quantity can be directly compared to experimental SCD values determined by 2H NMR or 1H–13C NMR. (77-80)SCD is a measure of the relative orientation of the C–D bonds with respect to the bilayer normal and was calculated according to(5)where θ is the angle between the bilayer normal and the vector joining Ci to its deuterium atom, and < > represents an ensemble average.

Figure 7

Figure 7. Simulation NMR order parameters for the six lipid systems and comparison to experiment. (77, 78, 80-84)

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Figure 7 shows the Lipid14 order parameters with comparison to experiment. All lipid systems follow the experimental order parameter trend. The carbon-2 atom of the sn-1 and sn-2 chains display markedly different order parameters owing to the different alignment of the acyl chains in this region. Experimentally, it has been found that the SCD order parameter of the C-D bonds near the headgroup in the sn-1 chains are greater than the sn-2 chains. (85, 86) Splitting of the order parameter value of the sn-2 chain from the sn-1 chain is observed for the simulated lipid systems. The unsaturated chain of the DOPC, POPC and POPE lipids show a distinctive drop at the carbon-9 and -10 positions due to the cis double bond. The SCD values for the sn-1 chain of POPE are a little high, indicating that POPE may be slightly too ordered. In agreement with Jämbeck et al., the two chains of DOPC show differing behavior, the sn-1 chain having higher SCD values about the double bond than the sn-2 chain. (87)
The conformation of the acyl chains may be examined by analyzing the rotamers and rotamer sequences along the lipid tails and comparing results to experimental data collected by Fourier transform infrared (FTIR) spectroscopy. (88) FTIR can determine the number of trans (t) and gauche (g) conformers and sequences of t and g (end gauche eg, double gauche gg, gtg, and kinks gtg′). The lipid bilayer simulations were analyzed by denoting torsion angles φ in the acyl chains as either t (φ< −150° or φ> 150°), g- (−90°≤ φ< −30°) or g+ (30°< φ≤90°). (89) The rotamer sequence gtg correspond to g+tg+ or g-tg- while the sequence (or kinks) gtg′ corresponds to g+tg- or g-tg+.
Results are shown in Table 8 and are in general satisfactorily close to available experimental values. The discrepancies observed between simulation and experimental values of gtg′ for DLPC and DPPC may result from the experimental ambiguity in assigning gtg and gtg′ wagging modes. (90) These results also confirm that the bilayers are in the correct phase, as the gel-to-liquid phase transition is associated with an increase in the number of gauche rotamers and kink rotamer sequences. (90-92) However the eg and gg results for POPE are not in accordance with the experimental values obtained by Senak et al. using FTIR, (88) who found a marked increase in eg, gg, and gtg′+gtg values going from DPPE to DPPC because of the tighter packing of the PE lipid in the Lα phase. The present simulation values for POPE and POPC, though, are similar.
Table 8. Analysis of Rotamers and Rotamer Sequences in the Acyl Chains of the Six Lipid Systems – End gauche (eg), Double gauche (gg), Kinks (gtg′), gtg′+gtg, and Number of gauche (ng)
lipid systemeggggtg′gtg′+gtgng
DLPC     
Lipid140.350.440.280.522.50
Expt (93)0.450.320.88*-2.85
DMPC     
Lipid140.340.480.350.622.82
Expt (94)0.380.67-0.442.6
DPPC     
Lipid140.360.660.470.833.58
Expt0.38, (94) 0.4, (88) 0.54 (93)0.4, (88, 93) 0.57 (94)1.19 (93)a0.46, (94) 1.0 (88)2.44, (94) 3.6–4.2, (95) 3.7, (93) 3.8 (82)
DOPC     
Lipid140.360.750.370.703.93
POPC     
Lipid140.360.690.410.753.73
POPE     
Lipid140.350.600.420.733.50
Expt (88)0.050.2-0.8-
a

The gtg′ sequence may be ascribed to a gtg′+gtg sequence. (90)

Electron Density Profiles

The electron density profiles (EDP) were calculated by assuming an electron charge equal to the atomic number minus the atomic partial charge, located at the center of each atom. Profiles have also been decomposed into contributions from the following groups: water, choline (CHOL), phosphate (PO4), glycerol (GLY), carbonyl (COO), methylene (CH2), unsaturated CH═CH and terminal methyls (CH3). These profiles, shown in Figure 8, are all symmetrical, with water penetrating up to the carbonyl groups, leaving the terminal methyl groups dehydrated in agreement with experimental findings. (54, 68, 61) The electron density profiles were then utilized for the calculation of scattering form factors using the SIMtoEXP software. (75)

Figure 8

Figure 8. The total and decomposed electron density profiles for each of the six lipid bilayer systems with contributions from water, choline (CHOL), phosphate (PO4), glycerol (GLY), carbonyl (COO), methylene (CH2), unsaturated CH═CH and terminal methyls (CH3).

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Scattering Form Factors

Scattering data allow direct comparison between lipid bilayer simulation and experiment, avoiding any intermediate modeling of experimental raw data. (57) X-ray and neutron scattering form factors can be computed by Fourier transformation of simulation electron density profiles and compared to experimental scattering data.
Recent work determined the areas per lipid (AX and AN) at which DOPC bilayer simulations best replicate the experimental X-ray scattering and neutron scattering data by varying the area per lipid through application of a surface tension, with the ideal situation being AX = AN = ANPT (bilayer is run in the tensionless NPT ensemble). (57) In this work we were concerned with validating the Lipid14 parameters for tensionless bilayer simulation only; thus we report the X-ray and neutron scattering form factors for ANPT only.

Figure 9

Figure 9. Simulation X-ray scattering form factors for the six lipid systems (black line) and comparison to experiment (54, 55, 62, 66, 68) (cyan circles). Inset: Simulation neutron scattering form factors at 100% D2O (black line), 70% D2O (red line), and 50% D2O (blue line) and comparison to experiment (55, 96) (black, red, and blue circles, respectively).

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It can be seen from Figure 9 that there is general agreement between both the X-ray and neutron scattering form factors for all lipids for which there is experimental scattering data available, indicating that the simulated bilayers have the correct structure. In general the minima of the experimental F(q) profiles are correctly reproduced, as are the relative lobe heights.
The quantity ΔDB-H was computed from the membrane thickness values (see Table 7). Agreement with X-ray scattering data is sensitive to the value of DHH, while agreement with neutron scattering data is sensitive to the value of DB. Therefore it has been proposed that bilayer simulations should aim to replicate experimental ΔDB-H values to best achieve agreement with both types of scattering data, where ΔDB-H = (DB-DHH)/2. (57) The GROMOS united-atom lipid force field has been shown to match experiment for simulation ΔDB-H results. (56, 57) As evidenced by Table 7, Lipid14 ΔDB-H values are lower than those found by experiment, though all simulation values do maintain a large standard deviation. In fact, analysis of ΔDB-H results for two other all-atom lipid force fields, CHARMM36 (8) and Slipids (10, 87) indicates that this quantity is difficult to reproduce using all-atom models, with only the Slipids POPC result falling close to experiment. Figure 10 plots ΔDB-H values against area per lipid for CHARMM36, (56) Slipids, (10, 87) and AMBER Lipid14, displaying a downward trend in ΔDB-H with increasing area per lipid, in disagreement with the experimental trend. Results for Lipid14 are similar to CHARMM36 and most Slipids values. Improving this discrepancy with experiment for Lipid14 may further improve the comparison with scattering data; however, present simulation scattering profiles are still seen to be in satisfactory agreement with experiment.

Figure 10

Figure 10. Plot of ΔDB-H versus area per lipid AL for the three all-atom lipid force fields CHARMM36 (squares), Slipids (diamonds), and AMBER Lipid14 (circles). Values shown for DLPC (green), DMPC (magenta), DPPC (blue), DOPC (red), and POPC (orange).

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Lipid Lateral Diffusion

To assess the ability of the Lipid14 parameters to reproduce dynamic lipid properties, the lipid lateral diffusion coefficient Dxy was calculated using the Einstein relation (eq 2) with two degrees of freedom (nf = 2). Diffusion coefficients were computed for each lipid as a block average over the five NPT production runs. The mean-square-displacement (MSD) curves were determined using window lengths spanning 20 ns and averaged over different time origins separated by 200 ps. The slope of this curve yields the diffusion coefficient using eq 2, with the linear 10–20 ns region used to perform the fit. Prior to the MSD calculation, the lipid coordinates were corrected to remove the artificial center of mass drift of each monolayer. (73)
Table 9. Lipid Lateral Diffusion Coefficients Calculated from NPT Runs, NVE Runs, and Experimental Values
lipid systemcalcd NPT Dxy (10-8 cm2 s-1)calcd NVE Dxy (10-8 cm2 s-1)simulation temp (K)exptl Dxy (10-8 cm2 s-1)exptl temp (K)
DLPC7.657.783038.5 (97)298
DMPC5.056.323035.95, (98) 9 (99, 100)303, 303
DPPC9.2111.9432312.5, (101) 15.2 (102)323, 323
DOPC6.489.4930311.5, (100) 17 (103)303, 308
POPC5.746.5430310.7 (100)303
POPE4.674.853105.2 (104)a305
a

Cell culture membrane containing 78% POPE at 305 K.

Results are of the same order of magnitude as experimental values; although in general they are underestimated. Unlike the bulk alkane work there is no correction term to account for collective motion which cannot be sampled using a periodic box of limited size. Accordingly, the underestimation may be a result of size effects. As highlighted by Poger et al. there is a widespread in experimental lipid lateral diffusion values in the literature, with a range of experimental techniques applied to the calculation of diffusion values. (105) Even different groups applying the same experimental technique do not necessarily yield comparable diffusion coefficients. Our calculated diffusion coefficients are nonetheless found to be in good agreement with other simulation values. (10, 23, 87, 105-107)
Given that the production runs were performed in the NPT ensemble and that temperature regulation methods such as Langevin dynamics, which randomizes particle velocities, may affect dynamic properties such as diffusion, the lipid lateral diffusion was also determined in the microcanonical (NVE) ensemble. A single production run of each lipid system was extended into the NVE ensemble for 100 ns using the same simulation settings as used for the alkane diffusion runs (see Parameterization Strategy). Resulting time averaged MSD curves are shown in Figure 11, and calculated diffusion coefficients are reported in Table 9. Although similar to the Dxy values determined from the NPT runs, the diffusion coefficients from the NVE runs are slightly higher, with the results for DPPC and DOPC showing the largest differences. This supports a recent study on the effect of temperature control on dynamic properties by Basconi et al., (108) who found that diffusion coefficients calculated from simulations applying Langevin dynamics approach the coefficients derived from NVE simulations, provided weak coupling is used for the temperature regulation.

Figure 11

Figure 11. Time averaged mean square displacement of the center of mass of the lipid molecules versus NVE simulation time.

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Lipid lateral diffusion is known to occur via two regimes: fast ‘rattling’ of the lipid in the local solvation cage (109) and slower, long distance diffusion in the plane of the bilayer. The two regimes are clearly observed in the MSD versus time curves (Figure 11) and are also revealed by computing the diffusion coefficients using different time ranges of the MSD curve. Figure 12 plots the diffusion coefficient Dxy against the starting time for fitting the MSD slope. Time windows were either 100 ps long (fit starts between 10 ps and 500 ps) or 500 ps long (fit starts between 500 ps and 20 ns). (23)Dxy values decrease smoothly and then converge at a value representing the long time diffusion of lipids in the bilayer plane.

Figure 12

Figure 12. Lateral diffusion coefficients for the six lipid types calculated using different time ranges of the mean square displacement curve for the linear fit.

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Conclusions

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The Lipid14 force field represents a significant advancement for the simulation of phospoholipids in the AMBER MD package. Hydrocarbon parameters have been refined, resulting in good reproduction of thermodynamic and dynamic properties for a number of simple carbon chains, thus we can be confident that the hydrocarbon region of the lipid membrane is correctly represented. Head group parameters have also been updated, with the final parameter set finding good agreement with experiment for a range of properties, including the area per lipid, volume per lipid, bilayer thickness, NMR order parameters, scattering data, and lipid lateral diffusion, without applying a surface tension in the simulations. Crucially, the experimental raw data that requires no empirical input to derive, namely the NMR order parameters and scattering data, are well reproduced. Results for POPE however indicate that PE lipids may require further attention, as the order parameter results for POPE indicate that it remains somewhat artificially ordered in comparison to experiment. Results from five GPU repeats and CPU runs are seen to be consistent (these additional results are provided in the Supporting Information), with a number of tests performed on GPUs using both different starting structures and extending production runs to 250 ns. Future improvements may involve further refinement of parameters in order to address the underestimation of the volume per lipid and bilayer Luzzati thickness values in addition to PE lipid types.
Although the present study only concerns the validation of Lipid14 for the simulation of three saturated and three unsaturated lipids, the modular nature of the Lipid14 force field allows for a number of different lipids to be constructed from headgroup and tail group ‘building blocks’ and for the easy insertion of new lipid species into the force field. The Lipid14 charge derivation follows the usual AMBER convention, making this force field compatible with other AMBER potentials, such as the General Amber Force Field (16) and the ff99SB protein force field. (14) As such, the interaction of other species, such as small molecules or proteins, with lipid membranes can be studied in AMBER using the Lipid14 force field.

Supporting Information

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Details of the Lipid14 atom types, partial charges, and force field parameters. Also included are the bilayer results for additional GPU and CPU runs. This material is available free of charge via the Internet at http://pubs.acs.org.

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Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Authors
    • Ian R. Gould - Department of Chemistry and Institute of Chemical Biology, Imperial College London, South Kensington SW7 2AZ, United Kingdom;  Email: [email protected]
    • Ross C. Walker - San Diego Supercomputer Center, University of California San Diego, 9500 Gilman Drive MC0505, La Jolla, California 92093-0505, United States;  Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive MC0505, La Jolla, California 92093-0505, United States;  Email: [email protected]
  • Authors
    • Callum J. Dickson - Department of Chemistry and Institute of Chemical Biology, Imperial College London, South Kensington SW7 2AZ, United Kingdom
    • Benjamin D. Madej - San Diego Supercomputer Center, University of California San Diego, 9500 Gilman Drive MC0505, La Jolla, California 92093-0505, United States;  Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive MC0505, La Jolla, California 92093-0505, United States
    • Åge A. Skjevik - San Diego Supercomputer Center, University of California San Diego, 9500 Gilman Drive MC0505, La Jolla, California 92093-0505, United States;  Department of Biomedicine, University of Bergen, N-5009 Bergen, Norway
    • Robin M. Betz - San Diego Supercomputer Center, University of California San Diego, 9500 Gilman Drive MC0505, La Jolla, California 92093-0505, United States
    • Knut Teigen - Department of Biomedicine, University of Bergen, N-5009 Bergen, Norway
  • Notes
    The authors declare no competing financial interest.

Acknowledgment

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We are very grateful to Dr. Hannes Loeffler of the Science and Technology Facilities Council, UK, for writing and maintaining the modified PTRAJ/CPPTRAJ routines which were used for much of the analysis in this work. C.J.D. wishes to thank the Institute of Chemical Biology, UK Biotechnology and Biological Sciences Research Council (BBSRC) and GlaxoSmithKline for the award of a studentship, and the High Performance Computing centre of Imperial College London for the provision of computing time. B.D.M. would like to acknowledge funding for this work provided by the NIH Molecular Biophysics Training Grant (T32 GM008326) and the NVIDIA Graduate Fellowship Program. R.M.B. was supported by a grant from the University of California Institute for Mexico and the United States (UC MEXUS) and the Consejo Nacional de Ciencia y Tecnología de México (CONACYT) (R.C.W.). We acknowledge the support of the Strategic Programme for International Research and Education (SPIRE) and the Meltzer Foundation for travel grants provided to Å.A.S. The Norwegian Metacenter for Computational Science (NOTUR) is acknowledged for allocation of computational resources. This work was supported by NSF SI2-SSE grants (NSF-1047875 and 1148276) to R.C.W. and by the University of California (UC Lab 09-LR-06-117793) grant to R.C.W. R.C.W. also acknowledges funding through the NSF XSEDE program and through a fellowship from NVIDIA, Inc. Additional computer time was provided by the San Diego Supercomputer Center and by XSEDE and TG-CHG13W10 to R.C.W.

References

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    Klauda, J. B.; Venable, R. M.; Freites, J. A.; O’Connor, J. W.; Tobias, D. J.; Mondragon-Ramirez, C.; Vorobyov, I.; MacKerell, A. D.; Pastor, R. W. Update of the CHARMM all-atom additive force field for lipids: Validation on Six lipid types J. Phys. Chem. B 2010, 114 (23) 7830– 7843
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    8
    Update of the CHARMM All-Atom Additive Force Field for Lipids: Validation on Six Lipid Types
    Klauda, Jeffery B.; Venable, Richard M.; Freites, J. Alfredo; O'Connor, Joseph W.; Tobias, Douglas J.; Mondragon-Ramirez, Carlos; Vorobyov, Igor; MacKerell, Alexander D., Jr.; Pastor, Richard W.
    Journal of Physical Chemistry B (2010), 114 (23), 7830-7843CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    A significant modification to the additive all-atom CHARMM lipid force field (FF) is developed and applied to phospholipid bilayers with both choline and ethanolamine contg. head groups and with both satd. and unsatd. aliph. chains. Motivated by the current CHARMM lipid FF (C27 and C27r) systematically yielding values of the surface area per lipid that are smaller than exptl. ests. and gel-like structures of bilayers well above the gel transition temp., selected torsional, Lennard-Jones and partial at. charge parameters were modified by targeting both quantum mech. (QM) and exptl. data. QM calcns. ranging from high-level ab initio calcns. on small mols. to semiempirical QM studies on a 1,2-dipalmitoyl-sn-phosphatidylcholine (DPPC) bilayer in combination with exptl. thermodn. data were used as target data for parameter optimization. These changes were tested with simulations of pure bilayers at high hydration of the following six lipids: DPPC, 1,2-dimyristoyl-sn-phosphatidylcholine (DMPC), 1,2-dilauroyl-sn-phosphatidylcholine (DLPC), 1-palmitoyl-2-oleoyl-sn-phosphatidylcholine (POPC), 1,2-dioleoyl-sn-phosphatidylcholine (DOPC), and 1-palmitoyl-2-oleoyl-sn-phosphatidylethanolamine (POPE); simulations of a low hydration DOPC bilayer were also performed. Agreement with exptl. surface area is on av. within 2%, and the d. profiles agree well with neutron and x-ray diffraction expts. NMR deuterium order parameters (SCD) are well predicted with the new FF, including proper splitting of the SCD for the aliph. carbon adjacent to the carbonyl for DPPC, POPE, and POPC bilayers. The area compressibility modulus and frequency dependence of 13C NMR relaxation rates of DPPC and the water distribution of low hydration DOPC bilayers also agree well with expt. Accordingly, the presented lipid FF, referred to as C36, allows for mol. dynamics simulations to be run in the tensionless ensemble (NPT), and is anticipated to be of utility for simulations of pure lipid systems as well as heterogeneous systems including membrane proteins.
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  9. 9
    Poger, D.; Van Gunsteren, W. F.; Mark, A. E. A new force field for simulating phosphatidylcholine bilayers J. Comput. Chem. 2010, 31 (6) 1117– 1125
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    9
    A new force field for simulating phosphatidylcholine bilayers
    Poger, David; Van Gunsteren, Wilfred F.; Mark, Alan E.
    Journal of Computational Chemistry (2010), 31 (6), 1117-1125CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    A new force field for the simulation of dipalmitoylphosphatidylcholine (DPPC) in the liq.-cryst., fluid phase at zero surface tension is presented. The structure of the bilayer with the area per lipid (0.629 Nm2; expt. 0.629-0.64 Nm2), the vol. per lipid (1.226 Nm3; expt. 1.229-1.232 Nm3), and the ordering of the palmitoyl chains (order parameters) are all in very good agreement with expt. Exptl. electron d. profiles are well reproduced in particular with regard to the penetration of water into the bilayer. The force field was further validated by simulating the spontaneous assembly of DPPC into a bilayer in water. Notably, the timescale on which membrane sealing was obsd. using this model appears closer to the timescales for membrane resealing suggested by electroporation expts. than previous simulations using existing models. © 2009 Wiley Periodicals, Inc.
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  10. 10
    Jämbeck, J. P. M.; Lyubartsev, A. P. Derivation and systematic validation of a refined all-atom force field for phosphatidylcholine lipids J. Phys. Chem. B 2012, 116 (10) 3164– 3179
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  11. 11
    Marrink, S. J.; Risselada, H. J.; Yefimov, S.; Tieleman, D. P.; de Vries, A. H. The MARTINI force field: Coarse grained model for biomolecular simulations J. Phys. Chem. B 2007, 111 (27) 7812– 7824
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    11
    The MARTINI Force Field: Coarse Grained Model for Biomolecular Simulations
    Marrink, Siewert J.; Risselada, H. Jelger; Yefimov, Serge; Tieleman, D. Peter; De Vries, Alex H.
    Journal of Physical Chemistry B (2007), 111 (27), 7812-7824CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    We present an improved and extended version of our coarse grained lipid model. The new version, coined the MARTINI force field, is parametrized in a systematic way, based on the reprodn. of partitioning free energies between polar and apolar phases of a large no. of chem. compds. To reproduce the free energies of these chem. building blocks, the no. of possible interaction levels of the coarse-grained sites has increased compared to those of the previous model. Application of the new model to lipid bilayers shows an improved behavior in terms of the stress profile across the bilayer and the tendency to form pores. An extension of the force field now also allows the simulation of planar (ring) compds., including sterols. Application to a bilayer/cholesterol system at various concns. shows the typical cholesterol condensation effect similar to that obsd. in all atom representations.
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  12. 12
    Orsi, M.; Essex, J. W. The ELBA force field for coarse-grain modeling of lipid membranes PLoS One 2011, 6 (12) e28637
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    12
    The ELBA force field for coarse-grain modeling of lipid membranes
    Orsi, Mario; Essex, Jonathan W.
    PLoS One (2011), 6 (12), e28637CODEN: POLNCL; ISSN:1932-6203. (Public Library of Science)
    A new coarse-grain model for mol. dynamics simulation of lipid membranes is presented. Following a simple and conventional approach, lipid mols. are modeled by spherical sites, each representing a group of several atoms. In contrast to common coarse-grain methods, two original (interdependent) features are here adopted. First, the main electrostatics are modeled explicitly by charges and dipoles, which interact realistically through a relative dielec. const. of unity (εr = 1). Second, water mols. are represented individually through a new parametrization of the simple Stockmayer potential for polar fluids; each water mol. is therefore described by a single spherical site embedded with a point dipole. The force field is shown to accurately reproduce the main phys. properties of single-species phospholipid bilayers comprising dioleoylphosphatidylcholine (DOPC) and dioleoylphosphatidylethanolamine (DOPE) in the liq. crystal phase, as well as distearoylphosphatidylcholine (DSPC) in the liq. crystal and gel phases. Insights are presented into fundamental properties and phenomena that can be difficult or impossible to study with alternative computational or exptl. methods. For example, we investigate the internal pressure distribution, dipole potential, lipid diffusion, and spontaneous self-assembly. Simulations lasting up to 1.5 μs were conducted for systems of different sizes (128, 512 and 1058 lipids); this also allowed us to identify size-dependent artifacts that are expected to affect membrane simulations in general. Future extensions and applications are discussed, particularly in relation to the methodol.'s inherent multiscale capabilities.
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  13. 13
    Chiu, S.-W.; Pandit, S. A.; Scott, H. L.; Jakobsson, E. An improved united atom force field for simulation of mixed lipid bilayers J. Phys. Chem. B 2009, 113 (9) 2748– 2763
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    13
    An Improved United Atom Force Field for Simulation of Mixed Lipid Bilayers
    Chiu, See-Wing; Pandit, Sagar A.; Scott, H. L.; Jakobsson, Eric
    Journal of Physical Chemistry B (2009), 113 (9), 2748-2763CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    We introduce a new force field (43A1-S3) for simulation of membranes by the Gromacs simulation package. Construction of the force fields is by std. methods of electronic structure computations for bond parameters and charge distribution and sp. vol.s and heats of vaporization for small-mol. components of the larger lipid mols. for van der Waals parameters. Some parameters from the earlier 43A1 force field are found to be correct in the context of these calcns., while others are modified. The validity of the force fields is demonstrated by correct replication of X-ray form factors and NMR order parameters over a wide range of membrane compns. in semi-isotropic NTP 1 atm simulations. 43-A1-S3 compares favorably with other force fields used in conjunction with the Gromacs simulation package with respect to the breadth of phenomena that it accurately reproduces.
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  14. 14
    Hornak, V.; Abel, R.; Okur, A.; Strockbine, B.; Roitberg, A.; Simmerling, C. Comparison of multiple Amber force fields and development of improved protein backbone parameters Proteins: Struct., Funct., Bioinf. 2006, 65 (3) 712– 725
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  15. 15
    Kirschner, K. N.; Yongye, A. B.; Tschampel, S. M.; González-Outeiriño, J.; Daniels, C. R.; Foley, B. L.; Woods, R. J. GLYCAM06: A generalizable biomolecular force field. Carbohydrates J. Comput. Chem. 2008, 29 (4) 622– 655
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  16. 16
    Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and testing of a general amber force field J. Comput. Chem. 2004, 25, 1157– 1174
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    16
    Development and testing of a general Amber force field
    Wang, Junmei; Wolf, Romain M.; Caldwell, James W.; Kollman, Peter A.; Case, David A.
    Journal of Computational Chemistry (2004), 25 (9), 1157-1174CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    We describe here a general Amber force field (GAFF) for org. mols. GAFF is designed to be compatible with existing Amber force fields for proteins and nucleic acids, and has parameters for most org. and pharmaceutical mols. that are composed of H, C, N, O, S, P, and halogens. It uses a simple functional form and a limited no. of atom types, but incorporates both empirical and heuristic models to est. force consts. and partial at. charges. The performance of GAFF in test cases is encouraging. In test I, 74 crystallog. structures were compared to GAFF minimized structures, with a root-mean-square displacement of 0.26 Å, which is comparable to that of the Tripos 5.2 force field (0.25 Å) and better than those of MMFF 94 and CHARMm (0.47 and 0.44 Å, resp.). In test II, gas phase minimizations were performed on 22 nucleic acid base pairs, and the minimized structures and intermol. energies were compared to MP2/6-31G* results. The RMS of displacements and relative energies were 0.25 Å and 1.2 kcal/mol, resp. These data are comparable to results from Parm99/RESP (0.16 Å and 1.18 kcal/mol, resp.), which were parameterized to these base pairs. Test III looked at the relative energies of 71 conformational pairs that were used in development of the Parm99 force field. The RMS error in relative energies (compared to expt.) is about 0.5 kcal/mol. GAFF can be applied to wide range of mols. in an automatic fashion, making it suitable for rational drug design and database searching.
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  17. 17
    Case, D. A.; Darden, T. A.; Cheatham, T. E., III; Simmerling, C. L.; Wang, J.; Duke, R. E.; Luo, R.; Walker, R. C.; Zhang, W.; Merz, K. M.; Roberts, B.; Hayik, S.; Roitberg, A.; Seabra, G.; Swails, J.; Goetz, A. W.; Kolossváry, I.; Wong, K. F.; Paesani, F.; Vanicek, J.; Wolf, R. M.; Liu, J.; Wu, X.; Brozell, S. R.; Steinbrecher, T.; Gohlke, H.; Cai, Q.; Ye, X.; Wang, J.; Hsieh, M.-J.; Cui, G.; Roe, D. R.; Mathews, D. H.; Seetin, M. G.; Salomon-Ferrer, R.; Sagui, C.; Babin, V.; Luchko, T.; Gusarov, S.; Kovalenko, A.; Kollman, P. A.AMBER 12; University of California: San Francisco, 2012.
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  18. 18
    Salomon-Ferrer, R.; Case, D. A.; Walker, R. C. An overview of the Amber biomolecular simulation package Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2013, 3 (2) 198– 210
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    18
    An overview of the amber biomolecular simulation package
    Salomon-Ferrer, Romelia; Case, David A.; Walker, Ross C.
    Wiley Interdisciplinary Reviews: Computational Molecular Science (2013), 3 (2), 198-210CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
    A review. Mol. dynamics (MD) allows the study of biol. and chem. systems at the atomistic level on timescales from femtoseconds to milliseconds. It complements expt. while also offering a way to follow processes difficult to discern with exptl. techniques. Numerous software packages exist for conducting MD simulations of which one of the widest used is termed Amber. Here, we outline the most recent developments, since version 9 was released in Apr. 2006, of the Amber and AmberTools MD software packages, referred to here as simply the Amber package. The latest release represents six years of continued development, since version 9, by multiple research groups and the culmination of over 33 years of work beginning with the first version in 1979. The latest release of the Amber package, version 12 released in Apr. 2012, includes a substantial no. of important developments in both the scientific and computer science arenas. We present here a condensed vision of what Amber currently supports and where things are likely to head over the coming years. Figure 1 shows the performance in ns/day of the Amber package version 12 on a single-core AMD FX-8120 8-Core 3.6GHz CPU, the Cray XT5 system, and a single GPU GTX680.
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  19. 19
    Götz, A. W.; Williamson, M. J.; Xu, D.; Poole, D.; Le Grand, S.; Walker, R. C. Routine microsecond molecular dynamics simulations with AMBER on GPUs. 1. Generalized Born J. Chem. Theory Comput. 2012, 8 (5) 1542– 1555
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    19
    Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 1. Generalized Born
    Gotz, Andreas W.; Williamson, Mark J.; Xu, Dong; Poole, Duncan; Le Grand, Scott; Walker, Ross C.
    Journal of Chemical Theory and Computation (2012), 8 (5), 1542-1555CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We present an implementation of generalized Born implicit solvent all-atom classical mol. dynamics (MD) within the AMBER program package that runs entirely on CUDA enabled NVIDIA graphics processing units (GPUs). We discuss the algorithms that are used to exploit the processing power of the GPUs and show the performance that can be achieved in comparison to simulations on conventional CPU clusters. The implementation supports three different precision models in which the contributions to the forces are calcd. in single precision floating point arithmetic but accumulated in double precision (SPDP), or everything is computed in single precision (SPSP) or double precision (DPDP). In addn. to performance, we have focused on understanding the implications of the different precision models on the outcome of implicit solvent MD simulations. We show results for a range of tests including the accuracy of single point force evaluations and energy conservation as well as structural properties pertaining to protein dynamics. The numerical noise due to rounding errors within the SPSP precision model is sufficiently large to lead to an accumulation of errors which can result in unphys. trajectories for long time scale simulations. We recommend the use of the mixed-precision SPDP model since the numerical results obtained are comparable with those of the full double precision DPDP model and the ref. double precision CPU implementation but at significantly reduced computational cost. Our implementation provides performance for GB simulations on a single desktop that is on par with, and in some cases exceeds, that of traditional supercomputers.
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  20. 20
    Salomon-Ferrer, R.; Götz, A. W.; Poole, D.; Le Grand, S.; Walker, R. C. Routine microsecond molecular dynamics simulations with Amber on GPUs. 2. Explicit solvent particle mesh Ewald J. Chem. Theory Comput. 2013, 9 (9) 3878– 3888
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    20
    Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 2. Explicit Solvent Particle Mesh Ewald
    Salomon-Ferrer, Romelia; Gotz, Andreas W.; Poole, Duncan; Le Grand, Scott; Walker, Ross C.
    Journal of Chemical Theory and Computation (2013), 9 (9), 3878-3888CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We present an implementation of explicit solvent all atom classical mol. dynamics (MD) within the AMBER program package that runs entirely on CUDA-enabled GPUs. First released publicly in Apr. 2010 as part of version 11 of the AMBER MD package and further improved and optimized over the last two years, this implementation supports the three most widely used statistical mech. ensembles (NVE, NVT, and NPT), uses particle mesh Ewald (PME) for the long-range electrostatics, and runs entirely on CUDA-enabled NVIDIA graphics processing units (GPUs), providing results that are statistically indistinguishable from the traditional CPU version of the software and with performance that exceeds that achievable by the CPU version of AMBER software running on all conventional CPU-based clusters and supercomputers. We briefly discuss three different precision models developed specifically for this work (SPDP, SPFP, and DPDP) and highlight the tech. details of the approach as it extends beyond previously reported work [Goetz et al., J. Chem. Theory Comput.2012, DOI: 10.1021/ct200909j; Le Grand et al., Comp. Phys. Comm.2013, DOI: 10.1016/j.cpc.2012.09.022].We highlight the substantial improvements in performance that are seen over traditional CPU-only machines and provide validation of our implementation and precision models. We also provide evidence supporting our decision to deprecate the previously described fully single precision (SPSP) model from the latest release of the AMBER software package.
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  21. 21
    Le Grand, S.; Götz, A. W.; Walker, R. C. SPFP: Speed without compromise—A mixed precision model for GPU accelerated molecular dynamics simulations Comput. Phys. Commun. 2013, 184 (2) 374– 380
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    21
    SPFP: Speed without compromise-A mixed precision model for GPU accelerated molecular dynamics simulations
    Le Grand, Scott; Gotz, Andreas W.; Walker, Ross C.
    Computer Physics Communications (2013), 184 (2), 374-380CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    A new precision model is proposed for the acceleration of all-atom classical mol. dynamics (MD) simulations on graphics processing units (GPUs). This precision model replaces double precision arithmetic with fixed point integer arithmetic for the accumulation of force components as compared to a previously introduced model that uses mixed single/double precision arithmetic. This significantly boosts performance on modern GPU hardware without sacrificing numerical accuracy. We present an implementation for NVIDIA GPUs of both generalized Born implicit solvent simulations as well as explicit solvent simulations using the particle mesh Ewald (PME) algorithm for long-range electrostatics using this precision model. Tests demonstrate both the performance of this implementation as well as its numerical stability for const. energy and const. temp. biomol. MD as compared to a double precision CPU implementation and double and mixed single/double precision GPU implementations.
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  22. 22
    Skjevik, Å. A.; Madej, B. D.; Walker, R. C.; Teigen, K. LIPID11: A modular framework for lipid simulations using Amber J. Phys. Chem. B 2012, 116 (36) 11124– 11136
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  23. 23
    Siu, S. W.; Vacha, R.; Jungwirth, P.; Bockmann, R. A. Biomolecular simulations of membranes: physical properties from different force fields J. Chem. Phys. 2008, 128 (12) 125103
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    23
    Biomolecular simulations of membranes: Physical properties from different force fields
    Siu, Shirley W. I.; Vacha, Robert; Jungwirth, Pavel; Boeckmann, Rainer A.
    Journal of Chemical Physics (2008), 128 (12), 125103/1-125103/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Phospholipid force fields are of ample importance for the simulation of artificial bilayers, membranes, and also for the simulation of integral membrane proteins. Here, we compare the two most applied at. force fields for phospholipids, the all-atom CHARMM27 and the united atom Berger force field, with a newly developed all-atom generalized AMBER force field (GAFF) for dioleoylphosphatidylcholine mols. Only the latter displays the exptl. obsd. difference in the order of the C2 atom between the two acyl chains. The interfacial water dynamics is smoothly increased between the lipid carbonyl region and the bulk water phase for all force fields; however, the water order and with it the electrostatic potential across the bilayer showed distinct differences between the force fields. Both Berger and GAFF underestimate the lipid self-diffusion. GAFF offers a consistent force field for the at. scale simulation of biomembranes. (c) 2008 American Institute of Physics.
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  24. 24
    Jójárt, B.; Martinek, T. A. Performance of the general amber force field in modeling aqueous POPC membrane bilayers J. Comput. Chem. 2007, 28 (12) 2051– 2058
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  25. 25
    Rosso, L.; Gould, I. R. Structure and dynamics of phospholipid bilayers using recently developed general all-atom force fields J. Comput. Chem. 2008, 29 (1) 24– 37
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  26. 26
    Dickson, C. J.; Rosso, L.; Betz, R. M.; Walker, R. C.; Gould, I. R. GAFFlipid: A general Amber force field for the accurate molecular dynamics simulation of phospholipid Soft Matter 2012, 8, 9617– 9627
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    26
    GAFFlipid: a General Amber Force Field for the accurate molecular dynamics simulation of phospholipid
    Dickson, Callum J.; Rosso, Lula; Betz, Robin M.; Walker, Ross C.; Gould, Ian R.
    Soft Matter (2012), 8 (37), 9617-9627CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
    Previous attempts to simulate phospholipid bilayers using the General Amber Force Field (GAFF) yielded many bilayer characteristics in agreement with expt., however when using a tensionless NPT ensemble the bilayer is seen to compress to an undesirable extent resulting in low areas per lipid and high order parameters in comparison to expt. In this work, the GAFF Lennard-Jones parameters for the simulation of acyl chains are cor. to allow the accurate and stable simulation of pure lipid bilayers. Lipid bilayers comprised of six phospholipid types were simulated for timescales approaching a quarter of a microsecond under tensionless const. pressure conditions using Graphics Processing Units. Structural properties including area per lipid, vol. per lipid, bilayer thickness, order parameter and headgroup hydration show favorable agreement with available exptl. values. Expanding the system size from 72 to 288 lipids and a more exptl. realistic 2 × 288 lipid bilayer stack induces little change in the obsd. properties. This preliminary work is intended for combination with the new AMBER Lipid11 modular force field as part of on-going attempts to create a modular phospholipid AMBER force field allowing tensionless NPT simulations of complex lipid bilayers.
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  27. 27
    Siu, S. W. I.; Pluhackova, K.; Böckmann, R. A. Optimization of the OPLS-AA force field for long hydrocarbons J. Chem. Theory Comput. 2012, 8 (4) 1459– 1470
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    27
    Optimization of the OPLS-AA Force Field for Long Hydrocarbons
    Siu, Shirley W. I.; Pluhackova, Kristyna; Boeckmann, Rainer A.
    Journal of Chemical Theory and Computation (2012), 8 (4), 1459-1470CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The all-atom optimized potentials for liq. simulations (OPLS-AA) force field is a popular force field for simulating biomols. However, the current OPLS parameters for hydrocarbons developed using short alkanes cannot reproduce the liq. properties of long alkanes in mol. dynamics simulations. Therefore, the extension of OPLS-AA to (phospho)lipid mols. required for the study of biol. membranes was hampered in the past. Here, we optimized the OPLS-AA force field for both short and long hydrocarbons. Following the framework of the OPLS-AA parametrization, we refined the torsional parameters for hydrocarbons by fitting to the gas-phase ab initio energy profiles calcd. at the accurate MP2/aug-cc-pVTZ theory level. Addnl., the depth of the Lennard-Jones potential for methylene hydrogen atoms was adjusted to reproduce the densities and the heats of vaporization of alkanes and alkenes of different lengths. Optimization of partial charges finally allowed to reproduce the gel-to-liq.-phase transition temp. for pentadecane and solvation free energies. The optimized parameter set (L-OPLS) yields improved hydrocarbon diffusion coeffs., viscosities, and gauche-trans ratios. Moreover, its applicability for lipid bilayer simulations is shown for a GMO bilayer in its liq.-cryst. phase.
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  28. 28
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    A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model
    Bayly, Christopher I.; Cieplak, Piotr; Cornell, Wendy; Kollman, Peter A.
    Journal of Physical Chemistry (1993), 97 (40), 10269-80CODEN: JPCHAX; ISSN:0022-3654.
    The authors present a new approach to generating electrostatic potential (ESP) derived charges for mols. The major strength of electrostatic potential derived charges is that they optimally reproduce the intermol. interaction properties of mols. with a simple two-body additive potential, provided, of course, that a suitably accurate level of quantum mech. calcn. is used to derive the ESP around the mol. Previously, the major weaknesses of these charges have been that they were not easily transferably between common functional groups in related mols., they have often been conformationally dependent, and the large charges that frequently occur can be problematic for simulating intramol. interactions. Introducing restraints in the form of a penalty function into the fitting process considerably reduces the above problems, with only a minor decrease in the quality of the fit to the quantum mech. ESP. Several other refinements in addn. to the restrained electrostatic potential (RESP) fit yield a general and algorithmic charge fitting procedure for generating atom-centered point charges. This approach can thus be recommended for general use in mol. mechanics, mol. dynamics, and free energy calcns. for any org. or bioorg. system.
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    Application of Molecular Dynamics Simulations in Molecular Property Prediction. 1. Density and Heat of Vaporization
    Wang, Junmei; Hou, Tingjun
    Journal of Chemical Theory and Computation (2011), 7 (7), 2151-2165CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Mol. mech. force field (FF) methods are useful in studying condensed phase properties. They are complementary to expts. and can often go beyond expts. in at. details. Even if a FF is specific for studying structures, dynamics, and functions of biomols., it is still important for the FF to accurately reproduce the exptl. liq. properties of small mols. that represent the chem. moieties of biomols. Otherwise, the force field may not describe the structures and energies of macromols. in aq. solns. properly. In this work, the authors have carried out a systematic study to evaluate the General AMBER Force Field (GAFF) in studying densities and heats of vaporization for a large set of org. mols. that covers the most common chem. functional groups. The latest techniques, such as the particle mesh Ewald (PME) for calcg. electrostatic energies and Langevin dynamics for scaling temps., have been applied in the mol. dynamics (MD) simulations. For d., the av. percent error (APE) of 71 org. compds. is 4.43% when compared with the exptl. values. More encouragingly, the APE drops to 3.43% after the exclusion of two outliers and four other compds. for which the exptl. densities have been measured with pressures higher than 1.0 atm. For the heat of vaporization, several protocols have been investigated, and the best one, P4/ntt0, achieves an av. unsigned error (AUE) and a root-mean-square error (RMSE) of 0.93 and 1.20 kcal/mol, resp. How to reduce the prediction errors through proper van der Waals (vdW) parametrization has been discussed. An encouraging finding in vdW parametrization is that both densities and heats of vaporization approach their "ideal" values in a synchronous fashion when vdW parameters are tuned. The following hydration free energy calcn. using thermodn. integration further justifies the vdW refinement. The authors conclude that simple vdW parametrization can significantly reduce the prediction errors. The authors believe that GAFF can greatly improve its performance in predicting liq. properties of org. mols. after a systematic vdW parametrization, which will be reported in a sep. paper.
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    Ryckaert, Jean Paul; Ciccotti, Giovanni; Berendsen, Herman J. C.
    Journal of Computational Physics (1977), 23 (3), 327-41CODEN: JCTPAH; ISSN:0021-9991.
    A numerical algorithm integrating the 3N Cartesian equation of motion of a system of N points subject to holonomic constraints is applied to mol. dynamics simulation of a liq. of 64 butane mols.
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    Journal of Chemical Physics (1984), 81 (8), 3684-90CODEN: JCPSA6; ISSN:0021-9606.
    In mol. dynamics (MD) simulations, the need often arises to maintain such parameters as temp. or pressure rather than energy and vol., or to impose gradients for studying transport properties in nonequil. MD. A method is described to realize coupling to an external bath with const. temp. or pressure with adjustable time consts. for the coupling. The method is easily extendable to other variables and to gradients, and can be applied also to polyat. mols. involving internal constraints. The influence of coupling time consts. on dynamical variables is evaluated. A leap-frog algorithm is presented for the general case involving constraints with coupling to both a const. temp. and a const. pressure bath.
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    Yeh, I.-C.; Hummer, G. System-size dependence of diffusion coefficients and viscosities from molecular dynamics simulations with periodic boundary conditions J. Phys. Chem. B 2004, 108 (40) 15873– 15879
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    System-Size Dependence of Diffusion Coefficients and Viscosities from Molecular Dynamics Simulations with Periodic Boundary Conditions
    Yeh, In-Chul; Hummer, Gerhard
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    We study the system-size dependence of translational diffusion coeffs. and viscosities in mol. dynamics simulations under periodic boundary conditions. Simulations of water under ambient conditions and a Lennard-Jones (LJ) fluid show that the diffusion coeffs. increase strongly as the system size increases. We test a simple analytic correction for the system-size effects that is based on hydrodynamic arguments. This correction scales as N-1/3, where N is the no. of particles. For a cubic simulation box of length L, the diffusion coeff. cor. for system-size effects is D0 = DPBC + 2.837297kBT/(6πηL), where DPBC is the diffusion coeff. calcd. in the simulation, kB the Boltzmann const., T the abs. temp., and η the shear viscosity of the solvent. For water, LJ fluids, and hard-sphere fluids, this correction quant. accounts for the system-size dependence of the calcd. self-diffusion coeffs. In contrast to diffusion coeffs., the shear viscosities of water and the LJ fluid show no significant system-size dependences.
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    Lipari, Giovanni; Szabo, Attila
    Biophysical Journal (1980), 30 (3), 489-506CODEN: BIOJAU; ISSN:0006-3495.
    The theory of fluorescent emission anisotropy (r(t)) of a cylindrical probe in a membrane suspension is developed. The limiting anisotropy (r(∞)) is proportional to the square of the order parameter of the probe. The order parameter dets. the 1st nontrivial term in the expansion of the equil. orientational distribution function of the probe in a series of Legendre polynomials. The motion of the probe is described as diffusion (wobbling) within a cone of semiangle θ0. Within the framework of this model, an accurate single-exponential approxn. for r(t) is considered. An analytic expression relating the effective relaxation time, which appears in the above approxn., to θ0 and the diffusion coeff. for wobbling is derived. The model is generalized to the situation where the probe is attached to a macromol. whose motion cannot be neglected on the time scale of the fluorescence expt. Finally, by exploiting the formal similarity between the theory of fluorescence depolarization and 13C NMR dipolar relaxation, expressions for spin-spin and spin-lattice relaxation times and the nuclear Overhauser enhancement are derived for a protonated C which is nonrigidly attached to a macromol. and undergoes librational motion described as diffusion on a spherical cap of semiangle θ0.
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    Ottiger, M.; Bax, A. Determination of Relative N–HN, N–C′, Cα–C′, and Cα–Hα effective bond lengths in a protein by NMR in a dilute liquid crystalline phase J. Am. Chem. Soc. 1998, 120 (47) 12334– 12341
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    Tofts, P. S.; Lloyd, D.; Clark, C. A.; Barker, G. J.; Parker, G. J. M.; McConville, P.; Baldock, C.; Pope, J. M. Test liquids for quantitative MRI measurements of self-diffusion coefficient in vivo Magn. Reson. Med. 2000, 43 (3) 368– 374
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    Test liquids for quantitative MRI measurements of self-diffusion coefficient in vivo
    Tofts, P. S.; Lloyd, D.; Clark, C. A.; Barker, G. J.; Parker, G. J. M.; McConville, P.; Baldock, C.; Pope, J. M.
    Magnetic Resonance in Medicine (2000), 43 (3), 368-374CODEN: MRMEEN; ISSN:0740-3194. (Wiley-Liss, Inc.)
    A range of liqs. suitable as quality control test objects for measuring the accuracy of clin. MRI diffusion sequences (both apparent diffusion coeff. and tensor) has been identified and characterized. The self-diffusion coeffs. for 15 liqs. (3 cyclic alkanes: cyclohexane to cyclooctane, 9 n-alkanes: n-octane to n-hexadecane, and 3 n-alcs.: ethanol to 1-propanol) were measured at 15-30° using an NMR spectrometer. Values at 22° range from 0.36 to 2.2 10-9 m2s-1. Typical 95% confidence limits are ±2%. Temp. coeffs. are 1.7-3.2%/°C. T1 and T2 values at 1.5 T and proton d. are given. N-tridecane has a diffusion coeff. close to that of normal white matter. The longer n-alkanes may be useful T2 stds. Measurements from a spin-echo MRI sequence agreed to within 2%.
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    CHARMM-GUI Membrane Builder for mixed bilayers and its application to yeast membranes
    Jo, Sunhwan; Lim, Joseph B.; Klauda, Jeffery B.; Im, Wonpil
    Biophysical Journal (2009), 97 (1), 50-58CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
    The CHARMM-GUI Membrane Builder (http://www.charmm-gui.org/input/membrane), an intuitive, straightforward, web-based graphical user interface, was expanded to automate the building process of heterogeneous lipid bilayers, with or without a protein and with support for up to 32 different lipid types. The efficacy of these new features was tested by building and simulating lipid bilayers that resemble yeast membranes, composed of cholesterol, dipalmitoylphosphatidylcholine, dioleoylphosphatidylcholine, palmitoyloleoylphosphatidylethanolamine, palmitoyloleoylphosphatidylamine, and palmitoyloleoylphosphatidylserine. Four membranes with varying concns. of cholesterol and phospholipids were simulated, for a total of 170 ns at 303.15 K. Unsatd. phospholipid chain concn. had the largest influence on membrane properties, such as av. lipid surface area, d. profiles, deuterium order parameters, and cholesterol tilt angle. Simulations with a high concn. of unsatd. chains (73%, membraneunsat) resulted in a significant increase in lipid surface area and a decrease in deuterium order parameters, compared with membranes with a high concn. of satd. chains (60-63%, membranesat). The av. tilt angle of cholesterol with respect to bilayer normal was largest, and the distribution was significantly broader for membraneunsat. Moreover, short-lived cholesterol orientations parallel to the membrane surface existed only for membraneunsat. The membranesat simulations were in a liq.-ordered state, and agree with similar exptl. cholesterol-contg. membranes.
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    Journal of Chemical Physics (1983), 79 (2), 926-35CODEN: JCPSA6; ISSN:0021-9606.
    Classical Monte Carlo simulations were carried out for liq. H2O in the NPT ensemble at 25° and 1 atm using 6 of the simpler intermol. potential functions for the dimer. Comparisons were made with exptl. thermodn. and structural data including the neutron diffraction results of Thiessen and Narten (1982). The computed densities and potential energies agree with expt. except for the original Bernal-Fowler model, which yields an 18% overest. of the d. and poor structural results. The discrepancy may be due to the correction terms needed in processing the neutron data or to an effect uniformly neglected in the computations. Comparisons were made for the self-diffusion coeffs. obtained from mol. dynamics simulations.
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    Joung, I. S.; Cheatham, T. E. Determination of alkali and halide monovalent ion parameters for use in explicitly solvated biomolecular simulations J. Phys. Chem. B 2008, 112 (30) 9020– 9041
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    Determination of Alkali and Halide Monovalent Ion Parameters for Use in Explicitly Solvated Biomolecular Simulations
    Joung, In Suk; Cheatham, Thomas E.
    Journal of Physical Chemistry B (2008), 112 (30), 9020-9041CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    Alkali (Li+, Na+, K+, Rb+, and Cs+) and halide (F-, Cl-, Br-, and I-) ions play an important role in many biol. phenomena, roles that range from stabilization of biomol. structure, to influence on biomol. dynamics, to key physiol. influence on homeostasis and signaling. To properly model ionic interaction and stability in atomistic simulations of biomol. structure, dynamics, folding, catalysis, and function, an accurate model or representation of the monovalent ions is critically necessary. A good model needs to simultaneously reproduce many properties of ions, including their structure, dynamics, solvation, and moreover both the interactions of these ions with each other in the crystal and in soln. and the interactions of ions with other mols. At present, the best force fields for biomols. employ a simple additive, nonpolarizable, and pairwise potential for at. interaction. In this work, the authors describe their efforts to build better models of the monovalent ions within the pairwise Coulombic and 6-12 Lennard-Jones framework, where the models are tuned to balance crystal and soln. properties in Ewald simulations with specific choices of well-known water models. Although it has been clearly demonstrated that truly accurate treatments of ions will require inclusion of nonadditivity and polarizability (particularly with the anions) and ultimately even a quantum mech. treatment, the authors' goal was to simply push the limits of the additive treatments to see if a balanced model could be created. The applied methodol. is general and can be extended to other ions and to polarizable force-field models. The authors' starting point centered on observations from long simulations of biomols. in salt soln. with the AMBER force fields where salt crystals formed well below their soly. limit. The likely cause of the artifact in the AMBER parameters relates to the naive mixing of the Smith and Dang chloride parameters with AMBER-adapted Aqvist cation parameters. To provide a more appropriate balance, the authors reoptimized the parameters of the Lennard-Jones potential for the ions and specific choices of water models. To validate and optimize the parameters, the authors calcd. hydration free energies of the solvated ions and also lattice energies (LE) and lattice consts. (LC) of alkali halide salt crystals. This is the first effort that systematically scans across the Lennard-Jones space (well depth and radius) while balancing ion properties like LE and LC across all pair combinations of the alkali ions and halide ions. The optimization across the entire monovalent series avoids systematic deviations. The ion parameters developed, optimized, and characterized were targeted for use with some of the most commonly used rigid and nonpolarizable water models, specifically TIP3P, TIP4PEW, and SPC/E. In addn. to well reproducing the soln. and crystal properties, the new ion parameters well reproduce binding energies of the ions to water and the radii of the first hydration shells.
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    Roe, D. R.; Cheatham, T. E. PTRAJ and CPPTRAJ: Software for processing and analysis of molecular dynamics trajectory data J. Chem. Theory Comput. 2013, 9 (7) 3084– 3095
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    PTRAJ and CPPTRAJ: Software for Processing and Analysis of Molecular Dynamics Trajectory Data
    Roe, Daniel R.; Cheatham, Thomas E.
    Journal of Chemical Theory and Computation (2013), 9 (7), 3084-3095CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We describe PTRAJ and its successor CPPTRAJ, two complementary, portable, and freely available computer programs for the anal. and processing of time series of three-dimensional at. positions (i.e., coordinate trajectories) and the data therein derived. Common tools include the ability to manipulate the data to convert among trajectory formats, process groups of trajectories generated with ensemble methods (e.g., replica exchange mol. dynamics), image with periodic boundary conditions, create av. structures, strip subsets of the system, and perform calcns. such as RMS fitting, measuring distances, B-factors, radii of gyration, radial distribution functions, and time correlations, among other actions and analyses. Both the PTRAJ and CPPTRAJ programs and source code are freely available under the GNU General Public License version 3 and are currently distributed within the AmberTools 12 suite of support programs that make up part of the Amber package of computer programs (see http://ambermd.org). This overview describes the general design, features, and history of these two programs, as well as algorithmic improvements and new features available in CPPTRAJ.
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    Braun, A. R.; Sachs, J. N.; Nagle, J. F. Comparing simulations of lipid bilayers to scattering data: The GROMOS 43A1-S3 force field J. Phys. Chem. B 2013, 117 (17) 5065– 5072
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    Comparing Simulations of Lipid Bilayers to Scattering Data: The GROMOS 43A1-S3 Force Field
    Braun, Anthony R.; Sachs, Jonathan N.; Nagle, John F.
    Journal of Physical Chemistry B (2013), 117 (17), 5065-5072CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    Simulations of DOPC at T = 303 K were performed using the united atom force field 43A1-S3 at six fixed projected areas, AP = 62, 64, 66, 68, 70, and 72 Å2, as well as a tensionless simulation that produced an av. ANPT = 65.8 Å2. After a small undulation correction for the system size consisting of 288 lipids, results were compared to exptl. data. The best, and excellent, fit to neutron scattering data occurs at an interpolated AN = 66.6 Å2 and the best, but not as good, fit to the more extensive x-ray scattering data occurs at AX = 68.7 Å2. The distance ΔDB-H between the Gibbs dividing surface for water and the peak in the electron d. profile agrees with scattering expts. The calcd. area compressibility KA = 277±10 mN/m is in excellent agreement with the micromech. expt. The vol. per lipid VL is smaller than vol. expts. which suggests a workaround that raises all the areas by about 1.5%. Although AX ≠ AN ≠ ANPT, this force field obtains acceptable agreement with expt. for AL = 67.5 Å2 (68.5 Å2 in the workaround), which we suggest is a better DOPC result from 43A1-S3 simulations than its value from the tensionless NPT simulation. However, nonsimulation modeling obtains better simultaneous fits to both kinds of scattering data, which suggests that the force fields can still be improved.
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    Rawicz, W.; Olbrich, K. C.; McIntosh, T.; Needham, D.; Evans, E. Effect of chain length and unsaturation on elasticity of lipid bilayers Biophys. J. 2000, 79 (1) 328– 339
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    Effect of chain length and unsaturation on elasticity of lipid bilayers
    Rawicz, W.; Olbrich, K. C.; McIntosh, T.; Needham, D.; Evans, E.
    Biophysical Journal (2000), 79 (1), 328-339CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    Micropipette pressurization of giant bilayer vesicles was used to measure both elastic bending kc and area stretch KA moduli of fluid-phase phosphatidylcholine (PC) membranes. Twelve diacyl PCs were chosen: eight with two 18 carbon chains and degrees of unsatn. from one double bond (C18:1/0, C18:0/1) to six double bonds per lipid (diC18:3), two with short satd. carbon chains (diC13:0, diC14:0), and two with long unsatd. carbon chains (diC20:4, diC22:1). Bending moduli were derived from measurements of apparent expansion in vesicle surface area under very low tensions (0.001-0.5 mN/m), which is dominated by smoothing of thermal bending undulations. Area stretch moduli were obtained from measurements of vesicle surface expansion under high tensions (>0.5 mN/m), which involve an increase in area per mol. and a small, but important, contribution from smoothing of residual thermal undulations. The direct stretch moduli varied little (< ± 10%) with either chain unsatn. or length about a mean of 243 mN/m. On the other hand, the bending moduli of satd./mono-unsatd. chain PCs increased progressively with chain length from 0.56 × 10-19 J for diC13:0 to 1.2 × 10-19 J for diC22:1. However, quite unexpectedly for longer chains, the bending moduli dropped precipitously to ∼0.4 × 10-19 J when two or more cis double bonds were present in a chain (C18:0/2, diC18:2, diC18:3, diC20:4). Given nearly const. area stretch moduli, the variations in bending rigidity with chain length and poly-unsatn. implied significant variations in thickness. To test this hypothesis, peak-to-peak headgroup thicknesses hpp of bilayers were obtained from x-ray diffraction of multibilayer arrays at controlled relative humidities. For satd./mono-unsatd. chain bilayers, the distances hpp increased smoothly from diC13:0 to diC22:1 as expected. Moreover, the distances and elastic properties correlated well with a polymer brush model of the bilayer that specifies that the elastic ratio (kc/KA)1/2 = (hpp - ho)/24, where ho ≈ 1 nm accounts for sepn. of the headgroup peaks from the deformable hydrocarbon region. However, the elastic ratios and thicknesses for diC18:2, diC18:3, and diC20:4 fell into a distinct group below the correlation, which showed that poly-cis unsatd. chain bilayers are thinner and more flexible than satd./mono-unsatd. chain bilayers.
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    Klauda, J. B.; Kučerka, N.; Brooks, B. R.; Pastor, R. W.; Nagle, J. F. Simulation-based methods for interpreting X-ray data from lipid bilayers Biophys. J. 2006, 90 (8) 2796– 2807
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    Simulation-based methods for interpreting X-ray data from lipid bilayers
    Klauda, Jeffery B.; Kucerka, Norbert; Brooks, Bernard R.; Pastor, Richard W.; Nagle, John F.
    Biophysical Journal (2006), 90 (8), 2796-2807CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    The fully hydrated liq. cryst. phase of the dimyristoylphosphatidylcholine lipid bilayer at 30° was simulated using mol. dynamics with the CHARMM potential for five surface areas per lipid (A) in the range 55-65 Å2 that brackets the previously detd. exptl. area 60.6 Å2. The results of these simulations are used to develop a new hybrid zero-baseline structural model, denoted H2, for the electron d. profile, p(z), for the purpose of interpreting x-ray diffraction data. H2 and also the older hybrid baseline model were tested by fitting to partial information from the simulation and various constraints, both of which correspond to those available exptl. The A, ρ(z), and F(q) obtained from the models agree with those calcd. directly from simulation at each of the five areas, thereby validating this use of the models. The new H2 was then applied to exptl. dimyristoylphosphatidylcholine data; it yields A = 60.6 ± 0.5 Å2, in agreement with the earlier est. obtained using the hybrid baseline model. The electron d. profiles also compare well, despite considerable differences in the functional forms of the two models. Overall, the simulated ρ(z) at A = 60.7 Å2 agrees well with expt., demonstrating the accuracy of the CHARMM lipid force field; small discrepancies indicate targets for improvements. Lastly, a simulation-based model-free approach for obtaining A is proposed. It is based on interpolating the area that minimizes the difference between the exptl. F(q) and simulated F(q) evaluated for a range of surface areas. This approach is independent of structural models and could be used to det. structural properties of bilayers with different lipids, cholesterol, and peptides.
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    Kučerka, N.; Tristram-Nagle, S.; Nagle, J. F. Closer look at structure of fully hydrated fluid phase DPPC bilayers Biophys. J. 2006, 90 (11) L83– L85
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    Kučerka, N.; Nagle, J. F.; Sachs, J. N.; Feller, S. E.; Pencer, J.; Jackson, A.; Katsaras, J. Lipid bilayer structure determined by the simultaneous analysis of neutron and X-ray scattering data Biophys. J. 2008, 95 (5) 2356– 2367
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    Pan, J.; Tristram-Nagle, S.; Kučerka, N.; Nagle, J. F. Temperature dependence of structure, bending rigidity, and bilayer interactions of dioleoylphosphatidylcholine bilayers Biophys. J. 2008, 94 (1) 117– 124
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    Kučerka, N.; Tristram-Nagle, S.; Nagle, J. F. Structure of fully hydrated fluid phase lipid bilayers with monounsaturated chains J. Membr. Biol. 2006, 208 (3) 193– 202
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    Structure of Fully Hydrated Fluid Phase Lipid Bilayers with Monounsaturated Chains
    Kucerka, Norbert; Tristram-Nagle, Stephanie; Nagle, John F.
    Journal of Membrane Biology (2006), 208 (3), 193-202CODEN: JMBBBO; ISSN:0022-2631. (Springer)
    Quant. structures are obtained at 30°C for the fully hydrated fluid phases of palmitoyloleoylphosphatidylcholine (POPC), with a double bond on the sn-2 hydrocarbon chain, and for dierucoylphosphatidylcholine (di22:1PC), with a double bond on each hydrocarbon chain. The form factors F(qz) for both lipids are obtained using a combination of 3 methods: (1) Volumetric measurements provide F(0), (2) x-ray scattering from extruded unilamellar vesicles provides |F(qz)| for low qz, (3) Diffuse x-ray scattering from oriented stacks of bilayers provides |F(qz)| for high qz. Also, data using method (2) are added to the authors' recent data for dioleoylphosphatidylcholine (DOPC) using methods (1) and (3); the new DOPC data agree very well with the recent data and with (4) the authors' older data obtained using a liq. crystallog. x-ray method. The authors used hybrid electron d. models to obtain structural results from these form factors. The result for area per lipid (A) for DOPC 72.4 ± 0.5 Å2 agrees well with the authors' earlier publications, and the authors find A = 69.3 ± 0.5 Å2 for di22:1PC and A = 68.3 ± 1.5 Å2 for POPC. The authors obtain the values for 5 different av. thicknesses: hydrophobic, steric, head-head, phosphate-phosphate and Luzzati. Comparison of the results for these 3 lipids and for the authors' recent dimyristoylphosphatidylcholine (DMPC) detn. provides quant. measures of the effect of unsatn. on bilayer structure. The authors' results suggest that lipids with one monounsatd. chain have quant. bilayer structures closer to lipids with 2 monounsatd. chains than to lipids with 2 completely satd. chains.
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    Binder, H.; Gawrisch, K. Effect of unsaturated lipid chains on dimensions, molecular order and hydration of membranes J. Phys. Chem. B 2001, 105 (49) 12378– 12390
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    Rappolt, M.; Hickel, A.; Bringezu, F.; Lohner, K. Mechanism of the lamellar/inverse hexagonal phase transition examined by high resolution X-ray diffraction Biophys. J. 2003, 84 (5) 3111– 3122
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    Mechanism of the lamellar/inverse hexagonal phase transition examined by high resolution X-ray diffraction
    Rappolt, Michael; Hickel, Andrea; Bringezu, Frank; Lohner, Karl
    Biophysical Journal (2003), 84 (5), 3111-3122CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    For the first time the electron d. of the lamellar liq. cryst. as well as of the inverted hexagonal phase could be retrieved at the transition temp. A reliable decompn. of the d-spacings into hydrophobic and hydrophilic structure elements could be performed owing to the presence of a sufficient no. of reflections. While the hydrocarbon chain length, dC, in the lamellar phase with a value of 14.5 Å lies within the extreme limits of the estd. chain length of the inverse hexagonal phase 10 Å < dC < 16 Å, the changes in the hydrophilic region vary strongly. During the lamellar-to-inverse hexagonal phase transition the area per lipid mol. reduces by ∼25%, and the no. of water mols. per lipid increases from 14 to 18. On the basis of the anal. of the structural components of each phase, the interface between the coexisting mesophases between 66 and 84° has been examd. in detail, and a model for the formation of the first rods in the matrix of the lamellar phospholipid stack is discussed. Judging from the structural relations between the inverse hexagonal and the lamellar phase, we suggest a cooperative chain reaction of rod formation at the transition midpoint, which is mainly driven by minimizing the interstitial region.
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    Lipid bilayer structure
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    Current Opinion in Structural Biology (2000), 10 (4), 474-480CODEN: COSBEF; ISSN:0959-440X. (Elsevier Science Ltd.)
    A review with 51 refs. Fluctuations, inherent in flexible and biol. relevant lipid bilayers, make quant. structure detn. challenging. Shortcomings in older methods of structure detn. have been realized and new methodologies have been introduced that take fluctuations into account. The large uncertainty in literature values of lipid bilayer structural parameters is being reduced.
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    Poger, D.; Mark, A. E. On the validation of molecular dynamics simulations of saturated and cis-monounsaturated phosphatidylcholine lipid bilayers: A comparison with experiment J. Chem. Theory Comput. 2009, 6 (1) 325– 336
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    Kučerka, N.; Katsaras, J.; Nagle, J. Comparing membrane simulations to scattering experiments: Introducing the SIMtoEXP software J. Membr. Biol. 2010, 235 (1) 43– 50
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    Comparing Membrane Simulations to Scattering Experiments: Introducing the SIMtoEXP Software
    Kucerka, Norbert; Katsaras, John; Nagle, John F.
    Journal of Membrane Biology (2010), 235 (1), 43-50CODEN: JMBBBO; ISSN:0022-2631. (Springer)
    SIMtoEXP is a software package designed to facilitate the comparison of biomembrane simulations with exptl. x-ray and neutron scattering data. It has the following features: (1) Accepts no. d. profiles from simulations in a std. but flexible format. (2) Calcs. the electron d. ε(z) and neutron scattering length d. ν(z) profiles along the z direction (i.e., normal to the membrane) and their resp. Fourier transforms (i.e., Fε [qz] and Fν[qz]). The resultant 4 functions are then displayed graphically. (3) Accepts exptl. Fε(qz) and Fν(qz) data for graphical comparison with simulations. (4) Allows for lipids and other large mols. to be parsed into component groups by the user and calcs. the component vols. following Petrache et al. The software then calcs. and displays the contributions of each component group as vol. probability profiles, ρ(z), as well as the contributions of each component to ε(z) and ν(z).
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    Perly, B.; Smith, I. C. P.; Jarrell, H. C. Acyl chain dynamics of phosphatidylethanolamines containing oleic acid and dihydrosterculic acid: deuteron NMR relaxation studies Biochemistry 1985, 24 (17) 4659– 4665
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    Lafleur, M.; Bloom, M.; Eikenberry, E. F.; Gruner, S. M.; Han, Y.; Cullis, P. R. Correlation between lipid plane curvature and lipid chain order Biophys. J. 1996, 70 (6) 2747– 2757
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    Correlation between lipid plane curvature and lipid chain order
    Lafleur, Michel; Bloom, Myer; Eikenberry, Eric F.; Gruner, Sol M.; Han, Yuqi; Cullis, Pieter R.
    Biophysical Journal (1996), 70 (6), 2747-2757CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    The 1-palmitoyl-2-oleoyl-phosphatidylethanolamine: 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPE:POPC) system has been investigated by measuring, in the inverted hexagonal (HII) phase, the intercylinder spacings (using x-ray diffraction) and orientational order of the acyl chains (using 2H NMR). The presence of 20% dodecane leads to the formation of a HII phase for the compn. range from 0 to 39 mol% of POPC in POPE, as ascertained by x-ray diffraction and 2H NMR. The addn. of the alkane induces a small decrease in chain order, consistent with less stretched chains. An increase in temp. or in POPE proportion leads to a redn. in the intercylinder spacing, primarily due to a decrease in the water core radius. A temp. increase also leads to a redn. in the orientational order of the lipid acyl chains, whereas in POPE proportion has little effect on chain order. A correlation is proposed to relate the radius of curvature of the cylinders in the inverted hexagonal phase to the chain order of the lipids adopting the HII phase. A simple geometrical model is proposed, taking into account the area occupied by the polar headgroup at the interface and the orientational order of the acyl chains reflecting the contribution of the apolar core. From these parameters, intercylinder spacings are calcd. that agree well with the values detd. exptl. by x-ray diffraction, for the variations of both temp. and POPE:POPC proportion. This model suggests that temp. increases the curvature of lipid layers, mainly by increasing the area subtended by the hydrophobic core through chain conformation disorder, whereas POPC content affects primarily the headgroup interface contribution. The frustration of lipid layer curvature is also shown to be reflected in the acyl chain order measured in the Lα phase, in the absence of dodecane; for a given temp., increased order is obsd. when the curling tendencies of the lipid plane are more pronounced.
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    Warschawski, D.; Devaux, P. Order parameters of unsaturated phospholipids in membranes and the effect of cholesterol: a 1H-13C solid-state NMR study at natural abundance Eur. Biophys. J. 2005, 34 (8) 987– 96
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    Order parameters of unsaturated phospholipids in membranes and the effect of cholesterol: a 1H-13C solid-state NMR study at natural abundance
    Warschawski, Dror E.; Devaux, Philippe F.
    European Biophysics Journal (2005), 34 (8), 987-996CODEN: EBJOE8; ISSN:0175-7571. (Springer)
    Most biol. phospholipids contain at least one unsatd. alkyl chain. However, few order parameters of unsatd. lipids have been detd. because of the difficulty assocd. with isotopic labeling of a double bond. Dipolar recoupling on axis with scaling and shape preservation (DROSS) is a solid-state NMR technique optimized for measuring 1H-13C dipolar couplings and order parameters in lipid membranes in the fluid phase. It has been used to det. the order profile of 1,2-dimyristoyl-sn-glycero-3-phosphocholine hydrated membranes. Here, we show an application for the measurement of local order parameters in multilamellar vesicles contg. unsatd. lipids. Taking advantage of the very good 13C chem. shift dispersion, one can easily follow the segmental order along the acyl chains and, particularly, around the double bonds where we have been able to det. the previously misassigned order parameters of each acyl chain of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). We have followed the variation of such order profiles with temp., unsatn. content and cholesterol addn. We have found that the phase formed by DOPC with 30% cholesterol is analogous to the liq.-ordered (lo) phase. Because these expts. do not require isotopic enrichment, this technique can, in principle, be applied to natural lipids and biomembranes.
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    Petrache, H. I.; Dodd, S. W.; Brown, M. F. Area per lipid and acyl length distributions in fluid phosphatidylcholines determined by (2)H NMR spectroscopy Biophys. J. 2000, 79 (6) 3172– 92
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    Area per lipid and acyl length distributions in fluid phosphatidylcholines determined by 2H NMR spectroscopy
    Petrache, Horia I.; Dodd, Steven W.; Brown, Michael F.
    Biophysical Journal (2000), 79 (6), 3172-3192CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    Deuterium (2H) NMR spectroscopy provides detailed information regarding the structural fluctuations of lipid bilayers, including both the equil. properties and dynamics. Exptl. 2H NMR measurements for the homologous series of 1,2-diacyl-sn-glycero-3-phosphocholines with perdeuterated satd. chains (from C12:0 to C18:0) have been performed on randomly oriented, fully hydrated multilamellar samples. For each lipid, the C-D bond order parameters have been calcd. from de-Paked 2H NMR spectra as a function of temp. The exptl. order parameters were analyzed using a mean-torque potential model for the acyl chain segment distributions, and comparison was made with the conventional diamond lattice approach. Statistical mech. principles were used to relate the measured order parameters to the lipid bilayer structural parameters: the hydrocarbon thickness and the mean interfacial area per lipid. At fixed temp., the area decreases with increasing acyl length, indicating increased van der Waals attraction for longer lipid chains. However, the main effect of increasing the acyl chain length is on the hydrocarbon thickness rather than on the area per lipid. Expansion coeffs. of the structural parameters are reported and interpreted using an empirical free energy function that describes the force balance in fluid bilayers. At the same abs. temp., the phosphatidylcholine (PC) series exhibits a universal chain packing profile that differs from that of phosphatidylethanolamines (PE). Hence, the lateral packing of phospholipids is more sensitive to the headgroup methylation than to the acyl chain length. A fit to the area per lipid for the PC series using the empirical free energy function shows that the PE area represents a limiting value for the packing of fluid acyl chains.
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    Douliez, J. P.; Léonard, A.; Dufourc, E. J. Restatement of order parameters in biomembranes: calculation of C-C bond order parameters from C-D quadrupolar splittings Biophys. J. 1995, 68 (5) 1727– 1739
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    Restatement of order parameters in biomembranes: calculation of C-C bond order parameters from C-D quadrupolar splittings
    Douliez, Jean-Paul; Leonard, Alain; Dufourc, Erick J.
    Biophysical Journal (1995), 68 (5), 1727-39CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    An expression for the C-C bond order parameter, SCC, of membrane hydrocarbon chains has been derived from the obsd. C-D bond order parameters. It allows calcn. of the probability of each of the C-C bond rotamers and, consequently, the no. of gauche defects per chain as well as their projected av. length onto the bilayer normal, thus affording the calcn. of accurate hydrophobic bilayer thicknesses. The effect of the temp. has been studied on dilauroyl-, dimyristoyl-, and dipalmitoylphosphatidylcholine (DLPC, DMPC, DPPC) membranes, as has the effect of cholesterol on DMPC. The salient results are as follows: (1) an odd-even effect is obsd. for the SCC vs. carbon position, k, whose amplitude increases with temp.; (2) calcn. of SCC, from nonequivalent deuterons on the sn-2 chain of lipids, S2CC, leads to neg. values, indicating the tendency for the C1-C2 bond to be oriented parallel to the bilayer surface; this bond becomes more parallel to the surface as the temp. increases or when cholesterol is added; (3) calcn. on the sn-2 chain length can be performed from C1 and Cn, where n is the no. of carbon atoms in the chain, and leads to 10.4, 12.2, and 13.8 Å for DLPC, DMPC, and DPPC close to the transition temp. TC, of each of the systems and to 9.4, 10.9, and 12.6 for T-TC = 30-40°, resp.; (4) sepn. of intra- and intermol. motions allows quantitation of the no. of gauche defects per chain, which is equal to 1.9, 2.7, and 3.5 for DLPC, DMPC, and DPPC near Tc and to 2.7, 3.5, and 4.4 at T - TC = 30-40°, resp. Finally, the validity of the model is discussed and compared with previously published models.
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    Aussenac, F.; Laguerre, M.; Schmitter, J.-M.; Dufourc, E. J. Detailed structure and dynamics of bicelle phospholipids using selectively deuterated and perdeuterated labels. 2H NMR and molecular mechanics study Langmuir 2003, 19 (25) 10468– 10479
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    Shaikh, S. R.; Brzustowicz, M. R.; Gustafson, N.; Stillwell, W.; Wassall, S. R. Monounsaturated PE does not phase-separate from the lipid raft molecules sphingomyelin and cholesterol: Role for polyunsaturation? Biochemistry 2002, 41 (34) 10593– 10602
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    The sensitivity of the structure and dynamics of a fully hydrated pure bilayer of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) in mol. dynamics simulations to changes in force-field and simulation parameters has been assessed. Three related force fields (the GROMOS 54A7 force field, a GROMOS 53A6-derived parameter set and a variant of the Berger parameters) in combination with either particle-mesh Ewald (PME) or a reaction field (RF) were compared. Structural properties such as the area per lipid, carbon-deuterium order parameters, electron d. profile and bilayer thicknesses, are reproduced by all the parameter sets within the uncertainty of the available exptl. data. However, there are clear differences in the ordering of the glycerol backbone and choline headgroup, and the orientation of the headgroup dipole. In some cases, the degree of ordering was reminiscent of a liq.-ordered phase. It is also shown that, although the lateral diffusion of the lipids in the plane of the bilayer is often used to validate lipid force fields, because of the uncertainty in the exptl. measurements and the fact that the lateral diffusion is dependent on the choice of the simulation conditions, it should not be employed as a measure of quality. Finally, the simulations show that the effect of small changes in force-field parameters on the structure and dynamics of a bilayer is more significant than the treatment of the long-range electrostatic interactions using RF or PME. Overall, the GROMOS 54A7 best reproduced the range of exptl. data examd.
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    Accelerated mol. dynamics (aMD) is an enhanced sampling technique that expedites conformational space sampling by reducing the barriers sepg. various low-energy states of a system. Here, the authors present the first application of the aMD method on lipid membranes. Altogether, ∼1.5 μs simulations were performed on three systems: a pure POPC bilayer, a pure DMPC bilayer, and a mixed POPC:DMPC bilayer. Overall, the aMD simulations are found to produce significant speedup in trans-gauche isomerization and lipid lateral diffusion vs. those in conventional MD (cMD) simulations. Further comparison of a 70-ns aMD run and a 300-ns cMD run of the mixed POPC:DMPC bilayer shows that the two simulations yield similar lipid mixing behaviors, with aMD generating a 2-3-fold speedup compared to cMD. The authors' results demonstrate that the aMD method is an efficient approach for the study of bilayer structural and dynamic properties. On the basis of simulations of the three bilayer systems, the authors also discuss the impact of aMD parameters on various lipid properties, which can be used as a guideline for future aMD simulations of membrane systems.
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    Basconi, J. E.; Shirts, M. R. Effects of temperature control algorithms on transport properties and kinetics in molecular dynamics simulations J. Chem. Theory Comput. 2013, 9 (7) 2887– 2899
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    Temp. control algorithms in mol. dynamics (MD) simulations are necessary to study isothermal systems. However, these thermostatting algorithms alter the velocities of the particles and thus modify the dynamics of the system with respect to the microcanonical ensemble, which could potentially lead to thermostat-dependent dynamical artifacts. In this study, we investigate how six well-established thermostat algorithms applied with different coupling strengths and to different degrees of freedom affect the dynamics of various mol. systems. We consider dynamic processes occurring on different times scales by measuring translational and rotational self-diffusion as well as the shear viscosity of water, diffusion of a small mol. solvated in water, and diffusion and the dynamic structure factor of a polymer chain in water. All of these properties are significantly dampened by thermostat algorithms which randomize particle velocities, such as the Andersen thermostat and Langevin dynamics, when strong coupling is used. For the solvated small mol. and polymer, these dampening effects are reduced somewhat if the thermostats are applied to the solvent alone, such that the solute's temp. is maintained only through thermal contact with solvent particles. Algorithms which operate by scaling the velocities, such as the Berendsen thermostat, the stochastic velocity rescaling approach of Bussi and co-workers, and the Nose-Hoover thermostat, yield transport properties that are statistically indistinguishable from those of the microcanonical ensemble, provided they are applied globally, i.e. coupled to the system's kinetic energy. When coupled to local kinetic energies, a velocity scaling thermostat can have dampening effects comparable to a velocity randomizing method, as we observe when a massive Nose-Hoover coupling scheme is used to simulate water. Correct dynamical properties, at least those studied in this paper, are obtained with the Berendsen thermostat applied globally, despite the fact that it yields the wrong kinetic energy distribution.
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  • Abstract

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    Figure 1

    Figure 1. A box of 144 pentadecane molecules simulated in the NPT ensemble at 298.15 K using the General Amber Force Field (16) to model the carbon chains.

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    Figure 2

    Figure 2. The energy profile for rotating about selected torsions of a cis-5-decene molecule. Energy evaluated using QM and the HM-IE method (filled triangle ▲), AMBER with standard GAFF parameters (dotted line), and AMBER with Lipid14 parameters (black line). Torsion fits from the top are as follows: CH2–CH–CH–CH2, CH–CH–CH2–CH2, and CH–CH2–CH2–CH2.

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    Figure 3

    Figure 3. Structure and charges of Lipid11/Lipid14 headgroup and tail group caps. (22)

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    Figure 4

    Figure 4. A capped lauroyl tail group residue was used to fit the oS-cC-cD-cD and oC-cC-cD-cD torsions.

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    Figure 5

    Figure 5. The energy profiles for rotating about selected torsions of a capped lauroyl tail group residue. Energy evaluated using QM and the HM-IE method (filled triangle ▲), AMBER with standard GAFF/Lipid11 parameters (dotted line), and AMBER with Lipid14 parameters (black line). Torsion fits from the top are oC-cC-cD-cD and oS-cC-cD-cD.

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    Figure 6

    Figure 6. Calculated 13C NMR T1 relaxation times for selected alkane chains and comparison to experiment. (47) Values at 312 K.

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    Figure 7

    Figure 7. Simulation NMR order parameters for the six lipid systems and comparison to experiment. (77, 78, 80-84)

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    Figure 8

    Figure 8. The total and decomposed electron density profiles for each of the six lipid bilayer systems with contributions from water, choline (CHOL), phosphate (PO4), glycerol (GLY), carbonyl (COO), methylene (CH2), unsaturated CH═CH and terminal methyls (CH3).

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    Figure 9

    Figure 9. Simulation X-ray scattering form factors for the six lipid systems (black line) and comparison to experiment (54, 55, 62, 66, 68) (cyan circles). Inset: Simulation neutron scattering form factors at 100% D2O (black line), 70% D2O (red line), and 50% D2O (blue line) and comparison to experiment (55, 96) (black, red, and blue circles, respectively).

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    Figure 10

    Figure 10. Plot of ΔDB-H versus area per lipid AL for the three all-atom lipid force fields CHARMM36 (squares), Slipids (diamonds), and AMBER Lipid14 (circles). Values shown for DLPC (green), DMPC (magenta), DPPC (blue), DOPC (red), and POPC (orange).

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    Figure 11

    Figure 11. Time averaged mean square displacement of the center of mass of the lipid molecules versus NVE simulation time.

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    Figure 12

    Figure 12. Lateral diffusion coefficients for the six lipid types calculated using different time ranges of the mean square displacement curve for the linear fit.

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  • References

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      19
      Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 1. Generalized Born
      Gotz, Andreas W.; Williamson, Mark J.; Xu, Dong; Poole, Duncan; Le Grand, Scott; Walker, Ross C.
      Journal of Chemical Theory and Computation (2012), 8 (5), 1542-1555CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      We present an implementation of generalized Born implicit solvent all-atom classical mol. dynamics (MD) within the AMBER program package that runs entirely on CUDA enabled NVIDIA graphics processing units (GPUs). We discuss the algorithms that are used to exploit the processing power of the GPUs and show the performance that can be achieved in comparison to simulations on conventional CPU clusters. The implementation supports three different precision models in which the contributions to the forces are calcd. in single precision floating point arithmetic but accumulated in double precision (SPDP), or everything is computed in single precision (SPSP) or double precision (DPDP). In addn. to performance, we have focused on understanding the implications of the different precision models on the outcome of implicit solvent MD simulations. We show results for a range of tests including the accuracy of single point force evaluations and energy conservation as well as structural properties pertaining to protein dynamics. The numerical noise due to rounding errors within the SPSP precision model is sufficiently large to lead to an accumulation of errors which can result in unphys. trajectories for long time scale simulations. We recommend the use of the mixed-precision SPDP model since the numerical results obtained are comparable with those of the full double precision DPDP model and the ref. double precision CPU implementation but at significantly reduced computational cost. Our implementation provides performance for GB simulations on a single desktop that is on par with, and in some cases exceeds, that of traditional supercomputers.
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    20. 20
      Salomon-Ferrer, R.; Götz, A. W.; Poole, D.; Le Grand, S.; Walker, R. C. Routine microsecond molecular dynamics simulations with Amber on GPUs. 2. Explicit solvent particle mesh Ewald J. Chem. Theory Comput. 2013, 9 (9) 3878– 3888
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      20
      Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 2. Explicit Solvent Particle Mesh Ewald
      Salomon-Ferrer, Romelia; Gotz, Andreas W.; Poole, Duncan; Le Grand, Scott; Walker, Ross C.
      Journal of Chemical Theory and Computation (2013), 9 (9), 3878-3888CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      We present an implementation of explicit solvent all atom classical mol. dynamics (MD) within the AMBER program package that runs entirely on CUDA-enabled GPUs. First released publicly in Apr. 2010 as part of version 11 of the AMBER MD package and further improved and optimized over the last two years, this implementation supports the three most widely used statistical mech. ensembles (NVE, NVT, and NPT), uses particle mesh Ewald (PME) for the long-range electrostatics, and runs entirely on CUDA-enabled NVIDIA graphics processing units (GPUs), providing results that are statistically indistinguishable from the traditional CPU version of the software and with performance that exceeds that achievable by the CPU version of AMBER software running on all conventional CPU-based clusters and supercomputers. We briefly discuss three different precision models developed specifically for this work (SPDP, SPFP, and DPDP) and highlight the tech. details of the approach as it extends beyond previously reported work [Goetz et al., J. Chem. Theory Comput.2012, DOI: 10.1021/ct200909j; Le Grand et al., Comp. Phys. Comm.2013, DOI: 10.1016/j.cpc.2012.09.022].We highlight the substantial improvements in performance that are seen over traditional CPU-only machines and provide validation of our implementation and precision models. We also provide evidence supporting our decision to deprecate the previously described fully single precision (SPSP) model from the latest release of the AMBER software package.
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    21. 21
      Le Grand, S.; Götz, A. W.; Walker, R. C. SPFP: Speed without compromise—A mixed precision model for GPU accelerated molecular dynamics simulations Comput. Phys. Commun. 2013, 184 (2) 374– 380
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      21
      SPFP: Speed without compromise-A mixed precision model for GPU accelerated molecular dynamics simulations
      Le Grand, Scott; Gotz, Andreas W.; Walker, Ross C.
      Computer Physics Communications (2013), 184 (2), 374-380CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
      A new precision model is proposed for the acceleration of all-atom classical mol. dynamics (MD) simulations on graphics processing units (GPUs). This precision model replaces double precision arithmetic with fixed point integer arithmetic for the accumulation of force components as compared to a previously introduced model that uses mixed single/double precision arithmetic. This significantly boosts performance on modern GPU hardware without sacrificing numerical accuracy. We present an implementation for NVIDIA GPUs of both generalized Born implicit solvent simulations as well as explicit solvent simulations using the particle mesh Ewald (PME) algorithm for long-range electrostatics using this precision model. Tests demonstrate both the performance of this implementation as well as its numerical stability for const. energy and const. temp. biomol. MD as compared to a double precision CPU implementation and double and mixed single/double precision GPU implementations.
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      Skjevik, Å. A.; Madej, B. D.; Walker, R. C.; Teigen, K. LIPID11: A modular framework for lipid simulations using Amber J. Phys. Chem. B 2012, 116 (36) 11124– 11136
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      Siu, S. W.; Vacha, R.; Jungwirth, P.; Bockmann, R. A. Biomolecular simulations of membranes: physical properties from different force fields J. Chem. Phys. 2008, 128 (12) 125103
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      Biomolecular simulations of membranes: Physical properties from different force fields
      Siu, Shirley W. I.; Vacha, Robert; Jungwirth, Pavel; Boeckmann, Rainer A.
      Journal of Chemical Physics (2008), 128 (12), 125103/1-125103/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Phospholipid force fields are of ample importance for the simulation of artificial bilayers, membranes, and also for the simulation of integral membrane proteins. Here, we compare the two most applied at. force fields for phospholipids, the all-atom CHARMM27 and the united atom Berger force field, with a newly developed all-atom generalized AMBER force field (GAFF) for dioleoylphosphatidylcholine mols. Only the latter displays the exptl. obsd. difference in the order of the C2 atom between the two acyl chains. The interfacial water dynamics is smoothly increased between the lipid carbonyl region and the bulk water phase for all force fields; however, the water order and with it the electrostatic potential across the bilayer showed distinct differences between the force fields. Both Berger and GAFF underestimate the lipid self-diffusion. GAFF offers a consistent force field for the at. scale simulation of biomembranes. (c) 2008 American Institute of Physics.
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      Jójárt, B.; Martinek, T. A. Performance of the general amber force field in modeling aqueous POPC membrane bilayers J. Comput. Chem. 2007, 28 (12) 2051– 2058
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      Rosso, L.; Gould, I. R. Structure and dynamics of phospholipid bilayers using recently developed general all-atom force fields J. Comput. Chem. 2008, 29 (1) 24– 37
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      Dickson, C. J.; Rosso, L.; Betz, R. M.; Walker, R. C.; Gould, I. R. GAFFlipid: A general Amber force field for the accurate molecular dynamics simulation of phospholipid Soft Matter 2012, 8, 9617– 9627
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      GAFFlipid: a General Amber Force Field for the accurate molecular dynamics simulation of phospholipid
      Dickson, Callum J.; Rosso, Lula; Betz, Robin M.; Walker, Ross C.; Gould, Ian R.
      Soft Matter (2012), 8 (37), 9617-9627CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
      Previous attempts to simulate phospholipid bilayers using the General Amber Force Field (GAFF) yielded many bilayer characteristics in agreement with expt., however when using a tensionless NPT ensemble the bilayer is seen to compress to an undesirable extent resulting in low areas per lipid and high order parameters in comparison to expt. In this work, the GAFF Lennard-Jones parameters for the simulation of acyl chains are cor. to allow the accurate and stable simulation of pure lipid bilayers. Lipid bilayers comprised of six phospholipid types were simulated for timescales approaching a quarter of a microsecond under tensionless const. pressure conditions using Graphics Processing Units. Structural properties including area per lipid, vol. per lipid, bilayer thickness, order parameter and headgroup hydration show favorable agreement with available exptl. values. Expanding the system size from 72 to 288 lipids and a more exptl. realistic 2 × 288 lipid bilayer stack induces little change in the obsd. properties. This preliminary work is intended for combination with the new AMBER Lipid11 modular force field as part of on-going attempts to create a modular phospholipid AMBER force field allowing tensionless NPT simulations of complex lipid bilayers.
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      Siu, S. W. I.; Pluhackova, K.; Böckmann, R. A. Optimization of the OPLS-AA force field for long hydrocarbons J. Chem. Theory Comput. 2012, 8 (4) 1459– 1470
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      Optimization of the OPLS-AA Force Field for Long Hydrocarbons
      Siu, Shirley W. I.; Pluhackova, Kristyna; Boeckmann, Rainer A.
      Journal of Chemical Theory and Computation (2012), 8 (4), 1459-1470CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The all-atom optimized potentials for liq. simulations (OPLS-AA) force field is a popular force field for simulating biomols. However, the current OPLS parameters for hydrocarbons developed using short alkanes cannot reproduce the liq. properties of long alkanes in mol. dynamics simulations. Therefore, the extension of OPLS-AA to (phospho)lipid mols. required for the study of biol. membranes was hampered in the past. Here, we optimized the OPLS-AA force field for both short and long hydrocarbons. Following the framework of the OPLS-AA parametrization, we refined the torsional parameters for hydrocarbons by fitting to the gas-phase ab initio energy profiles calcd. at the accurate MP2/aug-cc-pVTZ theory level. Addnl., the depth of the Lennard-Jones potential for methylene hydrogen atoms was adjusted to reproduce the densities and the heats of vaporization of alkanes and alkenes of different lengths. Optimization of partial charges finally allowed to reproduce the gel-to-liq.-phase transition temp. for pentadecane and solvation free energies. The optimized parameter set (L-OPLS) yields improved hydrocarbon diffusion coeffs., viscosities, and gauche-trans ratios. Moreover, its applicability for lipid bilayer simulations is shown for a GMO bilayer in its liq.-cryst. phase.
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      Klauda, J. B.; Brooks, B. R.; MacKerell, A. D.; Venable, R. M.; Pastor, R. W. An ab initio study on the torsional surface of alkanes and its effect on molecular simulations of alkanes and a DPPC bilayer J. Phys. Chem. B 2005, 109 (11) 5300– 5311
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      Betz, R. M.; Walker, R. C. Paramfit: Optimization of potential energy function parameters for molecular dynamics. Manuscript in preparation.
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      Bayly, C. I.; Cieplak, P.; Cornell, W.; Kollman, P. A. A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model J. Phys. Chem. 1993, 97 (40) 10269– 10280
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      A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model
      Bayly, Christopher I.; Cieplak, Piotr; Cornell, Wendy; Kollman, Peter A.
      Journal of Physical Chemistry (1993), 97 (40), 10269-80CODEN: JPCHAX; ISSN:0022-3654.
      The authors present a new approach to generating electrostatic potential (ESP) derived charges for mols. The major strength of electrostatic potential derived charges is that they optimally reproduce the intermol. interaction properties of mols. with a simple two-body additive potential, provided, of course, that a suitably accurate level of quantum mech. calcn. is used to derive the ESP around the mol. Previously, the major weaknesses of these charges have been that they were not easily transferably between common functional groups in related mols., they have often been conformationally dependent, and the large charges that frequently occur can be problematic for simulating intramol. interactions. Introducing restraints in the form of a penalty function into the fitting process considerably reduces the above problems, with only a minor decrease in the quality of the fit to the quantum mech. ESP. Several other refinements in addn. to the restrained electrostatic potential (RESP) fit yield a general and algorithmic charge fitting procedure for generating atom-centered point charges. This approach can thus be recommended for general use in mol. mechanics, mol. dynamics, and free energy calcns. for any org. or bioorg. system.
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      Sonne, J.; Jensen, M. Ø.; Hansen, F. Y.; Hemmingsen, L.; Peters, G. H. Reparameterization of all-atom dipalmitoylphosphatidylcholine lipid parameters enables simulation of fluid bilayers at zero tension Biophys. J. 2007, 92 (12) 4157– 4167
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      Klauda, J. B.; Garrison, S. L.; Jiang, J.; Arora, G.; Sandler, S. I. HM-IE: Quantum chemical hybrid methods for calculating interaction energies J. Phys. Chem. A 2003, 108 (1) 107– 112
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      Davis, J. E.; Warren, G. L.; Patel, S. Revised charge equilibration potential for liquid alkanes J. Phys. Chem. B 2008, 112 (28) 8298– 8310
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      Wang, J.; Hou, T. Application of molecular dynamics simulations in molecular property prediction. 1. density and heat of vaporization J. Chem. Theory Comput. 2011, 7 (7) 2151– 2165
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      Application of Molecular Dynamics Simulations in Molecular Property Prediction. 1. Density and Heat of Vaporization
      Wang, Junmei; Hou, Tingjun
      Journal of Chemical Theory and Computation (2011), 7 (7), 2151-2165CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Mol. mech. force field (FF) methods are useful in studying condensed phase properties. They are complementary to expts. and can often go beyond expts. in at. details. Even if a FF is specific for studying structures, dynamics, and functions of biomols., it is still important for the FF to accurately reproduce the exptl. liq. properties of small mols. that represent the chem. moieties of biomols. Otherwise, the force field may not describe the structures and energies of macromols. in aq. solns. properly. In this work, the authors have carried out a systematic study to evaluate the General AMBER Force Field (GAFF) in studying densities and heats of vaporization for a large set of org. mols. that covers the most common chem. functional groups. The latest techniques, such as the particle mesh Ewald (PME) for calcg. electrostatic energies and Langevin dynamics for scaling temps., have been applied in the mol. dynamics (MD) simulations. For d., the av. percent error (APE) of 71 org. compds. is 4.43% when compared with the exptl. values. More encouragingly, the APE drops to 3.43% after the exclusion of two outliers and four other compds. for which the exptl. densities have been measured with pressures higher than 1.0 atm. For the heat of vaporization, several protocols have been investigated, and the best one, P4/ntt0, achieves an av. unsigned error (AUE) and a root-mean-square error (RMSE) of 0.93 and 1.20 kcal/mol, resp. How to reduce the prediction errors through proper van der Waals (vdW) parametrization has been discussed. An encouraging finding in vdW parametrization is that both densities and heats of vaporization approach their "ideal" values in a synchronous fashion when vdW parameters are tuned. The following hydration free energy calcn. using thermodn. integration further justifies the vdW refinement. The authors conclude that simple vdW parametrization can significantly reduce the prediction errors. The authors believe that GAFF can greatly improve its performance in predicting liq. properties of org. mols. after a systematic vdW parametrization, which will be reported in a sep. paper.
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      Darden, T.; York, D.; Pedersen, L. Particle mesh Ewald: An N-log(N) method for Ewald sums in large systems J. Chem. Phys. 1993, 98 (12) 10089– 10092
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      Numerical integration of the Cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes
      Ryckaert, Jean Paul; Ciccotti, Giovanni; Berendsen, Herman J. C.
      Journal of Computational Physics (1977), 23 (3), 327-41CODEN: JCTPAH; ISSN:0021-9991.
      A numerical algorithm integrating the 3N Cartesian equation of motion of a system of N points subject to holonomic constraints is applied to mol. dynamics simulation of a liq. of 64 butane mols.
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      Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. Molecular dynamics with coupling to an external bath J. Chem. Phys. 1984, 81 (8) 3684– 3690
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      Molecular dynamics with coupling to an external bath
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      Journal of Chemical Physics (1984), 81 (8), 3684-90CODEN: JCPSA6; ISSN:0021-9606.
      In mol. dynamics (MD) simulations, the need often arises to maintain such parameters as temp. or pressure rather than energy and vol., or to impose gradients for studying transport properties in nonequil. MD. A method is described to realize coupling to an external bath with const. temp. or pressure with adjustable time consts. for the coupling. The method is easily extendable to other variables and to gradients, and can be applied also to polyat. mols. involving internal constraints. The influence of coupling time consts. on dynamical variables is evaluated. A leap-frog algorithm is presented for the general case involving constraints with coupling to both a const. temp. and a const. pressure bath.
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      Yeh, I.-C.; Hummer, G. System-size dependence of diffusion coefficients and viscosities from molecular dynamics simulations with periodic boundary conditions J. Phys. Chem. B 2004, 108 (40) 15873– 15879
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      System-Size Dependence of Diffusion Coefficients and Viscosities from Molecular Dynamics Simulations with Periodic Boundary Conditions
      Yeh, In-Chul; Hummer, Gerhard
      Journal of Physical Chemistry B (2004), 108 (40), 15873-15879CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      We study the system-size dependence of translational diffusion coeffs. and viscosities in mol. dynamics simulations under periodic boundary conditions. Simulations of water under ambient conditions and a Lennard-Jones (LJ) fluid show that the diffusion coeffs. increase strongly as the system size increases. We test a simple analytic correction for the system-size effects that is based on hydrodynamic arguments. This correction scales as N-1/3, where N is the no. of particles. For a cubic simulation box of length L, the diffusion coeff. cor. for system-size effects is D0 = DPBC + 2.837297kBT/(6πηL), where DPBC is the diffusion coeff. calcd. in the simulation, kB the Boltzmann const., T the abs. temp., and η the shear viscosity of the solvent. For water, LJ fluids, and hard-sphere fluids, this correction quant. accounts for the system-size dependence of the calcd. self-diffusion coeffs. In contrast to diffusion coeffs., the shear viscosities of water and the LJ fluid show no significant system-size dependences.
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      Effect of librational motion on fluorescence depolarization and nuclear magnetic resonance relaxation in macromolecules and membranes
      Lipari, Giovanni; Szabo, Attila
      Biophysical Journal (1980), 30 (3), 489-506CODEN: BIOJAU; ISSN:0006-3495.
      The theory of fluorescent emission anisotropy (r(t)) of a cylindrical probe in a membrane suspension is developed. The limiting anisotropy (r(∞)) is proportional to the square of the order parameter of the probe. The order parameter dets. the 1st nontrivial term in the expansion of the equil. orientational distribution function of the probe in a series of Legendre polynomials. The motion of the probe is described as diffusion (wobbling) within a cone of semiangle θ0. Within the framework of this model, an accurate single-exponential approxn. for r(t) is considered. An analytic expression relating the effective relaxation time, which appears in the above approxn., to θ0 and the diffusion coeff. for wobbling is derived. The model is generalized to the situation where the probe is attached to a macromol. whose motion cannot be neglected on the time scale of the fluorescence expt. Finally, by exploiting the formal similarity between the theory of fluorescence depolarization and 13C NMR dipolar relaxation, expressions for spin-spin and spin-lattice relaxation times and the nuclear Overhauser enhancement are derived for a protonated C which is nonrigidly attached to a macromol. and undergoes librational motion described as diffusion on a spherical cap of semiangle θ0.
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      Ottiger, M.; Bax, A. Determination of Relative N–HN, N–C′, Cα–C′, and Cα–Hα effective bond lengths in a protein by NMR in a dilute liquid crystalline phase J. Am. Chem. Soc. 1998, 120 (47) 12334– 12341
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      Tofts, P. S.; Lloyd, D.; Clark, C. A.; Barker, G. J.; Parker, G. J. M.; McConville, P.; Baldock, C.; Pope, J. M. Test liquids for quantitative MRI measurements of self-diffusion coefficient in vivo Magn. Reson. Med. 2000, 43 (3) 368– 374
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      Test liquids for quantitative MRI measurements of self-diffusion coefficient in vivo
      Tofts, P. S.; Lloyd, D.; Clark, C. A.; Barker, G. J.; Parker, G. J. M.; McConville, P.; Baldock, C.; Pope, J. M.
      Magnetic Resonance in Medicine (2000), 43 (3), 368-374CODEN: MRMEEN; ISSN:0740-3194. (Wiley-Liss, Inc.)
      A range of liqs. suitable as quality control test objects for measuring the accuracy of clin. MRI diffusion sequences (both apparent diffusion coeff. and tensor) has been identified and characterized. The self-diffusion coeffs. for 15 liqs. (3 cyclic alkanes: cyclohexane to cyclooctane, 9 n-alkanes: n-octane to n-hexadecane, and 3 n-alcs.: ethanol to 1-propanol) were measured at 15-30° using an NMR spectrometer. Values at 22° range from 0.36 to 2.2 10-9 m2s-1. Typical 95% confidence limits are ±2%. Temp. coeffs. are 1.7-3.2%/°C. T1 and T2 values at 1.5 T and proton d. are given. N-tridecane has a diffusion coeff. close to that of normal white matter. The longer n-alkanes may be useful T2 stds. Measurements from a spin-echo MRI sequence agreed to within 2%.
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      Jo, S.; Lim, J. B.; Klauda, J. B.; Im, W. CHARMM-GUI membrane builder for mixed bilayers and its application to yeast membranes Biophys. J. 2009, 97 (1) 50– 58
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      CHARMM-GUI Membrane Builder for mixed bilayers and its application to yeast membranes
      Jo, Sunhwan; Lim, Joseph B.; Klauda, Jeffery B.; Im, Wonpil
      Biophysical Journal (2009), 97 (1), 50-58CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
      The CHARMM-GUI Membrane Builder (http://www.charmm-gui.org/input/membrane), an intuitive, straightforward, web-based graphical user interface, was expanded to automate the building process of heterogeneous lipid bilayers, with or without a protein and with support for up to 32 different lipid types. The efficacy of these new features was tested by building and simulating lipid bilayers that resemble yeast membranes, composed of cholesterol, dipalmitoylphosphatidylcholine, dioleoylphosphatidylcholine, palmitoyloleoylphosphatidylethanolamine, palmitoyloleoylphosphatidylamine, and palmitoyloleoylphosphatidylserine. Four membranes with varying concns. of cholesterol and phospholipids were simulated, for a total of 170 ns at 303.15 K. Unsatd. phospholipid chain concn. had the largest influence on membrane properties, such as av. lipid surface area, d. profiles, deuterium order parameters, and cholesterol tilt angle. Simulations with a high concn. of unsatd. chains (73%, membraneunsat) resulted in a significant increase in lipid surface area and a decrease in deuterium order parameters, compared with membranes with a high concn. of satd. chains (60-63%, membranesat). The av. tilt angle of cholesterol with respect to bilayer normal was largest, and the distribution was significantly broader for membraneunsat. Moreover, short-lived cholesterol orientations parallel to the membrane surface existed only for membraneunsat. The membranesat simulations were in a liq.-ordered state, and agree with similar exptl. cholesterol-contg. membranes.
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      Journal of Chemical Physics (1983), 79 (2), 926-35CODEN: JCPSA6; ISSN:0021-9606.
      Classical Monte Carlo simulations were carried out for liq. H2O in the NPT ensemble at 25° and 1 atm using 6 of the simpler intermol. potential functions for the dimer. Comparisons were made with exptl. thermodn. and structural data including the neutron diffraction results of Thiessen and Narten (1982). The computed densities and potential energies agree with expt. except for the original Bernal-Fowler model, which yields an 18% overest. of the d. and poor structural results. The discrepancy may be due to the correction terms needed in processing the neutron data or to an effect uniformly neglected in the computations. Comparisons were made for the self-diffusion coeffs. obtained from mol. dynamics simulations.
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      Joung, I. S.; Cheatham, T. E. Determination of alkali and halide monovalent ion parameters for use in explicitly solvated biomolecular simulations J. Phys. Chem. B 2008, 112 (30) 9020– 9041
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      Determination of Alkali and Halide Monovalent Ion Parameters for Use in Explicitly Solvated Biomolecular Simulations
      Joung, In Suk; Cheatham, Thomas E.
      Journal of Physical Chemistry B (2008), 112 (30), 9020-9041CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      Alkali (Li+, Na+, K+, Rb+, and Cs+) and halide (F-, Cl-, Br-, and I-) ions play an important role in many biol. phenomena, roles that range from stabilization of biomol. structure, to influence on biomol. dynamics, to key physiol. influence on homeostasis and signaling. To properly model ionic interaction and stability in atomistic simulations of biomol. structure, dynamics, folding, catalysis, and function, an accurate model or representation of the monovalent ions is critically necessary. A good model needs to simultaneously reproduce many properties of ions, including their structure, dynamics, solvation, and moreover both the interactions of these ions with each other in the crystal and in soln. and the interactions of ions with other mols. At present, the best force fields for biomols. employ a simple additive, nonpolarizable, and pairwise potential for at. interaction. In this work, the authors describe their efforts to build better models of the monovalent ions within the pairwise Coulombic and 6-12 Lennard-Jones framework, where the models are tuned to balance crystal and soln. properties in Ewald simulations with specific choices of well-known water models. Although it has been clearly demonstrated that truly accurate treatments of ions will require inclusion of nonadditivity and polarizability (particularly with the anions) and ultimately even a quantum mech. treatment, the authors' goal was to simply push the limits of the additive treatments to see if a balanced model could be created. The applied methodol. is general and can be extended to other ions and to polarizable force-field models. The authors' starting point centered on observations from long simulations of biomols. in salt soln. with the AMBER force fields where salt crystals formed well below their soly. limit. The likely cause of the artifact in the AMBER parameters relates to the naive mixing of the Smith and Dang chloride parameters with AMBER-adapted Aqvist cation parameters. To provide a more appropriate balance, the authors reoptimized the parameters of the Lennard-Jones potential for the ions and specific choices of water models. To validate and optimize the parameters, the authors calcd. hydration free energies of the solvated ions and also lattice energies (LE) and lattice consts. (LC) of alkali halide salt crystals. This is the first effort that systematically scans across the Lennard-Jones space (well depth and radius) while balancing ion properties like LE and LC across all pair combinations of the alkali ions and halide ions. The optimization across the entire monovalent series avoids systematic deviations. The ion parameters developed, optimized, and characterized were targeted for use with some of the most commonly used rigid and nonpolarizable water models, specifically TIP3P, TIP4PEW, and SPC/E. In addn. to well reproducing the soln. and crystal properties, the new ion parameters well reproduce binding energies of the ions to water and the radii of the first hydration shells.
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      Roe, D. R.; Cheatham, T. E. PTRAJ and CPPTRAJ: Software for processing and analysis of molecular dynamics trajectory data J. Chem. Theory Comput. 2013, 9 (7) 3084– 3095
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      PTRAJ and CPPTRAJ: Software for Processing and Analysis of Molecular Dynamics Trajectory Data
      Roe, Daniel R.; Cheatham, Thomas E.
      Journal of Chemical Theory and Computation (2013), 9 (7), 3084-3095CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      We describe PTRAJ and its successor CPPTRAJ, two complementary, portable, and freely available computer programs for the anal. and processing of time series of three-dimensional at. positions (i.e., coordinate trajectories) and the data therein derived. Common tools include the ability to manipulate the data to convert among trajectory formats, process groups of trajectories generated with ensemble methods (e.g., replica exchange mol. dynamics), image with periodic boundary conditions, create av. structures, strip subsets of the system, and perform calcns. such as RMS fitting, measuring distances, B-factors, radii of gyration, radial distribution functions, and time correlations, among other actions and analyses. Both the PTRAJ and CPPTRAJ programs and source code are freely available under the GNU General Public License version 3 and are currently distributed within the AmberTools 12 suite of support programs that make up part of the Amber package of computer programs (see http://ambermd.org). This overview describes the general design, features, and history of these two programs, as well as algorithmic improvements and new features available in CPPTRAJ.
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      Kučerka, N.; Liu, Y.; Chu, N.; Petrache, H. I.; Tristram-Nagle, S.; Nagle, J. F. Structure of fully hydrated fluid phase DMPC and DLPC lipid bilayers using X-ray scattering from oriented multilamellar arrays and from unilamellar vesicles Biophys. J. 2005, 88 (4) 2626– 2637
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      Kučerka, N.; Nieh, M.-P.; Katsaras, J. Fluid phase lipid areas and bilayer thicknesses of commonly used phosphatidylcholines as a function of temperature Biochim. Biophys. Acta 2011, 1808 (11) 2761– 2771
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      Braun, A. R.; Sachs, J. N.; Nagle, J. F. Comparing simulations of lipid bilayers to scattering data: The GROMOS 43A1-S3 force field J. Phys. Chem. B 2013, 117 (17) 5065– 5072
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      Comparing Simulations of Lipid Bilayers to Scattering Data: The GROMOS 43A1-S3 Force Field
      Braun, Anthony R.; Sachs, Jonathan N.; Nagle, John F.
      Journal of Physical Chemistry B (2013), 117 (17), 5065-5072CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      Simulations of DOPC at T = 303 K were performed using the united atom force field 43A1-S3 at six fixed projected areas, AP = 62, 64, 66, 68, 70, and 72 Å2, as well as a tensionless simulation that produced an av. ANPT = 65.8 Å2. After a small undulation correction for the system size consisting of 288 lipids, results were compared to exptl. data. The best, and excellent, fit to neutron scattering data occurs at an interpolated AN = 66.6 Å2 and the best, but not as good, fit to the more extensive x-ray scattering data occurs at AX = 68.7 Å2. The distance ΔDB-H between the Gibbs dividing surface for water and the peak in the electron d. profile agrees with scattering expts. The calcd. area compressibility KA = 277±10 mN/m is in excellent agreement with the micromech. expt. The vol. per lipid VL is smaller than vol. expts. which suggests a workaround that raises all the areas by about 1.5%. Although AX ≠ AN ≠ ANPT, this force field obtains acceptable agreement with expt. for AL = 67.5 Å2 (68.5 Å2 in the workaround), which we suggest is a better DOPC result from 43A1-S3 simulations than its value from the tensionless NPT simulation. However, nonsimulation modeling obtains better simultaneous fits to both kinds of scattering data, which suggests that the force fields can still be improved.
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      Rawicz, W.; Olbrich, K. C.; McIntosh, T.; Needham, D.; Evans, E. Effect of chain length and unsaturation on elasticity of lipid bilayers Biophys. J. 2000, 79 (1) 328– 339
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      Rawicz, W.; Olbrich, K. C.; McIntosh, T.; Needham, D.; Evans, E.
      Biophysical Journal (2000), 79 (1), 328-339CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
      Micropipette pressurization of giant bilayer vesicles was used to measure both elastic bending kc and area stretch KA moduli of fluid-phase phosphatidylcholine (PC) membranes. Twelve diacyl PCs were chosen: eight with two 18 carbon chains and degrees of unsatn. from one double bond (C18:1/0, C18:0/1) to six double bonds per lipid (diC18:3), two with short satd. carbon chains (diC13:0, diC14:0), and two with long unsatd. carbon chains (diC20:4, diC22:1). Bending moduli were derived from measurements of apparent expansion in vesicle surface area under very low tensions (0.001-0.5 mN/m), which is dominated by smoothing of thermal bending undulations. Area stretch moduli were obtained from measurements of vesicle surface expansion under high tensions (>0.5 mN/m), which involve an increase in area per mol. and a small, but important, contribution from smoothing of residual thermal undulations. The direct stretch moduli varied little (< ± 10%) with either chain unsatn. or length about a mean of 243 mN/m. On the other hand, the bending moduli of satd./mono-unsatd. chain PCs increased progressively with chain length from 0.56 × 10-19 J for diC13:0 to 1.2 × 10-19 J for diC22:1. However, quite unexpectedly for longer chains, the bending moduli dropped precipitously to ∼0.4 × 10-19 J when two or more cis double bonds were present in a chain (C18:0/2, diC18:2, diC18:3, diC20:4). Given nearly const. area stretch moduli, the variations in bending rigidity with chain length and poly-unsatn. implied significant variations in thickness. To test this hypothesis, peak-to-peak headgroup thicknesses hpp of bilayers were obtained from x-ray diffraction of multibilayer arrays at controlled relative humidities. For satd./mono-unsatd. chain bilayers, the distances hpp increased smoothly from diC13:0 to diC22:1 as expected. Moreover, the distances and elastic properties correlated well with a polymer brush model of the bilayer that specifies that the elastic ratio (kc/KA)1/2 = (hpp - ho)/24, where ho ≈ 1 nm accounts for sepn. of the headgroup peaks from the deformable hydrocarbon region. However, the elastic ratios and thicknesses for diC18:2, diC18:3, and diC20:4 fell into a distinct group below the correlation, which showed that poly-cis unsatd. chain bilayers are thinner and more flexible than satd./mono-unsatd. chain bilayers.
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      Petrache, H. I.; Tristram-Nagle, S.; Nagle, J. F. Fluid phase structure of EPC and DMPC bilayers Chem. Phys. Lipids 1998, 95 (1) 83– 94
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      Klauda, J. B.; Kučerka, N.; Brooks, B. R.; Pastor, R. W.; Nagle, J. F. Simulation-based methods for interpreting X-ray data from lipid bilayers Biophys. J. 2006, 90 (8) 2796– 2807
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      Klauda, Jeffery B.; Kucerka, Norbert; Brooks, Bernard R.; Pastor, Richard W.; Nagle, John F.
      Biophysical Journal (2006), 90 (8), 2796-2807CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
      The fully hydrated liq. cryst. phase of the dimyristoylphosphatidylcholine lipid bilayer at 30° was simulated using mol. dynamics with the CHARMM potential for five surface areas per lipid (A) in the range 55-65 Å2 that brackets the previously detd. exptl. area 60.6 Å2. The results of these simulations are used to develop a new hybrid zero-baseline structural model, denoted H2, for the electron d. profile, p(z), for the purpose of interpreting x-ray diffraction data. H2 and also the older hybrid baseline model were tested by fitting to partial information from the simulation and various constraints, both of which correspond to those available exptl. The A, ρ(z), and F(q) obtained from the models agree with those calcd. directly from simulation at each of the five areas, thereby validating this use of the models. The new H2 was then applied to exptl. dimyristoylphosphatidylcholine data; it yields A = 60.6 ± 0.5 Å2, in agreement with the earlier est. obtained using the hybrid baseline model. The electron d. profiles also compare well, despite considerable differences in the functional forms of the two models. Overall, the simulated ρ(z) at A = 60.7 Å2 agrees well with expt., demonstrating the accuracy of the CHARMM lipid force field; small discrepancies indicate targets for improvements. Lastly, a simulation-based model-free approach for obtaining A is proposed. It is based on interpolating the area that minimizes the difference between the exptl. F(q) and simulated F(q) evaluated for a range of surface areas. This approach is independent of structural models and could be used to det. structural properties of bilayers with different lipids, cholesterol, and peptides.
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      Kučerka, N.; Nagle, J. F.; Sachs, J. N.; Feller, S. E.; Pencer, J.; Jackson, A.; Katsaras, J. Lipid bilayer structure determined by the simultaneous analysis of neutron and X-ray scattering data Biophys. J. 2008, 95 (5) 2356– 2367
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      Tristram-Nagle, S.; Petrache, H. I.; Nagle, J. F. Structure and interactions of fully hydrated dioleoylphosphatidylcholine bilayers Biophys. J. 1998, 75 (2) 917– 925
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      Kučerka, N.; Tristram-Nagle, S.; Nagle, J. F. Structure of fully hydrated fluid phase lipid bilayers with monounsaturated chains J. Membr. Biol. 2006, 208 (3) 193– 202
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      Structure of Fully Hydrated Fluid Phase Lipid Bilayers with Monounsaturated Chains
      Kucerka, Norbert; Tristram-Nagle, Stephanie; Nagle, John F.
      Journal of Membrane Biology (2006), 208 (3), 193-202CODEN: JMBBBO; ISSN:0022-2631. (Springer)
      Quant. structures are obtained at 30°C for the fully hydrated fluid phases of palmitoyloleoylphosphatidylcholine (POPC), with a double bond on the sn-2 hydrocarbon chain, and for dierucoylphosphatidylcholine (di22:1PC), with a double bond on each hydrocarbon chain. The form factors F(qz) for both lipids are obtained using a combination of 3 methods: (1) Volumetric measurements provide F(0), (2) x-ray scattering from extruded unilamellar vesicles provides |F(qz)| for low qz, (3) Diffuse x-ray scattering from oriented stacks of bilayers provides |F(qz)| for high qz. Also, data using method (2) are added to the authors' recent data for dioleoylphosphatidylcholine (DOPC) using methods (1) and (3); the new DOPC data agree very well with the recent data and with (4) the authors' older data obtained using a liq. crystallog. x-ray method. The authors used hybrid electron d. models to obtain structural results from these form factors. The result for area per lipid (A) for DOPC 72.4 ± 0.5 Å2 agrees well with the authors' earlier publications, and the authors find A = 69.3 ± 0.5 Å2 for di22:1PC and A = 68.3 ± 1.5 Å2 for POPC. The authors obtain the values for 5 different av. thicknesses: hydrophobic, steric, head-head, phosphate-phosphate and Luzzati. Comparison of the results for these 3 lipids and for the authors' recent dimyristoylphosphatidylcholine (DMPC) detn. provides quant. measures of the effect of unsatn. on bilayer structure. The authors' results suggest that lipids with one monounsatd. chain have quant. bilayer structures closer to lipids with 2 monounsatd. chains than to lipids with 2 completely satd. chains.
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      Rappolt, M.; Hickel, A.; Bringezu, F.; Lohner, K. Mechanism of the lamellar/inverse hexagonal phase transition examined by high resolution X-ray diffraction Biophys. J. 2003, 84 (5) 3111– 3122
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      Rappolt, Michael; Hickel, Andrea; Bringezu, Frank; Lohner, Karl
      Biophysical Journal (2003), 84 (5), 3111-3122CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
      For the first time the electron d. of the lamellar liq. cryst. as well as of the inverted hexagonal phase could be retrieved at the transition temp. A reliable decompn. of the d-spacings into hydrophobic and hydrophilic structure elements could be performed owing to the presence of a sufficient no. of reflections. While the hydrocarbon chain length, dC, in the lamellar phase with a value of 14.5 Å lies within the extreme limits of the estd. chain length of the inverse hexagonal phase 10 Å < dC < 16 Å, the changes in the hydrophilic region vary strongly. During the lamellar-to-inverse hexagonal phase transition the area per lipid mol. reduces by ∼25%, and the no. of water mols. per lipid increases from 14 to 18. On the basis of the anal. of the structural components of each phase, the interface between the coexisting mesophases between 66 and 84° has been examd. in detail, and a model for the formation of the first rods in the matrix of the lamellar phospholipid stack is discussed. Judging from the structural relations between the inverse hexagonal and the lamellar phase, we suggest a cooperative chain reaction of rod formation at the transition midpoint, which is mainly driven by minimizing the interstitial region.
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      Current Opinion in Structural Biology (2000), 10 (4), 474-480CODEN: COSBEF; ISSN:0959-440X. (Elsevier Science Ltd.)
      A review with 51 refs. Fluctuations, inherent in flexible and biol. relevant lipid bilayers, make quant. structure detn. challenging. Shortcomings in older methods of structure detn. have been realized and new methodologies have been introduced that take fluctuations into account. The large uncertainty in literature values of lipid bilayer structural parameters is being reduced.
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      Anézo, C.; de Vries, A. H.; Höltje, H.-D.; Tieleman, D. P.; Marrink, S.-J. Methodological issues in lipid bilayer simulations J. Phys. Chem. B 2003, 107 (35) 9424– 9433
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      Poger, D.; Mark, A. E. On the validation of molecular dynamics simulations of saturated and cis-monounsaturated phosphatidylcholine lipid bilayers: A comparison with experiment J. Chem. Theory Comput. 2009, 6 (1) 325– 336
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      Kučerka, N.; Katsaras, J.; Nagle, J. Comparing membrane simulations to scattering experiments: Introducing the SIMtoEXP software J. Membr. Biol. 2010, 235 (1) 43– 50
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      Comparing Membrane Simulations to Scattering Experiments: Introducing the SIMtoEXP Software
      Kucerka, Norbert; Katsaras, John; Nagle, John F.
      Journal of Membrane Biology (2010), 235 (1), 43-50CODEN: JMBBBO; ISSN:0022-2631. (Springer)
      SIMtoEXP is a software package designed to facilitate the comparison of biomembrane simulations with exptl. x-ray and neutron scattering data. It has the following features: (1) Accepts no. d. profiles from simulations in a std. but flexible format. (2) Calcs. the electron d. ε(z) and neutron scattering length d. ν(z) profiles along the z direction (i.e., normal to the membrane) and their resp. Fourier transforms (i.e., Fε [qz] and Fν[qz]). The resultant 4 functions are then displayed graphically. (3) Accepts exptl. Fε(qz) and Fν(qz) data for graphical comparison with simulations. (4) Allows for lipids and other large mols. to be parsed into component groups by the user and calcs. the component vols. following Petrache et al. The software then calcs. and displays the contributions of each component group as vol. probability profiles, ρ(z), as well as the contributions of each component to ε(z) and ν(z).
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      Shirts, M. R. Simple quantitative tests to validate sampling from thermodynamic ensembles J. Chem. Theory Comput. 2012, 9 (2) 909– 926
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      Seelig, J.; Waespe-Sarcevic, N. Molecular order in cis and trans unsaturated phospholipid bilayers Biochemistry 1978, 17 (16) 3310– 3315
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      Perly, B.; Smith, I. C. P.; Jarrell, H. C. Acyl chain dynamics of phosphatidylethanolamines containing oleic acid and dihydrosterculic acid: deuteron NMR relaxation studies Biochemistry 1985, 24 (17) 4659– 4665
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      Lafleur, M.; Bloom, M.; Eikenberry, E. F.; Gruner, S. M.; Han, Y.; Cullis, P. R. Correlation between lipid plane curvature and lipid chain order Biophys. J. 1996, 70 (6) 2747– 2757
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      Correlation between lipid plane curvature and lipid chain order
      Lafleur, Michel; Bloom, Myer; Eikenberry, Eric F.; Gruner, Sol M.; Han, Yuqi; Cullis, Pieter R.
      Biophysical Journal (1996), 70 (6), 2747-2757CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
      The 1-palmitoyl-2-oleoyl-phosphatidylethanolamine: 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPE:POPC) system has been investigated by measuring, in the inverted hexagonal (HII) phase, the intercylinder spacings (using x-ray diffraction) and orientational order of the acyl chains (using 2H NMR). The presence of 20% dodecane leads to the formation of a HII phase for the compn. range from 0 to 39 mol% of POPC in POPE, as ascertained by x-ray diffraction and 2H NMR. The addn. of the alkane induces a small decrease in chain order, consistent with less stretched chains. An increase in temp. or in POPE proportion leads to a redn. in the intercylinder spacing, primarily due to a decrease in the water core radius. A temp. increase also leads to a redn. in the orientational order of the lipid acyl chains, whereas in POPE proportion has little effect on chain order. A correlation is proposed to relate the radius of curvature of the cylinders in the inverted hexagonal phase to the chain order of the lipids adopting the HII phase. A simple geometrical model is proposed, taking into account the area occupied by the polar headgroup at the interface and the orientational order of the acyl chains reflecting the contribution of the apolar core. From these parameters, intercylinder spacings are calcd. that agree well with the values detd. exptl. by x-ray diffraction, for the variations of both temp. and POPE:POPC proportion. This model suggests that temp. increases the curvature of lipid layers, mainly by increasing the area subtended by the hydrophobic core through chain conformation disorder, whereas POPC content affects primarily the headgroup interface contribution. The frustration of lipid layer curvature is also shown to be reflected in the acyl chain order measured in the Lα phase, in the absence of dodecane; for a given temp., increased order is obsd. when the curling tendencies of the lipid plane are more pronounced.
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      Warschawski, D.; Devaux, P. Order parameters of unsaturated phospholipids in membranes and the effect of cholesterol: a 1H-13C solid-state NMR study at natural abundance Eur. Biophys. J. 2005, 34 (8) 987– 96
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      Order parameters of unsaturated phospholipids in membranes and the effect of cholesterol: a 1H-13C solid-state NMR study at natural abundance
      Warschawski, Dror E.; Devaux, Philippe F.
      European Biophysics Journal (2005), 34 (8), 987-996CODEN: EBJOE8; ISSN:0175-7571. (Springer)
      Most biol. phospholipids contain at least one unsatd. alkyl chain. However, few order parameters of unsatd. lipids have been detd. because of the difficulty assocd. with isotopic labeling of a double bond. Dipolar recoupling on axis with scaling and shape preservation (DROSS) is a solid-state NMR technique optimized for measuring 1H-13C dipolar couplings and order parameters in lipid membranes in the fluid phase. It has been used to det. the order profile of 1,2-dimyristoyl-sn-glycero-3-phosphocholine hydrated membranes. Here, we show an application for the measurement of local order parameters in multilamellar vesicles contg. unsatd. lipids. Taking advantage of the very good 13C chem. shift dispersion, one can easily follow the segmental order along the acyl chains and, particularly, around the double bonds where we have been able to det. the previously misassigned order parameters of each acyl chain of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). We have followed the variation of such order profiles with temp., unsatn. content and cholesterol addn. We have found that the phase formed by DOPC with 30% cholesterol is analogous to the liq.-ordered (lo) phase. Because these expts. do not require isotopic enrichment, this technique can, in principle, be applied to natural lipids and biomembranes.
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      Petrache, H. I.; Dodd, S. W.; Brown, M. F. Area per lipid and acyl length distributions in fluid phosphatidylcholines determined by (2)H NMR spectroscopy Biophys. J. 2000, 79 (6) 3172– 92
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      Area per lipid and acyl length distributions in fluid phosphatidylcholines determined by 2H NMR spectroscopy
      Petrache, Horia I.; Dodd, Steven W.; Brown, Michael F.
      Biophysical Journal (2000), 79 (6), 3172-3192CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
      Deuterium (2H) NMR spectroscopy provides detailed information regarding the structural fluctuations of lipid bilayers, including both the equil. properties and dynamics. Exptl. 2H NMR measurements for the homologous series of 1,2-diacyl-sn-glycero-3-phosphocholines with perdeuterated satd. chains (from C12:0 to C18:0) have been performed on randomly oriented, fully hydrated multilamellar samples. For each lipid, the C-D bond order parameters have been calcd. from de-Paked 2H NMR spectra as a function of temp. The exptl. order parameters were analyzed using a mean-torque potential model for the acyl chain segment distributions, and comparison was made with the conventional diamond lattice approach. Statistical mech. principles were used to relate the measured order parameters to the lipid bilayer structural parameters: the hydrocarbon thickness and the mean interfacial area per lipid. At fixed temp., the area decreases with increasing acyl length, indicating increased van der Waals attraction for longer lipid chains. However, the main effect of increasing the acyl chain length is on the hydrocarbon thickness rather than on the area per lipid. Expansion coeffs. of the structural parameters are reported and interpreted using an empirical free energy function that describes the force balance in fluid bilayers. At the same abs. temp., the phosphatidylcholine (PC) series exhibits a universal chain packing profile that differs from that of phosphatidylethanolamines (PE). Hence, the lateral packing of phospholipids is more sensitive to the headgroup methylation than to the acyl chain length. A fit to the area per lipid for the PC series using the empirical free energy function shows that the PE area represents a limiting value for the packing of fluid acyl chains.
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      Douliez, J. P.; Léonard, A.; Dufourc, E. J. Restatement of order parameters in biomembranes: calculation of C-C bond order parameters from C-D quadrupolar splittings Biophys. J. 1995, 68 (5) 1727– 1739
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      Restatement of order parameters in biomembranes: calculation of C-C bond order parameters from C-D quadrupolar splittings
      Douliez, Jean-Paul; Leonard, Alain; Dufourc, Erick J.
      Biophysical Journal (1995), 68 (5), 1727-39CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
      An expression for the C-C bond order parameter, SCC, of membrane hydrocarbon chains has been derived from the obsd. C-D bond order parameters. It allows calcn. of the probability of each of the C-C bond rotamers and, consequently, the no. of gauche defects per chain as well as their projected av. length onto the bilayer normal, thus affording the calcn. of accurate hydrophobic bilayer thicknesses. The effect of the temp. has been studied on dilauroyl-, dimyristoyl-, and dipalmitoylphosphatidylcholine (DLPC, DMPC, DPPC) membranes, as has the effect of cholesterol on DMPC. The salient results are as follows: (1) an odd-even effect is obsd. for the SCC vs. carbon position, k, whose amplitude increases with temp.; (2) calcn. of SCC, from nonequivalent deuterons on the sn-2 chain of lipids, S2CC, leads to neg. values, indicating the tendency for the C1-C2 bond to be oriented parallel to the bilayer surface; this bond becomes more parallel to the surface as the temp. increases or when cholesterol is added; (3) calcn. on the sn-2 chain length can be performed from C1 and Cn, where n is the no. of carbon atoms in the chain, and leads to 10.4, 12.2, and 13.8 Å for DLPC, DMPC, and DPPC close to the transition temp. TC, of each of the systems and to 9.4, 10.9, and 12.6 for T-TC = 30-40°, resp.; (4) sepn. of intra- and intermol. motions allows quantitation of the no. of gauche defects per chain, which is equal to 1.9, 2.7, and 3.5 for DLPC, DMPC, and DPPC near Tc and to 2.7, 3.5, and 4.4 at T - TC = 30-40°, resp. Finally, the validity of the model is discussed and compared with previously published models.
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      Aussenac, F.; Laguerre, M.; Schmitter, J.-M.; Dufourc, E. J. Detailed structure and dynamics of bicelle phospholipids using selectively deuterated and perdeuterated labels. 2H NMR and molecular mechanics study Langmuir 2003, 19 (25) 10468– 10479
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      Shaikh, S. R.; Brzustowicz, M. R.; Gustafson, N.; Stillwell, W.; Wassall, S. R. Monounsaturated PE does not phase-separate from the lipid raft molecules sphingomyelin and cholesterol: Role for polyunsaturation? Biochemistry 2002, 41 (34) 10593– 10602
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      Hitchcock, P. B.; Mason, R.; Thomas, K. M.; Shipley, G. G. Structural chemistry of 1,2 dilauroyl-DL-phosphatidylethanolamine: Molecular conformation and intermolecular packing of phospholipids Proc. Natl. Acad. Sci. U.S.A. 1974, 71 (8) 3036– 3040
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      Seelig, A.; Seelig, J. Bilayers of dipalmitoyl-3-sn-phosphatidylcholine: Conformational differences between the fatty acyl chains Biochim. Biophys. Acta 1975, 406 (1) 1– 5
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      Jämbeck, J. P. M.; Lyubartsev, A. P. An extension and further validation of an all-atomistic force field for biological membranes J. Chem. Theory Comput. 2012, 8 (8) 2938– 2948
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      Senak, L.; Davies, M. A.; Mendelsohn, R. A quantitative IR study of hydrocarbon chain conformation in alkanes and phospholipids: CH2 wagging modes in disordered bilayer and HII phases J. Phys. Chem. 1991, 95 (6) 2565– 2571
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      A quantitative IR study of hydrocarbon chain conformation in alkanes and phospholipids: CH2 wagging modes in disordered bilayer and HII phases
      Senak, Laurence; Davies, Mark A.; Mendelsohn, Richard
      Journal of Physical Chemistry (1991), 95 (6), 2565-71CODEN: JPCHAX; ISSN:0022-3654.
      A series of CH2 wagging modes in the 1320-1370-cm-1 region of alkane and phospholipid IR spectra characteristic of nonplanar conformers were used for quant. evaluation of conformational states in disordered (phospholipid Lα and HII and alkane liq.) phases. A quant. comparison of DPPC and 1,2-dipalmitoylphosphatidylethanolamine (DPPE) shows the former to have 0.4 double gauche (gg), 0.5 end gauche (eg), and ∼1.0 (kink + gtg) conformers per chain just above the gel0liq. crystal phase transition, while the more highly ordered DPPE Lα phase shows ∼0.2 gg, 0.1 eg, and 1.0 (kink + gtg) conformers. In all systems studied, the no. of allowed gg and eg forms that occur is reduced substantially. From those achieved in isotropic liq. alkanes. A study of the Lα → HII interconversion in 2 unsatd. (1-palmitoyl-2-oleoyl- and 1,2-dielaidoylphosphatidylethanolamine) shows a substantial increase in both gg and eg conformers near temp.3s leading to the inverted micellar state in each instance, with smaller percentage increases in (kink + gtg) states. Connections between these quant. observations with those of 2H NMR and other spectroscopies are presented. Finally, a temp.4 dependence inconsistent with the prediction of the rotational isomeric state model is noted for the 1368-cm-1 band characteristic of (kink + gtg) conformers in alkanes.
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      Cates, D. A.; Strauss, H. L.; Snyder, R. G. Vibrational modes of liquid n-alkanes: Simulated isotropic raman spectra and band progressions for C5H12-C20H42 and C16D34 J. Phys. Chem. 1994, 98 (16) 4482– 4488
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      Snyder, R. G.; Strauss, H. L.; Elliger, C. A. C-H stretching modes and the structure of n-alkyl chains. 1. Long, disordered chains J. Phys. Chem. 1982, 86, 5145– 5150
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      Mendelsohn, R.; Senak, L. Quantitative determination of conformational disorder in biological membranes by FTIR spectroscopy. In Biomolecular spectroscopy; Clark, R. J. H.; Hester, R. E., Eds.; Wiley: New York, 1993; pp 339– 380.
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      Casal, H. L.; McElhaney, R. N. Quantitative determination of hydrocarbon chain conformational order in bilayers of saturated phosphatidylcholines of various chain lengths by Fourier transform infrared spectroscopy Biochemistry 1990, 29 (23) 5423– 5427
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      Tuchtenhagen, J.; Ziegler, W.; Blume, A. Acyl chain conformational ordering in liquid-crystalline bilayers: comparative FT-IR and 2H-NMR studies of phospholipids differing in headgroup structure and chain length Eur. Biophys. J. 1994, 23 (5) 323– 335
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      Acyl chain conformational ordering in liquid-crystalline bilayers: comparative FT-IR and 2H-NMR studies of phospholipids differing in headgroup structure and chain length
      Tuchtenhagen, Juergen; Ziegler, Wolfgang; Blume, Alfred
      European Biophysics Journal (1994), 23 (5), 323-35CODEN: EBJOE8; ISSN:0175-7571.
      FT-IR spectroscopy has been used to evaluate the acyl chain conformational ordering of DMPC, DMPE, DMPA (pH 6 and 12), DMPG (pH 1 and 7), and DPPC, DPPE, DPPA (pH 6). The frequencies of the sym. and antisym. methylene stretching vibrations were detd. as a function of temp. In the liq.-cryst. phase the frequencies show a qual. dependence on the amt. of chain disorder. Quant. data for trans-gauche isomerization were obtained from the integral intensities of the conformation sensitive methylene wagging absorptions at ∼1368 cm-1 (gtg' and gtg sequences), 1356 cm-1 (double gauche) and 1342 cm-1 (end gauche). The integral band intensities were converted to the no. of gauche conformers per acyl chain using the calibration factors published by L. Senak et al. (1991). At 69° the highest no. of gauche conformers excluding contributions from single gauche conformers and jogs (g'tttg) were found for PCs (DMPC: 2.6; DPPC: 2.4), followed by DMPG- (2.0), phosphatidylethanolamines (DMPE: 1.4; DPPE: 2.0), protonated DMPG (1.5), and phosphatidic acids (DPPA-: 1.7; DMPA-: 1.4, DMPA2-: 1.7).
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      Mendelsohn, R.; Davies, M. A.; Brauner, J. W.; Schuster, H. F.; Dluhy, R. A. Quantitative determination of conformational disorder in the acyl chains of phospholipid bilayers by infrared spectroscopy Biochemistry 1989, 28 (22) 8934– 8939
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      Kučerka, N.; Gallová, J.; Uhríková, D.; Balgavý, P.; Bulacu, M.; Marrink, S.-J.; Katsaras, J. Areas of Monounsaturated Diacylphosphatidylcholines Biophys. J. 2009, 97 (7) 1926– 1932
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      Ratto, T. V.; Longo, M. L. Obstructed diffusion in phase-separated supported lipid bilayers: A combined atomic force microscopy and fluorescence recovery after photobleaching approach Biophys. J. 2002, 83 (6) 3380– 3392
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      Almeida, P. F. F.; Vaz, W. L. C.; Thompson, T. E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis Biochemistry 1992, 31 (29) 6739– 6747
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      Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis
      Almeida, Paulo F. F.; Vaz, Winchil L. C.; Thompson, T. E.
      Biochemistry (1992), 31 (29), 6739-47CODEN: BICHAW; ISSN:0006-2960.
      Fluorescence recovery after photobleaching is used to perform an extensive study of the lateral diffusion of a phospholipid probe in the binary mixt. dimyristoylphosphatidylcholine/cholesterol, above the melting temp. of the phospholipid. In the regions of the phase diagram where a single liq. phase exists, diffusion can be quant. described by free vol. theory, using a modified Macedo-Litovitz hybrid equation. In the liq.-liq. immiscibility region, the temp. dependence of the diffusion coeff. is in excellent agreement with current theories of generalized diffusivities in composite two-phase media. A consistent interpretation of the diffusion data can be provided based essentially on the idea that the primary effect of cholesterol addn. to the bilayer is to occupy free vol. On this basis, a general interpretation of the phase behavior of this mixt. is also proposed.
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      Orädd, G.; Lindblom, G.; Westerman, P. W. Lateral diffusion of cholesterol and dimyristoylphosphatidylcholine in a lipid bilayer measured by pulsed field gradient NMR spectroscopy Biophys. J. 2002, 83 (5) 2702– 2704
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      Filippov, A.; Orädd, G.; Lindblom, G. Influence of cholesterol and water content on phospholipid lateral diffusion in bilayers Langmuir 2003, 19 (16) 6397– 6400
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      Vaz, W. L. C.; Clegg, R. M.; Hallmann, D. Translational diffusion of lipids in liquid crystalline phase phosphatidylcholine multibilayers. A comparison of experiment with theory Biochemistry 1985, 24 (3) 781– 786
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      Translational diffusion of lipids in liquid crystalline phase phosphatidylcholine multibilayers. A comparison of experiment with theory
      Vaz, Winchil L. C.; Clegg, Robert M.; Hallmann, Dieter
      Biochemistry (1985), 24 (3), 781-6CODEN: BICHAW; ISSN:0006-2960.
      A systematic study of the translational diffusion of the phospholipid deriv., N-(7-nitro-2,1,3-benzoxadiazol-4-yl)phosphatidylethanolamine (NBD-PE), was undertaken in liq. cryst. phase phosphatidylcholine (PC) bilayers by using the fluorescence recovery after photobleaching technique. The exptl. results were then compared with the predictions of theor. models for diffusion in membranes. For NBD-PE, the dependence of the translational diffusion coeff. (Dt) upon the acyl chain length of the diffusant was not that predicted by continuum fluid hydrodynamic models for diffusion in membranes. Plots of Dt vs. 1/T (Arrhenius plots) were nonlinear in PC bilayers where the acyl chain compn. of the NBD-PE was matched with that of the host bilayer lipid. This suggested that a free vol. model may be appropriate for the description of lipid diffusion in lipid bilayers. In bilayers of PCs with satd. acyl chains at the same reduced temp., the magnitude of Dt followed the order: distearoyl-PC > dipalmitoyl-PC (DPPC) > dimyristoyl-PC (DMPC) > dilauroyl-PC (DLPC). This was the inverse of what might be expected from the hydrodynamic model, but was in agreement with the free vol. in these bilayers. A free vol. model that takes into account the frictional drag forces acting upon the diffusing NBD-PE at the membrane-water interface and also at the bilayer midplane adequately describes the diffusion results for NBD-PE mols. in DLPC, DMPC, DPPC, and 1-palmitoyl-2-oleoyl-PC bilayers in the liq.-cryst. phase.
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      Scheidt, H. A.; Huster, D.; Gawrisch, K. Diffusion of cholesterol and its precursors in lipid membranes studied by 1H pulsed field gradient magic angle spinning NMR Biophys. J. 2005, 89 (4) 2504– 2512
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      Kuśba, J.; Li, L.; Gryczynski, I.; Piszczek, G.; Johnson, M.; Lakowicz, J. R. Lateral diffusion coefficients in membranes measured by resonance energy transfer and a new algorithm for diffusion in two dimensions Biophys. J. 2002, 82 (3) 1358– 1372
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      Jin, A. J.; Edidin, M.; Nossal, R.; Gershfeld, N. L. A singular state of membrane lipids at cell growth temperatures Biochemistry 1999, 38 (40) 13275– 13278
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      A singular state of membrane lipids at cell growth temperatures
      Jin, A. J.; Edidin, M.; Nossal, R.; Gershfeld, N. L.
      Biochemistry (1999), 38 (40), 13275-13278CODEN: BICHAW; ISSN:0006-2960. (American Chemical Society)
      Cells adjust their membrane lipid compn. when they adapt to grow at different temps. The consequences of this adjustment for membrane properties and functions are not well understood. Our report shows that the temp. dependence of the diffusion of a probe mol. in multilayers formed from total lipid exts. of E. coli has an anomalous max. at a temp. corresponding to the growth temp. of each bacterial prepn. (25, 29, and 32 °C). This increase in the lateral diffusion coeff., D, is characteristic of membrane lipids in a crit. state, for which large fluctuations of mol. area in the plane of the bilayer are expected. Therefore, changes in lipid compn. may be due to a requirement that cells maintain their membranes in a state where mol. interactions and reaction rates are readily modulated by small, local perturbations of membrane organization.
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      Poger, D.; Mark, A. E. Lipid bilayers: The effect of force field on ordering and dynamics J. Chem. Theory Comput. 2012, 8 (11) 4807– 4817
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      Lipid Bilayers: The Effect of Force Field on Ordering and Dynamics
      Poger, David; Mark, Alan E.
      Journal of Chemical Theory and Computation (2012), 8 (11), 4807-4817CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The sensitivity of the structure and dynamics of a fully hydrated pure bilayer of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) in mol. dynamics simulations to changes in force-field and simulation parameters has been assessed. Three related force fields (the GROMOS 54A7 force field, a GROMOS 53A6-derived parameter set and a variant of the Berger parameters) in combination with either particle-mesh Ewald (PME) or a reaction field (RF) were compared. Structural properties such as the area per lipid, carbon-deuterium order parameters, electron d. profile and bilayer thicknesses, are reproduced by all the parameter sets within the uncertainty of the available exptl. data. However, there are clear differences in the ordering of the glycerol backbone and choline headgroup, and the orientation of the headgroup dipole. In some cases, the degree of ordering was reminiscent of a liq.-ordered phase. It is also shown that, although the lateral diffusion of the lipids in the plane of the bilayer is often used to validate lipid force fields, because of the uncertainty in the exptl. measurements and the fact that the lateral diffusion is dependent on the choice of the simulation conditions, it should not be employed as a measure of quality. Finally, the simulations show that the effect of small changes in force-field parameters on the structure and dynamics of a bilayer is more significant than the treatment of the long-range electrostatic interactions using RF or PME. Overall, the GROMOS 54A7 best reproduced the range of exptl. data examd.
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      Temp. control algorithms in mol. dynamics (MD) simulations are necessary to study isothermal systems. However, these thermostatting algorithms alter the velocities of the particles and thus modify the dynamics of the system with respect to the microcanonical ensemble, which could potentially lead to thermostat-dependent dynamical artifacts. In this study, we investigate how six well-established thermostat algorithms applied with different coupling strengths and to different degrees of freedom affect the dynamics of various mol. systems. We consider dynamic processes occurring on different times scales by measuring translational and rotational self-diffusion as well as the shear viscosity of water, diffusion of a small mol. solvated in water, and diffusion and the dynamic structure factor of a polymer chain in water. All of these properties are significantly dampened by thermostat algorithms which randomize particle velocities, such as the Andersen thermostat and Langevin dynamics, when strong coupling is used. For the solvated small mol. and polymer, these dampening effects are reduced somewhat if the thermostats are applied to the solvent alone, such that the solute's temp. is maintained only through thermal contact with solvent particles. Algorithms which operate by scaling the velocities, such as the Berendsen thermostat, the stochastic velocity rescaling approach of Bussi and co-workers, and the Nose-Hoover thermostat, yield transport properties that are statistically indistinguishable from those of the microcanonical ensemble, provided they are applied globally, i.e. coupled to the system's kinetic energy. When coupled to local kinetic energies, a velocity scaling thermostat can have dampening effects comparable to a velocity randomizing method, as we observe when a massive Nose-Hoover coupling scheme is used to simulate water. Correct dynamical properties, at least those studied in this paper, are obtained with the Berendsen thermostat applied globally, despite the fact that it yields the wrong kinetic energy distribution.
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