The force field jungle(2): lipids

I thought atomistic protein force fields were a jungle. They are more like a well maintained garden compared to their lipid counterparts. It seems this has three main reasons:

  1. Experimental data is unreliable and sparse. Estimates of, for example, the area per lipid vary greatly, depending on technique used and the lab where they were obtained. Furthermore, the list of properties one can measure and use to parametrize against is enormous.
  2. There a many different kinds of lipids, that all can be in different "states" depending on temperature, hydration level and other components they are mixed with.
  3. Lipids have not been the main focus of any of the "big" force fields and, arguably, of the community in general. This means that for most force fields there are no long standing, golden standard lipid parameters, that also see a steady improvement over time.

Due to these reasons many people have recently parameterized lipid forcefields, all with slightly different philosophies and/or goals. On top of that there are fewer papers comparing different lipid force fields, in comparison to the protein force fields. Therefore we'll first describe some of the available force fields based on the original papers.

CHARMM36 (Klauda et al, 10.1021/jp101759q, 10.1021/jp207925m, 10.1021/jp304056p). In this series of three papers with the same first author improvements to the existing CHARMM27r lipid force field are proposed. Selected charges, LJ and dihedral parameters are reparameterized by fitting to high level QM data of model compounds. Parameters are tested for 6 different lipid types (DPPC, DMPC, DLPC, DOPC, POPE and POPC) in the first paper. In the other papers parameters for SDPC/DAPC and cholesterol are added. Although the reparameterization seems to be done in an extensive and sturdy way, the test systems are small  (~72 lipids) and short (~40ns).

GAFFlipids/LIPID11 (AMBER) (Dickson, 10.1039/c2sm26007g, Skjevik, 10.1021/jp3059992). Amber did not have a designated lipid force field. Instead some lipids had been simulated using the Generalized Amber Force Field (GAFF), however these always gave a to small area per lipids or gell phase systems. Skjevik et al organized the GAFF based parameters in a structured, building block based lipid force field, however still using the old parameters. At the same time Dickson et al proposed new parameters for charges (RESP based) and LJ and torsion of the tails (based on density & free energy of vaporization of pentadecane), that would later be added to LIPID11. Parameters were tested for DOPC, DMPC, DPPC, DLPC, POPC and POPE.

Stockholm Lipids (AMBER) (Jämbeck, 10.1021/jp212503e, 10.1021/ct300342n10.1021/ct300777p). At the same time as the GAFF lipids Jämbeck and Lyubartsev published Amber compatible lipid parameters (RESP charges, same nonbonded fudge factors, but much longer cutoffs). Starting from CHARMM36 parameters, they recalculated charges and LJ+dihedrals parameters of the tails by fitting them to QM data. In three papers they publish and test parameters for DPPC, DLPC, DMPC, POPC, DOPC, SOPC, POPE, DOPE, sphingomylin, PG and PS headgroups and cholesterol. This work is the only paper that looks extensively at the behaviour at different temperatures, properties of the DPPC gel phase, multi component bilayers and protein lipid interactions.

Berger-lipids (Gromos, general) (Berger, 10.1016/S0006-3495(97)78845-3). The Berger force field is a united atom lipid force field often combined with Gromos protein parameters and is clearly the oldest set of parameters discussed here (1997). The original paper only contained parameters for DPPC, other parameters have later been added by various authors (POPC/DPPC/DMPC/DOPC/PLPC/POPE/DPC). Bonds, angles and dihedrals were taken from GROMOS87, tail dihedrals are taken from Rykaert (10.1016/0009-2614(75)85513-8, 10.1039/DC9786600095), LJ parameters were taken from OPLS, charges were taken from Chiu et al (10.1016/S0006-3495(95)80005-6). LJ parameters were optimized against volume and free energy of vaporization for pentadecane.

GROMOS43A1-S3 (Gromos43A1) (Chiu, 10.1021/jp807056c). A united atom force field that inculdes many new interactions, but is still compatible with the Gromos43A1 force field. Uses the same charges as the Berger force field (Chiu et al. 1995). Complete reparameterization using large set of small molecules, that can be combined into lipid parameters. Quite some QM and fitting to volume and heats of vaporization data. Parameters are available for PC/PE/sphingomyelin and cholesterol.

Gromos53A6-Kukol/Gromos-CKP (Gromos53A6) (Kukol, 10.1021/ct8003468, Piggot, 10.1021/jp207013v). Mostly uses the Gromos53A6 parameters and, again, the charges from Chiu et al. The size of the ester-carbonyl carbon VDW has been increased and new double bond bonded/torsion potentials have been derived. Parameters available for DMPC/DPPC/POPC/POPG and PE/PIP/PO/cardiolipin.

GROMOS54A7 (sometimes called GROMOS53A6L) (Poger, 10.1021/ct300675z, 10.1002/jcc.21396). Uses the same base parameters as the Kukol lipids above, except for the redefined interaction between choline, methyl and non-ester phosphate oxygen groups. Parameters exist for DPPC/DLPC/DMPC/DOPC/POPC.

As mentioned before there have been only very few papers comparing different lipid force fields. A recent, thorough comparison was done by Piggot et al. (10.1021/ct3003157). They started by finding optimal simulation settings for the different FFs (CHARMM36, Berger, G43A1-S3, Kukol/CKP and G54A7). With these optimal settings they simulated patches of fully hydrated DPPC and POPC and calculated a series of properties for these systems. They compare the values in a table, however to make things more clear we created a color coded matrix out of this table, where we compare deviation in percent from the experimental value. Green is 0%, red is 30% or more (sorry for the colorblind...). Since the experimental values vary greatly we used the average of the values reported by Piggot et al. In addition we added the values of these properties for GAFFlipids and Stockholm lipids (Slipids) obtained by the authors of these FFs (they are derived by other people and might thus be more or less reliable). The properties are: Area per lipids (AL), volume per lipid (VL), Isothermal area compressibility (Ka), P-N vector, Headgroup-Headgroup distance (DH-H) and Diffusion (Diff)

DPPC
dppc

POPC
dopc

It should be stressed that the spread in experimental values is not visible in this plot; for example the experimental values for diffusion differ more than the values obtained from simulations. Remarkable in these pictures is the relative good overal performance of Berger lipids and the Stokholm lipids. It should be noted that these force fields also have the longest cutoffs of all force fields.