Lennard-Jones Lattice Summation in Bilayer Simulations Has Critical Effects on Surface Tension and Lipid Properties

Abstract

The accuracy of electrostatic interactions in molecular dynamics advanced tremendously with the introduction of particle-mesh Ewald (PME) summation almost 20 years ago. Lattice summation electrostatics is now the de facto standard for most types of biomolecular simulations, and in particular, for lipid bilayers, it has been a critical improvement due to the large charges typically present in zwitterionic lipid headgroups. In contrast, Lennard-Jones interactions have continued to be handled with increasingly longer cutoffs, partly because few alternatives have been available despite significant difficulties in tuning cutoffs and parameters to reproduce lipid properties. Here, we present a new Lennard-Jones PME implementation applied to lipid bilayers. We confirm that long-range contributions are well approximated by dispersion corrections in simple systems such as pentadecane (which makes parameters transferable), but for inhomogeneous and anisotropic systems such as lipid bilayers there are large effects on surface tension, resulting in up to 5.5% deviations in area per lipid and order parameters-far larger than many differences for which reparameterization has been attempted. We further propose an approximation for combination rules in reciprocal space that significantly reduces the computational cost of Lennard-Jones PME and makes accurate treatment of all nonbonded interactions competitive with simulations employing long cutoffs. These results could potentially have broad impact on important applications such as membrane proteins and free energy calculations.

Direct-Space Corrections Enable Fast and Accurate Lorentz–Berthelot Combination Rule Lennard-Jones Lattice Summation

“…18 The structures simulated originally come from the work of Hub et al 25 These structures contain 128 POPC molecules and 5,262 SPC 26 water molecules. The systems were simulated for 100 ns at 298 K, using a time step of 2 fs.…”

“…In our previous work 18 we showed that when using LJ-PME with LB combination rules we only obtain 25% of the performance we get by using cutoffs, which makes it hard to motivate its use. However, we also noted that by using geometric combination rules for the reciprocal part of the potential, the performance could be increased up to almost 80% of the performance obtained using a twin-range 10/16Å cutoff.…”

“…18 The bilayer simulation using LB combination rules was extended for an additional 100 ns using three setups: (I) Full LB combination rules in both direct and reciprocal space, (II) approximation of reciprocal space with geometric combination rules, and (III) modified direct-space interactions together with geometric combination rules in reciprocal space. Since the force field parameters for these lipids originates from the Berger lipids, 28 and hence uses geometric combination rules, the errors introduced by the application of LB combination rules will have a small effect on the calculated properties.…”

“…In light of this, we recently presented an implementation in the Gromacs simulation package where the PME method was used to calculate long-range LJ interactions. 18 In this implementation we proposed to circumvent the expensive calculations for the reciprocal sum by approximating the reciprocal-space interaction coefficients with the geometric combination rules 19 even where the force field uses Lorentz-Berthelot rules 20 (LB). While this introduced slight errors in the entire reciprocal space component (which extends inside the cutoff too), we argued this was much smaller than the errors historically accepted with analytical dispersion correction.…”

Dispersion Corrections to the Surface Tension at Planar Surfaces

“…Although these kinds of methods may be applied for any kind of power-law potential, they have not until recently been effectively implemented for dispersion interactions in standard molecular dynamics software. 3 Therefore, it is still of interest to calculate long-range corrections. The cutoff affects energies, forces and pressures.…”