Comparison of the Extended Isotropic Periodic Sum and Particle Mesh Ewald Methods for Simulations of Lipid Bilayers and Monolayers

Abstract

3D-IPS/DFFT is an extension of the three dimensional Isotropic Periodic Sum (3D-IPS) for evaluation of electrostatic and Lennard-Jones interactions in heterogeneous systems; it utilizes a discrete fast Fourier transform (DFFT) for efficient calculation of the IPS potential with a large local region radius. The method is demonstrated to be highly accurate for simple bulk fluids, liquid/liquid and liquid/vapor interfaces, and lipid bilayers and monolayers. Values for rC (the cutoff distance for direct evaluation of pairs) and RC (the local region radius) equal to 10 Å and twice the longest edge of the periodic cell, respectively, provide excellent efficiency and accuracy. Dimyristoylphosphatidylcholine (DMPC) monolayers simulated with the CHARMM (Chemistry at HARvard Molecular Mechanics) C27r lipid parameter set and 3D-IPS/DFFT yield surface tensions approximately 8 dyn/cm higher than those simulated using Particle Mesh Ewald (PME), and with experiment. In contrast, surface tensions for DMPC bilayers are 16 dyn/cm/leaflet with both 3D-IPS/DFFT (rC = 10 and 12 Å) and PME (rC = 12 Å). This indicates that PME (rC = 12 Å) may be used for simulations of bilayers, but not monolayers, and that the large bilayer surface tension arising from C27r is incorrect.

Molecular Simulation with Discrete Fast Fourier Transform

“…Venable et al applied IPS/DFFT and PME methods for simulations of lipid bilayers and monolayers (Venable, Chen et al 2009). The method is demonstrated to be highly accurate for simple bulk fluids, liquid/liquid and liquid/vapor interfaces, and lipid bilayers and monolayers (Klauda, Wu et al 2007).…”

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

“…lipid bilayers) is troublesome since the assumption that g(r) is equal to unity beyond the cutoff inherently assumes that the system is homogeneous and isotropic, something that most definitely is not true for these systems. The implication of this for simulations containing lipid bilayers has not been given much attention in the past, but coupled to the development of alternative ways of treating long-range LJ interactions [10][11][12][13][14][15][16][17] the problem has started to become more apparent the last few years. 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.…”

Isotropic periodic sum for multipole interactions and a vector relation for calculation of the Cartesian multipole tensor

“…28,30 The IPS method makes long-ranged nonbonded interactions short-ranged so that they can be calculated as simply as with a cutoff method. Therefore, the IPS method has the accuracy of lattice sum methods and can be calculated as efficiently as the cutoff methods.…”

“…For heterogeneous systems, the discrete fast Fourier transform accelerated 3D IPS (3D IPS/DFFT) method 29 provides an efficient way to allow a local region large enough to contain the heterogeneity of a simulation system, for a more accurate calculation of longranged interactions. Venable and co-workers 30 have compared 3D-IPS/DFFT with PME and demonstrated that this method is highly accurate for simple bulk fluids, liquid/liquid, and liquid/vapor interfaces, as well as lipid bilayers and monolayers. For lipid monolayers, 3D-IPS/DFFT is recommended over PME.…”

“…For lipid monolayers, 3D-IPS/DFFT is recommended over PME. 30 Ojeda-May and Pu have extended the IPS method for quantum mechanical and molecular mechanical (QM/MM) simulation, demonstrating that the QM/MM-IPS method can be used as a reliable and efficient alternative to the QM/MMEwald method. 31,32 IPS is more convenient than PME in decomposing pairwise interactions, which is essential for some new simulation methods, such as the virtual mixture of multiple states (VMMS's) method.…”