Structural, dynamic, and electrostatic properties of fully hydrated DMPC bilayers from molecular dynamics simulations accelerated with graphical processing units (GPUs)

Abstract

We present results of molecular dynamics simulations of fully hydrated DMPC bilayers performed on graphics processing units (GPUs) using current state-of-the-art non-polarizable force fields and a local GPU-enabled molecular dynamics code named FEN ZI. We treat the conditionally convergent electrostatic interaction energy exactly using the particle mesh Ewald method (PME) for solution of Poisson's Equation for the electrostatic potential under periodic boundary conditions. We discuss elements of our implementation of the PME algorithm on GPUs as well as pertinent performance issues. We proceed to show results of simulations of extended lipid bilayer systems using our program, FEN ZI. We performed simulations of DMPC bilayer systems consisting of 17,004, 68,484, and 273,936 atoms in explicit solvent. We present bilayer structural properties (atomic number densities, electron density profiles), deuterium order parameters (S(CD)), electrostatic properties (dipole potential, water dipole moments), and orientational properties of water. Predicted properties demonstrate excellent agreement with experiment and previous all-atom molecular dynamics simulations. We observe no statistically significant differences in calculated structural or electrostatic properties for different system sizes, suggesting the small bilayer simulations (less than 100 lipid molecules) provide equivalent representation of structural and electrostatic properties associated with significantly larger systems (over 1000 lipid molecules). We stress that the three system size representations will have differences in other properties such as surface capillary wave dynamics or surface tension related effects that are not probed in the current study. The latter properties are inherently dependent on system size. This contribution suggests the suitability of applying emerging GPU technologies to studies of an important class of biological environments, that of lipid bilayers and their associated integral membrane proteins. We envision that this technology will push the boundaries of fully atomic-resolution modeling of these biological systems, thus enabling unprecedented exploration of meso-scale phenomena (mechanisms, kinetics, energetics) with atomic detail at commodity hardware prices.

Figure 01

Example of influence region of three charges. The combined effect of the multiple charges impacts the volume under intersection of neighborhoods.

Figure 02

Example of charge update for which only the affected lattice points are updated.

Figure 03

When a single cell is affected due to displacement of multiple charges, it is updated with the help of integer atomic intrinsics.

Figure 04

Visual representations of the lipid-bilayer systems considered in this study. The DMPC 1×1 system describes the smallest system of 72 lipid molecules (36 lipids/leaflet). DMPC 2×2 and 4×4 describe systems with 288 and 1152 lipid molecules, respectively.

Figure 05

Plot of the total energy fluctuations of DMPC 1×1 as a function of time step size for different time step size - i.e., 0.125 fs, 0.25 fs, 0.5 fs, 1 fs, and 2 fs using single and double precisions as well as two different sets of cutoff values.

Figure 06

Comparison of the temperature and energy profiles of DMPC 1×1 for 3 ns of NVT MD simulation with 1fs step size for CHARMM on single core, 64 bits and FEN ZI on GTX 480, 32 bits. Shown from left to right, top to bottom are the temperature, and bond, angle, Urey-Bradley, improper torsion, dihedral, Van Der Waals, electrostatic, particle-mesh Ewald energies for CHARMM (black) and FEN ZI (red). All energies are expressed in kcal/mol, and temperature is expressed in Kelvin.

Figure 07

Comparison of performance of DMPC 1×1 in terms of ns/day for CHARMM on 1, 2, 4, and 8 CPU cores versus FEN ZI on GTX 480 (Fermi chip).

Figure 08

Simulations of three lipid bilayer membranes (DMPC) with three different sizes, each four time larger than the previous.

Figure 09

Number density profiles for various headgroup atoms in small, medium and large DMPC systems. Number densities are expressed in units of atom/ų.

Figure 10

Electron density profiles for small, medium and large DMPC membranes. Experimental profile is derived from experimental form factors in Ref..

Figure 11

Average orientation of water molecules for small, medium and large DMPC membranes as a function of z position relative to the center of the bilayer (left panels). The right panels show the orientation profiles scaled by a factor, ζ = ρ_fit(z)/ρ_bulk. Here, ρ_fit(z) is taken from an error function fit (Eq. 11) to the z-dependent water density profile. The horizontal line denoting zero is included for clarity in the right panels.

Figure 12

Distribution of the angle formed between the $\overrightarrow{PN}$ vector and the z-axis for small, medium and large DMPC membranes.

Figure 13

sn − 1 and sn − 2 order parameters for small, medium and large DMPC membranes.

Figure 14

Average water dipole moment as a function of the z position relative to the center of the bilayer for small, medium and large DMPC membranes.

Figure 15

Surface potentials and contributions of water and DMPC to the surface potential for small, medium and large membranes. All potentials are expressed in Volts.

Figure 16

FEN ZI performance in ns/day of DHFR simulations using different time steps and GPUs.