Table 2 lists simulations of pure DHPC and pure DPPC bilayers presented in this study. Structural and mechanical properties calculated include form factors (
), SDP,
, and
. Properties focusing on the interaction of water with the ether and ester linkages are: pair-correlation functions,
, of the ether oxygen (in DHPC) and ester and carbonyl oxygens (in DPPC) with water; and z-profiles of the electrostatic potential (
), water potential of mean force (
), and density-weighted orientation of water dipole,
.
Bilayer simulations contained a total of 80 lipids (40 per leaflet) and 30 waters per lipid. Initial coordinates were produced by the CHARMM-GUI
28 (link)Membrane Builder29 (link)–31 (link) for DPPC. Necessary atom-type substitutions and deletions were made to produce the ether linkage of DHPC. “C36” denotes partial-charge assignments based on C36 charges for PEG and unchanged dihedral parameters (see
Sec. S2 and
Table S1). “C36e” denotes the new partial-charge and dihedral parameters found in Sec. 3.1. Simulations were run in NAMD using a 2-fs timestep and Langevin damping coefficient of 1/ps. Data were analyzed after equilibration, from 30 – 100 ns. Standard errors between replicates were calculated for
and scattering parameters, and from uncorrelated blocks for
. “NBFIX” parameters for carboxylate, ester, and phosphate oxygens
32 were used in simulations with NaCl.
The scattering densities of functional groups from simulation were obtained with the software package SIMtoEXP.
33 (link) For ready comparison with the experimental SDP,
12 (link) three Gaussians were used to describe the volume probabilities of the lipid headgroup: one each for the glycerol and ether linkage (G1), the phosphate and CH
2CH
2N moiety (G2), and the trimethyl groups of the terminal choline (G3). For calculating the bilayer hydrocarbon thickness (2D
C), the total hydrocarbon region was represented by an error function. Matlab R2016a
34 was used to fit the Gaussian and error functions and obtain the difference between electron density maxima (D
HH). X-ray and neutron form factors were calculated using SIMtoEXP
33 (link) with a Fourier transform of the total densities.
Area compressibility moduli of DHPC and DPPC bilayers were calculated using fluctuations in area:
35 Here,
is the mean square fluctuation in area per lipid,
nL is the number of lipids per leaflet, and
kB is Boltzmann’s constant.
The electrostatic potential profile along the bilayer normal was calculated by integration of the Poisson equation:
where
is the total time-averaged charge density and
is the permittivity of free space.
is greater at the center of the membrane than in bulk water. The total dipole potential drop across the membrane,
, is here defined as the difference in the electrostatic potential of bulk water,
, from that inside the membrane:
36 CHARMM
20 (link) was used to find the water density and dipole orientation with respect to position along the bilayer normal,
The software package Visual Molecular Dynamics (VMD)
37 (link) was used to find the pair-correlation functions,
, for ether oxygens of DHPC and carbonyl and ester oxygens of DPPC with water hydrogens, and to capture images of the bilayers. Peak positions and integrals of
were computed with Matlab R2016a.
34
Leonard A.N., Pastor R.W, & Klauda J.B. (2018). Parameterization of the CHARMM All-Atom Force Field for Ether Lipids and Model Linear Ethers. The journal of physical chemistry. B, 122(26), 6744-6754.