Computational analysis of local membrane properties

Abstract

In the field of biomolecular simulations, dynamics of phospholipid membranes is of special interest. A number of proteins, including channels, transporters, receptors and short peptides are embedded in lipid bilayers and tightly interact with phospholipids. While the experimental measurements report on the spatial and/or temporal average membrane properties, simulation results are not restricted to the average properties. In the current study, we present a collection of methods for an efficient local membrane property calculation, comprising bilayer thickness, area per lipid, deuterium order parameters, Gaussian and mean curvature. The local membrane property calculation allows for a direct mapping of the membrane features, which subsequently can be used for further analysis and visualization of the processes of interest. The main features of the described methods are highlighted in a number of membrane systems, namely: a pure dimyristoyl-phosphatidyl-choline (DMPC) bilayer, a fusion peptide interacting with a membrane, voltage-dependent anion channel protein embedded in a DMPC bilayer, cholesterol enriched bilayer and a coarse grained simulation of a curved palmitoyl-oleoyl-phosphatidyl-choline lipid membrane. The local membrane property analysis proves to provide an intuitive and detailed view on the observables that are otherwise interpreted as averaged bilayer properties.

Fig. 1

Representation of a cis double bond in an unsaturated lipid acyl chain. x, y and z axis define a molecular frame, C _i denotes carbon atom, D _j depicts deuterium atom

Fig. 2

Analysis of the local thickness and APL of a pure DMPC bilayer. A MD simulation trajectory was divided in two 80 ns parts and local properties for both parts were evaluated separately. The area of the box was 5.3 × 5.3 nm² and 100 bins were used along x and y axes. a Local thickness of the bilayer averaged over time. Average thickness values calculated from the grid elements were 3.61 and 3.59 nm for the first and second part, respectively. b Local APL of the membrane averaged over time. c Phosphorus atom densities averaged over time and over all lipids. Thickness values evaluated from the 1D densities. d Change of the APL, averaged over lipids, in time: the black curve depicts the mean APL value, the red and blue curves denote the maximal and minimal APL values, respectively. e Standard deviations of the local membrane thickness. f Standard deviations of the local membrane APL

Fig. 3

Local properties of a membrane with an inserted fusion peptide. The box area was 6.0 × 6.3 nm² and 50 bins were used along x and y axes. a The first 12 amino acids of a GP41 peptide inserted in a DMPC membrane patch. The peptide is in an α-helical cartoon representation with the amino acid side chains represented as sticks. Lipids are shown as transparent sticks with hydrogens omitted and phosphorus atoms are depicted as spheres. b The time averaged local bilayer thickness shows a perturbation of the membrane around the peptide. The experimentally determined thickness of the pure DMPC membrane is shown as a dotted line in the scale bar. c Area per lipid values in each leaflet display an asymmetric distribution of lipids around the peptide. The experimental APL value of pure DMPC is shown as the dotted line in the scale bar. d Local deuterium order parameters of the carbon atoms in positions 2, 7 and 13 of each acyl chain (sn-1 & sn-2) are shown, considering the grid-mapped values within 1 nm of the peptide

Fig. 4

Local membrane properties of a bilayer with an embedded membrane protein VDAC. a The voltage dependent anion channel (VDAC) is shown in a cartoon β-barrel representation. Residue E73 and the water molecules nearby are represented as spheres. Serine and threonine residues constituting hydrophilic area close to E73 are shown in ball and stick representation. In the snapshot, a DMPC lipid is shown flipping close to the E73 and K110 residues. The box area was 11.5 × 11.5 nm² and 100 bins were used along x and y axes. b Top view perspectives of the circular representation of the local thickness, calculated considering phosphorus atoms, and area per lipid, calculated considering the COMs of the lipids. The properties were estimated for the simulations of the E73V, uncharged E73° and charged E73⁻ variants of VDAC. The arrow indicates the position of E73X residue (sphere representation). c Circular representation of the deuterium order parameters for selected carbons around VDAC

Fig. 5

S _CD order parameter analysis of a cholesterol enriched DMPC bilayer. Order parameter values for the C10 carbon of the acyl chain sn-1 are shown. The box area was 5.6 × 5.6 nm² and 50 bins were used along x and y axes. a Local deuterium order parameters of a pure DMPC membrane averaged over a 100 ns MD trajectory. b Local S _CD order parameters for a 20 mol% DMPC bilayer averaged over a 10 ns MD trajectory excerpt. The cholesterol molecules represented as lines are overlayed for all the frames. The enlarged view figures emphasize the areas where cholesterol (visualized as sticks) decreases ordering of the lipid chains on the opposite leaflet

Fig. 6

Curvature of a coarse grained POPC bilayer simulation. a The whole simulated system containing a SNARE protein complex holding a POPE lipid vesicle and POPC bilayer in a pre-stalk formation phase. The box area was 30 × 30 nm² and 100 bins were used along x and y axes. b. A POPC bilayer with only the beads representing the amine (blue) and phosphate (gray) groups is shown. The characteristic high curvature ‘dimple’ region is highlighted. c Gaussian and mean curvatures after applying a low pass filter. d Gaussian and mean curvatures after applying a band pass filter. e Gaussian and mean curvatures after applying a high pass filter

Fig. 7

Dependence of the calculated area per lipid/protein on the user defined grid cell number. A molecular dynamics trajectory of a protein VDAC embedded in a DMPC bilayer was analysed by calculating local area per lipid/protein using different number of grid cells. Both, the membrane area occupied by the protein and the local APL of three randomly selected lipids converge for the grid cells with area smaller than 10 Å²