The analysis of basic membrane properties, i.e., lipid area per lipid (APL), curved APL, volume per lipid (VPL), lipid diffusion, membrane thickness, and water permeability, was performed as previously described [73]. If not stated otherwise, the standard deviations of the estimated properties at atomistic resolution were calculated from intervals of all production run simulations at a given temperature. In detail, 100 ns block averages were used at AA resolution after exclusion of initial 100 ns (in case of 1 μs long simulations the initial 200 ns were excluded). Water permeation events were counted over the whole production simulations after exclusion of the initial 100 ns. Structural properties of CG membranes were evaluated over the last microsecond of the simulations and the standard deviations were evaluated from ten 100 ns intervals. Water permeation events at CG resolution were estimated for 1 μs windows after exclusion of the first μs.

In order to be able to compare the hydrophobic membrane thickness to the estimates given in the Orientations of Proteins in Membranes (OPM) database [79], a hydrophobic boundary was defined as the mid distance between the carbonyl carbon and the first methylene carbon in AA representation and glycerol and C1 bead in CG representation for each tail. The hydrophobic thickness amounts to the local distance of these boundaries in the upper and the lower leaflet. The local membrane thickness around AQP1 was calculated on 1 nm sized grid as the difference in the z position of phosphorus atoms found either within 0.5 nm or within 1 nm of the protein in the upper and the lower leaflet.

The lipid tail ordering was estimated by evaluation of the fraction of lipid tail dihedral angles along the tail in trans orientation. To this end, the dihedral angles formed by carbons between positions 2 and 16 were evaluated for every single lipid tail and every dihedral angle at every time point of the simulation. Next, all data for individual analysis intervals were combined and the number of trans conformations (i.e., dihedral angles from the interval < 130,230 > relative to the total number of dihedral angle values in the same time interval) was estimated. Assessment of trans fraction of lipid tail dihedral angles was chosen instead of evaluation of order parameters due to its independence of lipid tilt relative to the membrane normal and due to the possibility to estimate a global ordering characteristic independent of the number of different lipids, the presence of double bonds and cyclopropane units, and their localization in the lipid tail.

The order parameters, P2, of CG lipids were calculated according to

where θ is the angle between the vector along the bond of interest and the membrane normal. Random orientation is indicated by P2=0, perfect alignment along the membrane normal by P2=1 and perfect anti-alignment by P2=−0.5.

The isothermal membrane area compressibility, κT, was determined from the fluctuations of the area per lipid using the equation

where k B is the Boltzmann constant, T the simulation temperature, 〈AL〉 the average area per lipid, and sAL the standard error of A L.

Lipid diffusion was estimated individually for each lipid type and temperature on a molecular basis from the Einstein equation as a slope of the lipid mean square displacement versus time (see [73] for more details). The sampling was improved by restarting the calculation every 1 ns. In atomistic resolution, the interval between 10 and 30 ns was used for the fit, while in CG resolution the interval between 100 and 300 ns was utilized.

The activation energies, E a, of water permeability and lipid diffusion were estimated from the Arrhenius plot

where k is the rate constant, A the pre-exponential factor, R the gas constant, and T the absolute temperature in K.

Lipid interdigitation of the two membrane leaflets was previously estimated as the overlap of the density distributions of the two leaflets [128]. In order to enable simple quantification of interdigitation, we suggest here a method in which the number of contacts between lipid tail carbon atoms after exclusion of the terminal methyls (or C4 beads in the CG resolution) between the two leaflets are counted and normalized to one lipid tail.

Lipid clustering was quantified by evaluation of lipid enrichment/depletion in lipid neighborhood. In detail, the number of headgroup contacts within 0.9 nm (i.e., the size of the first solvation shell of CLs’ GL1 bead connecting the two phosphate beads) of each lipid type were calculated using the program gmx mindist. As headgroups, the phosphate atoms (or beads in CG resolution) of PG and PE lipids are taken, while for CL, the central carbon of the glycerol connecting the two phosphate units was used (or the corresponding glycerol bead GL1 in CG resolution). For two lipid types, X and Y, the average number of contacts of Y with X per one lipid was estimated in each frame, and then normalized by the average number of contacts of Y lipids to any type of lipid. The plots were generated using R [86, 129], the curved lipid areas were estimated using a home-written code [73] in an idl demo version [130]. Pictures were rendered in PyMOL [131]

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