Tight cohesion between glycolipid membranes results from balanced water–headgroup interactions

Membrane systems that naturally occur as densely packed membrane stacks contain high amounts of glycolipids whose saccharide headgroups display multiple small electric dipoles in the form of hydroxyl groups. Experimentally, the hydration repulsion between glycolipid membranes is of much shorter range than that between zwitterionic phospholipids whose headgroups are dominated by a single large dipole. Using solvent-explicit molecular dynamics simulations, here we reproduce the experimentally observed, different pressure-versus-distance curves of phospholipid and glycolipid membrane stacks and show that the water uptake into the latter is solely driven by the hydrogen bond balance involved in non-ideal water/sugar mixing. Water structuring effects and lipid configurational perturbations, responsible for the longer-range repulsion between phospholipid membranes, are inoperative for the glycolipids. Our results explain the tight cohesion between glycolipid membranes at their swelling limit, which we here determine by neutron diffraction, and their unique interaction characteristics, which are essential for the biogenesis of photosynthetic membranes.


Supplementary Note 1: Thermal expansion of the area per DGDG lipid
The thermal expansion coefficient of the DGDG bilayer was determined by performing simulations at three different temperatures: 280 K, 300 K, and 320 K. The lengths of the simulations were between 200 and 600 ns and the error associated with the area per lipid was estimated by block averaging. The resulting area per lipid is shown in Supplementary Fig. 1. From the linear fit (dashed straight line) we obtain the thermal expansion coefficient of the area per lipid.

Supplementary Note 2: Sensitivity to the simulation parameters
The force field used for DGDG is based on GROMOS 53a6 [1], which was developed in combination with the Simple Point Charge (SPC) water model, a Lennard-Jones (LJ) cutoff distance of r LJ = 1.4 nm and a Coulomb interaction modified by a reaction field (RF) contribution. In order to be consistent with the PC lipid membrane simulations and with previous studies [2,3], we instead use the SPC/E water model, Particle-Mesh-Ewald (PME) electrostatics, and r LJ = 0.9 nm. In the following, we examine the sensitivity of the DGDG area per lipid upon the force field variations mentioned above. Figure 2a in the main text shows the area per DGDG averaged over simulation times of around 80 ns.
In addition, we performed longer simulations of 1 μs, for which the results are shown in Supplementary Fig. 2 by red open square symbols. In these additional simulations we estimated the errors associated with the area per lipid by the block averaging method. As seen, the obtained error bars are comparable to those from the main text where they were estimated by the scatter of data points. To determine the effect of variations in the simulation parameters, we first extended the LJ cutoff distance to r LJ = 1.4 nm, which results in the values represented by green open circles. The area per lipid in this case decreases a bit, which can be explained by a longer-ranged lipid-lipid attraction due to the larger LJ cutoff distance. Nevertheless, in both cases, the simulation data points lie close to the experimental values (orange open squares), albeit slightly above in the former and slightly below in the latter case. Further, switching from SPC/E to SPC water and from PME to RF electrostatics (blue triangles) does not influence the final results significantly. The good match between simulated and experimental area per lipid and the fact that the force-field-related differences in the final results seen above are small suggest that the above-mentioned force-field modifications are acceptable. In fact, it was shown that minor variations in the area per lipid have negligible influence on the membrane interaction forces [3].

Supplementary Note 3: Hydrogen bonds in hydrated PC lipid membranes
In the same way as in Fig. 4a in the main text for DGDG, we show in Supplementary Fig. 3  with D W . It reaches a saturation value at much larger separations than in the DGDG case. Fitting an exponential curve to the points gives a decay length of λ = 0.43 nm. The fit is, however, not as good as for DGDG in the main text. The inset shows the decomposition of the total number of HBs into water-water (ww) and lipid-water (lw) contributions. Note that the lipid-lipid (ll) contribution is zero, as PC lipids possess only proton acceptors and therefore cannot form HBs among themselves.
The exponential fits (dashed lines) with decay lengths λ = 0.36 nm (ww) and λ = 0.33 nm (lw) match the data points very well.

Supplementary Note 4: Water orientation profiles within the water layer
As shown in Fig. 5b in the main text, the degree of water orientation is much higher in hydrated PC lipid membranes than in hydrated DGDG membranes for the same water layer thickness. In Supplementary Fig. 4, which shows a close-up view of the water orientation within the water slab, it can be seen that for PC lipid membranes significant orientation extends virtually all the way to the centre of the water layer, where it has to vanish by symmetry. For DGDG, on the other hand, orientation within the water layer is almost immeasurably weak.

Supplementary Note 5: Head group angular distributions compared at the same pressure
In Fig. 5c in the main text we compare the angular distributions of DGDG and PC lipid headgroups with respect to the membrane normal at same separations, that is, D w = 2.3 nm and 0.6 nm. Here, Supplementary Fig. 5 shows a similar comparison but at the same equivalent interaction pressures of Π ≈ 0 and Π ≈ 600 bar, respectively. For the former condition we choose the separation D W = 2.3 nm, whereas the second one corresponds to D w = 0.3 nm and 0.6 nm for DGDG and PC lipids, respectively. Even when bringing the DGDG membranes down to a 0.3 nm separation, the impact on the angular distribution is still much weaker than for PC lipids at 0.6 nm.

Supplementary Note 6: Decomposition of the interaction free energy
It can be instructive to decompose the membrane interaction into its enthalpic and entropic contributions. For this purpose, we first quantify the interaction free energy ( which we can also evaluate via water chemical potential μ and the number of water molecules in the water layer N W as: In the next step, we evaluate the enthalpy H of the system in dependence of D w , where we account also for the enthalpy of the water molecules transferred into the bulk where H 0 is the total enthalpy of the simulation box and h w = −38.9038 kJ/mol is the enthalpy per water molecule in bulk, evaluated from independent bulk water MD simulations. The entropic contribution of the interaction, −TS, then follows as −TS = G−H. Supplementary Fig. 6a shows G, H, and −TS as functions of D w for DGDG membranes. Consistent with the rapidly decaying interaction pressure, G is seen to be immeasurably small for D w > 0.6 nm. This does not apply, however, to H and −TS, which assume magnitudes of 1-1.5 kJ/mol/lipid up to D w ≈ 0.9 nm, but are of opposite sign and exhibit virtually complete cancellation. The significant repulsion (dG/dD w < 0) for D w < 0.6 nm is driven by the enthalpy, dH/dD w < 0. In contrast, the entropic contribution is attractive, −TdS/ dD w > 0, but sub-dominant. For D w > 0.6 nm the situation is opposite (dH/dD w > 0 and −TdS/dD w < 0). For a comparison with the commonly studied PC lipid membranes, Supplementary Fig. 6b shows the same enthalpy-entropy decomposition for PC lipids. The overall picture is qualitatively similar for DGDG and PC lipids. In both cases we notice enthalpic repulsion dominating over entropic attraction at low hydration and a turnover to the opposite situation at larger hydration. However, since for PC lipids the entropic repulsion significantly dominates over the enthalpic attraction at large hydration, G for PC lipids assumes substantially positive values in a much wider hydration range, measurable even for D w > 1.5 nm. This substantial entropic repulsion at higher hydration has been discussed previously [2,4].