Exploring the Properties of Curved Lipid Membranes: Comparative Analysis of Atomistic and Coarse-Grained Force Fields

Curvature emerges as a fundamental membrane characteristic crucial for diverse biological processes, including vesicle formation, cell signaling, and membrane trafficking. Increasingly valuable insights into atomistic details governing curvature-dependent membrane properties are provided by computer simulations. Nevertheless, the underlying force field models are conventionally calibrated and tested in relation to experimentally derived parameters of planar bilayers, thereby leaving uncertainties concerning their consistency in reproducing curved lipid systems. In this study we compare the depiction of buckled phosphatidylcholine (POPC) and POPC–cholesterol membranes by four popular force field models. Aside from agreement with respect to general trends in curvature dependence of a number of parameters, we observe a few qualitative differences. Among the most prominent ones is the difference between atomistic and coarse grained force fields in their representation of relative compressibility of the polar headgroup region and hydrophobic lipid core. Through a number of downstream effects, this discrepancy can influence the way in which curvature modulates the behavior of membrane bound proteins depending on the adopted simulation model.


Simulated systems
2 Membrane shape approximation Membrane shape was approximated by a linear combination of n sinus functions with wavelengths chosen to fit into the x-dimension of the simulation box, L x : In order to establish the number of necessary components we took into account two opposing effects that arise with increasing n.First is the ability of the fitted function to represent membrane surface, which can be quantified by the root mean square deviations (RMSD) of distances of atomic positions in xz-plane from Z(x).Second is the tendency to capture short wave membrane fluctuations that are registered as spurious, locally high curvatures.The higher number of components obviously allows better shape approximation evidenced by lower RMSD (Fig. S1A), however, at the same time leads to an increase in the amount of surface area whose curvature falls outside the range considered for analysis (Fig. S1BC).To arrive at the final number of n = 6 components, we assumed that sufficiently low RMSD would correspond to that obtained by approximating the surface of a flat 3 nm × 3 nm membrane patch by a planar surface, which turned out to be 0.2 nm (assessed based on flat membrane simulations).Under this assumption more than 85 % of membrane surface was mapped as having the curvature K ∈ [−0.25, 0.25] nm −1 , which we deemed satisfactory.
In order to assess the effect of increasing the number of components used for membrane shape approximation, we compared the results obtained for bilayer thickness and surface area per lipid, that is two basic parameters characterizing transverse and lateral membrane parameters.Both sets of plots (Fig. S2) reveal the same qualitative differences between atomistic and coarse grained force fields.We note that quantitative differences obtained for membrane thickness, are in the order on 0.03 nm (for the overall thickness of ∼ 4 nm) that is similar to the one resulting from using different algorithms to assess the thickness of a flat membrane.Table S3: Atoms used for calculation of lipid acyl chain ordering -S CC

Figure
Figure S1: A) RMSD between phosphorus atoms positions and their fitted analytic curve as a function of the number n of considered sinus components.Blue horizontal line denotes an average RMSD for for phosphorus atoms positions within flat membrane, fitted to 3 nm × 3 nm square surface parallel to the membrane plane.B) The distribution of curvature probability density obtained with an increasing number of sinus components.Dashed lines denote |K| = 0.25 nm −1 , that is the limiting value of curvature used for analysis.C) The fraction of curvature probability density falling between K = ±0.25 nm −1 .

Figure S2 :
Figure S2: Relative membrane thickness (upper row) and normalized surface area per lipid (lower row) as a function of membrane curvature, obtained using membrane shape approximation based on n sinus components (Eq.1).

Figure S3 :
Figure S3: Sample monolayer atomic number densities along curved surfaces fitted to their positions in the xz-plane.

Figure S4 :
Figure S4: Slopes of atomic number densities obtained by linear function fit over K ∈ [−0.15, 0.15] nm −1 , as a function of respective average atomic positions along membrane normal, z, with z = 0 corresponding to the bilayer midplane.Dashed line indicates the depth at which the slope would be 0, i.e. an approximate location of the pivotal plane, z p .

Figure S5 :
Figure S5: Left: mean S CH values for flat systems -sn1 chain.Right: mean S CH values for flat systems -sn2 chain.Experimental data are from Seelig et al. [1]

Table S1 :
Details of considered curved systems and simulations.L21 -Amber Lipid 21 force field, C36 -Charmm36m force field, M2, M3 -Martini 2 and 3 force fields.Note that the M2 and M3 models use water beads equivalent to 4 explicit water molecules.

Table S2 :
Details of considered flat systems and simulations.

Table S4 :
Atoms used for calculation of hydration of lipid heads and acyl chains

Table S5 :
Numerical values for membrane descriptors obtained for buckled membranes at K = 0 nm −1 .

Table S6 :
Numerical values for membrane descriptors obtained for flat POPC membranes.