Amphipathic Helices Can Sense Both Positive and Negative Curvatures of Lipid Membranes

Curvature sensing is an essential ability of biomolecules to preferentially localize to membrane regions of a specific curvature. It has been shown that amphipathic helices (AHs), helical peptides with both hydrophilic and hydrophobic regions, could sense a positive membrane curvature. The origin of this AH sensing has been attributed to their ability to exploit lipid-packing defects that are enhanced in regions of positive curvature. In this study, we revisit an alternative framework where AHs act as sensors of local internal stress within the membrane, suggesting the possibility of an AH sensing a negative membrane curvature. Using molecular dynamics simulations, we gradually tuned the hydrophobicity of AHs, thereby adjusting their insertion depth so that the curvature preference of AHs is switched from positive to negative. This study suggests that highly hydrophobic AHs could preferentially localize proteins to regions of a negative membrane curvature.

choline beads.After the peptide placement, the system was again equilibrated for 20 ns.The equilibration was followed by 20 µs long production run.For the production, Parinello-Rahman barostat 13,14 was used instead of Berendsen barostat with a coupling constant of 12 ps.All system coordinates were saved every 2 ns (1 ns for all-atom systems) for subsequent analysis.The first 5 µs were discarded from the analysis as additional equilibration.Three independent replicas were constructed for all MARTINI systems.
For MARTINI 3 systems, we used the final structures from the simulation of an empty buckled membrane simulated with MARTINI 2 parameters.The systems were simulated with MARTINI 3 (v3.0.0) 15 parameters for 20 µs, first 5 µs were discarded as equilibration.For the coarse-graining of the peptides generated from the sequence martinize2.py 16was used.Apart from the aforementioned details, the simulation parameters were identical to MARTINI 2.
For all-atom simulations, similarly to MARTINI 3, two di↵erent snapshots from MARTINI 2 trajectories were selected and backmapped to all-atom using CHARMM-GUI All-atom converter, 17 which employs backward.py 18to transform CG proteins into all-atom representation.As a result, we obtained systems of approximately half a million atoms.CHARMM36m 19 parameters were used to describe the system.Verlet integrator with a 2 fs integration step was employed.Electrostatic interactions were treated using PME 20 with a cut-o↵ of 1.2 nm.The system's temperature was kept at 310 K using stochastic velocity rescaling thermostat 10 with separate coupling for solvent, membrane, and peptides.Semiisotropic pressure coupling was used with the Parinello-Rahman barostat 13,14 to maintain the pressure of 1 bar.Constraints were applied to bonds containing hydrogen atoms using the LINCS 21,22 algorithm.SETTLE 23 algorithm was used for water molecules.To preserve the buckled membrane shape, compressibility in the XY plane was set to zero as in CG systems, while the pressure in the Z-direction was allowed to fluctuate.The systems were simulated up to 6.5 µs.The first 1 µs was discarded as equilibration.
To analyze the membrane curvatures we employed approach used in previous work by Bhaskara et al. 3 based on the MemCurv scripts (https://github.com/bio-phys/MemCurv).The membrane shape from each trajectory frame was approximated by a 2D Fourier series, which was optimized using the least squares method with respect to the positions of phosphate beads or phosphorus atoms in the case of all-atom.
To precisely capture the local membrane shape, each membrane leaflet was fitted individually.Resulting di↵erentiable surfaces were then used to calculate principal curvatures at the position of the peptide's center of mass (and corresponding mean and Gaussian curvatures).
The distance from bilayer midplane was calculated as a minimal distance between peptide backbone COM and the bilayer midplane as described by curved surface fitted to positions of innermost lipid tail beads.Similarly, the insertion depth was calculated as minimal distance between peptide backbone COM and the curved surface fitted to positions of phosphate beads or phosporus atoms, in the case of CG MARTINI and all-atom simulations, respectively.
Mean values and standard deviations were calculated from the average values for individual peptide copies in each replica and from independent replicas, three for CG systems and two for all-atom systems, resulting in overall n=6 and n=4 for CG and all-atom, respectively.
To predict the secondary structure of peptides from the all-atom trajectories, implementation of DSSP algorithm 24 (version 4.0.0) was used.Snapshots of the simulation systems were obtained using Visual Molecular Dynamics (VMD) software (version 1.9.3) and composed together in Inkscape (version 1.46.2).Analysis and plots were performed using Python 3, namely matplotlib (version 3.6.3),seaborn (version 0.12.2), and scipy (version 1.10.0)packages.

Analysis of accessible curvature and weighting
To obtain the accessible membrane curvature, we created a grid with equidistantly spaced points along the membrane buckle (X-direction).First, the trajectory of the membrane buckle was aligned according to the bilayer midplane (positions of C4A and C4B lipid beads).Subsequently, all frames were overlayed, and individual leaflets were fitted (positions of PO4 beads) using Fourier series (undulations in the Y direction are assumed to average out).We then selected points along the curve corresponding to the XZ profile of the membrane, dividing the curve into intervals of equal arc length.The points along the Y direction were generated equidistantly.The resulting grid had 102 points in X and 62 in Y direction.Mean membrane curvature was then calculated at each grid node for every 100th frame of the simulation trajectory, providing us with the distribution of accessible curvature.
To filter the e↵ect of accessible curvature, we used the distribution of curvature present on the membrane surface (surface given by fitting PO4 beads of upper or lower leaflet) and inverted it to give higher weight to the less represented curvature values.To avoid overemphasizing the curvatures that arose only transiently, the curvature values visited less than in 0.1% of the frames were discarded from the reweighing.Some peptides have ability to generate and stabilize certain curvatures, a↵ecting the overall distribution.However, in our systems, there concentration of peptides was low and the same applied for the di↵erence between the respective distributions.A common reference distribution was therefore used, in our case LS4.
Table S1: Summary of peptide labels used in this work, together with corresponding amino acid sequences, mean hydrophobicity according to the Wimley-White hydrophobicity scale, 25 and mean hydrophobic moment, hµi.   Figure S3: Time evolution of ↵-helical propensity in all-atom simulations of ALPS, LS11, and LS4, evaluated using DSSP algorithm. 24Data for copies of peptides on both membrane leaflets and independent replicas are shown separately.Trajectory frames were analyzed every 100 ns.

Figure S1 :
FigureS1: Helical wheel representations of control peptides, amphipathic lipid packing sensor of ArfGAP1 (ALPS) and amphipathic helix derived from the nonstructural protein NS5A of hepatitis C virus.Residues are colored according to their properties: acidic (red), basic (blue), nonpolar (white), and polar (green).

Figure S2 :
Figure S2: Summary of distributions of sampled mean membrane curvatures by di↵erent peptides in MARTINI 2. Data for peptide copies in individual leaflets are plotted separately.The red line serves as a guide for the eye and shows the position of zero mean curvature.

Figure S4 :
Figure S4: Distributions of sampled mean membrane curvatures by di↵erent peptides in MARTINI 2 shown for individual replicas.Data for peptide copies in individual leaflets are plotted separately.The dotted grey line serves as a guide for the eye and shows the position of zero mean curvature.

Figure S5 :
Figure S5: Distributions of sampled mean membrane curvatures by di↵erent peptides in MARTINI 2 shown for individual replicas.Data for peptide copies in individual leaflets are plotted separately.The dotted grey line serves as a guide for the eye and shows the position of zero mean curvature.

Figure S7 :
Figure S7: Distributions of sampled mean membrane curvatures by di↵erent peptides in all-atom CHARMM36m.Data for peptide copies in individual leaflets are shown.The dotted grey line serves as a guide for the eye and shows the position of zero mean curvature.

Figure S8 :
Figure S8: Plots showing the distributions of reweighted/normalized mean membrane curvatures by di↵erent peptides, together with raw sampled data and distribution of accessible curvature on membrane surface (phosphate beads) in coarse-grained MARTINI 2 force field.Data for peptide copies in individual leaflets are shown.The dotted grey line serves as a guide for the eye and shows the position of zero mean curvature.

Figure S9 :
Figure S9: Time evolution of the membrane mean curvature sampled by the individual peptides in all-atom representation on buckled membrane shown as a 200 ns moving average.Data from both replicas are shown.

Table S2 :
Summary of performed simulations, specifying if the simulation was run using MARTINI 2 (M2), MARTINI 3 (M3), or all-atom CHARMM36m (AA).The number of lipid molecules and the overall size of the system (beads or atoms) along with the simulation time are listed as well.