# Insights into Membrane Damage by \(\alpha\)-Helical and \(\beta\)-Sheet Peptides
## 2 Materials and Methods
### Simulation Setup  
All-atom molecular dynamics simulations were performed using GROMACS 2021 [48; 49] with the atomic interactions modeled via the CHARMM36m force field that provides robust parameterization for both peptides and lipid systems [50]. The bilayer contained 200 lipids that were either 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) or 1-Palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol (POPG). It was made using a 7:3 POPC-POPG lipid ratio, which is commonly employed to study biologically relevant membrane.  
The initial box size for the simulations was approximately 12 \(\times\) 12 \(\times\) 12 nm\({}^{3}\), and it contained \(\sim\)20,000 TIP3P water molecules. Prior to peptide insertion, the lipid bilayer was equilibrated at 350 K under NVT and NPT conditions for a total of 500 ns to ensure membrane stability.  
The leap-frog algorithm was used to integrate the equations of motion, with a time step of 2 femtoseconds. Long-range electrostatic interactions were treated using the Particle Mesh Ewald (PME) technique, with a Fourier grid spacing of 0.12 nm and a short-range cut-off of 1.2 nm [51]. Van der Waals forces were smoothly switched to zero between 1.0 nm and 1.2 nm. A Nose-Hoover thermostat (\(\tau_{T}\) = 1 ps) was used to maintain the temperature of the membrane, solvent, and peptides at 350 K [52; 53]. A semi-isotropic Parrinello-Rahman barostat (\(\tau_{P}\) = 5 ps) was used to maintain the pressure in the system at 1 atm [54; 55].  
Molecular dynamics simulations were performed in four steps of 1 us, designed to mimic gradual adsorption of peptides onto the membrane [28]. At the beginning of each of these steps, 0.4 amino acids per lipid were randomly added to the solution, which accounted for ten M01 or M02 peptides, and five M03 or M04 peptides. At the end of each 1 us step, the peptides were found to adsorb onto the membrane, which accounted for 320 amino acids in the last simulation step, i.e., forty M01 or M02 peptides and twenty M03 or M04 peptides. At the end of the fourth step, the simulations were extended by an additional 3 us to study peptide aggregation and pore formation on the membrane. Three independent simulations were performed for M03 and M04 peptides, showing a consistent membrane permeation effect- Figure 2. An additional 1 us step was also simulated for the M04 peptides to show its membrane damaging effect at higher concentrations, consistently with the experiments.  
The adopted simulation protocol favored a pathway in which peptides first adsorb onto the membrane before self-assembling. This pathway is expected to dominate in experiments performed at low concentration, where the membrane behaves as a sink that gradually adsorbs peptides. This pathway may also be dominant in amyloid diseases, where peptides are initially found in healthy individuals at nano-molar concentrations, i.e., below the critical concentration for fibril formation. It is only over the time-frame of several years that this concentration reaches the micromolar range in the case of the A\(\beta\) protein in the brain [56; 57; 58]. However, alternative pathways of membrane damage are also possible due to the complexity of in vivo conditions [2; 59]. Notice that most computational studies start with peptides already embedded onto the membrane [60; 61; 62], which can lead to biases.  
Water permeation was computed using the perm-md-count code that is publicly available on git-hub [63]. It defines a permeation event as the translocation of one water molecule across the entire lipid bilayer along the membrane normal (z-axis), moving from one side of the membrane to the other. Before analysis, the membrane is centered along the z-axis using MDAnalysis, and only the phosphorus atoms of the lipid headgroups within a layer around the membrane midplane are used to define the bilayer region. This setup allowed the robust identification of water molecules that fully crossed the membrane.