Supplementary Information for " Effects of Stretching Speed on Mechanical Rupture of Phospholipid/cholesterol Bilayers: Molecular Dynamics Simulation "

Initial system construction and equilibration The procedure for the construction of pure DPPC and DPPC/cholesterol bilayer systems, with almost identical planar bilayer areas and square bilayer shapes, is briefly explained in this section. The fundamental procedure is the same as in our previous study 1. First, two monolayers were constructed by placing DPPC and cholesterol molecules rotated around their long axis on a 88 grid. These monolayers contained the same number of cholesterol molecules and the position of each molecule was assigned randomly. The two monolayers were then stacked up to build a bilayer and the entire system was energy minimized. The bilayer was solvated with water molecules, which immersed the polar head group of DPPC and the cholesterol molecules. The solvated system was energy minimized again and equilibrated by NPT MD simulation for more than 100 ns. At this point, the pure DPPC bilayer consisted of 128 DPPC and 4,955 water molecules, and the DPPC/cholesterol bilayer of 76

DPPC, 52 cholesterol, and 4,864 water molecules. Additionally, the bilayer areas of the pure DPPC and DPPC/cholesterol bilayer systems at equilibrium state were 41.87 and 25.12 nm 2 , respectively. To reduce the difference in bilayer areas, we developed the DPPC/cholesterol bilayer system further. The square DPPC/cholesterol bilayer system was replicated along the direction parallel to the bilayer plain and a rectangular bilayer system was thus formed. The rectangular bilayer system was deformed using the MD simulation with the deform option, implemented in GROMACS codes, to obtain a square bilayer system. Then, three DPPC and two cholesterol molecules per leaflet were randomly removed from the deformed square bilayer system and the system was equilibrated by NPT MD simulation for 10 ns. Once again, eight DPPC and six cholesterol molecules per leaflet were removed and the system was equilibrated for 20 ns. The DPPC/cholesterol bilayer consisted of 128 DPPC and 86 cholesterol molecules. Finally, water molecules were added to both the pure DPPC and DPPC/cholesterol bilayer systems. Both the systems were equilibrated using NPT MD simulation for more than 100 ns.

Equilibrium simulation parameters
Unless otherwise mentioned, all MD calculations were carried out under the conditions shown below. The leap-frog algorithm was used for numerical solution of the equations of motion and the time step was set to 2.0 fs. The PME method 2 with periodic boundary conditions in all directions was used to calculate the Coulombic interactions with 0.12 nm of the maximum Fourier spacing and fitting function in the fourth order. A 1.0-nm cutoff was employed for both van del Waals and short-range Coulombic interactions. The neighbor list was updated every 10 steps and the center of mass motion was removed after every step. All bonds were constrained using the linear constraint solver (LINCS) 3 for the DPPC and cholesterol molecules, and the SETTLE algorithm 4 for the water molecules. The temperatures of DPPC, cholesterol, and water were maintained individually at 323 K using the velocity rescaling method 5 with a 0.2 ps coupling constant. The pressure normal and lateral to the bilayer plane were individually maintained at 1 bar using the Berendsen method 6 with a 0.5-ps coupling constant.

Structural parameters of the bilayers
To validate the bilayer structures of the pure DPPC and DPPC/cholesterol bilayers before stretching, we evaluated the typical structural parameters, i.e., area per molecule, bilayer thickness, and the order parameter for the lipid tails. The areas per molecule are 0.656 and 0.391 nm 2 for the pure DPPC and DPPC/cholesterol bilayers, respectively. These are in good agreement with a recent MD simulation study for a DPPC/cholesterol bilayer at 323 K (0.657 and 0.389 nm 2 ) 7 . However, the area per molecule for the DPPC/cholesterol bilayer is slightly smaller than those obtained in experiments for similar lipid mixtures 8,9 , whereas that for the pure DPPC bilayer is in good agreement with those obtained in experiments (summarized by Nagle and Tristram-Nagle 10 ). The bilayer thicknesses are 3.70 and 4.68 nm for the pure DPPC and DPPC/cholesterol bilayers, respectively. As with the area per molecule, the bilayer thicknesses for both bilayers are in good agreement with those obtained in a recent MD simulation study 7 and that for the pure DPPC bilayer is in agreement with experiments for similar lipid bilayers 9 . However, the thickness of the DPPC/cholesterol bilayer is slightly larger than those obtained in experiments with similar lipid mixtures 9 . The averaged order parameter of DPPC tails are 0.16 and 0.38 for the pure DPPC and DPPC/cholesterol bilayers, respectively. These are in good agreement with the recent MD simulation study 7 and in qualitative agreement with experimental measurements 11 . In summary, whereas the structural parameters for the pure DPPC bilayer are in good agreement with those obtained in experiments, those for the DPPC/cholesterol bilayer are slightly different. In particular, the DPPC/cholesterol bilayer in MD simulation tends to be overly condensed, which may be caused by a mismatch in the force field between the DPPC and cholesterol molecules.
Meanwhile, the trends in the bilayer structure changes induced by the inclusion of cholesterol are in agreement with both simulations and experimental studies. In this study, we conclude that the bilayer systems used in this study can represent real bilayers, without departing from the accuracy of the current MD simulation for lipid mixtures.

Detailed results of statistical analyses
In this section, the set of critical areal strains obtained in stretching simulations for a given simulation condition is written as c(, c).  is a bilayer composition parameter, which is 0 for the pure

Overlap of DPPC tails between the upper and lower monolayer
In the interdigitated gel-phase-like structure of the DPPC/cholesterol bilayers under lower speed stretching, the DPPC tails penetrate into the opposite monolayer across the mid-plane of the bilayer, resulting in the overlap of the tails between the upper and lower monolayers ( Fig. 1c and g). We defined the overlap length Dol as Dol = zlowerzupper, where zlower and zupper are the average z-positions of the terminal methyl groups of the DPPC tails in the lower and upper monolayers, respectively. Dol will be positive when the tails are interdigitated and will be negative when the tails do not. Figure S1