Molecular Dynamics Simulations

Molecular Dynamic Simulations were used to study the interaction between the M2 AH peptide and a buckled membrane. Coarse-grained simulations and the analysis protocol for simulating curvature sensing by single peptides was performed as previously described (Gómez-Llobregat et al. 2016) by collaborators, Dr Jordi Gómez-Llobregat and Dr Martin Lindén at Stockholm University using the Swedish National Infrastructure for Computing at the National Supercomputer Centre.

2.2.6.1 Simulation parameters

Coarse-grained simulations were performed using GROMACS 4.6.1 (Pronk et al. 2013) and the MARTINI force-field (version 2.P) with polarizable water (Kawaoka and Neumann 2012, Kikuchi et al. 2012, Neumann et al. 2012), and a relative dielectric constant of 2.5 (Kawaoka and Neumann 2012). Standard parameters were used for lipids POPC and POPG (Nidom et al. 2012, Victor et al. 2012) and for peptides (Murakami et al. 2012). The M2AH peptide structure was obtained from PDB 2L0J (Sharma et al. 2010), and was coarse-grained with the martinize script provided by the MARTINI developers. Constant temperature was maintained with the velocity rescaling thermostat (Kawai et al. 2012) with a 1.0 ps time constant, and pressure was controlled with the Berendsen barostat (Shi et al. 2012) using a time constant of 12 ps and a compressibility of 3 x10-4 bar-1. Peptide (when present), lipids and solvent were coupled separately to the temperature bath. Coulomb interactions were modelled with the particle mesh Ewald method (Noda et al. 2012) setting the real-space cut to 1.4 nm and the Fourier grid spacing to 0.12 nm. Lennard-Jones interactions were shifted to zero between 0.9 and 1.2 nm. A time step of 25 fs was used in all simulations.

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2.2.6.2 Lipid bilayer equilibration

First two coarse-grained symmetric lipid bilayers twice as large than wide (Lx = 2Ly)

were built, consisting of 1024 lipids, one with a 4:1 molar ratio of POPC:POPG and another with POPC-only. The systems were solvated with ≈ β1,β50 coarse-grained water beads and neutralised with sodium and chloride ion beads. The bilayer systems were then equilibrated for 25 ns in an NPT ensemble at 300 K and 1 bar, with pressure coupling applied semi-isotropically.

2.2.6.3 Membrane buckling and peptide addition

After equilibration, both systems were laterally compressed in the x direction by a factor = (L-LX)/L = 0.2, where L is the linear size of the flat system in the x direction,

and LX the size of the simulation box in the x direction. This was done by scaling all

x-coordinates, and the system size LX, by a factor 1- = 0.8 at the end of the

equilibration run, yielding LX = 21.03 and 20.93 nm for the mixed and pure membrane

patches, respectively. After rescaling, the compressibilities were set to 0 in the x and y directions to keep the system size constant in those directions for subsequent simulations. Pressure coupling was then applied anisotropically in the z direction only. An energy minimisation and a short equilibration run (25 ns) was then performed to let the bilayer buckle. Next the M2 AH peptide was added to each system. The peptide was initially placed 3 nm above the membrane surface, but quickly attached to the membrane-water interface. After the binding event, the system was equilibrated for another 5 s before starting a production run of 35 s, where the data was collected every 5 ns.

2.2.6.4 Membrane alignment and peptide tracking

The buckled membrane profile diffuses during the simulation, but curvature sensing by the M2AH peptide is reflected in its distribution relative to the buckled shape, and the buckled configurations must therefore be aligned in order to extract useful information. Previous protocol (Gómez-Llobregat et al. 2016) was used to fit the xz profile of the membrane by the ground state of the Helfrich model with periodic boundary conditions, which is one of the Euler buckling profiles of an elastic beam

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(Shinya et al. 2012, Hu et al. 2013). This shape depends only on the dimensionless buckling parameter , where = 0 is the flat state. Thus, if one period of the buckling profile for LX = 1 is given by a parameter curve x = s +  (s, ), z =  (s, ), 0 < s < 1,

the general case LX ≠1 can be obtained by shifting and scaling. For fast evaluation, (s, ) and  (s, ) were expanded in truncated Fourier series in s, and created look-up tables for Fourier coefficients versus . The arc-length coordinate s was scaled to have period one independent of the overall system size, and defined such that the curve z(x) has a maximum at s = 0.5, minima at s = 0, 1, and inflection points at s = 0.5 ± 0.25. The buckled shapes were aligned by fitting the bilayer in each frame to the buckling profile and aligning the inflection points. Specifically, the buckling profile was fit to the innermost tail beads of all lipids in each frame using least-squares in the x and z directions, i.e., minimising

with respect to , the translations x0, z0, and the projected arc-length coordinates si of

each bead (xi, zi are bead positions). The arclength position s of the peptide was

computed by projecting the peptide centre of mass onto the buckled profile fitted to the membrane midplane in every frame (Fig. 3.3-19 B). The in-plane orientation was computed by fitting a line through the backbone particles of the alpha-helical part of the peptide and projecting this line to the tangent plane defined by the tangent vector t and the y unit vector, taking to be the angle between the projected line and the tangent vector, in the tangent plane. Variations in the buckling parameter (std[ ] ≈ 0.005) reflect small shape and area fluctuations, that was neglected by using the average buckling parameter values for curvature analysis, [ ] = 0.β16 and [ ] = 0.ββ5 for the POPC:POPG and pure POPC systems, respectively. The local curvature, shown in Figure 3.3-19 D, is then given by C(s)=(1−[ ])/Lx d /ds, where is the tangent

angle in Figure 3.3-19 B (also computed using average compression factors). Molecular graphics were generated using Visual Molecular Dynamics (VMD) (Langel et al. 2008).

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