The MemCurv software package contains three python programs used to describe membrane shapes and quantify their curvature properties from MD simulations using the coarse-grained MARTINI model. The individual python programs

1. Compute Mean (Constant) curvature of the discontinuous membrane system by fitting membrane shape to spherical surfaces.
2. 1. Fit shape profiles of curved or buckled membranes under periodic boundary conditions to obtain optimized Fourier representation of the curved surface.
   2. Compute local curvature properties of protein inclusions in curved or buckled membranes from optimized height profiles.

For a detailed description of the procedures and the algorithm, we refer to [Bhaskara et al, 2019].

This software contains two Python packages:

• "Fit_bicelle_sph_cap.py" provides algorithm for description of shape changes of a discontinuous membrane patch. For.e.g. bicelle-to-vesicle conversion by patch-closure. The program uses least square fits for curved membrane-patches to spherical cup/cap shaped surfaces, to compute the constant mean curvature.

• "Get_mem_profile_hcf_abcd.py" and "Cal_local_curv_props_abcd.py" are part of a combined package which provide algorithms for description of curved membrane surfaces under periodic boundary conditions. They can be used independently with a trajectory of curved membrane to quantify the membrane shapes and to compute local curvature properties of protein inclusion.

Please, if you have an issue with the software, open an issue here on the git-hub repository https://github.com/bio-phys/MemCurv/issues .

• Python 2.7
• Python packages: numpy, scipy, MDAnalysis, pandas

No installation required. Directly run the Python programs if the dependencies are installed before.

1. Example input files from MD simulations of a discontinuous membrane system using MARTINI force-field, for e.g. bicelle/bilayer patches (GROMACS formatted .gro and .xtc).

• fam_bicelle.gro, a configuration file containing FAM134B embedded in bicelle (DMPC+DHPC)
• fam_bicelle.xtc, a processed GROMACS trajectory of the bicelle.

python Fit_bicelle_sph_cap.py

The output file contains

2. Example input files from MD simulations of a curved membrane under periodic boundary conditions using MARTINI force-field (GROMACS formatted .gro and .xtc).

• fam_buckle.gro, a configuration file of the curved bilayer with protein (FAM134B) inclusion.
• fam_buckle_100ns.xtc, a processed GROMACS trajectory of the curved membrane simulation.

python Get_mem_profile_hcf_abcd.py
python Cal_local_curv_props_abcd.py

Depending on membrane composition, the selection of atom type constituting the mid-plane of the bilayer needs to be selected.

In curvature computations, If protein coordinates is provided, the local curvature is computed at the centre of mass of the protein atoms.

Three output files are generated with default names.

"Fit_bicelle_sph_cap.py" generates an output file "bicelle_curv_ts.dat" which contains the following tab delimited data.

"Get_mem_profile_hcf_abcd.py" generates an output file "popf_1ns_k3_abcd_fam_buckled.dat" which contains optimized height coefficients describing the membrane shape profile.

"Cal_local_curv_props_abcd.py" generates an output file "fam_1ns_abcd_k3_curv_props.dat" which contains the local curvature properties of the sampled protein curvatures (tab delimited file).

Q: How is the sign of the bicelle curvature decided?

A: Lipid flip-flop at the open edge merges the two leaflets. Therefore, we use the identity as defined in the start frame (by lipid assignment). If more than 50 % of upper leaflet lipids remain above the fitted spherical surface of the membrane-patch, then the curvature is positive, else it is negative.

Q: My curvature values are negative instead of positive. What is going on?

A: In the Monge representation, using a height function, such that z=h(x,y) and positive, to represent the membrane shape, the default curvature values represent the curvature along the lower leaflet and its inverse represent curvature along the upper leaflet. To compute curvatures along upper leaflet, as in the manuscript (Bhaskara et al, 2019), we multiply the Shape operator with -1 (S = -1*S).