Membrane Interfacial Potential Governs Surface Condensation and Fibrillation of α-Synuclein in Neurons

Model to study surface condensation of 𝛼-synuclein on a lipid bilayer. The membrane is composed of two kinds of lipids (DOPC and DOPS) and is represented via a 2D Ising model (lipid-lipid interaction Jm). 𝛼-synuclein proteins are represented using a 3D lattice-gas model (protein-protein interaction Jp). The proteins interact with the membrane via tethers (protein-tether interaction Jt) The custom code was written in Julia (Version 1.10.9) and executed on a standard desktop (32 GB RAM, 12th Gen Intel(R) Core(TM) i7-12700) running Debian 12.11. It was also tested on a Lenovo laptop with 32 GB RAM and Intel(R) Core(TM) Ultra 9 185H processor, with Ubuntu 22.04.5 LTS operating system. To run the code, just save the .jl file to a machine with Julia installed (https://julialang.org/install/). Specify the parameters and either run output = main() in the REPL, or include a line to save the output data in a preferred format and analyse later. For Julia code, JLD is a recommended format. The output gives the state of the system: particle and tether positions, and the membrane states. The excess density is computed from this, as mentioned in the manuscript. On a standard desktop as mentioned above, a typical run for the lattice sizes and parameters mentioned in the manuscript takes around 2-3hours.