OrganL: Dynamic Triangulation of Biomembranes using Curved Elements

We describe a method for simulating biomembranes of arbitrary shape. In contrast to other dynamically triangulated surface (DTS) algorithms, our method provides a rich, quasi tangent-continuous, yet local description of the surface. We use curved Nagata triangles, which we generalize to cubic order to achieve the requisite flexibility. The resulting interpolation can be constructed locally without iterations. This allows us to provide a parallelized and fine-tuned Monte Carlo implementation. As a first example of the potential benefits of the enhanced description, our method supports inhomogeneous lipid properties as well as lipid mixing. It also supports restraints and constraints of various types and is constructed to be as easily extensible as possible. We validate the approach by testing its numerical accuracy, followed by reproducing the known Helfrich solutions for shapes with rotational symmetry. Finally, we present some example applications, including curvature-driven demixing and stylized effects of proteins. Input files for these examples, as well as the implementation itself, are freely available for researchers under the name OrganL. Our method provides a straightforward way to simulate any biomembrane geometry. It overcomes some of the limitations of previous dynamically triangulated surface (DTS) Monte Carlo schemes by providing a surface that contains an interpolant which allows to assign meaningful functions of curvature to almost every point of the discretization, yet keeps much of the simplicity of the common DTS schemes by not requiring any nonlocal information or iterations for its construction. Our tool is easily extensible and facilitates the simulation of complex lipid and protein compositions on membrane surfaces at any scale. ### Competing Interest Statement The authors have declared no competing interest.