Towards Sub-cellular Modeling with Delaunay Triangulation

G. Grise^* and M. Meyer-Hermann

Frankfurt Institute for Advanced Studies, Goethe University Ruth-Moufang Strasse 1, 60438 Frankfurt, Germany

^* Corresponding author. E-mail: grise@fias.uni-frankfurt.de

Abstract

In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –, distinguished by specific interaction potentials and, eventually, also by the use of modified interaction criteria. For example, membrane sub-particles may interact only on a two-dimensional surface embedded on three-dimensional space, described via a restricted Delaunay triangulation. The model can be used not only to study cell shape and movement, but also has the potential to investigate the coupling between internal space-resolved movement of molecules and determined cell behaviors.