Topology-based Geometric Modelling for Biological Cellular Processes
Mathieu Poudret, Jean‐Paul Comet, Pascale Le Gall, Mathieu Poudret, Jean-paul Comet, Pascale Le Gall, Mathieu Poudret, Jean-paul Comet, Pascale Le Gall · 2007
Abstract. In this paper, we present a framework to simulate biological cellular processes involving a strong topological and geometric struc-turation. Our framework is based on topology-based geometric mod-elling. The edge labels of a graph sub-class, the n-dimensional general-ized maps, model the neighbouring relations between biological compart-ments. Thus, membranes become topological objects of the n-dimensional generalized maps representation and can be handled just as compart-ments. The evolutions of the underlying topology during the simulation are expressed by using graph transformation rules. These rules are con-ditioned by geometric properties and molecular concentrations bound to the vertices of the graph. A simplified example, inspired by the phe-nomenon of gap junctions, illustrates how topological and geometric pa-rameters are involved in the simulation of biological cellular processes controlled by the concentrations of molecules in the compartments. Key words: topology-based geometric modelling, graph transforma-tion, generalized map, simulation of biological processes