We evaluate different mechanisms for spatial domain formation of guanosine triphosphatases (GTPases) on cellular membranes. A kinetic model of the basic guanine-nucleotide cycle common to all GTPases is developed and coupled along a one-dimensional axis by diffusion of inactive and activated GTPases. We ask whether a parameter set exists such that domain formation is possible by Turing’s mechanism, i.e., purely by reactions and diffusion, and show that the Turing instability does not occur in this model for any parameter combination. But, as revealed by stability and bifurcation analysis, domain formation is reproduced after augmenting the model with combinations of two spatial interaction mechanisms: 1. attraction and 2. adhesion among active GTPases. These interactions can be mediated by effector proteins that bind active GTPases, and the model therefore predicts domains to disintegrate if effector binding is inhibited.
|Title of host publication
|Mathematical Modeling of Biological Systems
|Andreas Deutsch, Lutz Brusch, Helen Byrne, Gerda de Vries, Hanspeter Herzel
|Place of Publication
|Number of pages
|Published - 2006
|Modeling and Simulation in Science, Engineering and Technology (MSSET)