title: A model for spatio-temporal dynamics in a regulatory network for cell polarity.
abstract: Cell polarity in Myxococcus xanthus is crucial for the directed motility of individual cells. The polarity system is characterised by a dynamic spatio-temporal localisation of the regulatory proteins MglA and MglB at opposite cell poles. In response to signalling by the Frz chemosensory system, MglA and MglB are released from the poles and then rebind at the opposite poles. Thus, over time MglA and MglB oscillate irregularly between the poles in synchrony but out of phase. A minimal macroscopic model of the Mgl/Frz regulatory system based on a reaction-diffusion PDE system is presented. Mathematical analysis of the steady states derives conditions on the reaction terms for formation of dynamic localisation patterns of the regulatory proteins under different biologically-relevant regimes, i.e. with and without Frz signalling. Numerical simulations of the model system produce either a stationary pattern in time (fixed polarity), periodic solutions in time (oscillating polarity), or excitable behaviour (irregular switching of polarity).
authors.affiliation: Department of Mathematics and Informatics, Philipps-Universität Marburg, Hans-Meerwein-Str., 35032 Marburg, Germany. Electronic address: rashkov@mathematik.uni-marburg.de.
authors.forename: Peter
authors.initials: P
authors.lastname: Rashkov
authors.affiliation: Department of Mathematics and Informatics, Philipps-Universität Marburg, Hans-Meerwein-Str., 35032 Marburg, Germany.
authors.forename: Bernhard A
authors.initials: BA
authors.lastname: Schmitt
authors.affiliation: Max Planck Institute for Terrestrial Microbiology, Karl-von-Frisch-Str. 10, 35043 Marburg, Germany.
authors.forename: Daniela
authors.initials: D
authors.lastname: Keilberg
authors.forename: Kristof
authors.initials: K
authors.lastname: Beck
authors.affiliation: Max Planck Institute for Terrestrial Microbiology, Karl-von-Frisch-Str. 10, 35043 Marburg, Germany.
authors.forename: Lotte
authors.initials: L
authors.lastname: Søgaard-Andersen
authors.affiliation: Department of Mathematics and Informatics, Philipps-Universität Marburg, Hans-Meerwein-Str., 35032 Marburg, Germany.
authors.forename: Stephan
authors.initials: S
authors.lastname: Dahlke
mesh_terms: D001426:Bacterial Proteins / Q000378:metabolism*; D016764:Cell Polarity / Q000502:physiology*; D008954:Models, Biological; D016941:Myxococcus xanthus / Q000378:metabolism*
chemical_list: D001426:Bacterial Proteins
keywords: Biological modelling; Dynamical systems; Excitable system; Oscillatory behaviour; Protein dynamics; Regulatory network