Modelling Protein Oscillations in Myxococcus xanthus
DOI:
https://doi.org/10.11145/88Abstract
Spatio-temporal oscillations of proteins in bacterial cells play an importantrole in fundamental biological processes. Motility of the rod-shaped bacterium Myxococcus xanthus is due to two motility systems: an A-motilitysystem and a type-4 pili system [1]. Both motility systems depend on the correct localisation of regulatory proteins at the cell poles which set up apolarity (front-to-back) axis. The oscillatory motion of the individual cel lresults from dynamic inversion of the polarity axis due to a spatio-temporal oscillation of the regulatory proteins between the cell poles. A mathematical framework for a minimal macroscopic model is presented which produces self-sustained oscillations of the protein concentrations. The mathematicalmodel is based on a reaction-diusion system and is independent of external triggers. Necessary conditions on the reaction terms leading to oscillating solutions are derived theoretically. Several possible cases are studied based on dierent rates of interaction between the regulatory proteins. The interaction laws are then chosen according to mathematical analysis to produce dierent spatio-temporal oscillation patterns [2]. The dierent scenarios are numerically tested for robustness against parameter variation. Finally,possible extensions of the model will be addressed.This is joint work with B. A. Schmitt, S. Dahlke, P. Lenz, L. Sgaard-Andersen. This work has been supported by the Centre for Synthetic Microbiologyin Marburg, promoted by the LOEWE Excellence Program ofthe state of Hessen, Germany
References
[1] P. Lenz, L. Sgaard-Andersen, Temporal and spatial oscillations in bac-teria, Nat. Rev. Microbiol. 9 565{577, 2011.
[2] P. Rashkov, B.A. Schmitt, L. Sgaard-Andersen, P. Lenz, S. Dahlke, Amodel of oscillatory protein dynamics in bacteria, Bull. Math. Biol. 742183{2203, 2012.
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