Mathematical Modelling of Protein Oscillations in Bacteria

Peter Rashkov
Institute of Mathematics and Informatics – Bulgarian Academy of Sciences
Associate Professor

“Pole-to-pole oscillations of protein concentrations are observed in connection with cell division or movement and mathematical models have been proposed for different types of bacteria. We consider a layout where protein transport in the cytoplasm is driven by diffusion while the main interaction between proteins is restricted to small regions at the two cell poles. We present a general framework for analysing the dynamics of such models. Based on this analysis a minimal model using two proteins is constructed that shows regular oscillations whose robustness is shown for two possible scenarios. The model gives an affirmative answer to the question whether the motility system in mutant strains of Myxococcus xanthus may be driven by dynamics of this kind. We also discuss generalisations for adjusting the model to more detailed experimental observations, involving reaction terms in the cytoplasm and stochastic effects”.