Effects of Cell Growth on Min-Protein Oscillation in \textit{E. coli}

A coarse-grained model for cell growth via elongation is implemented to study the effects of dynamic cell geometry on the spatio-temporal oscillations of the Min system of proteins in \textit{Escherichia coli}. Using a well studied reaction-diffusion model for the oscillations, numerical solutions of a system of coupled non-linear PDEs are solved with dynamic boundary conditions. The model for elongation correctly captures the behavior of wild-type cells and predicts the emergence of multi-node oscillations in filamentous mutants. Comparisons are made with results of fixed-length calculations for long filamentous cells.