Robust and resource-optimal dynamic pattern formation of Min proteins in vivo

The Min system in Escherichia coli plays a crucial role in cellular reproduction by preventing minicell formation through pole-to-pole oscillations. Despite extensive research, the predicting the onset of Min protein concentrations required at the onset of for oscillation are unknown and understanding the system's robustness under physiological perturbations remains challenging. Our study aims to address these gaps. We show that the Min system's dynamic pattern formation is robust across a wide range of Min protein levels and varying growth physiology. Using genetically engineered E. coli strains, we independently modulated the expression of minCD and minE in E. coli under both fast and slow growth conditions. This led to the construction of a MinD-MinE phase diagram, which revealed not just a large oscillation regime but also complex dynamic patterns such as traveling and standing waves. Interestingly, we found that the natural expression level of Min proteins is both robust to changes in protein concentration and resource-optimalnearly optimal. Our work combines experimental findings with biophysical theory based on reaction-diffusion models, reproducing the experimental phase diagram and other key quantitative properties quantitatively. This includes the observation of an invariant wavelength of dynamic Min patterns across our phase diagram. Crucially, the success of the our model depends on the switching of MinE between its latent and active states, indicating its essential role as a robustness module for Min oscillation in vivo. Our results underline the potential of integrating quantitative cell physiology and biophysical modeling in understanding the fundamental mechanisms controlling cell division machinery, offering insights applicable to other biological processes.