Interplay between the Localization and Kinetics of Phosphorylation in Flagellar Pole Development of the Bacterium <em>Caulobacter crescentus</em>

<div><p>Bacterial cells maintain sophisticated levels of intracellular organization that allow for signal amplification, response to stimuli, cell division, and many other critical processes. The mechanisms underlying localization and their contribution to fitness have been difficult to uncover, due to the often challenging task of creating mutants with systematically perturbed localization but normal enzymatic activity, and the lack of quantitative models through which to interpret subtle phenotypic changes. Focusing on the model bacterium <em>Caulobacter crescentus</em>, which generates two different types of daughter cells from an underlying asymmetric distribution of protein phosphorylation, we use mathematical modeling to investigate the contribution of the localization of histidine kinases to the establishment of cellular asymmetry and subsequent developmental outcomes. We use existing mutant phenotypes and fluorescence data to parameterize a reaction-diffusion model of the kinases PleC and DivJ and their cognate response regulator DivK. We then present a systematic computational analysis of the effects of changes in protein localization and abundance to determine whether PleC localization is required for correct developmental timing in <em>Caulobacter</em>. Our model predicts the developmental phenotypes of several localization mutants, and suggests that a novel strain with co-localization of PleC and DivJ could provide quantitative insight into the signaling threshold required for flagellar pole development. Our analysis indicates that normal development can be maintained through a wide range of localization phenotypes, and that developmental defects due to changes in PleC localization can be rescued by increased PleC expression. We also show that the system is remarkably robust to perturbation of the kinetic parameters, and while the localization of either PleC or DivJ is required for asymmetric development, the delocalization of one of these two components does not prevent flagellar pole development. We further find that allosteric regulation of PleC observed <em>in vitro</em> does not affect the predicted <em>in vivo</em> developmental phenotypes. Taken together, our model suggests that cells can tolerate perturbations to localization phenotypes, whose evolutionary origins may be connected with reducing protein expression or with decoupling pre- and post-division phenotypes.</p>