Mathematical Model of the Cell Cycle Control and Asymmetry Development in Caulobacter crescentus

Caulobacter crescentus goes through a classic dimorphic cell division cycle to adapt to the stringent environment and reduce intraspecific competition. Caulobacter mother cell gives rise to two progenies with distinct morphology - a motile swarmer cell equipped with a flagellum and a sessile stalked cell equipped with a stalk. Because of the nature of dimorphic lifestyle, Caulobacter becomes a model bacterium to study the cell differentiation, signalling transduction, stress response, and asymmetry development of prokaryotes. The dimorphic cell cycle of Caulobacter is driven by the elaborate spatiotemporal organization of regulatory molecules through regulations of synthesis, degradation, phosphorelay, and localization. There is a wealth of experimental observations about gene/protein interactions and localizations accumulated in recent decades, while several mathematical models have been proposed to study the cell cycle progression in Caulobacter. However, the specific control mechanisms of stress response and spatial asymmetry establishment are yet clearly elucidated, while these mechanisms are of fundamental importance to understanding the bacterial survival strategy and developing the microbial industry.

Here we utilize mathematical modeling to study the regulatory network of cell cycle control in C. crescentus, focusing on the stress response and asymmetry development. First, we investigate the starvation response of Caulobacter through the connection of phosphotransferase systems (PTS) and guanine nucleotide-based second messenger system. We have developed a mathematical model to capture the temporal dynamics of vital regulatory second messengers, c-di-GMP (cdG) and guanosine pentaphosphate or tetraphosphate (pppGpp or ppGpp), under normal and stressful conditions. This research suggests that the RelA-SpoT homolog enzymes have the potential to effectively influence the cell cycle in response to nutrition changes by regulating cdG and (p)ppGpp levels. We further integrate the second messenger network into a temporal cell cycle model to investigate molecular mechanisms underlying responses of Caulobacter to nutrition starvation. Our model suggests that the cdG-relevant starvation signal is essential but not sufficient to robustly arrest the cell cycle of Caulobacter. We also demonstrate that there may be unknown pathway(s) reducing CtrA under starvation conditions, which results in delayed cytokinesis in starved stalked cells.

The cell cycle development of Caulobacter is determined by the periodical activation and deactivation of the master regulator CtrA. cdG is an essential component of the ClpXP pro- tease complex, which is specifically responsible for the degradation of CtrA. We propose a mathematical model for the hierarchical assembly of ClpXP complexes, together with modeling DNA replication, transcription, and protein interactions, to characterize the Caulobacter cell cycle. Our model suggests that the ClpXP-based proteolysis system contributes to the timing and robustness of the cell cycle progression.

Furthermore, we construct a spatiotemporal model with Turing-pattern mechanism to study the morphogenesis and asymmetry establishment during the cell cycle of Caulobacter. We apply reaction-diffusion equations to capture the spatial dynamics of scaffolding proteins PodJ, PopZ, and SpmX, which organize two distinct poles of Caulobacter. The spatial regulations influence the activity and distribution of key cell cycle regulators, governing the dimorphic lifestyle of Caulobacter. Our model captures major spatiotemporal experimental observations of wild-type and mutant cells. It provides predictions of novel mutant strains and explains the spatial regulatory mechanisms of bacterial cell cycle progression.