A Mass Conserved Reaction–Diffusion System Captures Properties of Cell Polarity

Cell polarity is a general cellular process that can be seen in various cell types such as migrating neutrophils and Dictyostelium cells. The Rho small GTP(guanosine 5′-tri phosphate)ases have been shown to regulate cell polarity; however, its mechanism of emergence has yet to be clarified. We first developed a reaction–diffusion model of the Rho GTPases, which exhibits switch-like reversible response to a gradient of extracellular signals, exclusive accumulation of Cdc42 and Rac, or RhoA at the maximal or minimal intensity of the signal, respectively, and tracking of changes of a signal gradient by the polarized peak. The previous cell polarity models proposed by Subramanian and Narang show similar behaviors to our Rho GTPase model, despite the difference in molecular networks. This led us to compare these models, and we found that these models commonly share instability and a mass conservation of components. Based on these common properties, we developed conceptual models of a mass conserved reaction–diffusion system with diffusion–driven instability. These conceptual models retained similar behaviors of cell polarity in the Rho GTPase model. Using these models, we numerically and analytically found that multiple polarized peaks are unstable, resulting in a single stable peak (uniqueness of axis), and that sensitivity toward changes of a signal gradient is specifically restricted at the polarized peak (localized sensitivity). Although molecular networks may differ from one cell type to another, the behaviors of cell polarity in migrating cells seem similar, suggesting that there should be a fundamental principle. Thus, we propose that a mass conserved reaction–diffusion system with diffusion-driven instability is one of such principles of cell polarity.: Eukaryotic cells such as neutrophils and Dictyostelium cells respond to temporal and spatial gradients of extracellular signals with directional movements. In a migrating cell, specific molecular events take place at the front and back edges. The spatially distinctive molecular accumulation inside cells is known as cell polarity. Despite numerous experimental and theoretical studies, its mechanism of emergence has yet to be clarified. We first developed a mathematical model of the Rho small GTP(guanosine 5′-tri phosphate)ases that cooperatively regulate cell polarity, and showed that the model generates specific spatial accumulation of the molecules. Based on our Rho GTPases model and other models, we further established a conceptual model, a mass conserved reaction–diffusion system, and showed that diffusion-driven instability and a mass conservation of molecules that have active and inactive states are sufficient for polarity formation. We numerically and analytically found that molecular accumulations at multiple sites are unstable, resulting in a single stable front–back axis, and that sensitivity toward changes of a signal gradient is specifically restricted at the front of a polarized cell. We propose that a mass conserved reaction–diffusion system is one of the fundamental principles of cell polarity.