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

Abstract

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.

Self-organization and advective transport in the cell polarity formation for asymmetric cell division

“…In the bistable region, we have two stable states: the anterior-domain state with low ½P m and the posterior-domain state with high ½P m . The property of the bistability with mass conservation can form AP polarity in our model, as the previous studies (Mori et al, 2008;Otsuji et al, 2007;Trong et al, 2014).…”

“…Dawes and Munro (2011) also has shown that cortical flow is not required for the establishment of the AP polarity pattern, but a bistable switch mechanism of PAR proteins are important. Mori et al (2008) and Otsuji et al (2007) have suggested the mathematical structure for cell polarity patten, and showed that the mass-conservation and the bistability in chemical reaction are sufficient, in the absence of the advective transport. Tostevin and Howard (2008) have considered the formation of the anterior-posterior polarity pattern using a model combined with the effect of actomyosin contraction which directly influences a biochemical reaction of polarity proteins, but the effect of advective transport was not supposed into the model.…”

Cell Polarity in Yeast

“…Remarkably, a similar phenomenon occurs in some computational models of positive feedback by local activation (Goryachev & Pokhilko 2008, Otsuji et al 2007). This suggests that both the growth of clusters and their winnowing down to yield a single cluster might be intrinsic to this positive feedback mechanism.…”

A dual role model for active Rac1 in cell migration

“…52 This model belongs to a class of mass-conserved reaction-diffusion models where negative regulation of a component in a reaction system can be traced back to its limited supply. 53 We propose that the regulation of spatiotemporal dynamics of Rac1 activity is governed by a similar mechanism (Fig. 3B).…”