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 59-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.

Coupling actin flow, adhesion, and morphology in a computational cell motility model

“…Since actin monomers diffuse rapidly, we will assume that this monomer concentration is uniform. The mass-conserving function f is chosen to be bistable with solutions corresponding to small and large actin concentrations (35,36). Choosing the total actin concentration neither too large nor too small leads to a symmetry broken solution in which one part of the cell has a high actin concentration and the remainder has a small actin concentration.…”

Pattern Formation at Cellular Membranes by Phosphorylation and Dephosphorylation of Proteins

“…We analyze two different mechanisms of pattern formation for protein at membranes: A long wave instability and a bistability-related mechanism, previously described in models of cell polarization [20] and [23] respectively. The conditions of the model to fulfill the requirements for pattern formation are simple and generic:…”

“…Phosphorylation by kinases regulates multiple processes in living cells, e.g. the formation of polarity of cells induced by PAR proteins [19], the cyclic dynamics of Rho GTPases [20] or the regulation of the cell division of E. Coli controlled by the Min proteins [36].…”

“…One possibility is the use of non-flux boundaries in a one-dimensional approach of the cell, see Fig.8(a). This type of models are commonly used for the description of cell polarity [20,23,19,25]. We employ this model for the calculation of the linear stability analysis in Sec.4.1.…”

“…The interactions between these two components, which are highly non-linear, produce a Turing-like instability of the homogeneous solution [20,21,22] or a wave-pinning dynamics due to the frustration under bistable conditions of the wave between both stable solution due to a mass-conservation condition [19,23,24,25].…”