A Bistable Model of Cell Polarity

Abstract

Ultrasensitivity, as described by Goldbeter and Koshland, has been considered for a long time as a way to realize bistable switches in biological systems. It is not as well recognized that when ultrasensitivity and reinforcing feedback loops are present in a spatially distributed system such as the cell plasmamembrane, they may induce bistability and spatial separation of the system into distinct signaling phases. Here we suggest that bistability of ultrasensitive signaling pathways in a diffusive environment provides a basic mechanism to realize cell membrane polarity. Cell membrane polarization is a fundamental process implicated in several basic biological phenomena, such as differentiation, proliferation, migration and morphogenesis of unicellular and multicellular organisms. We describe a simple, solvable model of cell membrane polarization based on the coupling of membrane diffusion with bistable enzymatic dynamics. The model can reproduce a broad range of symmetry-breaking events, such as those observed in eukaryotic directional sensing, the apico-basal polarization of epithelium cells, the polarization of budding and mating yeast, and the formation of Ras nanoclusters in several cell types.

Beyond symmetry-breaking: competition and negative feedback in GTPase regulation

“…The number of domains generated by Turing models depends on the size of the cell: small cells generate only one domain (if the cell is smaller than the characteristic spacing between domains), while larger cells generate more [14]. However, other computational models predict that there will be a “winner-takes-all” competition between GTPase clusters no matter how large the cell [16, 17]. A key feature of such models is that larger clusters have a competitive advantage in recruiting and retaining cytoplasmic polarity factors (like the GEF-effector complexes in yeast), so that the largest cluster wins.…”

Motif for controllable toggle switch in gene regulatory networks

“…Bistability has been shown in many studies to be caused by a positive feedback loop composed of two genes (nodes) with a double negative feedback loop (DNFL) [29][30][31][32][33]. A set of ordinary differential equations has been widely used for describing genomic regulation [28,34,35], this approach adopts an 'OR' gate between all repressive and active regulations.…”

Robust polarity establishment occurs via an endocytosis-based cortical corralling mechanism

“…However, when a Cdc42 diffusion rate of 0.036 µm 2 s 1 is incorporated, as has been measured in vivo, Turing-based models predict significant loss of polarity (Goryachev and Pokhilko, 2008;Howell et al, 2009;Savage et al, 2012). Without excluding the possibility that a Turing-based mechanism may contribute to polarity establishment, we present here an alternative regimen of the same autoamplification module where polarity emerges from a multistable reaction network (M&M; Semplice et al, 2012). The autoamplification module stimulates exocytosis in two ways.…”

“…However, the analysis of the biochemical reaction network described in the previous section revealed the potential for an alternative mechanism for spontaneous symmetry breaking. This mechanism is based on multistability, the existence of multiple stable uniform steady-states (Semplice et al, 2012). In the (uniform) steady-state, the system of equations for Cdc42 autoamplification reduces to the following: Table 1), the system shows multiple solutions.…”