The mechanisms and design principles of regulatory systems establishing stable polarized protein patterns within cells are well studied. However, cells can also dynamically control their cell polarity.Here, we ask how an upstream signaling system can switch the orientation of a polarized pattern.We use a mathematical model of a core polarity system based on three proteins as the basis to study different mechanisms of signal-induced polarity switching. The analysis of this model reveals four general classes of switching mechanisms with qualitatively distinct behaviors: the transient oscillator switch, the reset switch, the prime-release switch, and the push switch. Each of these regulatory mechanisms effectively implements the function of a spatial toggle switch, however with different characteristics in their nonlinear and stochastic dynamics. We identify these characteristics and also discuss experimental signatures of each type of switching mechanism.1 Cell polarity is manifested in molecular and morphological asymmetries of the cell. From bacterial to mammalian cells, cell polarity is essential in a multitude of functional contexts, including cell migration, cell division and differentiation, cell-cell signaling, development and tissue homeostasis [1,2]. One fundamental question related to cell polarity is how an initially symmetrical cell can establish a polarized state and subsequently maintain it [3].However, cells are also known to dynamically change their polarity, e.g. reversing polarity in response to external or internal signals to control motility [4][5][6]. This raises a second fundamental question: Which mechanisms permit reliable switching of cell polarity?The first question, about establishing and maintaining cell polarity, is well studied, both on the conceptual level with theoretical approaches and on the experimental level by characterizing model systems. The polarization of an initially nonpolarized cell is a symmetry breaking phenomenon: In the case of essentially isotropic cells, e.g. budding yeast or epithelial cells [3], the continuous angular symmetry is broken by polarization, whereas discrete symmetry breaking occurs for rod-shaped bacterial cells [7]. Symmetry breaking can occur spontaneously [8], but is often controlled by upstream guiding cues [9]. While the detailed molecular mechanisms underlying cell polarization differ between organisms, they often incorporate conserved G-protein based signaling systems that use multiple feedback interactions to generate asymmetric distributions on the cell membrane via a Turing instability [10]. A class of simple networks that can achieve cell polarization was explored in a synthetic biology study [11], which first showed computationally that all such networks feature one or more of the three minimal motifs 'positive feedback', 'mutual inhibition', or 'inhibition with positive feedback', and that combinations of these motifs generally polarize more reliably. The study also corroborated the latter finding experimentally, recapitulating the basic ...