Polarization is a crucial component in cell differentiation, development, and motility and its details are not yet well understood. At the onset of cell locomotion, cells break symmetry to form a well-defined cell front and rear. This polarity establishment varies across cell types: in Dictyostelium discoideum cells, it is mediated by biochemical signaling pathways and can function in the absence of a cytoskeleton, while in keratocytes it is tightly connected to cytoskeletal dynamics and mechanics. Theoretical models that have been developed to understand the onset of polarization have explored either signaling or mechanical pathways, yet few have explored mechanochemical mechanisms. However, many motile cells rely on both signaling modules and actin cytoskeleton to break symmetry and achieve a stable polarized state. We propose a general mechanochemical polarization model based on the coupling between a stochastic model for the segregation of signaling molecules and a simplified mechanical model for actin cytoskeleton network competition. We find that local linear coupling between minimally nonlinear signaling and cytoskeletal systems, separately not supporting stable polarization, yields a robustly polarized cell state.The ability to spontaneously break symmetry is fundamental to most eukaryotic cells and plays an important role in embryogenesis, cell differentiation, cell division, and migration. Intrinsically motile cells can spontaneously switch to a migratory polarized phenotype [47]. Understanding complex molecular circuits employed by a cell to establish polarization has been studied both theoretically [2,19,31,32,36,42] and experimentally [6,45,49,70].Polarity establishment arises primarily through the localization of particular proteins and lipids in the cell to specific regions of the plasma membrane, and often precedes motility. Experiments have identified a few conserved sets of proteins involved in polarization including the PAR system [37, 44], the Wnt system [28], the Scribble complex [3,58], and the Rho system [6,55]. Here, we focus on the Rho molecular circuit whose dynamics can lead to cell polarization at the onset of cell motility. The Rho family of GTPases is a family of small proteins that act as molecular switches [22,55]. Three important members of the family have been studied in detail: Cdc42, Rac1, and RhoA [55]. These proteins cycle between an inactive (GDP) cytosolic and an active (GTP) membrane-bound form that signals to the actin cytoskeleton and other downstream targets. Mutual antagonistic interactions between Rac1 and RhoA were identified, as well as spatial and/or temporal exclusions that produce a tendency for them to segregate to the front versus rear of a polarized cell [6, 7,65,72]. From previous theoretical work, it is well known that mutually inhibitory circuits, like those in Rac1/RhoA, could yield a robustly polarized system [14,29].Cell polarization is also associated with the rearrangement of the actin cytoskeleton during polarization, branched actin filaments form at ...