Robustness of Spontaneous Polarization Through Nonlinear Directional Antagonism Without Global Inhibition

ABSTRACT Life depends on the ability of a single cell to respond to a cue—whether a uniform signal or a gradient—and to polarize along a specific axis. Conventional models explain this behavior through reaction–diffusion instabilities characterized by local activation with nonlinear positive feedback and global inhibition mechanisms. To enhance the global effect, these models often incorporate long‐range transport via cable‐ or tubule‐like cytoskeletal structures as part of the positive feedback mechanism, treating the transport implicitly as a function of surface molecular reactions. However, the formation of these extended cytoskeletal structures may require more time than surface molecular reactions, and reliance on diffusion limits the robustness of conventional models across a wide range of parameters, particularly concerning cell sizes and stimulation strengths. Here, we adopt a reverse approach by treating cytoskeletal structure formation as the primary variable and incorporating nonlinear, orientation‐dependent antagonism among these structures. By assuming that long cytoskeletal structures growing in similar orientations stabilize each other, while those oriented differently tend to destabilize one another, we demonstrate that robust polarization can spontaneously arise over a broad range of parameter values, even in the absence of nonlinear positive feedback and global inhibition.