Effect of spatial heterogeneities on minimal stochastic models of cell polarity
Asymmetric self-organization is a hallmark of cell polarity, yet the diversity of observed polarization patterns is frequently attributed to specialized, complex biochemical mechanisms motifs beyond simple positive feedback. Here, we demonstrate that spatial heterogeneity alone fundamentally reshapes polarization dynamics within minimal stochastic reaction-diffusion processes. We show that weak differences in reaction rates between distinct spatial domains strongly bias polarization timing and determine which region ultimately polarizes. In systems containing two distant favored regions, a "stochastic winner-takes-all" mechanism--driven by long-range competition mediated by a shared cytoplasmic pool--induces stochastic switching that manifests as pole-to-pole oscillations. By relaxing the assumption of a perfectly mixed cytoplasm and incorporating finite cytoplasmic diffusion, we reveal a qualitative shift in this competitive dynamic. Specifically, as the total particle abundance increases, the system transitions from monopolar to bipolar activation, capturing the essence of the New-End Take-Off (NETO) phenomenon during cell growth and provides a physical basis for pole coexistence. These results demonstrate that spatial heterogeneity alone can strongly influence polarization dynamics in minimal models, highlighting the potential importance of quenched spatial variability in biological reaction-diffusion systems. Author summaryCells often need to choose a specific site for growth, division, or shape change. This process, known as cell polarization, is a fundamental organizing principle in biology. The wide variety of polarization patterns seen in living cells is often explained by proposing complex biochemical mechanisms beyond basic positive feedback among signaling molecules. In this work, we asked whether some of this diversity could instead arise from a simpler source: fixed spatial differences within the cell. Using minimal stochastic reaction-diffusion models, we found that even small local differences can strongly influence where polarization appears and how quickly it develops. When two favored sites are present, they can compete for a shared pool of molecules in cytoplasm, so that one site dominates at a time and the polarized state can switch stochastically between them. We also found that this competition changes when the shared molecular pool does not mix instantly: under these conditions, two polarized sites can start to coexist. This behavior offers a simple physical explanation for phenomena such as the appearance of a new growth site during cell development. Our results show that spatial heterogeneity alone can generate behaviors that might otherwise seem to require much more complicated biochemical mechanisms.