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In this paper, we study the dynamics of a localized unimodal pattern in reaction-diffusion systems with mass conservation, which are mathematical models for the polarity formation of cells. Our result provides a quantitatively precise characterization of the motion of the localized unimodal pattern, which suggests that the location of polarity peaks can be determined universally in a site where the maximal extracellular signal is present regardless of the details of the signaling pathways.

Dynamics of Localized Unimodal Patterns in Reaction-Diffusion Systems for Cell Polarization by Extracellular Signaling