Andrea Gamba , Igor Kolokolov, Vladimir Lebedev, Giovanni Ortenzi
    Politecnico di Torino     Landau Institute, Moscow

Abstract

Eukaryotic cells possess an extremely sensible chemical compass allowing them to orient toward sources of soluble chemicals. This property is key to the assembly of complex, multicellular organisms. The extracellular chemical signal triggers separation of the cell membrane into two domains populated by different phospholipid molecules and oriented along the signal anisotropy. We propose a universal description of this polarization pro- cess, based on the theory of phase ordering in first-order phase transitions. This descrip- tion implies the existence of two clearly separated polarization regimes depending on the presence or absence of a gradient in the activation pattern produced by the extracel- lular attractant, and the existence of a sensitivity threshold for the gradient. Simple scaling laws are found: the polarization time $t_\epsilon$ depends on the gradient steepness $\epsilon$ through the power law $t _\epsilon\propto \epsilon^{-2}$, while the smallest detectable gradient scales as $\epsilon_\mathrm{th} \propto R^{-1}$, where $R$ is the size of the cell. Our results are in agreement with existing experimental data.