Spatial signal amplification in cell biology: a lattice-gas model for self-tuned phase ordering

Experiments show that the movement of eukaryotic cells is regulated by a process of phase separation of two competing enzymes on the cell membrane, that effectively amplifies shallow external gradients of chemical attractant. Notably, the cell is able to self-tune the final enzyme concentrations to an equilibrium state of phase coexistence, for a wide range of the average attractant concentration. We propose a simple lattice model in which, together with a short-range attraction between enzymes, a long-range repulsion naturally arises from physical considerations, that easily explains such observed behavior.