Supporting Information: Information processing and signal integration in bacterial quorum sensing

We model receptors using a simple two-state model in which receptors exist in two states: a low kinase activity state we call “off” and a high kinase activity state, we call “on” (Swem et al., 2008; Keymer et al., 2006). Ligands, in our case autoinducers, act by binding to the receptor protein and changing the free energies and therefore the thermal occupancies of the two activity states. There are a total of four free-energy states with corresponding free energies: (i) on without ligand-bound E, (ii) on with ligand-bound E − log ([L]/K), (iii) off without ligand-bound E , and (iv) off with ligand bound E − log ([L]/K). In the absence of ligands, the receptors favor the on state but ligand causes switching to the off state. This implies that K K and that E < E . At equilibrium, the probability that a receptor is in the on state is a function of the difference in free energies between the “on” state and the “off” state: