Adaptive Ising Model and Bacterial Chemotactic Receptor Network

We present a so-called adaptive Ising model (AIM) to provide a unifying explanation for sensitivity and perfect adaptation in bacterial chemotactic signalling, based on coupling among receptor dimers. In an AIM, an external field, representing ligand binding, is randomly applied to a fraction of spins, representing the states of the receptor dimers, and there is a delayed negative feedback from the spin value on the local field. This model is solved in an adiabatic approach. If the feedback is slow and weak enough, as indeed in chemotactic signalling, the system evolves through quasi-equilibrium states and the ``magnetization'', representing the signal, always attenuates towards zero and is always sensitive to a subsequent stimulus.