  Many of the processes that underly neural computation are carried out by ion
channels embedded in the plasma membrane, a two-dimensional liquid that
surrounds all cells. Recent experiments have demonstrated that this membrane is
poised close to a liquid-liquid critical point in the Ising universality class.
Here we use both exact and stochastic techniques on the lattice Ising model to
explore the ramifications of proximity to criticality for proteins that are
allosterically coupled to Ising composition modes. Owing to diverging
generalized susceptibilities, such a protein's activity becomes strongly
influenced by perturbations that influence the two relevant parameters of the
critical point, especially the critical temperature. In addition, the protein's
kinetics acquire a range of time scales from its surrounding membrane,
naturally leading to non-Markovian dynamics.
