Clusters of calcium release channels harness the Ising phase transition to confine their elementary intracellular signals

Abstract: Intracellular Ca signals represent a universal mechanism of cell function. Messages carried by Ca are local, rapid, and powerful enough to be delivered over the thermal noise. A higher signal to noise ratio is achieved by a cooperative action of Ca release channels such as IP3 receptors or ryanodine receptors arranged in clusters or release units containing a few to several hundred release channels. The release channels synchronize their openings via Ca-induced-Ca-release, generating high-amplitude local Ca signals known as puffs in neurons or sparks in muscle cells. Despite the high release amplitude and positive feedback nature of the activation, Ca signals are strictly confined in time and space by an unexplained termination mechanism. Here we show that the collective transition of release channels from an open to a closed state is identical to the phase transition associated with the reversal of magnetic field in an Ising ferromagnet. We demonstrate this mechanism using numerical model simulations of Ca sparks over a wide range of cluster sizes from 25 to 169 release channels. While prior studies suggested contributions of stochastic attrition and Ca store depletion, our new simple quantitative criterion closely predicts the depletion level required for spark termination for each cluster size. We further formulate exact requirements for a cluster of release channels to follow the Ising model in any cell type. Thus we describe deterministically the behaviour of a system on a coarser scale (release unit) which is random on a finer scale (release channels), bridging the gap between scales. Our results provide the first exact mapping of a nanoscale biological signalling model to an interacting particle system in statistical physics, making the extensive mathematical apparatus available to quantitative biology.