Using Statistical Mechanics to Understand Calcium Sparks

Abstract

The crucial importance of local Ca signaling for regulation of cardiac muscle contraction was theoretically predicted in 1992 as part of local control theory and validated by the experimental discovery of Ca sparks. Sparks are generated by release channel clusters in the form of localized Ca releases from junctional sarcoplasmic reticulum (SR). As release channels interact, the spark is an emergent behavior of the collective, rather than a property of an individual channel. This nanoscale system of interacting molecules which generates elementary biological signals is particularly interesting because this is where physics meets biology. We have constructed an exact mapping of the release channel cluster to a famous model of an interacting particle system in statistical physics, namely the Ising model. We demonstrated that the channel synchronization that corresponds to termination of signals is described by the same equation as the phase transition associated to the change of magnetic field in an Ising ferromagnet. Our Ising-based theory predicts the critical level of SR [Ca] that is required for spark termination. If the SR depletion does not reach this level the spark does not terminate and becomes metastable. The prediction was confirmed by numerical simulations using 2013 Stern et al. spark model. In an ongoing work, we explore the fine structure of calcium sparks using Peierl's contour analysis to investigate the famous Onsager's phase transition to describe the transition from ordered to disordered sparks as a function of β (effective inverse temperature). The disordered sparks were manifested in numerical simulations by the presence of Ca embers, i.e. small clusters of opened channels. In summary, we describe deterministically the behavior of a system on a coarser scale (release unit) that is random on a finer scale (release channels), bridging the gap between scales.