Calcium Concentration Fluctuations and Subspace Volume Influence Calcium-Regulated Calcium Channel Gating and Subspace Dynamics

Abstract

Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough that local signaling may involve 1-100 calcium ions. Therefore, the question arises: is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of subspace calcium concentration and channel open probability (a result that accounts for the small subspace volume and concentration fluctuations) with the corresponding deterministic model (an approximation that assumes large system size and ignores concentration fluctuations). When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium-binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast, demonstrating that the calcium concentration fluctuations and subspace volume influence channel gating and subspace dynamics. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers [Tadross, Dick, Yue. Cell 133: 1228-40, 2008]. Additional work will consider the influence of slow and rapid buffers present in the subspace and whether and under what conditions these buffers mitigate the effects of concentration fluctuations on channel gating and subspace dynamics.