Spatial Modeling of IP3 Channel Clusters and Calcium Puffs

Abstract

Using detailed numerical analysis as well as strongly reduced models we study release of calcium from clusters of IP3 receptor channels. In the first part we present hybrid stochastic-deterministic simulations of release from a cluster of nine channels. We adopt recent advances in imaging of calcium release, which showed a considerable spatial separation of channels. We find that, due to the separation of channels and the three-dimensional transport of calcium away from the source area, the calcium concentration is generally heterogeneous in the cluster area. Based on a Markovian description of channel gating and a fitting of ligand/channel reactions to single-channel data, we obtain puffs that strongly resemble recent recordings in neuroblastoma cells. We conclude that spatial heterogeneity is crucial part of the understanding of puffs. In a second part of this work we take up the issue of deriving a reduced model in terms of a discrete or continuous description of gating variables. We argue that lack of homogeneity in [Ca2+] obtained in the detailed simulations obliterates the assumption of mixing of reactants (here ligands and channels) and thus the validity of the law of mass action. Effective reaction kinetics can be derived, however, by distinguishing concentrations of self-feedback of channels and coupling to different channels, thus eliminating detailed balance. We infer a minimal Markovian model as well as a corresponding Langevin model. Importantly, only the Markovian description reproduces calcium puffs, while a Langevin model wrongly predicts a stationary regime of high inhibition. The analysis of the Markovian model allows further insight into the functioning of calcium puffs.