Explicit Theoretical Analysis of How the Rate of Exocytosis Depends on Local Control by Ca²⁺ Channels

Hormones and neurotransmitters are released from cells by calcium-regulated exocytosis, and local coupling between Ca²⁺ channels (CaVs) and secretory granules is a key factor determining the exocytosis rate. Here, we devise a methodology based on Markov chain models that allows us to obtain analytic results for the expected rate. First, we analyze the property of the secretory complex obtained by coupling a single granule with one CaV. Then, we extend our results to a more general case where the granule is coupled with n CaVs. We investigate how the exocytosis rate is affected by varying the location of granules and CaVs. Moreover, we assume that the single granule can form complexes with inactivating or non-inactivating CaVs. We find that increasing the number of CaVs coupled with the granule determines a much higher rise of the exocytosis rate that, in case of inactivating CaVs, is more pronounced when the granule is close to CaVs, while, surprisingly, in case of non-inactivating CaVs, the highest relative increase in rate is obtained when the granule is far from the CaVs. Finally, we exploit the devised model to investigate the relation between exocytosis and calcium influx. We find that the quantities are typically linearly related, as observed experimentally. For the case of inactivating CaVs, our simulations show a change of the linear relation due to near-complete inactivation of CaVs.