Ca2+Current versus Ca2+Channel Cooperativity of Exocytosis

Recently there has been significant interest and progress in the study of spatiotemporal dynamics of Ca2+that triggers exocytosis at a fast chemical synapse, which requires understanding the contribution of individual calcium channels to the release of a single vesicle. Experimental protocols provide insight into this question by probing the sensitivity of exocytosis to Ca2+influx. While varying extracellular or intracellular Ca2+concentration assesses the intrinsic biochemical Ca2+cooperativity of neurotransmitter release, varying the number of open Ca2+channels using pharmacological channel block or the tail current titration probes the cooperativity between individual Ca2+channels in triggering exocytosis. Despite the wide use of these Ca2+sensitivity measurements, their interpretation often relies on heuristic arguments. Here we provide a detailed analysis of the Ca2+sensitivity measures probed by these experimental protocols, present simple expressions for special cases, and demonstrate the distinction between the Ca2+current cooperativity, defined by the relationship between exocytosis rate and the whole-terminal Ca2+current magnitude, and the underlying Ca2+channel cooperativity, defined as the average number of channels involved in the release of a single vesicle. We find simple algebraic expressions that show that the two are different but linearly related. Further, we use three-dimensional computational modeling of buffered Ca2+diffusion to analyze these distinct Ca2+cooperativity measures, and demonstrate the role of endogenous Ca2+buffers on such measures. We show that buffers can either increase or decrease the Ca2+current cooperativity of exocytosis, depending on their concentration and the single-channel Ca2+current.