Ca2+ current versus Ca2+ channel cooperativity of exocytosis

Recently there has been significant interest and progress in the study of spatiotemporal dynamics of Ca(2+) 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 Ca(2+) influx. While varying extracellular or intracellular Ca(2+) concentration assesses the intrinsic biochemical Ca(2+) cooperativity of neurotransmitter release, varying the number of open Ca(2+) channels using pharmacological channel block or the tail current titration probes the cooperativity between individual Ca(2+) channels in triggering exocytosis. Despite the wide use of these Ca(2+) sensitivity measurements, their interpretation often relies on heuristic arguments. Here we provide a detailed analysis of the Ca(2+) sensitivity measures probed by these experimental protocols, present simple expressions for special cases, and demonstrate the distinction between the Ca(2+) current cooperativity, defined by the relationship between exocytosis rate and the whole-terminal Ca(2+) current magnitude, and the underlying Ca(2+) 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 Ca(2+) diffusion to analyze these distinct Ca(2+) cooperativity measures, and demonstrate the role of endogenous Ca(2+) buffers on such measures. We show that buffers can either increase or decrease the Ca(2+) current cooperativity of exocytosis, depending on their concentration and the single-channel Ca(2+) current.