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 Ca ²⁺ concentration assesses the intrinsic biochemical Ca²⁺ 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 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 Ca ²⁺ 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 Ca ²⁺ current cooperativity of exocytosis, depending on their concentration and the single-channel Ca²⁺ current.