Calcium Current versus Calcium Cooperativity of Exocytosis

Victor Matveev, Richard Bertram, Arthur Sherman

Recently there has been significant interest and progress in the study of spatio-temporal dynamics of calcium 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 calcium influx. While varying extracellular or intracellular calcium concentration assesses the intrinsic biochemical calcium cooperativity of neurotransmitter release, varying the number of open calcium channels using pharmacological channel block or the tail current titration probes the cooperativity between individual calcium channels in triggering exocytosis. Despite the wide use of these calcium sensitivity measurements, their interpretation often relies on heuristic arguments. Here we provide a detailed analysis of the calcium sensitivity measures probed by these experimental protocols, present simple expressions for special cases, and demonstrate the distinction between the calcium current cooperativity, defined by the relationship between exocytosis rate and the whole-terminal calcium current magnitude, and the underlying calcium 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 3D computational modeling of buffered calcium diffusion to analyze these distinct calcium cooperativity measures, and demonstrate the role of endogenous calcium buffers on such measures. We show that buffers can either increase or decrease the calcium current cooperativity of exocytosis, depending on their concentration and the single-channel calcium current.