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The Journal of Neuroscience, September 30, 2009, 29(39):12196-12209; doi:10.1523/JNEUROSCI.0263-09.2009

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Cellular/Molecular
Ca²⁺ Current versus Ca²⁺ Channel Cooperativity of Exocytosis

Victor Matveev,¹ Richard Bertram,^2,3,4 and Arthur Sherman⁵

¹Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102-1982, ²Department of Mathematics and Programs in ³Neuroscience and ⁴Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, and ⁵Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892

Correspondence should be addressed to Victor Matveev, Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102-1982. Email: matveev{at}njit.edu

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.

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Received Jan. 15, 2009; revised Aug. 7, 2009; accepted Aug. 19, 2009.

Correspondence should be addressed to Victor Matveev, Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102-1982. Email: matveev{at}njit.edu

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