A quantitative model for presynaptic free Ca2+ dynamics during different stimulation protocols

The presynaptic free Ca2+ dynamics of neurons due to various stimulation protocols is investigated in a mathematical model. The model includes Ca2+ influx through voltage-dependent Ca2+ channels, Ca2+ buffering by endogenous and exogenous buffers as well as Ca2+ efflux through ATP-driven plasma membrane Ca2+ pumps and Na+/Ca2+ exchangers. We want to support a specific way of modeling which starts on the level of single proteins. Each protein is represented by characteristics that are determined by single protein experiments and that are considered to be widely independent of neuron types. This allows the applications of the model to different classes of neurons and experiments. The procedure is demonstrated for single boutons of pyramidal neurons of the rat neocortex. The corresponding fluorescence measurements of Koester and Sakmann (J. Physiol. 529 (2000) 625) are quantitatively reproduced. The model enables us to reconstruct the free Ca2+ dynamics in neurons as it would have been without fluorescence indicators starting from the fluorescence data. We discuss the different Ca2+ responses and find that during high-frequency stimulation an accumulation of free Ca2+ occurs above some threshold stimulation frequency. The threshold frequency depends on the amount of fluorescence indicator used in the experiment.

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