This thesis deals with a newly-developed model for the spatiotemporal calcium dynamics within presynaptic terminals. The model is based on single-protein kinetics and has been used to successfully describe different neuron types such as pyramidal neurons in the rat neocortex and the Calyx of Held of neurons from the rat brainstem. A limited number of parameters had to be adjusted to fluorescence measurements of the calcium concentration. These values can be interpreted as a prediction of the model, and in particular the protein densities can be compared to independent experiments. The contribution of single proteins to the total calcium dynamics has been analysed in detail for voltage-dependent calcium channel, plasma-membrane calcium ATPase, sodium-calcium exchanger, and endogenous as well as exogenous buffer proteins. The model can be used to reconstruct the unperturbed calcium dynamics from measurements using fluorescence indicators. The calcium response to different stimuli has been investigated in view of its relevance for synaptic plasticity. This work provides a first step towards a description of the complete synaptic transmission using single-protein data.

Synaptic long-term modifications following neuronal activation are believed to be at the origin of learning and long-term memory. Recent experiments suggest that these long-term synaptic changes are all-or-none switch-like events between discrete states of a single synapse. The biochemical network involving calcium/calmodulin-dependent protein kinase II (CaMKII) and its regulating protein signaling cascade has been hypothesized to durably maintain the synaptic state in form of a bistable switch. Furthermore, it has been shown experimentally that CaMKII and associated proteins such as protein kinase A and calcineurin are necessary for the induction of long-lasting increases (long-term potentiation, LTP) and/or long-lasting decreases (long-term depression, LTD) of synaptic efficacy. However, the biochemical mechanisms by which experimental LTP/LTD protocols lead to corresponding transitions between the two states in realistic models of such networks are still unknown. We present a detailed biochemical model of the calcium/calmodulin-dependent autophosphorylation of CaMKII and the protein signaling cascade governing the dephosphorylation of CaMKII. As previously shown, two stable states of the CaMKII phosphorylation level exist at resting intracellular calcium concentrations. Repetitive high calcium levels switch the system from a weakly- to a highly phosphorylated state (LTP). We show that the reverse transition (LTD) can be mediated by elevated phosphatase activity at intermediate calcium levels. It is shown that the CaMKII kinase-phosphatase system can qualitatively reproduce plasticity results in response to spike-timing dependent plasticity (STDP) and presynaptic stimulation protocols. A reduced model based on the CaMKII system is used to elucidate which parameters control the synaptic plasticity outcomes in response to STDP protocols, and in particular how the plasticity results depend on the differential activation of phosphatase and kinase pathways and the level of noise in the calcium transients. Our results show that the protein network including CaMKII can account for (i) induction - through LTP/LTD-like transitions - and (ii) storage - due to its bistability - of synaptic changes. The model allows to link biochemical properties of the synapse with phenomenological 'learning rules' used by theoreticians in neural network studies.