The dopamine-dependent plasticity of the cortico-striatal synapses is considered as the cellular mechanism crucial for reinforcement learning. The dopaminergic inputs and the calcium responses affect the synaptic plasticity by way of the signaling cascades within the synaptic spines. The calcium concentration within synaptic spines, however, is dependent on multiple factors including the calcium influx through ionotropic glutamate receptors, the intracellular calcium release by activation of metabotropic glutamate receptors, and the opening of calcium channels by EPSPs and back-propagating action potentials. Furthermore, dopamine is known to modulate the efficacies of NMDA receptors, some of the calcium channels, and sodium and potassium channels that affect the back propagation of action potentials. Here we construct an electric compartment model of the striatal medium spiny neuron with a realistic morphology and predict the calcium responses in the synaptic spines with variable timings of the glutamatergic and dopaminergic inputs and the postsynaptic action potentials. The model was validated by reproducing the responses to current inputs and could predict the electric and calcium responses to glutamatergic inputs and back-propagating action potential in the proximal and distal synaptic spines during up- and down-states. We investigated the calcium responses by systematically varying the timings of the glutamatergic and dopaminergic inputs relative to the action potential and found that the calcium response and the subsequent synaptic potentiation is maximal when the dopamine input precedes glutamate input and action potential. The prediction is not consistent with the hypothesis that the dopamine input provides the reward prediction error for reinforcement learning. The finding suggests that there is an unknown learning mechanisms at the network level or an unknown cellular mechanism for calcium dynamics and signaling cascades.
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