Depolarization block in the endocannabinoid system of the hippocampus

Depolarization block is such a mechanism that the firing activity of a neuronal system is stopped for particular values of the input current. It is important to block epilepsy or unpleasant firing rates. We investigate this property for a non-linear model of CA3 hippocampal neurons under the action of endocannabinoid transmitters. The aim is to discover if they induce depolarization block, a property already seen in other neuronal models and observed in some experiments, signifying that the neural population increases its spiking frequency as some main parameter changes until reaching a situation of no firing. The results is theoretical and it could be useful for investigating real system of neurons of the hippocampus. In some papers it has been shown that this property is connected with bistability, which means that the system has two equilibrium states for some ranges of its parameters. Endocannabinoids influence the learning and memory process and so we concentrate our attention on the CA3 neurons of the hippocampus. We find bistability and depolarization block for the considered model, which is a generalization of the Wilson-Cowan model. The model describes average properties of neurons divided in three classes: the excitatory neuronal population (CA3 neurons) and two types of inhibitory neuron populations (basket cells). The exogenous concentration of cannabinoids is the parameter that controls bistability. This result can be used for an experiment that could give information for medical therapy. We study the time evolution of the synapses connecting the excitatory population with two types of basket cells. The evolution of synaptic weights is considered to be a toy model of the learning process. But this model cannot encompass the complexity and diversity of exogenous and endogenous endocannabinoids effects in vivo