Beyond average firing rate, other measurable signals of neuronal activity are fundamental to an understanding of behavior. Recently, hidden Markov models (HMMs) have been applied to neural recordings and have described how neuronal ensembles process information by going through sequences of different states. Such collective dynamics are impossible to capture by just looking at the average firing rate. To estimate how well HMMs can decode information contained in single trials, we compared HMMs with a recently developed classification method based on the peristimulus time histogram (PSTH). The accuracy of the two methods was tested by using the activity of prefrontal neurons recorded while two monkeys were engaged in a strategy task. In this task, the monkeys had to select one of three spatial targets based on an instruction cue and on their previous choice. We show that by using the single trial's neural activity in a period preceding action execution, both models were able to classify the monkeys' choice with an accuracy higher than by chance. Moreover, the HMM was significantly more accurate than the PSTH-based method, even in cases in which the HMM performance was low, although always above chance. Furthermore, the accuracy of both methods was related to the number of neurons exhibiting spatial selectivity within an experimental session. Overall, our study shows that neural activity is better described when not only the mean activity of individual neurons is considered and that therefore, the study of other signals rather than only the average firing rate is fundamental to an understanding of the dynamics of neuronal ensembles.
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.
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