Interspike intervals in neuronal networks with self-organized criticality

The distribution of interspike intervals (ISI) for individual neurons is a standard measure in neuroscience. Recently the idea that neuronal networks works near the critical point of an absorbing state transition has been explored, with a lot of theoretical and experimental results. Surprisingly, it appears that the distribution of ISI for neurons pertaining to a critical network has not been measured yet. Here, we model the generation of interspike intervals in neuronal systems with self-organized criticality by two methods. First, we use a simple stochastic model where interavalanches intervals (IAI) are generated from a power law distribution, and interspike intervals are sums of IAI between two times where a neuron spikes because it pertains to an avalanche (modeled by a neuronal size avalanche distribution $P(S) = c S^{-3/2}$). Second, we perform a full simulation in a network of excitable elements (neurons) with dynamical synapses which presents well behaved self-organized criticality. In this simulation we define avalanches as sequential activity above some threshold level of active sites. This enables us to define interavalanches (IAI) and interspikes intervals (ISI) and construct histograms for them. We compare these results with ISI distributions that present power law tails from real neurons from cortical and thalamic areas of freely behaving rats. We find that self-organized criticality can explain power laws in the tail of ISI distributions of neurons and that such power laws in single neurons could suggest the presence of criticality at the network level.