Vinicius L. Cordeiro, Renan O. Shimoura, Nilton L. Kamiji, Osame Kinouchi and Antonio C. Roque
Experimental evidence suggests that neurons and neural circuits display stochastic variability  and, therefore, it is important to have neural models that capture this stochasticity. There are basically two types of noise model for a neuron : (1) spike generation is modeled deterministically and noise enters the dynamics via additional stochastic terms; or (2) spike generation is directly modeled as a stochastic process. Recently, Galves and Löcherbach  introduced a neural model of the latter type in which the firing of a neuron at a given time t is a random event with probability given by a monotonically increasing function of its membrane potential V. The model of Galves and Löcherbach (GL) has as one of its components a graph of interactions between neurons. In this work we consider that this graph has the structure of the Potjans and Diesmann network model of a cortical column . The model of Potjans and Diesmann has four layers and two neuron types, excitatory and inhibitory, so that there are eight cell populations. The population-specific neuron densities and connectivity are taken from comprehensive anatomical and electrophysiological studies [5-6], and the model has approximately 80,000 neurons and 300,000,000 synapses. We adjusted the parameters of the firing probability of the GL model to reproduce the firing behavior of regular (excitatory) and fast (inhibitory) spiking neurons . Then, we replaced the leaky integrate-and-fire neurons of the original Potjans-Diesmann model by these stochastic neurons to obtain a stochastic version of the Potjans-Diesmann model. The parameters of the model are the weights we and wi of the excitatory and inhibitory synaptic weights of the GL model . We studied the firing patterns of the eight cell populations of the stochastic model in the absence of external input and characterized their behavior in the two-dimensional diagram spanned by the excitatory and inhibitory synaptic weights. For a balanced case in which the network activity is asynchronous and irregular the properties of the stochastic model are similar to the properties of the original Potjans-Diesmann model. Different neural populations have different firing rates and inhibitory neurons have higher firing rates than excitatory neurons. In particular, the stochastic model emulates the very low firing rates of layer 2/3 observed in the original model and also experimentally . We also submitted the network to random input spikes applied to layers 4 and 6 to mimic thalamic inputs, as done by Potjans and Diesmann , and studied the propagation of activity across layers. In conclusion, the stochastic version of the Potjans-Diesmann model can be a useful replacement for the original Potjans-Diesmann model in studies that require a comparison between stochastic and deterministic models.