Integrate-and-Fire-type models are usually criticized because of their simplicity. On the other hand, the Integrate-and-Fire model is the basis of most of the theoretical studies on spiking neuron models. Here, we develop a sequential procedure to quantitatively evaluate an equivalent Integrate-and-Fire-type model based on intracellular recordings of cortical pyramidal neurons. We find that the resulting effective model is sufficient to predict the spike train of the real pyramidal neuron with high accuracy. In in vivo-like regimes, predicted and recorded traces are almost indistinguishable and a significant part of the spikes can be predicted at the correct timing. Slow processes like spike-frequency adaptation are shown to be a key feature in this context since they are necessary for the model to connect between different driving regimes.

Rate models are often used to study the behavior of large networks of spiking neurons. Here we propose a procedure to derive rate models that take into account the fluctuations of the input current and firing-rate adaptation, two ubiquitous features in the central nervous system that have been previously overlooked in constructing rate models. The procedure is general and applies to any model of firing unit. As examples, we apply it to the leaky integrate-and-fire (IF) neuron, the leaky IF neuron with reversal potentials, and to the quadratic IF neuron. Two mechanisms of adaptation are considered, one due to an afterhyperpolarization current and the other to an adapting threshold for spike emission. The parameters of these simple models can be tuned to match experimental data obtained from neocortical pyramidal neurons. Finally, we show how the stationary model can be used to predict the time-varying activity of a large population of adapting neurons.

Numerous animal behaviors, such as locomotion in vertebrates, are produced by rhythmic contractions that alternate between two muscle groups. The neuronal networks generating such alternate rhythmic activity are generally thought to rely on pacemaker cells or well-designed circuits consisting of inhibitory and excitatory neurons. However, experiments in organotypic cultures of embryonic rat spinal cord have shown that neuronal networks with purely excitatory and random connections may oscillate due to their synaptic depression, even without pacemaker cells. In this theoretical study, we investigate what happens if two such networks are symmetrically coupled by a small number of excitatory connections. We discuss a time-discrete mean-field model describing the average activity and the average synaptic depression of the two networks. Depending on the parameter values of the depression, the oscillations will be in phase, antiphase, quasiperiodic, or phase trapped. We put forward the hypothesis that pattern generators may rely on activity-dependent tuning of synaptic depression.