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Minimal Models of Adapted Neuronal Response to In Vivo–Like Input Currents

lacamera{at}cns.unibe.ch, Institute of Physiology, University of Bern, CH-3012 Bern, Switzerland

Alexander Rauch

rauch{at}pyl.unibe.ch, Institute of Physiology, University of Bern, CH-3012 Bern, Switzerland

Hans-R. Lüscher

luescher{at}pyl.unibe.ch, Institute of Physiology, University of Bern, CH-3012 Bern, Switzerland

Walter Senn

wsenn{at}cns.unibe.ch, Institute of Physiology, University of Bern, CH-3012 Bern, Switzerland

Stefano Fusi

fusi{at}cns.unibe.ch, Institute of Physiology, University of Bern, CH-3012 Bern, Switzerland

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.

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