Institute for Complex Systems, Paris Ile-de-France, France

Statistical Physics Laboratory, CNRS, Ecole Normale Superieure, Paris, France

Neurobiology Laboratory, CNRS, Ecole Normale Superieure, Paris, France

Neurons

We study analytically the stochastic dynamics of the membrane potential distribution between two successive action potentials, for an integrate-and-fire neuron receiving noisy synaptic inputs. We find that for long enough periods since the firing of the previous action potential, the dynamics converge to a quasi-stationary state, in which the membrane potential distribution becomes independent of time except for a global exponential decay. Once this quasi-stationary distribution has been reached, the firing probability per unit time becomes constant, and the subsequent firing is a Poisson process with a rate that depends on the amplitude of background noise. For

The fast convergence to the quasi-stationary state has important implications on the response properties of the neuron. We examine the spike-time dependent response (SDR), which we define as the modification in the timing of the next AP due to a given synaptic input, as function of the timing of this input. In absence of noise, the SDR is equivalent to the well studied Phase Response Curve and the response depends strongly on the timing of the input. In contrast, for

Acknowledgements

We thank Boris Barbour and Nicolas Brunel for useful discussions. Financial support was provided by Agence Nationale de la Recherche and Région Ile-de-France.