  Single neuron models have a long tradition in computational neuroscience.
Detailed biophysical models such as the Hodgkin-Huxley model as well as
simplified neuron models such as the class of integrate-and-fire models relate
the input current to the membrane potential of the neuron. Those types of
models have been extensively fitted to in vitro data where the input current is
controlled. Those models are however of little use when it comes to
characterize intracellular in vivo recordings since the input to the neuron is
not known. Here we propose a novel single neuron model that characterizes the
statistical properties of in vivo recordings. More specifically, we propose a
stochastic process where the subthreshold membrane potential follows a Gaussian
process and the spike emission intensity depends nonlinearly on the membrane
potential as well as the spiking history. We first show that the model has a
rich dynamical repertoire since it can capture arbitrary subthreshold
autocovariance functions, firing-rate adaptations as well as arbitrary shapes
of the action potential. We then show that this model can be efficiently fitted
to data without overfitting. Finally, we show that this model can be used to
characterize and therefore precisely compare various intracellular in vivo
recordings from different animals and experimental conditions.
