A nonautonomous phenomenological model for On and Off responses of cells in sensory system

Many neurons in mammalian sensory systems exhibit On and Off responses when given appropriate excitatory and inhibitory stimuli. In some instances, such neurons can also exhibit a Mixed response where diminished On and Off responses are both present. In this manuscript, we present a simple single cell model for these ubiquitous stimulus-response patterns. The model is nonautonomous consisting of two fast variables (one being the voltage), one slow recovery variable, and a time dependent stimuli current I(t). For piecewise constant I(t), On and Off responses can be reproduced and it is shown that their dependence on both the duration and the intensity of the input can be derived using singular perturbation techniques. Furthermore, we show that for certain stimuli I(t) the voltage has spike trains both during and immediately after the stimuli is presented. Such Mixed responses have also been measured experimentally, and the current model reproduces all three responses robustly for different net synaptic currents I(t).