Adaptive processes over many timescales endow neurons with sensitivity to stimulus changes over a similarly wide range of scales. Although spike timing of single neurons can precisely signal rapid fluctuations in their inputs, the mean firing rate can convey information about slower-varying properties of the stimulus. Here, we investigate the firing rate response to a slowly varying envelope of whisker motion in two processing stages of the rat vibrissa pathway. The whiskers of anesthetized rats were moved through a noise trajectory with an amplitude that was sinusoidally modulated at one of several frequencies. In thalamic neurons, we found that the rate response to the stimulus envelope was also sinusoidal, with an approximately frequency-independent phase advance with respect to the input. Responses in cortex were similar but with a phase shift that was about three times larger, consistent with a larger amount of rate adaptation. These response properties can be described as a linear transformation of the input for which a single parameter quantifies the phase shift as well as the degree of adaptation. These results are reproduced by a model of adapting neurons connected by synapses with short-term plasticity, showing that the observed linear response and phase lead can be built up from a network that includes a sequence of nonlinear adapting elements. Our study elucidates how slowly varying envelope information under passive stimulation is preserved and transformed through the vibrissa processing pathway.
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