Voltage-dependent ion channels as operators
Yes, they are nonlinear filters, which are operators on temporal signals. I have not seen a single ion channel analyzed as nonlinear filter though. Most of the time, a system containing ion channels (such as some neuron's membrane) is analyzed as such. Papers describing the biophysics of neurons and their function as filtering devices has been one of the topics in computational neuroscience.


Gerstner, W. and Kistler, W. M. (2002). Spiking Neuron Models. Cambridge University Press
Marmarelis, V. Z. (2004). Nonlinear dynamic modeling of physiological systems.