  The conventional impedance profile of a neuron can identify the presence of
resonance and other properties of the neuronal response to oscillatory inputs,
such as nonlinear response amplifications, but it cannot distinguish other
nonlinear properties such as asymmetries in the shape of the voltage response
envelope. Experimental observations have shown that the response of neurons to
oscillatory inputs preferentially enhances either the upper or lower part of
the voltage envelope in different frequency bands. These asymmetric voltage
responses arise in a neuron model when it is submitted to high enough amplitude
oscillatory currents of variable frequencies. We show how the nonlinearities
associated to different ionic currents or present in the model as captured by
its voltage equation lead to asymmetrical response and how high amplitude
oscillatory currents emphasize this response. We propose a geometrical
explanation for the phenomenon where asymmetries result not only from
nonlinearities in their activation curves but also from nonlinearites captured
by the nullclines in the phase-plane diagram and from the system's time-scale
separation. In addition, we identify an unexpected frequency-dependent pattern
which develops in the gating variables of these currents and is a product of
strong nonlinearities in the system as we show by controlling such behavior by
manipulating the activation curve parameters. The results reported in this
paper shed light on the ionic mechanisms by which brain embedded neurons
process oscillatory information.
