  Many neuron types exhibit preferred frequency responses in their voltage
amplitude (resonance) or phase shift to subthreshold oscillatory currents, but
the effect of biophysical parameters on these properties is not well
understood. We propose a general framework to analyze the role of different
ionic currents and their interactions in shaping the properties of impedance
amplitude and phase in linearized biophysical models and demonstrate this
approach in a two-dimensional linear model with two effective conductances gL
and g1. We compute the key attributes of impedance and phase (resonance
frequency and amplitude, zero-phase frequency, selectivity, etc.) in the gL-g1
parameter space. Using these attribute diagrams we identify two basic
mechanisms for the generation of resonance: an increase in the resonance
amplitude as g1 increases while the overall impedance is decreased, and an
increase in the maximal impedance, without any change in the input resistance,
as the ionic current time constant increases. We use the attribute diagrams to
analyze resonance and phase of the linearizations of two biophysical models
that include resonant (Ih or slow potassium) and amplifying currents
(persistent sodium). In the absence of amplifying currents, the two models
behave similarly as the conductances of the resonant currents is increased
whereas, with the amplifying current present, the two models have qualitatively
opposite responses. This work provides a general method for decoding the effect
of biophysical parameters on linear membrane resonance and phase by tracking
trajectories, parametrized by the relevant biophysical parameter, in
pre-constructed attribute diagrams.
