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Many neuron types exhibit preferred frequency responses in their voltageamplitude (resonance) or phase shift to subthreshold oscillatory currents, butthe effect of biophysical parameters on these properties is not wellunderstood. We propose a general framework to analyze the role of differentionic currents and their interactions in shaping the properties of impedanceamplitude and phase in linearized biophysical models and demonstrate thisapproach in a two-dimensional linear model with two effective conductances gLand g1. We compute the key attributes of impedance and phase (resonancefrequency and amplitude, zero-phase frequency, selectivity, etc.) in the gL-g1parameter space. Using these attribute diagrams we identify two basicmechanisms for the generation of resonance: an increase in the resonanceamplitude as g1 increases while the overall impedance is decreased, and anincrease in the maximal impedance, without any change in the input resistance,as the ionic current time constant increases. We use the attribute diagrams toanalyze resonance and phase of the linearizations of two biophysical modelsthat include resonant (Ih or slow potassium) and amplifying currents(persistent sodium). In the absence of amplifying currents, the two modelsbehave similarly as the conductances of the resonant currents is increasedwhereas, with the amplifying current present, the two models have qualitativelyopposite responses. This work provides a general method for decoding the effectof biophysical parameters on linear membrane resonance and phase by trackingtrajectories, parametrized by the relevant biophysical parameter, inpre-constructed attribute diagrams.

Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents