Journal of Computational Neuroscience

, Volume 37, Issue 1, pp 9–28 | Cite as

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

  • Horacio G. Rotstein
  • Farzan Nadim


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 g L and g 1. We compute the key attributes of impedance and phase (resonance frequency and amplitude, zero-phase frequency, selectivity, etc.) in the g L  − g 1 parameter space. Using these attribute diagrams we identify two basic mechanisms for the generation of resonance: an increase in the resonance amplitude as g 1 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 linearization of two biophysical models that include resonant (I h 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.


Resonance Subthreshold oscillations Zero phase frequency Impedance Model neuron 



The authors thank Diana Martinez and David Fox for their comments on this manuscript.


Supported by NSF DMS1313861 (HGR) and NIH MH060605, NS083319 (FN).

Conflict of interest statement

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNew Jersey Institute of TechnologyNewarkUSA
  2. 2.Department of Biological SciencesNew Jersey Institute of Technology, and Rutgers University-NewarkNewarkUSA

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