# The effect of dendritic voltage-gated conductances on the neuronal impedance: a quantitative model

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## Abstract

Neuronal impedance characterizes the magnitude and timing of the subthreshold response of a neuron to oscillatory input at a given frequency. It is known to be influenced by both the morphology of the neuron and the presence of voltage-gated conductances in the cell membrane. Most existing theoretical accounts of neuronal impedance considered the effects of voltage-gated conductances but neglected the spatial extent of the cell, while others examined spatially extended dendrites with a passive or spatially uniform quasi-active membrane. We derived an explicit mathematical expression for the somatic input impedance of a model neuron consisting of a somatic compartment coupled to an infinite dendritic cable which contained voltage-gated conductances, in the more general case of non-uniform dendritic membrane potential. The validity and generality of this model was verified through computer simulations of various model neurons. The analytical model was then applied to the analysis of experimental data from real CA1 pyramidal neurons. The model confirmed that the biophysical properties and predominantly dendritic localization of the hyperpolarization-activated cation current *I* _{h} were important determinants of the impedance profile, but also predicted a significant contribution from a depolarization-activated fast inward current. Our calculations also implicated the interaction of *I* _{h} with amplifying currents as the main factor governing the shape of the impedance-frequency profile in two types of hippocampal interneuron. Our results provide not only a theoretical advance in our understanding of the frequency-dependent behavior of nerve cells, but also a practical tool for the identification of candidate mechanisms that determine neuronal response properties.

## Keywords

Impedance Cable theory Quasi-active membrane Hippocampus## Notes

### Acknowledgements

We are grateful to Dr Norbert Hájos for initiating the project and for helpful discussions and comments regarding the manuscript. We thank Katalin Lengyel and Erzsébet Gregori for their excellent technical assistance. This work was supported by the Hungarian Scientific Research Fund (OTKA T049517, OTKA K60927, OTKA K83251).

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