Volume 14 Supplement 1

## Abstracts from the Twenty Second Annual Computational Neuroscience Meeting: CNS*2013

- Poster presentation
- Open Access

# Predicting the firing phase of an oscillatory neuron from its impedance profile

- Farzan Nadim
^{1, 2}Email author, - Horacio G Rotstein
^{2}and - David Fox
^{1}

**14 (Suppl 1)**:P132

https://doi.org/10.1186/1471-2202-14-S1-P132

© Nadim et al; licensee BioMed Central Ltd. 2013

**Published:**8 July 2013

## Keywords

- Current Input
- Impedance Profile
- Biological Neuron
- Oscillatory Neuron
- Spike Threshold

The activity phase of a neuron in an oscillatory network often determines what the neuron codes [1, 2]. We are interested in understanding the effect of subthreshold factors that influence this activity phase. Here we develop a first-order approximation of the activity phase of a neuron receiving oscillatory input using its subthreshold impedance profile.

A neuron's subthreshold membrane potential response to sinusoidal current input with frequency *f* is sinusoidal (to first order) with amplitude and phase-shift approximated by the impedance value at *f*:${Z}_{f}=\u2225{Z}_{f}\u2225{e}^{i{\phi}_{f}}$. If a neuron receives suprathreshold oscillatory input at frequency *f*, the resulting change in membrane potential can be approximated with a similar amplitude and phase-shift up to the time point *t*_{
spike
} where spike threshold is reached. This results in the following simple equation: ${V}_{m}\left({t}_{spike}\right)={V}_{rest}+{A}_{in}\u2225{Z}_{f}\u2225\mathsf{\text{sin}}\left(2\pi f\cdot {t}_{spike}+{\phi}_{f}\right)={V}_{thresh}$ where *A*_{
in
} is the amplitude of the input current. Assuming the reference time point of *t*_{0} = 0 in the cycle, the spike phase can be approximated as ${\phi}_{spike}=f\cdot {t}_{spike}=\frac{1}{2\pi}\left(\mathsf{\text{arcsin}}\frac{{V}_{thresh}-\phantom{\rule{2.77695pt}{0ex}}{V}_{rest}}{{A}_{in}\u2225{Z}_{f}\u2225}-{\phi}_{f}\right)$. This approximation is valid so long as the argument of arcsin is <1 in absolute value.

As proof of principle, we used the impedance profile of a model neuron exhibiting subthreshold resonance to approximate the spike phase with a given preset spike threshold (Figure A). We also used this approximation to predict the phase of the first spike in bursting PY neurons in the crab pyloric CPG, when synaptically isolated and subjected to a sinusoidal current input at different frequencies (0.1-4 Hz; see [3]for method). The PY impedance was measured from its subthreshold response.

To our knowledge this method, despite its simplicity, has not been previously used for the approximation of spike phase using the impedance profile. The usefulness of this approximation is that changes in membrane properties due to network activity or neuromodulation can be readily measured in the impedance profile and this knowledge can be used to predict how the neuron changes its response phase during network activity.

## Declarations

### Acknowledgements

Supported by NIH MH060605 (FN), NSF DMS0817241 (HGR).

## Authors’ Affiliations

## References

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## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.