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Fast-slow analysis as a technique for understanding the neuronal response to current ramps

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Abstract

The standard protocol for studying the spiking properties of single neurons is the application of current steps while monitoring the voltage response. Although this is informative, the jump in applied current is artificial. A more physiological input is where the applied current is ramped up, reflecting chemosensory input. Unsurprisingly, neurons can respond differently to the two protocols, since ion channel activation and inactivation are affected differently. Understanding the effects of current ramps, and changes in their slopes, is facilitated by mathematical models. However, techniques for analyzing current ramps are under-developed. In this article, we demonstrate how current ramps can be analyzed in single neuron models. The primary issue is the presence of gating variables that activate on slow time scales and are therefore far from equilibrium throughout the ramp. The use of an appropriate fast-slow analysis technique allows one to fully understand the neural response to ramps of different slopes. This study is motivated by data from olfactory bulb dopamine neurons, where both fast ramp (tens of milliseconds) and slow ramp (tens of seconds) protocols are used to understand the spiking profiles of the cells. The slow ramps generate experimental bifurcation diagrams with the applied current as a bifurcation parameter, thereby establishing asymptotic spiking activity patterns. The faster ramps elicit purely transient behavior that is of relevance to most physiological inputs, which are short in duration. The two protocols together provide a broader understanding of the neuron’s spiking profile and the role that slowly activating ion channels can play.

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Data availability

The data sets generated for this study are available on request.

Code availability

The XPPAUT code can be downloaded as freeware from www.math.fsu.edu/~bertram/software/neuron. All simulation data available upon request.

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Acknowledgements

We thank Dr. Laura Blakemore for her careful reading of the manuscript and helpful comments, and Dr. Theodore Vo for initial discussions. This work was supported by the FSU Chemosensory Training Program (CTP) Grant Award T32 DC000044 from the National Institutes of Health (NIH/NIDCD), NIH Grant R21DA044442 to PQT and RB, and grant number DMS 1853342 from the National Science Foundation to RB.

Funding

This work was supported by the FSU Chemosensory Training Program (CTP) Grant Award T32 DC000044 from the National Institutes of Health (NIH/NIDCD), NIH Grant R21DA044442 to PQT and RB, and grant number DMS 1853342 from the National Science Foundation to RB.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Ottawa, Ottawa, ON, K1N 6N5, Canada

    Kelsey Gasior

  2. Department of Biological Science and Program in Neuroscience, Florida State University, Tallahassee, FL, 32306, USA

    Kirill Korshunov & Paul Q. Trombley

  3. Department of Mathematics and Programs in Neuroscience and Molecular Biophysics, Florida State University, Tallahassee, FL, 32306, USA

    Richard Bertram

Authors
  1. Kelsey Gasior
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  2. Kirill Korshunov
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  3. Paul Q. Trombley
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  4. Richard Bertram
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Contributions

KG performed simulations and helped with writing the manuscript. KK performed experiments and helped with writing the manuscript. PQT oversaw the laboratory and helped with writing the manuscript. RB helped with simulations and writing the manuscript.

Corresponding author

Correspondence to Richard Bertram.

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Ethics approval

All experiments were carried out in accordance with the National Institutes of Health Guide for the Care and Use of Laboratory Animals (8th edition). Approval was granted by the Florida State University Institutional Animal Care and Use Committee (Date: 12/18/18/Protocol #1845).

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The authors declare no conflict of interest.

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Action Editor: Frances K. Skinner.

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Gasior, K., Korshunov, K., Trombley, P.Q. et al. Fast-slow analysis as a technique for understanding the neuronal response to current ramps. J Comput Neurosci 50, 145–159 (2022). https://doi.org/10.1007/s10827-021-00799-0

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  • DOI: https://doi.org/10.1007/s10827-021-00799-0

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