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P178: Neuronal resonance may not be apparent, but still present, for realistic input signals using standard impedance measurements
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Rodrigo Pena, **Ulises Chialva**, **Horacio Rotstein**

The impedance of a neuron reflects the frequency-dependent input-output relationships and is typically computed using sinusoidal inputs [1]. Oscillatory currents with gradually increasing frequencies or broadband noise have been used so the response is equally tested at all frequencies [2,3]. The ability of a neuron to amplify its response to specific non-zero input frequencies (resonance) has been questioned [4]. The question arises of whether the differences in the type of response (low- vs. band-pass) can be ascribed to the type of input and not necessarily to the details of the frequency content. More specifically, whether and how the use of different types of biophysically plausible periodic inputs (e.g., sinusoidal, synaptic- like) produce qualitatively different frequency-dependent input-output curves. We address these issues by injecting different types of inputs to biophysically plausible neuronal models including currents that are known to produce subthreshold (membrane potential) resonance in response to sinusoidal inputs. All input signals have the same amplitude and frequency content, but the frequencies may come in “different order” (e.g., monotonically increasing, randomly distributed or “shuffled”). The waveforms include sinusoidal, square- waves and synaptic-like functions. The impedance is computed either (i) as the ratio of the Fourier transforms (FT) of the voltage ( _V_ ) and the current ( _I_ ) or (ii) by the difference in the amplitude envelope responses normalized by the input amplitude.

We show that if the inputs involve abrupt changes (e.g., square-waves, synaptic-like), transients contribute to the output signal, which qualitatively modify the impedance profile. This can cause a mismatch between the impedance computed using (i) vs. (ii) given that the FT captures these transients as higher harmonics (Fig. 1). Therefore, a resonance observed in the response pattern may not be captured by the impedance using standard definitions and may require a more careful analysis. Furthermore, when input frequencies are presented in a “shuffled” order, these transient effects produce responses with additional amplification to the higher frequency responses.

Our results highlight both the flexibility and limitations of the impedance profile measurements and demonstrate that resonance may be present in neuronal systems, but are not apparent unless one uses the appropriate types of inputs and output metrics. Furthermore, our results question the ability of the standard impedance metric to make predictions for a more general class of inputs.

**Acknowledgment**

This work was supported by the National Science Foundation grant DMS-1608077 (HGR).

**References**

[1] Hutcheon, B. Yarom, Y. Resonance, oscillation and the intrinsic frequency preferences of neurons. Trends Neurosci. 2000, 23, 216–222.

[2] Kispersky, T.J., Fernandez, F.R., Economo, M.N., et al. Spike resonance properties in hippocampal o-lm cells are dependent on refractory dynamics. J Neurosci. 2012, 32, 3637–3651.

[3] Schreiber, S., Erchova, I., Heinemann, U., et al. Subthreshold resonance explains the frequency-dependent integration of periodic as well as random stimuli in the entorhinal cortex. J Neurophysiol. 2004, 92, 408–415.

[4] Zemankovics, R., Káli, S., Paulsen, O., et al. Differences in subthreshold resonance of hippocampal pyramidal cells and interneurons: the role of h‐current and passive membrane characteristics. J Physiol. 2010, 588, 2109-2132.

**Speakers**
## Rodrigo Pena

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Rodrigo Pena

The impedance of a neuron reflects the frequency-dependent input-output relationships and is typically computed using sinusoidal inputs [1]. Oscillatory currents with gradually increasing frequencies or broadband noise have been used so the response is equally tested at all frequencies [2,3]. The ability of a neuron to amplify its response to specific non-zero input frequencies (resonance) has been questioned [4]. The question arises of whether the differences in the type of response (low- vs. band-pass) can be ascribed to the type of input and not necessarily to the details of the frequency content. More specifically, whether and how the use of different types of biophysically plausible periodic inputs (e.g., sinusoidal, synaptic- like) produce qualitatively different frequency-dependent input-output curves. We address these issues by injecting different types of inputs to biophysically plausible neuronal models including currents that are known to produce subthreshold (membrane potential) resonance in response to sinusoidal inputs. All input signals have the same amplitude and frequency content, but the frequencies may come in “different order” (e.g., monotonically increasing, randomly distributed or “shuffled”). The waveforms include sinusoidal, square- waves and synaptic-like functions. The impedance is computed either (i) as the ratio of the Fourier transforms (FT) of the voltage ( _V_ ) and the current ( _I_ ) or (ii) by the difference in the amplitude envelope responses normalized by the input amplitude.

We show that if the inputs involve abrupt changes (e.g., square-waves, synaptic-like), transients contribute to the output signal, which qualitatively modify the impedance profile. This can cause a mismatch between the impedance computed using (i) vs. (ii) given that the FT captures these transients as higher harmonics (Fig. 1). Therefore, a resonance observed in the response pattern may not be captured by the impedance using standard definitions and may require a more careful analysis. Furthermore, when input frequencies are presented in a “shuffled” order, these transient effects produce responses with additional amplification to the higher frequency responses.

Our results highlight both the flexibility and limitations of the impedance profile measurements and demonstrate that resonance may be present in neuronal systems, but are not apparent unless one uses the appropriate types of inputs and output metrics. Furthermore, our results question the ability of the standard impedance metric to make predictions for a more general class of inputs.

This work was supported by the National Science Foundation grant DMS-1608077 (HGR).

[1] Hutcheon, B. Yarom, Y. Resonance, oscillation and the intrinsic frequency preferences of neurons. Trends Neurosci. 2000, 23, 216–222.

[2] Kispersky, T.J., Fernandez, F.R., Economo, M.N., et al. Spike resonance properties in hippocampal o-lm cells are dependent on refractory dynamics. J Neurosci. 2012, 32, 3637–3651.

[3] Schreiber, S., Erchova, I., Heinemann, U., et al. Subthreshold resonance explains the frequency-dependent integration of periodic as well as random stimuli in the entorhinal cortex. J Neurophysiol. 2004, 92, 408–415.

[4] Zemankovics, R., Káli, S., Paulsen, O., et al. Differences in subthreshold resonance of hippocampal pyramidal cells and interneurons: the role of h‐current and passive membrane characteristics. J Physiol. 2010, 588, 2109-2132.

Postdoc, Federated Department of Biological Sciences, New Jersey Institute of Technology

Post-Doctoral Research Associate at Computational Neuroscience, BioDatanamics Lab (H. G. Rotstein)orcid.org/0000-0002-2037-9746

CNS2020
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Monday July 20, 2020 8:00pm - 9:00pm CEST

Slot 02

Slot 02