Slowly activating outward membrane currents generate input-output sub-harmonic cross frequency coupling in neurons

Nirvik Sinha, C. J. Heckman, Yuan Yang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A major challenge in understanding spike-time dependent information encoding in the neural system is the non-linear firing response to inputs of the individual neurons. Hence, quantitative exploration of the putative mechanisms of this non-linear behavior is fundamental to formulating the theory of information transfer in the neural system. The objective of this simulation study was to evaluate and quantify the effect of slowly activating outward membrane current, on the non-linearity in the output of a one-compartment Hodgkin-Huxley styled neuron. To evaluate this effect, the peak conductance of the slow potassium channel (gK-slow) was varied from 0% to 200% of its normal value in steps of 33%. Both cross- and iso-frequency coupling between the input and the output of the simulated neuron was computed using a generalized coherence measure, i.e., n:m coherence. With increasing gK-slow, the amount of sub-harmonic cross-frequency coupling, where the output frequencies (1–8 Hz) are lower than the input frequencies (15–35 Hz), increased progressively whereas no change in iso-frequency coupling was observed. Power spectral and phase-space analysis of the neuronal membrane voltage vs. slow potassium channel activation variable showed that the interaction of the slow channel dynamics with the fast membrane voltage dynamics generates the observed sub-harmonic coupling. This study provides quantitative insights into the role of an important membrane mechanism i.e. the slowly activating outward current in generating non-linearities in the output of a neuron.

Original languageEnglish (US)
Article number110509
JournalJournal of Theoretical Biology
StatePublished - Jan 21 2021


  • Cross-frequency coupling
  • Hodgkin-Huxley neuron
  • Slow potassium conductance
  • Sub-harmonic coupling

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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