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Inward rectifier potassium channels interact with calcium channels to promote robust and physiological bistability.

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Paper

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The authors' code

Julia · 30 lines · 841 B · MIT

  1. include("gates.jl")
  2. function INa(gNa,mNa,hNa,V,eNa)
  3. INa = gNa*mNa^3*hNa*(V-eNa) # [µA/cm^2]
  4. return INa
  5. end
  6. function IKDR(gKDR,mKDR,V,eK)
  7. IKDR = gKDR*mKDR^4*(V-eK) # [µA/cm^2]
  8. return IKDR
  9. end
  10. function ICaLf(pCaLf,mCaLf,hCaLf,V,Ca,Ca_o)
  11. ICaLf = pCaLf*mCaLf^2*hCaLf*ghk_LeFranc(V, Ca, Ca_o) *1000 # [µA/cm^2] instead of [mA/cm^2]
  12. return ICaLf
  13. end
  14. function ICaLs(pCaLs,mCaLs,hCaLs,V,Ca,Ca_o)
  15. ICaLs = pCaLs*mCaLs*hCaLs*ghk_LeFranc(V, Ca, Ca_o) *1000 # [µA/cm^2] instead of [mA/cm^2]
  16. return ICaLs
  17. end
  18. function IKir(gKir,mKir,V,eK)
  19. IKir = gKir*mKir*(V-eK) # [µA/cm^2]
  20. return IKir
  21. end
  22. function IKM(gKM,mKM,V,eK)
  23. IKM = gKM*mKM*(V-eK) # [µA/cm^2]
  24. return IKM
  25. end
  26. function Ileak(gleak,V,eleak)
  27. Ileak = gleak*(V-eleak) # [µA/cm^2]
  28. return Ileak
  29. end

currents.jl at commit a4cb390, under MIT · at the source

Overview

Authors: Anaëlle De Worm1, Guillaume Drion1, Pierre Sacré1
  1. Department of Electrical Engineering and Computer Science, University of Liège, Liège, Belgium
Institutions: University of Liège (Belgium)
Journal: PLoS computational biology, volume 22, issue 7, article e1014549
Dates: received 23 May 2025; accepted 8 July 2026; published online 28 July 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1371/journal.pcbi.1014549 · PMID 42520078 · PMCID PMC13441080 · OpenAlex W7171485400
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: cellular / molecular (subfield)
MeSH: Calcium Channels*, Models, Neurological*, Potassium Channels, Inwardly Rectifying*, Action Potentials, Animals, Computational Biology (* major topic)
Topic: Neural dynamics and brain function (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: Waalse Gewest; Belgian Federal Science Policy Office (NEMODEI2)
Citations: not cited yet (Europe PMC); 42 references in the paper

Abstract

Projection neurons in the dorsal horn relay nociceptive input to supraspinal centers. During central sensitization, a subset of them switches from tonic firing to plateau potentials with sustained afterdischarges, a change that requires intrinsic bistability between a resting and a spiking state. Voltage-gated L-type calcium (CaL) channels can produce bistability, but reach physiological resting states only when paired with voltage-gated potassium channels, most of which simultaneously shrink the bistability window. How robust, physiological bistability arises has therefore remained unclear. Using a minimal conductance-based model, we show that inward rectifier potassium (Kir) channels enlarge the bistability window when combined with CaL channels, while M-type potassium (KM) channels slightly reduce it. Within the parameter region where bistability is both robust and physiological, both channel types can sustain bistability, but the CaL + Kir combination produces a substantially larger window and is more robust to noise and intrinsic variability. This window-enlarging effect traces to a shape feature of the outward Kir steady-state current: like the CaL current, it has a region of negative differential conductance around the spike threshold, a feature absent from KM and from most other voltage-gated potassium currents. Bifurcation analysis further shows that the two pairs support qualitatively distinct excitability: plateau-generating bistability for CaL + Kir and resonator-like dynamics for CaL + KM. These conclusions hold in a two-compartment model of deep projection neurons with realistic ion channel complements, and identify the CaL + Kir pair as a candidate intrinsic mechanism for central sensitization.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above.

anadew2/cal-kir-bistability

License: MIT
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: a4cb390e5a4593adef0c85c91b7069c717aafe9c, 29 April 2026
Languages: Julia (163), Shell (56)
Size: 860 files, 219 scripts
Software Heritage: not archived
Found in: the text, “Software”
Holds: README, license file, environment (.vscode/env/Manifest.toml, .vscode/env/Project.toml), tests
Not found: CITATION.cff, continuous integration, documentation
Tools: Plots.jl (81 files), DifferentialEquations.jl (60 files), DataFrames.jl (6 files), Distributions.jl (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
221 files

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 219 scripts, each with its path and the digest of its content;
  • no match between paragraphs and code yet;
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data Availability

All data and code used for running experiments and plotting are available at https://github.com/anadew2/cal-kir-bistability/tree/main.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 2, 28 September 2026

  • Funding: added Waalse Gewest; Belgian Federal Science Policy Office: NEMODEI2

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 6 MeSH terms, 41 references.

Cite

This paper

De Worm, A., Drion, G., & Sacré, P. (2026). Inward rectifier potassium channels interact with calcium channels to promote robust and physiological bistability. PLoS computational biology, 22(7), e1014549. https://doi.org/10.1371/journal.pcbi.1014549

BibTeX

@article{deworm2026inward,
author = {De Worm, Anaëlle and Drion, Guillaume and Sacré, Pierre},
title = {{Inward rectifier potassium channels interact with calcium channels to promote robust and physiological bistability}},
journal = {PLoS computational biology},
year = {2026},
month = jul,
volume = {22},
number = {7},
pages = {e1014549},
publisher = {PLOS},
issn = {1553-734X},
doi = {10.1371/journal.pcbi.1014549},
url = {https://doi.org/10.1371/journal.pcbi.1014549},
pmid = {42520078},
pmcid = {PMC13441080}
}

RIS

TY - JOUR
AU - De Worm, Anaëlle
AU - Drion, Guillaume
AU - Sacré, Pierre
TI - Inward rectifier potassium channels interact with calcium channels to promote robust and physiological bistability
T2 - PLoS computational biology
J2 - PLoS Comput Biol
PY - 2026
DA - 2026/07/28
VL - 22
IS - 7
SP - e1014549
SN - 1553-734X
PB - PLOS
DO - 10.1371/journal.pcbi.1014549
UR - https://doi.org/10.1371/journal.pcbi.1014549
LA - en
ER -

CSL-JSON

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"container-title-short": "PLoS Comput Biol",
"volume": "22",
"issue": "7",
"page": "e1014549",
"DOI": "10.1371/journal.pcbi.1014549",
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"PMCID": "PMC13441080",
"ISSN": "1553-734X",
"publisher": "PLOS",
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