Ligand-gated ion channels (LGICs) are regularly oligomers containing between two and five binding sites for ligands. Neither in homomeric nor heteromeric LGICs the activation process evoked by the ligand binding is fully understood. Here, we show on theoretical grounds that for LGICs with two to five binding sites, the cooperativity upon channel activation can be determined in considerable detail. The main requirements for our strategy are a defined number of binding sites in a channel, which can be achieved by concatenation, a systematic mutation of all binding sites and a global fit of all concentration–activation relationships (CARs) with corresponding intimately coupled Markovian state models. We take advantage of translating these state models to cubes with dimensions 2, 3, 4, and 5. We show that the maximum possible number of CARs for these LGICs specify all 7, 13, 23, and 41 independent model parameters, respectively, which directly provide all equilibrium constants within the respective schemes. Moreover, a fit that uses stochastically varied scaled unitary start vectors enables the determination of all parameters, without any bias imposed by specific start vectors. A comparison of the outcome of the analyses for the models with 2 to 5 binding sites showed that the identifiability of the parameters is best for a case with 5 binding sites and 41 parameters. Our strategy can be used to analyze experimental data of other LGICs and may be applicable to voltage-gated ion channels and metabotropic receptors.
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October 26 2023
Identifiability of equilibrium constants for receptors with two to five binding sites
Klaus Benndorf
,
(Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Validation, Visualization, Writing - original draft, Writing - review & editing)
1
Institute of Physiology II, Jena University Hospital, Friedrich Schiller University Jena
, Jena, Germany
Correspondence to Klaus Benndorf: klaus.benndorf@med.uni-jena.de
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Eckhard Schulz
Eckhard Schulz
(Conceptualization, Methodology, Writing - original draft)
2
Faculty of Electrical Engineering, Schmalkalden University of Applied Sciences
, Schmalkalden, Germany
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Klaus Benndorf
Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Validation, Visualization, Writing - original draft, Writing - review & editing
1
Institute of Physiology II, Jena University Hospital, Friedrich Schiller University Jena
, Jena, Germany
Eckhard Schulz
Conceptualization, Methodology, Writing - original draft
2
Faculty of Electrical Engineering, Schmalkalden University of Applied Sciences
, Schmalkalden, Germany
Correspondence to Klaus Benndorf: klaus.benndorf@med.uni-jena.de
Disclosures: The authors declare no competing interests exist.
Received:
May 26 2023
Revision Received:
August 22 2023
Revision Received:
September 27 2023
Accepted:
October 07 2023
Online ISSN: 1540-7748
Print ISSN: 0022-1295
Funding
Funder(s):
Deutsche Forschungsgemeinschaft
- Award Id(s): project P2
© 2023 Benndorf and Schulz
2023
Benndorf and Schulz
This article is distributed under the terms of an Attribution–Noncommercial–Share Alike–No Mirror Sites license for the first six months after the publication date (see http://www.rupress.org/terms/). After six months it is available under a Creative Commons License (Attribution–Noncommercial–Share Alike 4.0 International license, as described at https://creativecommons.org/licenses/by-nc-sa/4.0/).
J Gen Physiol (2023) 155 (12): e202313423.
Article history
Received:
May 26 2023
Revision Received:
August 22 2023
Revision Received:
September 27 2023
Accepted:
October 07 2023
Citation
Klaus Benndorf, Eckhard Schulz; Identifiability of equilibrium constants for receptors with two to five binding sites. J Gen Physiol 4 December 2023; 155 (12): e202313423. doi: https://doi.org/10.1085/jgp.202313423
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