June 2024 Analyzing cross-talk between superimposed signals: Vector norm dependent hidden Markov models and applications to ion channels
Laura Jula Vanegas, Benjamin Eltzner, Daniel Rudolf, Miroslav Dura, Stephan E. Lehnart, Axel Munk
Author Affiliations +
Ann. Appl. Stat. 18(2): 1445-1470 (June 2024). DOI: 10.1214/23-AOAS1842


We propose and investigate a hidden Markov model (HMM) for the analysis of dependent, aggregated, superimposed two-state signal recordings. A major motivation for this work is that often these signals cannot be observed individually but only their superposition. Among others, such models are in high demand for the understanding of cross-talk between ion channels, where each single channel cannot be measured separately. As an essential building block, we introduce a parameterized vector norm dependent Markov chain model and characterize it in terms of permutation invariance as well as conditional independence. This building block leads to a hidden Markov chain sum process which can be used for analyzing the dependence structure of superimposed two-state signal observations within an HMM. Notably, the model parameters of the vector norm dependent Markov chain are uniquely determined by the parameters of the sum process and are, therefore, identifiable. We provide algorithms to estimate the parameters, discuss model selection and apply our methodology to real-world ion channel data from the heart muscle, where we show competitive gating.

Funding Statement

The authors acknowledge support of the DFG CRC 803 project Z02, DFG CRC 1456 projects A01, B02, B04 and C06 and the DFG Cluster of Excellence 2067 MBExC. The data set was provided by Lehnart’s Lab from the Cellular Biophysics and Translational Cardiology Section in the Heart Research Center Göttingen (HRCG). S. E. Lehnart was supported by Deutsche Forschungsgemeinschaft SPP1926 Next Generation Optogenetics. The authors contributed equally.


We are grateful to Housen Li and Robin Requadt for helpful discussions and validation of our software package. M. Dura, S. E. Lehnart and A. Munk are additionally affiliated with the DFG Cluster of Excellence “Multiscale Bioimaging: from molecular Machines to Networks of excitable cells” at the University Medical Center Göttingen. D. Rudolf and A. Munk are additionally affiliated with the Felix-Bernstein-Institute for Mathematical Statistics in the Biosciences at the University of Göttingen.


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Laura Jula Vanegas. Benjamin Eltzner. Daniel Rudolf. Miroslav Dura. Stephan E. Lehnart. Axel Munk. "Analyzing cross-talk between superimposed signals: Vector norm dependent hidden Markov models and applications to ion channels." Ann. Appl. Stat. 18 (2) 1445 - 1470, June 2024. https://doi.org/10.1214/23-AOAS1842


Received: 1 August 2022; Revised: 1 October 2023; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/23-AOAS1842

Keywords: Aggregated data , crosstalk , Hidden Markov models , Ion channels , lumping property , permutation invariance , vector norm dependency

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 2 • June 2024
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