Analyzing cross-talk between superimposed signals: Vector norm dependent hidden Markov models and applications to ion channels

TL;DR

This paper introduces a novel vector norm dependent hidden Markov model to analyze superimposed two-state signals, particularly useful for studying ion channel cross-talk where individual signals are unobservable.

Contribution

It develops a new parameterized Markov chain model with permutation invariance and conditional independence, enabling analysis of dependent superimposed signals within an HMM framework.

Findings

Model parameters are uniquely identifiable from the sum process.

Algorithms for parameter estimation are provided.

Application to real ion channel data shows effective analysis of gating behavior.

Abstract

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.