Statistical Approach to Incorporating Experimental Variability into a Mathematical Model of the Voltage-Gated Na+ Channel and Human Atrial Action Potential.

Daniel Gratz,Thomas J Hund,Alexander J Winkle,Seth H Weinberg

doi:10.3390/cells10061516

Abstract

The voltage-gated Na+ channel Nav1.5 is critical for normal cardiac myocyte excitability. Mathematical models have been widely used to study Nav1.5 function and link to a range of cardiac arrhythmias. There is growing appreciation for the importance of incorporating physiological heterogeneity observed even in a healthy population into mathematical models of the cardiac action potential. Here, we apply methods from Bayesian statistics to capture the variability in experimental measurements on human atrial Nav1.5 across experimental protocols and labs. This variability was used to define a physiological distribution for model parameters in a novel model formulation of Nav1.5, which was then incorporated into an existing human atrial action potential model. Model validation was performed by comparing the simulated distribution of action potential upstroke velocity measurements to experimental measurements from several different sources. Going forward, we hope to apply this approach to other major atrial ion channels to create a comprehensive model of the human atrial AP. We anticipate that such a model will be useful for understanding excitability at the population level, including variable drug response and penetrance of variants linked to inherited cardiac arrhythmia syndromes.

Highlights

Atrial fibrillation (AF) is the most common sustained arrhythmia in the U.S, and is associated with a range of comorbidities, including increased risk for heart failure and ischemic stroke
Voltage-gated Na+ channels are required for normal atrial excitability and defects in the function of the primary cardiac Na+ channel Nav 1.5 have been linked to increased risk for AF
While a variety of Nav models have been published for use in simulations of the cardiac action potential (Figure 2), we proposed a novel formulation (Figure 2A) that sought to balance simplicity of Hodgkin-Huxley type models with channel gating assumed to occur via independent processes (Figure 2B) [20] and Markov Chain models in which gating is represented as transitions between dependent states (Figure 2C) [21,22]

Summary

Introduction

Atrial fibrillation (AF) is the most common sustained arrhythmia in the U.S, and is associated with a range of comorbidities, including increased risk for heart failure and ischemic stroke. Voltage-gated Na+ channels are required for normal atrial excitability and defects in the function of the primary cardiac Na+ channel Nav 1.5 have been linked to increased risk for AF. Nav 1.5 are commonly used in AF patients without structural heart disease [2,3]. Mathematical modeling has proven valuable in understanding the role of Nav 1.5 in regulating cardiac excitability in normal and diseased states, including in the discovery and testing of novel drugs and therapies (e.g., CiPA project) [4,5,6,7]

Objectives

Methods

Results

Conclusion