scholarly journals The cardiac Na+/K+ ATPase: An updated, thermodynamically consistent model

2020 ◽  
Author(s):  
Michael Pan ◽  
Peter J. Gawthrop ◽  
Joseph Cursons ◽  
Kenneth Tran ◽  
Edmund J. Crampin
Keyword(s):  
Cardiac Electrophysiology ◽  
Extracellular Potassium ◽  
Potassium Accumulation ◽  
Pumping Rate ◽  
Matlab Code ◽  
Consistent Model ◽  
Wide Range ◽  
Original Manuscript ◽  
Metabolite Concentrations ◽  
Cellular Energetics

The Na+/K+ATPase is an essential component of cardiac electrophysiology, maintaining physiological Na+ and K+ concentrations over successive heart beats. Terkildsen et al. (2007) developed a model of the ventricular myocyte Na+/K+ ATPase to study extracellular potassium accumulation during ischaemia, demonstrating the ability to recapitulate a wide range of experimental data, but unfortunately there was no archived code associated with the original manuscript. Here we detail an updated version of the model and provide CellML and MATLAB code to ensure reproducibility and reusability. We note some errors within the original formulation which have been corrected to ensure that the model is thermodynamically consistent, and although this required some reparameterisation, the resulting model still provides a good fit to experimental measurements that demonstrate the dependence of Na+/K+ ATPase pumping rate upon membrane voltage and metabolite concentrations. To demonstrate thermodynamic consistency we also developed a bond graph version of the model. We hope that these models will be useful for community efforts to assemble a whole-cell cardiomyocyte model which facilitates the investigation of cellular energetics.

scholarly journals The cardiac Na+/K+ ATPase: An updated, thermodynamically consistent model

2020 ◽  
Author(s):  
Michael Pan ◽  
Peter J. Gawthrop ◽  
Joseph Cursons ◽  
Kenneth Tran ◽  
Edmund J. Crampin
Keyword(s):  
Cardiac Electrophysiology ◽  
Extracellular Potassium ◽  
Potassium Accumulation ◽  
Pumping Rate ◽  
Matlab Code ◽  
Consistent Model ◽  
Wide Range ◽  
Original Manuscript ◽  
Metabolite Concentrations ◽  
Cellular Energetics

The Na+/K+ATPase is an essential component of cardiac electrophysiology, maintaining physiological Na+ and K+ concentrations over successive heart beats. Terkildsen et al. (2007) developed a model of the ventricular myocyte Na+/K+ ATPase to study extracellular potassium accumulation during ischaemia, demonstrating the ability to recapitulate a wide range of experimental data, but unfortunately there was no archived code associated with the original manuscript. Here we detail an updated version of the model and provide CellML and MATLAB code to ensure reproducibility and reusability. We note some errors within the original formulation which have been corrected to ensure that the model is thermodynamically consistent, and although this required some reparameterisation, the resulting model still provides a good fit to experimental measurements that demonstrate the dependence of Na+/K+ ATPase pumping rate upon membrane voltage and metabolite concentrations. To demonstrate thermodynamic consistency we also developed a bond graph version of the model. We hope that these models will be useful for community efforts to assemble a whole-cell cardiomyocyte model which facilitates the investigation of cellular energetics.

scholarly journals Potassium diffusive coupling in neural networks

2010 ◽  
Vol 365 (1551) ◽  
pp. 2347-2362 ◽  
Author(s):  
Dominique M. Durand ◽  
Eun-Hyoung Park ◽  
Alicia L. Jensen
Keyword(s):  
Neural Networks ◽  
Neural Activity ◽  
Neuronal Excitability ◽  
Epileptiform Activity ◽  
Lateral Diffusion ◽  
Normal Activity ◽  
Ionic Concentration ◽  
Extracellular Potassium ◽  
Potassium Accumulation ◽  
Diffusive Coupling

Conventional neural networks are characterized by many neurons coupled together through synapses. The activity, synchronization, plasticity and excitability of the network are then controlled by its synaptic connectivity. Neurons are surrounded by an extracellular space whereby fluctuations in specific ionic concentration can modulate neuronal excitability. Extracellular concentrations of potassium ([K + ] o ) can generate neuronal hyperexcitability. Yet, after many years of research, it is still unknown whether an elevation of potassium is the cause or the result of the generation, propagation and synchronization of epileptiform activity. An elevation of potassium in neural tissue can be characterized by dispersion (global elevation of potassium) and lateral diffusion (local spatial gradients). Both experimental and computational studies have shown that lateral diffusion is involved in the generation and the propagation of neural activity in diffusively coupled networks. Therefore, diffusion-based coupling by potassium can play an important role in neural networks and it is reviewed in four sections. Section 2 shows that potassium diffusion is responsible for the synchronization of activity across a mechanical cut in the tissue. A computer model of diffusive coupling shows that potassium diffusion can mediate communication between cells and generate abnormal and/or periodic activity in small (§3) and in large networks of cells (§4). Finally, in §5, a study of the role of extracellular potassium in the propagation of axonal signals shows that elevated potassium concentration can block the propagation of neural activity in axonal pathways. Taken together, these results indicate that potassium accumulation and diffusion can interfere with normal activity and generate abnormal activity in neural networks.

scholarly journals The Cardiac Electrophysiology Web Lab

2015 ◽  
Author(s):  
Jonathan Cooper ◽  
Martin Scharm ◽  
Gary R Mirams
Keyword(s):  
Cardiac Electrophysiology ◽  
Computational Modelling ◽  
Cell Types ◽  
Virtual Experiments ◽  
Online Resource ◽  
Voltage Curve ◽  
Current Voltage ◽  
Wide Range ◽  
Current Voltage Curve ◽  
The Mathematical Model

Computational modelling of cardiac cellular electrophysiology has a long history, with many models now available for different species, cell types, and experimental preparations. This success brings with it a challenge: how do we assess and compare the underlying hypotheses and emergent behaviours, in order to choose a model as a suitable basis for a new study, or characterize how a particular model behaves in different scenarios? We have created an online resource for the characterization and comparison of electrophysiological cell models under a wide range of experimental scenarios. The details of the mathematical model (quantitative assumptions and hypotheses formulated as ordinary differential equations) are separated from the experimental protocol being simulated. Each model and protocol is then encoded in computer-readable formats. A simulation tool runs virtual experiments on models, and a website – https://chaste.cs.ox.ac.uk/FunctionalCuration – provides a friendly interface, allowing users to store and compare results. The system currently contains a sample of 36 models and 23 protocols, including current-voltage curve generation, action potential properties under steady pacing at different rates, restitution properties, block of particular channels, and hypo-/hyper-kalaemia. This resource is publicly available, open source, and free; and we invite the community to use it and become involved in future developments. Those interested in comparing competing hypotheses using models can make a more informed decision; those developing new models can upload them for easy evaluation under the existing protocols, and even add their own protocols.

scholarly journals Bond graph modelling of the cardiac action potential: implications for drift and non-unique steady states

2018 ◽  
Vol 474 (2214) ◽  
pp. 20180106 ◽  
Author(s):  
Michael Pan ◽  
Peter J. Gawthrop ◽  
Kenneth Tran ◽  
Joseph Cursons ◽  
Edmund J. Crampin
Keyword(s):  
Action Potential ◽  
Conservation Laws ◽  
Cardiac Electrophysiology ◽  
Bond Graph ◽  
Steady States ◽  
Cardiac Action Potential ◽  
Bond Graphs ◽  
Charge Conservation ◽  
Cardiac Action ◽  
Wide Range

Mathematical models of cardiac action potentials have become increasingly important in the study of heart disease and pharmacology, but concerns linger over their robustness during long periods of simulation, in particular due to issues such as model drift and non-unique steady states. Previous studies have linked these to violation of conservation laws, but only explored those issues with respect to charge conservation in specific models. Here, we propose a general and systematic method of identifying conservation laws hidden in models of cardiac electrophysiology by using bond graphs, and develop a bond graph model of the cardiac action potential to study long-term behaviour. Bond graphs provide an explicit energy-based framework for modelling physical systems, which makes them well suited for examining conservation within electrophysiological models. We find that the charge conservation laws derived in previous studies are examples of the more general concept of a ‘conserved moiety’. Conserved moieties explain model drift and non-unique steady states, generalizing the results from previous studies. The bond graph approach provides a rigorous method to check for drift and non-unique steady states in a wide range of cardiac action potential models, and can be extended to examine behaviours of other excitable systems.

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