Date of Award

Winter 12-15-2021

Author's School

McKelvey School of Engineering

Author's Department

Biomedical Engineering

Degree Name

Doctor of Philosophy (PhD)

Degree Type



Voltage-gated ion channels carry transmembrane current and underlie the voltages changes seen during the action potential. The ion channels open and close precisely, or gate, in response to voltage to create the specific cellular action potential waveform. The first models of voltage-gated ion channels gating dynamics were described by Hodgkin and Huxley when studying the neuronal action potential in the squid giant axon. While the probabilistic gating variables cleverly imagined by Hodgkin and Huxley to describe channel gating are still used today to describe cardiac ionic currents, Markov (or state-dependent) models provide a more accurate representation of channel dynamics. As experimentalists have learned more about channel dynamics and function throughout many decades of experimentation, these Markov models have gained complexity to account for these new observations. These models successfully represent the stages of channel activation, deactivation, and inactivation, and when inserted to models the cardiac action potential, one can make higher dimensional membrane excitability predictions. However, as the amount of experimental data to model increases, the complexity of these models has increased without bound. These large models are computationally inefficient to solve and often suffer from poor parameter identifiability when simulating the cellular and tissue levels. Thus, while human intuition has usually informed model structure, with so many current protocols to reproduce, and new structural information, this human intuition has begun to break down.

A study published in 2009 first suggested optimizing the Markov model rate parameters and topology, the number of states and edges and connections between them. The optimization method used to screen various Markov model topologies was probabilistically based and not as thorough as a systematic search. In this thesis, I begin by formulating the topological search problem is terms of a rooted, connected, and unlabeled graphs. One may enumerate the unique rooted topologies as a function of the number of states to allow for a more efficient, systematic evaluation of model structures of varying complexity.

Starting from this enumeration of unique rooted structures, I first detail further parsing of these structures through biophysically inspired restrictions inspired by decades of experimentation. With the focused collection of possible Markov structures, I systematically optimize rate parameters for various structures in order of increasing complexity. I use canonical voltage-clamp protocol datasets of human transient outward potassium currents (Ito,f), atrial mouse myocyte sodium currents (INa), and heterologously expressed sodium currents in HEK293 cells to screen the structural candidates as potential Markov models. I include quantitative measures of optimization progress and generalization loss to prevent model overfitting. I categorize model structures that acceptably and unacceptably fit the training voltage-clamp protocols and suggest a point of complexity that balances model fitting fidelity against the potential to overfit parameters. I then explore how various acceptable and unacceptable structural models perform at the cellular and tissue levels. Variability in these higher dimensional stimulations validate the previous categorization of the acceptable and unacceptable topologies and illustrate the need for more sophisticated voltage-clamp protocols to train kinetic models for cellular and tissue simulations.

In the following chapter, I then apply our model search algorithm to a large electrophysiological hERG experimental dataset. I notably independently identify a common structural model for a wild-type and mutant hERG dataset. I then validate the kinetic models by simulating an action potential clamp protocol to predict cellular level excitability effects. This study not only demonstrates the usefulness of this novel model structure search routine but also suggests a dataset driven approach to identify a common wild-type and modulated channel structure.

Finally, I provide a step-by-step to guide to allow others to use my novel topology search algorithm with their own voltage-clamp datasets. By lowering the barrier to entry to start creating kinetic models, I hope that more channel scientists may be able to use my routine than providing source code alone. I hope others may readily use this tool to suggest model structures of varying complexity for their dataset followed by conducting and suggesting further experiments to validate the potential structures as Markov channel models.

The modeler has unprecedented amount of functional channel, and eventually molecular detail, to reproduce when creating kinetic Markov models. The novel topology search algorithm presented here suggests Markov structures of varying complexity needed for a modeling study with varying goals. I hope that these Markov models may be part of a pipeline that readily connects the channel and tissue levels to predict membrane excitability effects.


English (en)


Jonathan R. Silva

Committee Members

Renato Feres


Update embargo

Available for download on Wednesday, December 20, 2023

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