Modeling Sodium Channel Functional Variation in Garter Snakes With Known Tetrodotoxin Resistance Mutations
Authors
Gustafson, Ryan
Issue Date
2023
Type
Thesis
Language
Keywords
Hodgkin-Huxley , Identifiability , Mechanistic Model , Sodium Channel , Tetrodotoxin , Thamnophis
Alternative Title
Abstract
The action potential is fundamental to animal life as it gives a mechanism for rapid communication between cells, organs, and body regions, and a means for rapid muscular and nervous activity. Action potentials are bioelectrical signals that are carried through the body via neurons or other excitable cells and work by displacing ions in across cells which creates a propagating charge gradient. Interfering with the machinery that makes action potentials possible can be detrimental to organisms, even fatal. Sodium ion channels (Na\textsubscript{V}) are key players in the production of action potentials (as well as potassium ion channels). These channels allow for a voltage-gated regulation of the distribution of sodium and potassium ions in nerve and muscle cells. Opening these channels allows for rapid influx (Na\textsuperscript{+}) and a rapid efflux (K\textsuperscript{+}) of ions across the cell membrane. This rapid movement of ions creates the propagating electrical current in the nerve and muscle cells, indicating the intent to fire or contract. Without this signal, nerves and muscles remain inactive. Because this conserved molecular machinery is needed for organismal function, it has become the target of a host of neurotoxins. Indeed, Pacific newts (\textit{Taricha}) possess tetrodotoxin (TTX). TTX blocks the pore of the sodium ion channels, stopping the flow of ions across the membrane, and rendering any newt predator paralyzed. This includes respiratory and cardiac muscles which leads to asphyxiation and cardiac arrest -- death. However, there are some populations of garter snakes (\textit{Thamnophis}) that can prey upon these deadly newts. Evolution has offered a partial solution to these predators in the form of a handful of mutations in the sodium ion channels of the snake's muscle cells. These mutations decrease the ability for TTX to bind to sodium-ion channels which allows the snake to remain mobile even with TTX in its system (referred to a ''TTX-resistance"). But, this small change in the shape of the pore of the sodium-ion channel affects the ability of the channel to conduct sodium ions in the absence of TTX. So, snakes with these modifications have a lessened baseline muscle function. So, there is a trade-off that occurs where the TTX-resistant snakes have an expanded menu, but they lose some motility (which could result in their own predation). In this thesis, the aim is to determine if the action potentials from the aquatic garter snake (\textit{Thamnophis atratus}) with a single point mutation are phenotypically different from those \textit{T.atratus} with no mutation (referred to as ''conserved" or ''TTX-sensitive"). To do this, a model using first-order linear differential equations will be produced that approximates experimentally collected action potential data (sometimes referred to as a trace). This model will then be simplified to use the least number of parameters possible. With the simplified equations, the model will be fit to the experimental data via an optimization routine that uses least squares as its objective function. At this point, it will be apparent that there are practical identifiability issues where the model does not produce a unique solution for the same action potential trace when given different starting points. This issue will be mitigated by only optimizing a subset of the possible parameters and by implementing a multi-start approach. The parameters that are optimized are the free parameters. This means that some parameters will be set to some fixed value during the optimization. Because some parameters will be fixed, and the true value of those parameters is unknown (because of the identifiability issue) many different fixed parameter sets will be generated, and the free parameters (once optimized) will all be traded as part of a group, sampled from a single population. This will be done on both the TTX-sensitive action potential data and the TTX-resistant action potential data. With those two groups, a group-level comparison will be performed (via a linear mixed effects model), and the differences that are found between the two groups will be the basis for explaining the differences between the group. It was found that the parameter that describes the conductance of sodium ($ G_{Na} $), in the mechanistic model, was less in the mutant snakes than in the snakes with the ancestral condition of no sodium channel mutations. This provides evidence that the modifications that confer resistance to TTX reduce the ability of those snakes to conduct sodium ions and have enough impact to be quantified by the ensemble phenotype of the action potential. In addition to the sodium conductance, two other parameters in the mechanistic model were found to be significantly different between the groups. In both cases the parameter change indicated that the sodium ion channel exists in a less permissive (to sodium ions) state in the mutant snakes, further corroborating the initial finding. This also opens up the doors for further research into the true action of the sodium-ion channels in the mutant snakes in order to find a biochemical reason for this restriction of ion flow.
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Creative Commons Attribution-ShareAlike 4.0 United States