Matching Items (32)
Description
The primary channel responsible for cold thermo-transduction in mammals is the transient receptor potential melastatin 8 (TRPM8) channel. TRPM8 is a polymodal, nonselective cation channel with an activation that is dependent on a variety of signals, including the membrane potential, calcium concentration, temperature, and ligands such as menthol. Mathematical modeling provides valuable insight into biochemical phenomena, such as the activity of these channels, which are difficult to observe experimentally. Here, we propose a TRPM8 gating model, represented as a system of ordinary differential equations with menthol, calcium, voltage, and temperature dependencies. We use voltage-clamp data from transfected HEK293 cells in the presence of menthol to create a menthol-dependent voltage shift of activation. We fit the parameters of the TRPM8 gating model to replicate experimental TRPM8 transfected HEK293 cell voltage clamp electrophysiology data using a genetic algorithm. Using k-means clustering, we note eight clusters within 110 total parameter sets consisting of parameter solutions that provide a good fit to the experimental data. We then replicate novel fixed-voltage temperature ramp and fixed-temperature voltage ramp experimental data, demonstrating that our model can replicate the dynamic behaviors of TRPM8. With this TRPM8 gating model, we analyze the various parameter sets obtained from the genetic algorithm and find that different parameter combinations of calcium decay, calcium voltage shift of activation, and temperature sensitivity are able to match static voltage clamp data although differ in their effects on hysteresis and maximal current within prolonged temperature ramp simulations.
ContributorsDudebout, Eric (Author) / Crook, Sharon (Thesis director) / Van Horn, Wade (Committee member) / Barrett, The Honors College (Contributor) / School of Molecular Sciences (Contributor)
Created2024-05
Description
The study of hyperbolic manifolds, and more generally hyperbolic orbifolds, is inti-mately bound to the study of discrete subgroups of the isometry group of hyperbolic
n-space. In the wake of certain rigidity theorems due to Mostow et al., a new program
of study has developed in recent decades for the characterization of hyperbolic mani-
folds by investigating certain invariants arising from the theory of numbers. Critical
to the arithmetic study of hyperbolic manifolds are those discrete subgroups of the
isometry group which have finite co-volume under the Haar metric, sometimes called
lattices. These correlate to a particular tiling of hyperbolic space with a certain fun-
damental domain. The simplest non-trivial example of these for hyperbolic orbifolds
are triangle groups. These triangle groups, or more properly arithmetic Fuchsian tri-
angle groups, were first classified by Takeuchi in 1983. In the proceeding manuscript,
a concise introduction to the geometry of hyperbolic manifolds and orbifolds is put
forth. The two primary invariants used in the study of the hyperbolic lattices, the
invariant trace field and the invariant quaternion algebra, are then defined. There-
after, a hyperbolic triangle group is constructed from the tessellation of the hyperbolic
plane by hyperbolic triangles. A version of the classification theorem of arithmetic
Fuchsian triangle groups is stated and proved. The paper concludes with a brief
discussion regarding non-arithmetic lattices.
ContributorsMagaña, Jerry Paul (Author) / Pauper, Julien (Thesis advisor) / Kotschwar, Brett (Thesis advisor) / Crook, Sharon (Committee member) / Arizona State University (Publisher)
Created2024