Geometry and nonlinear dynamics underlying excitability phenotypes in biophysical models of membrane potential

Persistent Link:
http://hdl.handle.net/10150/312741
Title:
Geometry and nonlinear dynamics underlying excitability phenotypes in biophysical models of membrane potential
Author:
Herrera-Valdez, Marco Arieli
Issue Date:
2014
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Embargo:
Release 09-Jun-2014
Abstract:
The main goal of this dissertation was to study the bifurcation structure underlying families of low dimensional dynamical systems that model cellular excitability. One of the main contributions of this work is a mathematical characterization of profiles of electrophysiological activity in excitable cells of the same identified type, and across cell types, as a function of the relative levels of expression of ion channels coded by specific genes. In doing so, a generic formulation for transmembrane transport was derived from first principles in two different ways, expanding previous work by other researchers. The relationship between the expression of specific membrane proteins mediating transmembrane transport and the electrophysiological profile of excitable cells is well reproduced by electrodiffusion models of membrane potential involving as few as 2 state variables and as little as 2 transmembrane currents. Different forms of the generic electrodiffusion model presented here can be used to study the geometry underlying different forms of excitability in cardiocytes, neurons, and other excitable cells, and to simulate different patterns of response to constant, time-dependent, and (stochastic) time- and voltage-dependent stimuli. In all cases, an initial analysis performed on a deterministic, autonoumous version of the system of interest is presented to develop basic intuition that can be used to guide analyses of non-autonomous or stochastic versions of the model. Modifications of the biophysical models presented here can be used to study complex physiological systems involving single cells with specific membrane proteins, possibly linking different levels of biological organization and spatio-temporal scales.
Type:
text; Electronic Dissertation
Keywords:
Computational neurosciences; Dynamical systems; Electrodiffusion; Excitability phenotype; Membrane potential; Mathematics; Bifurcation
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Lega, Joceline

Full metadata record

DC FieldValue Language
dc.language.isoen_USen
dc.titleGeometry and nonlinear dynamics underlying excitability phenotypes in biophysical models of membrane potentialen_US
dc.creatorHerrera-Valdez, Marco Arielien_US
dc.contributor.authorHerrera-Valdez, Marco Arielien_US
dc.date.issued2014-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.releaseRelease 09-Jun-2014en_US
dc.description.abstractThe main goal of this dissertation was to study the bifurcation structure underlying families of low dimensional dynamical systems that model cellular excitability. One of the main contributions of this work is a mathematical characterization of profiles of electrophysiological activity in excitable cells of the same identified type, and across cell types, as a function of the relative levels of expression of ion channels coded by specific genes. In doing so, a generic formulation for transmembrane transport was derived from first principles in two different ways, expanding previous work by other researchers. The relationship between the expression of specific membrane proteins mediating transmembrane transport and the electrophysiological profile of excitable cells is well reproduced by electrodiffusion models of membrane potential involving as few as 2 state variables and as little as 2 transmembrane currents. Different forms of the generic electrodiffusion model presented here can be used to study the geometry underlying different forms of excitability in cardiocytes, neurons, and other excitable cells, and to simulate different patterns of response to constant, time-dependent, and (stochastic) time- and voltage-dependent stimuli. In all cases, an initial analysis performed on a deterministic, autonoumous version of the system of interest is presented to develop basic intuition that can be used to guide analyses of non-autonomous or stochastic versions of the model. Modifications of the biophysical models presented here can be used to study complex physiological systems involving single cells with specific membrane proteins, possibly linking different levels of biological organization and spatio-temporal scales.en_US
dc.typetexten
dc.typeElectronic Dissertationen
dc.subjectComputational neurosciencesen_US
dc.subjectDynamical systemsen_US
dc.subjectElectrodiffusionen_US
dc.subjectExcitability phenotypeen_US
dc.subjectMembrane potentialen_US
dc.subjectMathematicsen_US
dc.subjectBifurcationen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorLega, Jocelineen_US
dc.contributor.committeememberCushing, Jimen_US
dc.contributor.committeememberWatkins, Josephen_US
dc.contributor.committeememberSecomb, Timothy W.en_US
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