Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department


Major Professor

Ghanim Ullah, Ph.D.

Committee Member

Martin Muschol, Ph.D.

Committee Member

Chad Dube, Ph.D.

Committee Member

Robert Hoy, Ph.D.

Committee Member

Garrett Matthews, Ph.D.


Na+ Dynamics, Neurodegenerative diseases, HData-Driven Modeling


One of the defining features of Alzheimer’s disease (AD) is the increased cleavage of the amyloid precursor protein (APP), causing abnormally high levels of the aggregation form of amyloid beta (Aβ ). Many studies have shown that both AD patients and AD mice models exhibit abnormal network activity, including hypersynchronous excitatory neuron behavior, altered brain rhythms, and in some instances epileptic seizures when exposed to high levels of Aβ In particular, strong experimental evidence suggests that it is the small globular amyloid oligomers (gOs) and curvilinear fibrils (CFs) rather than the more stable, late stage rigid fibrils (RFs) that cause cytotoxicity. Half-time scaling analysis implies that gOs/CFs grow along a separate pathway (off-pathway) and do not facilitate RF growth. However, whether these two species of Aβ interact directly or through the competition for available monomers is still incompletely understood. In the first part of this work we present a self-assembly model to recreate RF assembly under initial conditions that do and do not facilitate gOs/CFs growth, for both hen egg white lysozyme (HewL) and Aβ aggregation. The model presented in this work recreates many of the salient experimental features such as a salt concentration dependent boundary below which gOs/CFs growth does not occur. In addition, the results of our model, as well as others, require primary and secondary nucleation rates vary nonlinearly with respect to initial monomer concentration, suggesting the existence of growth mechanisms not present in popular protein aggregation models. Finally, nonlinear variation of growth kinetics as well as half-time scaling analysis of experimental results suggests that the presence of gOs/CFs inhibit the growth of RFs.

In the next part of this work we examine how Aβ changes the intrinsic properties of inhibitory neurons, making for one of the main causes of impaired network activity. However, the specific molecular mechanisms leading to interneuronal dysfunction are not completely understood. Utilizing an augmented Hodgkin-Huxley (HH) formalism and patch-clamp experiments, we identify specific neurological pathways that lead to AD-like behavior. In particular, interneurons in AD mice models exhibit the inability to reliably produce action potentials, as well as, a significantly depolarized resting membrane potential. We use these two features as criteria to identify potential pathways affected by Aβ accumulation. Our model suggest that increases in the amount of Na+ leakage into the interneuron reproduce abnormalities observed in APPSWE/PSEN1DeltaE9 (APdE9) AD mice model. We remark that the hyperpolarization activated cyclic nucleotide-gated (HCN) ion channel also recreated APdE9 neuronal behavior, however, it required an unphysiologically large increase in channel conductance. No other pathways observed fulfilled our criteria.

Strong experimental evidence suggests that Aβ has a significant effect on voltage-gated sodium channel (VGSC) function. Since VGSCs are responsible for action potential (AP) initiation we examine the phase space behavior of APdE9 mice. Our experimental results show that AP initiation in interneurons from APdE9 mice are significantly different from that of NTG mice. We observe a transition from a rapid monophasic onset that occurs over a wide range of membrane potentials in non-transgenic mice (NTG) to a slower biphasic onset that occurs over a narrower ranger of membrane potentials in APdE9 mice. By altering the fraction of VGSCs that behave cooperatively we are able to reproduce the phase space behavior of NTG mice and the transition to APdE9 mice behavior.

The work up to this point highlights the strong impact that Na+ dynamics have on network activity, especially when colocalized with inhibitory neurons. In the next part of this work we extend our non-cooperative Hodgkin-Huxley formalism to a multi-neuron network model to study the spontaneous Na+ oscillations that occur in the CA1 pyramidal neurons within the hippocampus of postnatal mice (2- days old). Experimentally, the frequency of these oscillations are very low (∼2/h), and can last minutes with amplitudes of 1-3 mM, and disappear after the first week postnatal. This phenomena stems from the inversion of the reversal potential of chloride, resulting in the inhibitory neurotransmitter gamma amino butyric acid (GABA), having an excitatory effect. An extensive pharmacological study shows that when excitatory receptors are blocked these oscillations persist, furthermore, blocking either GABA or VGSC receptors abolished Na+ oscillations. These results support the hypothesis that the Na+ oscillations observed in neonatal mice are the result of local action potential activity, as well as, excitatory GABAergic behavior. Our study also suggests that neural networks exhibiting these dynamics are susceptible to hyperactive, epileptic activity.

In the final part of this work we increase the fidelity of our extended Hodgkin-Huxley formalism through the addition of neurotransmitter dynamics. We apply this augmented network model to Dravet syndrome (DS) mouse model, an epileptic encephalopathy. Similar to AD patients and AD mice models, inhibitory neurons of mice with this disease exhibit dysfunction of Nav1.1 VGSCs, resulting in abnormal brain rhythms and epileptic activity. Most notably, we observe a disruption of the hippocampal theta-gamma coupling observed in DS mice compared to the NTG control. Our model is able to recreate the theta-gamma coupling observed experimentally by reducing Na+ conductance in inhibitory interneurons within our network.