Control of clustered action potential firing in a mathematical model of entorhinal cortex stellate cells

•An SDE model of entorhinal cortex (EC) stellate cells is proposed.•Experimentally observed action potential clustering is investigated in the model.•Clusters are generated by subcritical-Hopf/homoclinic type bursting.•Potential mechanisms underlying changes in EC dynamics in dementia are presented....

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Bibliographic Details
Published in:Journal of theoretical biology 2018-07, Vol.449, p.23-34
Main Authors: Tait, Luke, Wedgwood, Kyle, Tsaneva-Atanasova, Krasimira, Brown, Jon T., Goodfellow, Marc
Format: Article
Language:English
Subjects:
Action Potentials
Animals
Bifurcation analysis
Bursting
Dementia
Dementia - pathology
Dementia - physiopathology
Entorhinal Cortex - pathology
Entorhinal Cortex - physiopathology
Gamma Rhythm
Humans
Models, Neurological
Neuron model
Subthreshold oscillations
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Summary:•An SDE model of entorhinal cortex (EC) stellate cells is proposed.•Experimentally observed action potential clustering is investigated in the model.•Clusters are generated by subcritical-Hopf/homoclinic type bursting.•Potential mechanisms underlying changes in EC dynamics in dementia are presented. The entorhinal cortex is a crucial component of our memory and spatial navigation systems and is one of the first areas to be affected in dementias featuring tau pathology, such as Alzheimer’s disease and frontotemporal dementia. Electrophysiological recordings from principle cells of medial entorhinal cortex (layer II stellate cells, mEC-SCs) demonstrate a number of key identifying properties including subthreshold oscillations in the theta (4–12 Hz) range and clustered action potential firing. These single cell properties are correlated with network activity such as grid firing and coupling between theta and gamma rhythms, suggesting they are important for spatial memory. As such, experimental models of dementia have revealed disruption of organised dorsoventral gradients in clustered action potential firing. To better understand the mechanisms underpinning these different dynamics, we study a conductance based model of mEC-SCs. We demonstrate that the model, driven by extrinsic noise, can capture quantitative differences in clustered action potential firing patterns recorded from experimental models of tau pathology and healthy animals. The differential equation formulation of our model allows us to perform numerical bifurcation analyses in order to uncover the dynamic mechanisms underlying these patterns. We show that clustered dynamics can be understood as subcritical Hopf/homoclinic bursting in a fast-slow system where the slow sub-system is governed by activation of the persistent sodium current and inactivation of the slow A-type potassium current. In the full system, we demonstrate that clustered firing arises via flip bifurcations as conductance parameters are varied. Our model analyses confirm the experimentally suggested hypothesis that the breakdown of clustered dynamics in disease occurs via increases in AHP conductance.
ISSN:0022-5193
1095-8541
DOI:10.1016/j.jtbi.2018.04.013