A Quantitative Model of Cortical Spreading Depression Due to Purinergic and Gap-Junction Transmission in Astrocyte Networks

Abstract

Spreading depression (SD), a propagating wave of electrical silence in the cortex and archicortex, involves depolarization of neurons and astrocytes for approximately 1 min, due principally to a large increase in extracellular K+. SD is accompanied by large increases in extracellular ATP and is blocked by glutamate N-methyl-D-aspartate receptor antagonists. As a principal means of transmission between astrocytes is through their release of ATP, we have investigated if a model in which SD is driven by the effects of astrocyte waves of ATP interacting with waves of glutamate release from neurons and astrocytes can give a quantitative account of experimental observations on SD. We show that the characteristics of SD and the accompanying extracellular ionic changes can be accommodated by such a model-whether astrocyte transmission is principally through the release of ATP, as in archicortex (hippocampus) and spinal cord, or via gap junctions, as in the neocortex. Furthermore, these models give quantitative accounts of the effects on the characteristics of SD of agents toxic for astrocytes and of gap-junction blockers. Finally, an additional series of critical tests of the model is suggested.

Mathematical approaches to modeling of cortical spreading depression

“…This glutamate acts on the NMDA receptors of neurons to trigger a large depolarization of the membrane potential (via massive redistribution of ions) and release of glutamate from the neurons, which leads to additional releases of ATP from astrocytes that complete the cycle. 4 While there is strong evidence in favor of the glutamate hypothesis, other experimental work also supports the potassium mechanism even though the details of the original theory may not be correct. 50 It is very likely that both glutamate and potassium are important and there is evidence in favor of the dual hypothesis.…”

“…4, it was proposed that glutamate released by astrocytes is the main agent responsible for the propagation of CSD, along with the ATP released by neurons. The model consists of a one-dimensional array of astrocytes and neurons, which are coupled via a two-way communication.…”

Cortical spreading depression and mitochondrial dysfunction with aging: lessons from ethanol abuse

“…This phenomenon has a duration of approximately 1 min and very slow propagation (2–5 mm/min) when compared to action potentials, resulting in a suppression of electrical activity and disruption of ion homeostasis (Bennett et al, 2008; Seidel and Shuttleworth, 2011). This depolarization occurs when the extracellular K + concentrations increase above a threshold of 40 mM, causing the CSD wave propagation into adjacent cells.…”

Variation of repetitive cortical spreading depression waves is related with relative refractory period: a computational study

“…Here, blood vessels were not included in this model. Since astrocytes play an important role in CSD [39,47] ] o respectively represent as the extracellular potassium concentration, the astrocytic calcium concentration, the neuronal calcium concentration, and the extracellular calcium concentration. We did not take the change of the volume of the three compartments into account during CSD.…”