Abstract
Amyloids β (Aβ) are a hallmark of Alzheimer's disease. They affect the communication between neurons. They can also bind to neuronal targets and thereby affect both intracellular signalling and neuronal electrical activity. During the onset of Alzheimer's disease, a positive feedback loop between Aβ40/42 and cytosolic calcium is thoughtto accelerate the progression of the disease. If intracellular calcium and Aβ reinforce themselves through this mechanism, one would expect that the neurons targets of Aβ may display an altered electrical activity caused by the increase in cytoplasmic calcium as it is known that there is a tight coupling between calcium dynamics and the electrical excitabilty. The aim of this work is to test this assumption when considering one of the privileged target of Aβ, the activity of extrasynaptic NMDA receptors. Our theoretical model is a simple description of neuronal electrical activity based on the Hodgkin-Huxley like formalism, including a term that corresponds to the activity of the NMDA receptor and a cytosolic calcium compartment. When the tonic activity of extrasynaptic NMDA receptors is increased, neurons are less excitable. This is a counterintuive result as NMDA receptors exert an excitatory effect. Further analysis show that this inhibitory effect is due to the activation of calcium-dependent potassium channels, which hyperpolarize the neurons. Activation of extrasynaptic NMDA receptors also provokes a marked increase in intracellular calcium concentration, thus reinforcing the feed-forward relation between Aβ production and calcium.
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