Impact of β-Amyloids Induced Disruption of Ca²⁺ Homeostasis in a Simple Model of Neuronal Activity

Alzheimer's disease is characterized by a marked dysregulation of intracellular Ca²⁺ homeostasis. In particular, toxic β-amyloids (Aβ) perturb the activities of numerous Ca²⁺ transporters or channels. Because of the tight coupling between Ca²⁺ dynamics and the membrane electrical activity, such perturbations are also expected to affect neuronal excitability. We used mathematical modeling to systematically investigate the effects of changing the activities of the various targets of Aβ peptides reported in the literature on calcium dynamics and neuronal excitability. We found that the evolution of Ca²⁺ concentration just below the plasma membrane is regulated by the exchanges with the extracellular medium, and is practically independent from the Ca²⁺ exchanges with the endoplasmic reticulum. Thus, disruptions of Ca²⁺ homeostasis interfering with signaling do not affect the electrical properties of the neurons at the single cell level. In contrast, the model predicts that by affecting the activities of L-type Ca²⁺ channels or Ca²⁺-activated K⁺ channels, Aβ peptides promote neuronal hyperexcitability. On the contrary, they induce hypo-excitability when acting on the plasma membrane Ca²⁺ ATPases. Finally, the presence of pores of amyloids in the plasma membrane can induce hypo- or hyperexcitability, depending on the conditions. These modeling conclusions should help with analyzing experimental observations in which Aβ peptides interfere at several levels with Ca²⁺ signaling and neuronal activity.