Mathematical Model Shows How Sleep May Affect Amyloid-β Fibrillization

Abstract

Deposition of amyloid-β (Aβ) fibers in the extracellular matrix of the brain is a ubiquitous feature associated with several neurodegenerative disorders, especially Alzheimer's disease (AD). Although many of the biological aspects that contribute to the formation of Aβ plaques are well addressed at the intra- and intercellular levels in short timescales, an understanding of how Aβ fibrillization usually starts to dominate at a longer timescale despite the presence of mechanisms dedicated to Aβ clearance is still lacking. Furthermore, no existing mathematical model integrates the impact of diurnal neural activity as emanated from circadian regulation to predict disease progression due to a disruption in the sleep-wake cycle. In this study, we develop a minimal model of Aβ fibrillization to investigate the onset of AD over a long timescale. Our results suggest that the diseased state is a manifestation of a phase change of the system from soluble Aβ (sAβ) to fibrillar Aβ (fAβ) domination upon surpassing a threshold in the production rate of sAβ. By incorporating the circadian rhythm into our model, we reveal that fAβ accumulation is crucially dependent on the regulation of the sleep-wake cycle, thereby indicating the importance of good sleep hygiene in averting AD onset. We also discuss potential intervention schemes to reduce fAβ accumulation in the brain by modification of the critical sAβ production rate.