Mathematical model shows how sleep may affect amyloid β fibrillization

Deposition of amyloid {beta} (A{beta}) fibers in extra-cellular matrix of the brain is a ubiquitous feature associated with several neurodegenerative disorders, especially Alzheimers disease (AD). While many of the biological aspects that contribute to the formation of A{beta} plaques are well addressed at the intra- and inter-cellular level in short timescales, an understanding of how A{beta} fibrillization usually starts to dominate at a longer timescale in spite of the presence of mechanisms dedicated to A{beta} 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 sleep-wake cycle. In this study, we develop a minimal model of A{beta} fibrillization to investigate the onset of AD over a long time-scale. Our results suggest that the diseased state is a manifestation of a phase change of the system from soluble A{beta} (sA{beta}) to fibrillar A{beta} (fA{beta}) domination upon surpassing a threshold in the production rate of soluble A{beta}. By incorporating the circadian rhythm into our model, we reveal that fA{beta} accumulation is crucially dependent on the regulation of sleep-wake cycle, thereby indicating the importance of a good sleep hygiene in averting AD onset. We also discuss potential intervention schemes to reduce fA{beta} accumulation in the brain by modification of the critical sA{beta} production rate.