Mathematical model of the brain immune system in the course of Alzheimer’s disease
Alzheimer's disease (AD) is considered the most common cause of dementia in elderly, accounting for 60-80% of the cases. Yet, no treatment is available for the disease and with the current demographic shift towards an elderly population, the total cost of care for AD patients increases. Finding an early biomarker for AD would be helpful to prevent or delay the course of the disease. A well-known biomarker of AD is the accumulation of Amyloid-β (Aβ) plaques in the interstitial fluid (ISF), followed by the accumulation of τ-protein tangles inside neurons. Aβ accumulation is estimated either by measuring its soluble-form concentration in cerebrospinal fluid (CSF) or by imaging (PET or MRI). There is little knowledge about how the immune system of the brain evolves during the onset of AD. Our goal is to derive a mathematical model for the disease to understand and suggest treatment or prevention strategies.
Deposition of amyloid beta (Aβ) fibers in the extra-cellular matrix of the brain is a ubiquitous feature associated with several neurodegenerative disorders, especially AD. While many of the biological aspects that contribute to the formation of Aβ plaques are well in short timescales, how Aβ fibrillization dominates over mechanisms of Aβ clearance remains unclear. Although there is increasing evidence for a contribution of disrupted sleep-wake cycles, the role of circadian regulation has not been addressed quantitatively.
We develop a minimal model of Aβ fibrillization to investigate the onset of AD over a long timescale. Incorporating the circadian rhythm into our model, we reveal that fibrillar Aβ accumulation is crucially dependent on the regulation of sleep-wake cycle, underscoring the role of chronobiology in AD prevention. Fibrillar Aβ accumulation further depends critically on the production rate of soluble Aβ, suggesting the latter as a potential target for causal therapies.
We further investigate the amyloid cascade hypothesis in a set of partial differential equations. Our model predicts amyloid plaque formation and neural atrophy to depend on the secretion rate of amyloid beta, which is proportional to the product of neural density and neural activity. The spatial distribution of amyloid plaques and neural death is investigated in silico, considering brain geometry, synaptic density, and microglia activation. The model explains amyloidosis patterns in patients and suggests a role of other factors such as τ-protein aggregation or neuroinflammation.
Tanmay Mitra, Sahamoddin Khailaie, Michael Meyer-Hermann
Martin Korte (TU Braunschweig)
Hoore M, Khailaie S, Montaseri G, Mitra T, Meyer-Hermann M. Mathematical model shows how sleep may affect amyloid β fibrillization. BioRxiv (2019)
- System-Immunologie- Prof. Dr. Michael Meyer-Hermann
Geldgeber / Förderer