The role of clearance mechanisms in the kinetics of pathological protein aggregation involved in neurodegenerative diseases.

The deposition of pathological protein aggregates in the brain plays a central role in cognitive decline and structural damage associated with neurodegenerative diseases. In Alzheimer's disease, the formation of amyloid-β plaques and neurofibrillary tangles of the tau protein is associated with the appearance of symptoms and pathology. Detailed models for the specific mechanisms of aggregate formation, such as nucleation and elongation, exist for aggregation in vitro where the total protein mass is conserved. However, in vivo, an additional class of mechanisms that clear pathological species is present and is believed to play an essential role in limiting the formation of aggregates and preventing or delaying the emergence of disease. A key unanswered question in the field of neuro-degeneration is how these clearance mechanisms can be modeled and how alterations in the processes of clearance or aggregation affect the stability of the system toward aggregation. Here, we generalize classical models of protein aggregation to take into account both production of monomers and the clearance of protein aggregates. We show that, depending on the specifics of the clearance process, a critical clearance value emerges above which accumulation of aggregates does not take place. Our results show that a sudden switch from a healthy to a disease state can be caused by small variations in the efficiency of the clearance process and provide a mathematical framework to explore the detailed effects of different mechanisms of clearance on the accumulation of aggregates.