The role of clearance mechanisms in the kinetics of toxic protein aggregates 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-beta 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 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 modelled and how alterations in the processes
of clearance or aggregation affect the stability of the system towards 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 in which to explore the detailed effects of
different mechanisms of clearance on the accumulation of aggregates.