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We introduce a stochastic model describing aggregation of misfolded proteinsand degradation by the protein quality control system in a single cell. Inanalogy with existing literature, aggregates can grow, nucleate and fragmentstochastically. We assume that the quality control system acts as an enzymethat can degrade aggregates at different stages of the growth process, with anefficiency that decreases with the size of the aggregate. We show how thisstochastic dynamics, depending on the parameter choice, leads to twoqualitatively different behaviors: a homeostatic state, where the qualitycontrol system is stable and aggregates of large sizes are not formed, and anoscillatory state, where the quality control system periodically breaks down,allowing for the formation of large aggregates. We discuss how these periodicbreakdowns may constitute a mechanism for the sporadic development ofneurodegenerative diseases.

Quality Control System Response to Stochastic Growth of Amyloid Fibrils