Quality Control System Response to Stochastic Growth of Amyloid Fibrils

Abstract: We introduce a stochastic model describing aggregation of misfolded proteins and degradation by the protein quality control system in a single cell. In analogy with existing literature, aggregates can grow, nucleate and fragment stochastically. We assume that the quality control system acts as an enzyme that can degrade aggregates at different stages of the growth process, with an efficiency that decreases with the size of the aggregate. We show how this stochastic dynamics, depending on the parameter choice, leads to two qualitatively different behaviors: a homeostatic state, where the quality control system is stable and aggregates of large sizes are not formed, and an oscillatory state, where the quality control system periodically breaks down, allowing for the formation of large aggregates. We discuss how these periodic breakdowns may constitute a mechanism for the sporadic development of neurodegenerative diseases.