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Several neurological disorders are associated with the aggregation ofaberrant proteins, often localized in intracellular organelles such as theendoplasmic reticulum. Here we study protein aggregation kinetics by mean-fieldreactions and three dimensional Monte carlo simulations of diffusion-limitedaggregation of linear polymers in a confined space, representing theendoplasmic reticulum. By tuning the rates of protein production anddegradation, we show that the system undergoes a non-equilibrium phasetransition from a physiological phase with little or no polymer accumulation toa pathological phase characterized by persistent polymerization. A combinationof external factors accumulating during the lifetime of a patient can thusslightly modify the phase transition control parameters, tipping the balancefrom a long symptomless lag phase to an accelerated pathological development.The model can be successfully used to interpret experimental data onamyloid-\b{eta} clearance from the central nervous system.

Protein accumulation in the endoplasmic reticulum as a non-equilibrium phase transition