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