Liquid cellular compartments spatially segregate from the cytoplasm and can
regulate aberrant protein aggregation, a process linked to several medical
conditions, including Alzheimer's and Parkinson's diseases. Yet the mechanisms
by which these droplet-like compartments affect protein aggregation remain
unknown. Here, we combine kinetic theory of protein aggregation and
liquid-liquid phase separation to study the spatial control of irreversible
protein aggregation in the presence of liquid compartments. We find that, even
for weak interactions between the compartment constituents and the aggregating
monomers, aggregates are strongly enriched inside the liquid compartment
relative to the surrounding cytoplasm. We show that this enrichment is caused
by a positive feedback mechanism of aggregate nucleation and growth which is
mediated by a flux maintaining the phase equilibrium between the compartment
and the cytoplasm. Our model predicts that the compartment volume that
maximizes aggregate enrichment in the compartment is determined by the reaction
orders of aggregate nucleation. The underlying mechanism of aggregate
enrichment could be used to confine cytotoxic protein aggregates inside
droplet-like compartments suggesting potential new avenues against aberrant
protein aggregation. Our findings could also represent a common mechanism for
the spatial control of irreversible chemical reactions in general
