The maintenance of a folded proteome is of principle importance for cell viability. The systems that govern protein-folding homeostasis (proteostasis) are dynamic and can respond to stresses. They can also become chronically maladapted leading to proteome instability and aggregation, which is a hallmark of neurodegenerative diseases. Yet a quantitative understanding of the effectiveness of proteostasis is not able to be readily measured. To address this goal we have built a novel biosensor system that defines the free capacity of proteins regulating proteostasis (such as chaperones). The biosensor comprises a series of barnase mutants tuned to different free energies of folding that act as baits to quality control engagement. By sandwiching the bait between two fluorescent proteins, fluorescence resonance energy transfer enabled measurement of both foldedness and aggregation of the baits in cells. We have established a mathematical model to that mechanistically defines the change in chaperone engagement with the biosensor under steady state conditions that affects foldedness. However, we have not yet extended this model to the kinetic framework including aggregation. Here we describe our work towards quantitatively modelling the aggregation process of the biosensor.