Overexpression of the de-ubiquitinating enzyme UCH-L1 leads to inclusion formation in response to proteasome impairment. These inclusions contain components of the ubiquitin-proteasome system and α-synuclein confirming that the ubiquitin-proteasome system plays an important role in protein aggregation. The processes involved are very complex and so we have chosen to take a systems biology approach to examine the system whereby we combine mathematical modelling with experiments in an iterative process. The experiments show that cells are very heterogeneous with respect to inclusion formation and so we use stochastic simulation. The model shows that the variability is partly due to stochastic effects but also depends on protein expression levels of UCH-L1 within cells. The model also indicates that the aggregation process can start even before any proteasome inhibition is present, but that proteasome inhibition greatly accelerates aggregation progression. This leads to less efficient protein degradation and hence more aggregation suggesting that there is a vicious cycle. However, proteasome inhibition may not necessarily be the initiating event. Our combined modelling and experimental approach show that stochastic effects play an important role in the aggregation process and could explain the variability in the age of disease onset. Furthermore, our model provides a valuable tool, as it can be easily modified and extended to incorporate new experimental data, test hypotheses and make testable predictions.