A Mathematical Model of Cellular Aggregation Predicts Patterns of Tau Accumulation in Neurodegenerative Disease

Protein aggregates are a hallmark of neurodegenerative disease, yet the molecular processes that control their appearance remain incompletely characterized. In particular, it is unknown to what degree the development of aggregates in one cell is triggered by nearby aggregate-containing cells, as opposed to proceeding cell-autonomously. Here, a minimal, bottom-up computational model is developed that is characterized by just two parameters: the relative rate of cell autonomous and cell-to-cell triggers of aggregation and a length scale of cell-to-cell interactions. Its applicability is demonstrated in the primary tauopathy Progressive Supranuclear Palsy by extracting mechanistic information from the distribution of tau aggregates at different disease stages from post-mortem human brain. Despite its simplicity, the model is able to reproduce the aggregate patterns observed in the data and reveals that the triggering of aggregation by nearby aggregated cells, over distances of ≈100 µm, is the major driver of disease progression once a low threshold level of aggregates is reached. The model also provides a natural explanation for an increase in the rate of disease progression when this threshold is reached, providing fundamental new insights into disease mechanisms and predicting the efficiency of different therapeutic strategies.