Two for tau: Automated model discovery reveals two-stage tau aggregation dynamics in Alzheimer’s disease

Abstract

Alzheimer’s disease is a neurodegenerative disorder characterized by the presence of amyloid-$\beta$ plaques and the accumulation of misfolded tau proteins and neurofibrillary tangles in the brain. A thorough understanding of the local accumulation of tau is critical to develop effective therapeutic strategies. Tau pathology has traditionally been described using reaction–diffusion models, which succeed in capturing the global spread, but fail to accurately describe the local aggregation dynamics. Current mathematical models enforce a single-peak behavior in tau aggregation, which does not align well with clinical observations. Here we identify a more accurate description of tau aggregation that reflects the complex patterns observed in patients. We propose an innovative approach that uses constitutive neural networks to autonomously discover bell-shaped aggregation functions with multiple peaks from clinical positron emission tomography (PET) data of misfolded tau protein. Our method reveals previously overlooked two-stage aggregation dynamics by uncovering a two-term ordinary differential equation that links the local accumulation rate to the tau concentration. When trained on data from amyloid-$\beta$ positive and negative subjects, the neural network clearly distinguishes between both groups and uncovers a more subtle relationship between amyloid-$\beta$ and tau than previously postulated. In line with the amyloid–tau dual pathway hypothesis, our results show that the presence of toxic amyloid-$\beta$ influences the accumulation of tau, particularly in the earlier disease stages. We expect that our approach to autonomously discover the accumulation dynamics of pathological proteins will improve simulations of tau dynamics in Alzheimer’s disease and provide new insights into disease progression.

Significance Statement

In Alzheimer’s disease, understanding the local dynamics of tau protein aggregation is crucial for developing effective treatments. Traditional models for tau protein dynamics use reaction–diffusion models that fail to accurately capture these local patterns. Our study introduces a novel approach that leverages constitutive neural networks to autonomously discover the complex, multi-peak aggregation dynamics from clinical PET data. This method reveals a previously overlooked two-stage tau accumulation process and a nuanced relationship between amyloid-$\beta$ and tau. By distinguishing between amyloid-$\beta$ positive and negative subjects, our model supports the amyloid–tau dual pathway hypothesis and offers novel insights into tau protein aggregation that have the potent to advance our understanding of Alzheimer’s disease progression.