A Network-Based Study of the Dynamics of Aβ and τ Proteins in Alzheimer's Disease

Due to the extreme complexity of Alzheimer's disease (AD), the etiology of which is not yet known, and for which there are no known effective treatments, mathematical modeling can be very useful. Indeed, mathematical models, if deemed reliable, can be used to test medical hypotheses that could be difficult to verify directly. In this context, it is important to understand how A beta and tau proteins, which, in abnormal aggregate conformations, are hallmarks of the disease, interact and spread. We are particularly interested, in this paper, in studying the spreading of misfolded tau. To this end, we present four different mathematical models, all on networks on which the protein evolves. The models differ in both the choice of network and diffusion operator. Through comparison with clinical data on tau concentration, which we carefully obtained with multimodal analysis techniques, we show that some models are more adequate than others to simulate the dynamics of the protein. This type of study may suggest that, when it comes to modeling certain pathologies, the choice of the mathematical setting must be made with great care if comparison with clinical data is considered decisive.