A network based study of the dynamics ofAβand τ proteins in Alzheimer’s disease

Abstract Due to the extreme complexity of Alzheimer’s disease (AD), the aetiology of which is not yet known, nor are there any known effective treatments, mathematical modelling 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 Aβ and τ 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 τ . 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 τ concentration, that 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 modelling certain pathologies, the choice of the mathematical setting must be made with great care if comparison with clinical data is considered decisive. Competing Interest Statement The authors have declared no competing interest.