A[formula omitted]-protein polymerization in Alzheimer disease: Optimal control for nucleation parameter estimation

Abstract

In this paper, we are interested in the modeling of Alzheimer’s disease from the angle of the amyloid cascade hypothesis, where the pathogenic agent is the Aβ protein in its oligomeric form. The formation dynamics of this pathogenic form is modeled by a Becker–Doring type model where APP (Amyloid Precursor Protein) protein, after cleavage by specific enzymes, forms monomeric Aβ proteins, which, by polymerization and/or nucleation, lead to the formation of oligomeric Aβ. We propose an optimal control problem to estimate the rate of nucleation which seems to be at the base of this amyloid cascade hypothesis and for which no (experimental) measurement exists for the moment.