Mathematical modeling of APP processing influenced by SORLA in Alzheimer\u27s disease: When one pathway is not enough

Background: Alzheimer\u27s disease (AD) is a neurodegenerative disorder characterized by amyloid plaques in the brain of affected individuals. Our study aims at (i) modeling the interactome of neuronal factors central to the proteolytic processing of amyloid precursor protein (APP) and (ii) evaluating the influence of SORLA/SORL1, an inhibitor of APP processing and important genetic risk factor. Results: Based on a panel of cell lines in which the amount of APP and of accessory factors can be varied, we have established a model, based on nonlinear Ordinary Differential Equations (ODE), describing the kinetics of APP processing and the influence of SORLA on the processing. The parameter values of the simplified ODE model are estimated by optimization from dose-response series for sAPPα and sAPPβ as a function of total amount of APP for cells with or without SORLA. We have systematically compared the goodness of fit of (a) model with only monomer processing, (b) model with only dimer processing, and (c) combined model with both monomer and dimer processing, on a series of dose-response data. In the combined model, the dimeric forms of the secretases only act on the dimeric form of APP and the monomeric forms of the secretases only act on the monomeric form of APP. The complexity of data and model made it necessary to also consider partial local parameter estimations in able to capture the dynamical behavior of the experimental data. We performed purely global parameter estimations for all three models and global-local parameter estimation for the combined model. For global-local parameter estimation, all parameters except the parameters describing β-secretase activity in the presence or absence of SORLA are estimated locally. Conclusions: The simulations, together with our experimental data, support a model whereby SORLA prevents APP oligomerization, thereby causing secretases to switch from allosteric to non-allosteric mode of action. We also performed simulations for intermediate concentrations of SORLA on the combined model with global-local estimate. We predicted a switch from cooperative to less efficient non-cooperative processing on a low amount of SORLA concentration