Model for competing pathways in protein-aggregation: role of membrane bound proteins

Motivated by the biologically important and complex phenomena of A{\beta} peptide aggregation in Alzheimer's disease, we introduce and simulate a protein aggregation model that includes extra-cellular aggregation, aggregation on the cell-surface assisted by a membrane bound protein, and in addition, supply, clearance, production and sequestration of peptides and proteins. The model is used to produce equilibrium and kinetic-aggregation phase diagrams for the onset of aggregation and of reduced stable A{\beta} monomer concentrations due to aggregation. We identify ranges of parameter values which give monomer concentration depletion upon aggregation similar to that observed in Alzheimer's disease. We show how very different behavior can be obtained as we vary reaction parameters and protein concentrations, and discuss the difficulty this creates in relating results from two vastly different concentration regimes. The latter is an important general issue in relating in-vitro and mice based experiments to humans.