  Motivated by the biologically important and complex phenomena of A\beta\
peptide aggregation in Alzheimer's disease, we introduce a model and simulation
methodology for studying protein aggregation 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 aggregation onset and of reduced stable
A\beta\ monomer concentrations due to aggregation. The methodology we
implemented permits modeling of a phenomenon involving orders of magnitude
differences in time scales and concentrations which can be retained in the
simulation. We demonstrate how to identify ranges of parameter values that give
monomer concentration depletion upon aggregation similar to that observed in
Alzheimer's disease. We show how very different behavior can be obtained as
reaction parameters and protein concentrations vary, and discuss the difficulty
reconciling results of experiments from two vastly different concentration
regimes. The latter is an important general issue in relating in-vitro and mice
based experiments to humans.
