  Amyloid fibrillation is a protein self-assembly phenomenon that is intimately
related to well-known human neurodegenerative diseases. During the past few
decades, striking advances have been achieved in our understanding of the
physical origin of this phenomenon and they constitute the contents of this
review. Starting from a minimal model of amyloid fibrils, we explore
systematically the equilibrium and kinetic aspects of amyloid fibrillation in
both dilute and semi-dilute limits. We then incorporate further molecular
mechanisms into the analyses. We also discuss the mathematical foundation of
kinetic modeling based on chemical mass-action equations, the quantitative
linkage with experimental measurements, as well as the procedure to perform
global fitting.
