  X-ray crystallography, NMR (Nuclear Magnetic Resonance) spectroscopy, and
dual polarization interferometry, etc are indeed very powerful tools to
determine the 3D structures of proteins (including the membrane proteins),
though they are time-consuming and costly. However, for some proteins, due to
their unstable, noncrystalline and insoluble nature, these tools cannot work.
Under this condition, mathematical and physical theoretical methods and
computational approaches allow us to obtain a description of the protein 3D
structure at a submicroscopic level. This Chapter presents some practical and
useful mathematical optimization computational approaches to produce 3D
structures of the Prion AGAAAAGA Amyloid Fibrils, from a potential energy
minimization point of view.
  X-ray crystallography finds the X-ray final structure of a protein, which
usually need refinements in order to produce a better structure. The
computational methods presented in this Chapter can be also acted as a tool for
the refinements.
