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