Mathematical Formulas for All PrP Peptides’ Cross-β Structures

Abstract

PrP has two regions: unstructured region PrP(1–120) and structured region PrP(119–231). In the structured region, there are many segments which have the property of amyloid fibril formation. By theoretical calculations, PrP(126–133), PrP(137–143), PrP(168–176), PrP(170–175), PrP(177–182), PrP(211–216) have the amyloid fibril forming property. PrP(142–166) has a X-ray crystallography experimental β-hairpin structure, instead of a pure cross-β amyloid fibril structure; thus we cannot clearly find it by our theoretical calculations. However, we can predict that there must be a laboratory X-ray crystal structure in PrP(184–192) segment that will be produced in the near future. The experiments of X-ray crystallography laboratories are agreeing with our theoretical calculations. This article summarized mathematical formulas of prion amyloid fibril cross-β structures of all the above PrP segments currently listed in the Protein Data Bank. There must be a laboratory X-ray crystal structure in PrP(184–192) segment that will be produced in the near future. The peptide PrP(113–120) (i.e. the AGAAAAGA palindrome of PrP) has no structures known, but is an inhibitor or blocker to control the formation of prion diseases. At the end of this Chapter we build an AGAAAAGA model and then do QM studies for it.