Mathematical Formulas for Prion All Cross-Structures Listed in the Protein Data Bank

Abstract

Prion protein (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(170-175), PrP(177-182), PrP(211-216) have the amyloid fibril forming property. PrP(142-166) has a X-ray crystallography experimentalβ-hairpin structure, instead of a pure cross-βamyloid 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.Key words: PrP structured region; amyloid fibril formation peptides; theoretical calculations; experimental laboratories; mathematical formulasThe Medicinal Chemistryjournal: submitted on Feb-20-2016, revisedon Mar-29-2016, acceptedon Apr-04-2016Table 1 lists the cross-βstructures of all PrP segments that were listed in the Protein Data Bank (PDB, www.rcsb.org), produced by X-ray crystallography experiments. In the below, 01~24give some mathematical formulas to describe all these cross-βstructures.