Dominance of irregular structures in the formation of intramolecular antiparallel β sheets by homopolyamino acids

Abstract

A matrix formulation of the conformational partition function is used to assess the influence of irregular structures on the formation of intramolecular antiparallel β sheets. An antiparallel sheet is considered to be irregular if any pair of contiguous strands has an unequal number of residues. The regular structures in the model consist of antiparallel sheets in which every strand contains the same number of residues. Aside from a growth parameter t, the model contains two parameters that account for the influence of edge effects. Each tight turn contributes a factor δ, and each residue in the sheet that does not have a partner in a preceding strand contributes a factor τ. When τ < δ = 1, preferred sheets consist of an extremely large number of very short strands. Such sheets resemble those found in cross-β fibers. Irregular structures increase the cooperativity of the formation of cross-β fibers. They cause the fibers that are formed to be longer (have more strands) and thicker (have more residues per strand) than if all antiparallel sheets were regular. A much different result is obtained if end effects are modified so that the antiparallel sheets formed resemble those found in globular proteins. Formation of antiparallel sheets remains cooperative, but irregular sheets now markedly reduce the cooperativity of the transition. At high antiparallel-sheet content, irregular structures cause typical antiparallel sheets to be smaller. The behavior of the conformational partition function shows that irregular structures make the dominant contribution to both transitions. Therefore, formulations that restrict consideration to regular structures may provide a misleading picture of antiparallel-sheet formation.