| Abstract: | A matrix formulation of the conformational partition function has been used to examine helix ? sheet transitions in homopolyamino acids. α-Helices are weighted by Zimm-Bragg parameters σ and s. Antiparallel β-sheets with tight bends are weighted by the parameters t, δ, and τ, where t is the propagation parameter. In addition, each bend contributes a factor δ, and each residue in the sheet that does not have a partner in the preceding strand contributes a factor τ. The helix can be the dominant conformation in a long chain only if two conditions are satisfied simultaneously: (i) s > 1 , and (ii) either s > t, or σ, δ, and τ are assigned values that inflict a greater penalty on antiparallel sheets than on helices. The maximum amount of coil developed during the helix ? sheet transition is strongly influenced by the size of τ, but it is only weakly dependent on the size of δ. Previously reported optical rotatory dispersion, CD, laser Raman, and nmr studies of thermally induced α ? β transitions in homopolyamino acids, notably poly(L -lysine), demonstrate that little random coil is present. If the random coil content is to remain small during the helix ? sheet transition, τ must be significantly less than unity. A small value for τ means that there is a significant penalty assessed to lysyl residues in an antiparallel sheet that do not have a partner in a preceding strand. |
