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The theory of transition between $\alpha$-helix, $\beta$-sheet and randomcoil conformation of a protein is discussed through a simple model, thatincludes both short and long-range interactions. Besides the bonding parameterand helical initiation factor in Zimm-Bragg model, three new parameters areintroduced to describe beta structure: the local constraint factor for a singleresidue to be contained in a $\beta$-strand, the long-range bonding parameterthat accounts for the interaction between a pair of bonded $\beta$-strands, anda correction factor for the initiation of a $\beta$-sheet. Either increasinglocal constraint factor or long-range bonding parameter can cause a transitionfrom $\alpha$-helix or random coil conformation to $\beta$-sheet conformation.The sharpness of transition depends on the competition between short andlong-range interactions. Other effective factors, such as the chain length andtemperature, are also discussed. In this model, the entropy due to differentways to group $\beta$-strands into different $\beta$-sheets gives rise tosignificant contribution to partition function, and makes major differencesbetween beta structure and helical structure.

A Unified Model of $\alpha$-Helix/$\beta$-Sheet/Random-Coil Transition in Proteins