  Understanding the mechanism of protein secondary structure formation is an
essential part of protein-folding puzzle. Here we describe a simple model for
the formation of the $\beta$-hairpin, motivated by the fact that folding of a
$\beta$-hairpin captures much of the basic physics of protein folding. We argue
that the coupling of ``primary'' backbone stiffness and ``secondary'' contact
formation (similar to the coupling between the ``secondary'' and ``tertiary''
structure in globular proteins), caused for example by side-chain packing
regularities, is responsible for producing an all-or-none 2-state
$\beta$-hairpin formation. We also develop a recursive relation to compute the
phase diagram and single exponential folding/unfolding rate arising via a
dominant transition state.
