Abstract
We study two models for the formation and packing of helices and sheets in globular (compact) proteins. These models, based on weighted Hamiltonian paths on a regular lattice both exhibit a first order transition between a compact high temperature phase, with no extended secondary structures, and a quasi-frozen compact phase, with secondary structures invading the whole lattice. The quasi-frozen phase with very weak temperature dependence, is identified as the native phase of proteins, whereas the high-temperature phase may be relevant to the so-called molten globule state of proteins
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