  In view of the important role helix-sheet transitions play in protein
aggregation, we introduce a simple model to study secondary structural
transitions of helix-coil-sheet systems using a Potts model starting with an
effective Hamiltonian. This energy function depends on four parameters that
approximately describe entropic and enthalpic contributions to the stability of
a polypeptide in helical and sheet conformations. The sheet structures involve
long-range interactions between residues which are far in sequence, but are in
contact in real space. Such contacts are included in the Hamiltonian. Using
standard statistical mechanical techniques, the partition function is solved
exactly using transfer matrices. Based on this model, we study thermodynamic
properties of polypeptides, including phase transitions between helix, sheet,
and coil structures.
