Statistical Thermodynamics

13Helix–Coil Transition

Transition from a helix conformation to a coil conformation of a polypeptide and vice versa is another phenomenon that a theoretical treatment similar to the one we learned in the 1D Ising model is effective. The theory was developed by Zimm and Bragg several decades ago [23]. The intuition they instilled in the model appears out‐of‐worldly, but it works and explains experimental results beautifully. We learn their model in this chapter.

13.1 Historical Background

A protein molecule is a sequence of amino acid residues (–NH–CHR–CO–, where R varies from residue to residue), and its sequence is given. Interactions between atoms or groups of atoms within the molecule force it to adopt a specific structure in three dimensions when the large molecule folds. We recognize a helix form (called α‐helix) and a sheet form (β‐sheet) in some parts of the folded structure. The α‐helix is made possible through a twist favored by bulky side groups R bonded to the chiral carbon atom and supported by hydrogen bonds between the proton in NH within the residue and the oxygen atom in CO a few residues away along the linear‐chain backbone (see Figure 13.1).

Figure 13.1 α‐Helix in a protein molecule. A hydrogen bond forms between the proton in NH and the oxygen atom in C = O across a few residues. Hydrogen atoms on the carbon atoms bonded to side groups R are not shown.