AbstractApplication of statistical mechanical theory gives the expressionr2= 27.9n− 20.3 relating the mean square end‐to‐end length,r2, of a random polypeptide chain in thetrans‐form andn, the number of amino acid residues in the chain. The corresponding expressions for thecisand nonplanar forms arer2= 8.6n− 0.8 andr2= 15.5n− 4.8 rrespectively. The first of these equations has been used to obtain an expression for the fractional decrease in length of a crosslinked, aligned α‐helical structure when it is converted to the random coil form. The assumptions made are that the crosslinkages undergo little lateral displacement and that the volume remains constant. The expression so obtained is\documentclass{article}\pagestyle{empty}\begin{document}$l/l_{0} = {{\left\{ {23.7n - 17.3 - [10\sqrt {l//l_0 } - 7]^2 } \right\}^{1/2} } \mathord{\left/ {\vphantom {{\left\{ {23.7n - 17.3 - [10\sqrt {l//l_0 } - 7]^2 } \right\}^{1/2} } {1.5n}}} \right. \kern-\nulldelimiterspace} {1.5n}} $\end{document}wherelis the supercontracted length of the polypeptide fiber,l0is its original length andnis the number of amino acid residues between