Solution (source code)

= Solution

On releasing the tensile load, the extended chain first retracts towards less aligned conformations because they have much greater configurational multiplicity. Viscous <friction> and internal relaxation determine the time course; stored <free energy> is dissipated as <heat>. An unconstrained <ideal chain> does not shrink to a point: its <mean vector> is zero but its <root mean square> end-to-end length is $b\sqrt N\simeq2.37\,\mathrm{nm}$ for the supplied ideal-chain parameters.

A real <polypeptide> also has sequence-dependent interactions. If the original native structure is the stable state in the prevailing <solvent> and the molecule remains intact and capable of folding, it can subsequently refold, gaining favourable intramolecular and <solvent> <free energy>. The folded state is not selected by chain <entropy> alone, and formation of native contacts need not be instantaneous. Kinetic traps, <proline> <isomerization>, <protein aggregation>, misfolding, surface attachments or chemical damage may prevent complete recovery or produce <hysteresis>. Thus reversible refolding is a physically motivated possibility, not guaranteed simply by removal of <force>. This distinction connects the recoil of a stretched polymer to the thermodynamics discussed in Question 6(c).