A synthetic elastin-like polypeptide chain is used as a temperature-sensitive…

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Physical foundations of the living cell · Macromolecules, membranes and cell architecture

Life at Thermal Energy, Ch Entropy, free energy and the forces that counting produces

Problem

A synthetic elastin-like polypeptide chain is used as a temperature-sensitive molecular actuator. It behaves as an entropic spring of

N=150

links, each of length

\ell=0.40\,\mathrm{nm}

, and is held at a fixed extension

x=6.0\,\mathrm{nm}

by a clamp, well short of its full contour length. A colleague argues: "Raising the temperature loosens the thermal jostling along the chain, so the clamp should feel less force at

340\,\mathrm{K}

than at

300\,\mathrm{K}

, the same way heating a stretched metal wire very slightly reduces the pull needed to hold it." ((a)) Calculate the force the clamp must supply to hold this extension at

T=300\,\mathrm{K}

and at

T=340\,\mathrm{K}

. ((b)) Say whether the colleague is right, and give the physical reason your two numbers show.

Browse the problem library