A poster shows a ligand binding to a receptor in two panels

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 poster shows a ligand binding to a receptor in two panels, given here as data. Panel A (bar chart): at

298\,\mathrm{K}

the reaction has

\Delta H = +40\,\mathrm{kJ\,mol^{-1}}

(one bar) and

T\Delta S = +55\,\mathrm{kJ\,mol^{-1}}

(a second, taller bar). Panel B (saturation curve): the fractional occupancy

\theta

of the receptor's single binding site rises smoothly with ligand concentration

c

, and the curve crosses

\theta = 0.5

c = 5.0\,\mathrm{\mu M}

. ((a)) Using panel A, calculate

\Delta G

for the binding reaction at

298\,\mathrm{K}

, state whether it proceeds on its own, and say which term (enthalpy or entropy) drives it. ((b)) Using panel B, read off the dissociation constant

K_d

and calculate the fractional occupancy at a ligand concentration of

20\,\mathrm{\mu M}

Browse the problem library