A biochemistry handout shows two panels for a proposed metabolic step

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 biochemistry handout shows two panels for a proposed metabolic step, redrawn here as data. Panel A (bar chart): at

298\,\mathrm{K}

the step has

\Delta H = +20\,\mathrm{kJ\,mol^{-1}}

and

\Delta S = +40\,\mathrm{J\,K^{-1}\,mol^{-1}}

, shown as two bars. Panel B (saturation curve): a regulatory protein's single binding site shows fractional occupancy

\theta

against substrate concentration

c

, crossing

\theta = 0.5

c = 2.0\,\mathrm{mM}

. ((a)) Using panel A, calculate

\Delta G

for the step at

298\,\mathrm{K}

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

K_d

and calculate the fractional occupancy at a substrate concentration of

6.0\,\mathrm{mM}

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