A report on a repressor-DNA complex states: "

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Thermodynamic potentials and the formal structure of thermodynamics · Thermodynamic potentials and the formal structure of thermodynamics

Forces, Machines and Signals, Ch Free energy at work: states, weights and entropic forces

Problem

A report on a repressor-DNA complex states: "Kd=50 nMK_d = 50\,\mathrm{nM}, so ΔG∘=kBTln⁡(50)=+9.7 kJ mol−1\Delta G^\circ = k_BT\ln(50) = +9.7\,\mathrm{kJ\,mol^{-1}} at 298 K298\,\mathrm{K}, meaning binding is unfavourable." ((a)) Find the error in this working. ((b)) Using the standard state c∘=1 Mc^\circ = 1\,\mathrm{M}, calculate the correct ΔGbind∘\Delta G^\circ_{\rm bind} in kBTk_BT and in kJ mol−1\mathrm{kJ\,mol^{-1}} at 298 K298\,\mathrm{K}. ((c)) Show that plugging the same KdK_d quoted as 0.05 μM0.05\,\mathrm{\mu M} into the flawed formula kBTln⁡(number)k_BT\ln(\text{number}) gives a different answer, and explain why this proves a standard state must always be stated.

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