A thermal denaturation experiment on a small designed protein gave the fraction…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture

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

Problem

A thermal denaturation experiment on a small designed protein gave the fraction unfolded fuf_u at two temperatures. Data: T=300 KT=300\,\mathrm K, fu=0.02f_u=0.02; T=320 KT=320\,\mathrm K, fu=0.50f_u=0.50. Treat the protein as a two-state system, folded and unfolded, with unfolding free energy ΔGunf(T)≈ΔHm(1−T/Tm)\Delta G_{\rm unf}(T)\approx \Delta H_m(1-T/T_m) near the melting temperature TmT_m, where ΔHm\Delta H_m is the enthalpy of unfolding at TmT_m. ((a)) Read TmT_m directly from the table. ((b)) Use the reading at 300 K300\,\mathrm{K} to find ΔHm\Delta H_m, quoting it in kJ mol−1\mathrm{kJ\,mol^{-1}} and in kBTk_BT at 298 K298\,\mathrm{K} (use R=8.314 J mol−1 K−1R=8.314\,\mathrm{J\,mol^{-1}\,K^{-1}} and 1kBT=2.48 kJ mol−11k_BT=2.48\,\mathrm{kJ\,mol^{-1}} at 298 K298\,\mathrm{K}). ((c)) Predict the fraction unfolded at body temperature, 310 K310\,\mathrm{K}.

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