A biosynthetic step has at and

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 biosynthetic step X+Y→ZX + Y \to Z has ΔG∘′=+20.0 kJ mol−1\Delta G^{\circ\prime} = +20.0\,\mathrm{kJ\,mol^{-1}} at pH 7\mathrm{pH}\,7 and 310 K310\,\mathrm{K}, and is unfavourable on its own. It is coupled, through a shared phosphate intermediate, to ATP hydrolysis, ATP→ADP+Pi\mathrm{ATP} \to \mathrm{ADP} + P_i, with ΔGATP∘′=−30.5 kJ mol−1\Delta G^{\circ\prime}_{\rm ATP} = -30.5\,\mathrm{kJ\,mol^{-1}}, so that the overall reaction is X+Y+ATP→Z+ADP+PiX + Y + \mathrm{ATP} \to Z + \mathrm{ADP} + P_i. ((a)) Find ΔGtot∘′\Delta G^{\circ\prime}_{\rm tot} for the coupled reaction in standard conditions. ((b)) At stated cellular concentrations [X]=5 mM[X]=5\,\mathrm{mM}, [Y]=2 mM[Y]=2\,\mathrm{mM}, [Z]=0.5 mM[Z]=0.5\,\mathrm{mM}, [ATP]=3 mM[\mathrm{ATP}]=3\,\mathrm{mM}, [ADP]=0.3 mM[\mathrm{ADP}]=0.3\,\mathrm{mM}, [Pi]=10 mM[P_i]=10\,\mathrm{mM}, all at 310 K310\,\mathrm{K}, find ΔGtot\Delta G_{\rm tot} in kJ mol−1\mathrm{kJ\,mol^{-1}} and in kBTk_BT.

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