Four short, independent…

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Molecular machines, transport and bioenergetics · Molecular machines, transport and bioenergetics

Forces, Machines and Signals, Ch Proton gradients, ATP synthesis and photosynthesis

Problem

Four short, independent calculations. ((a)) Cytochrome

c

has

E^{\circ\prime} = +0.25\,\mathrm{V}

and passes one electron to

\mathrm{O_2/H_2O}

E^{\circ\prime} = +0.82\,\mathrm{V}

. Calculate

\Delta G

for this one-electron transfer, in

\mathrm{kJ\,mol^{-1}}

. ((b)) A bacterium at

310\,\mathrm{K}

has

\Delta\psi = 170\,\mathrm{mV}

(inside negative) and

\Delta\mathrm{pH} = 0.5

units (inside more alkaline), each pH unit worth

61.5\,\mathrm{mV}

at this temperature. Calculate the magnitude of the proton-motive force

|\Delta p|

\mathrm{mV}

. ((c)) Yeast ATP synthase has a ring of

n_c = 10

subunits. Using

|\Delta p| = 200\,\mathrm{mV}

(

7.5k_BT

per proton) and an ATP cost in the cytosol of

21k_BT

, test the free-energy balance

(n_c/3 + 1)e|\Delta p| \ge \Delta G_{\rm ATP}^{\rm cyt}

and state the margin per ATP in

k_BT

. ((d)) A chlorophyll with absorption cross-section

\sigma = 3.8\times10^{-20}\,\mathrm{m^2}

sits in deep shade receiving

0.5

per cent of the full-sunlight photosynthetically active flux of

1.2\times10^{21}\,\mathrm{photons\,m^{-2}\,s^{-1}}

. Calculate its absorption rate in photons per second.

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