In E coli oxidationreduction reactions or ATP hydrolysis wit

In E. coli, oxidation-reduction reactions (or ATP hydrolysis) within the cell membrane generates a pH of 1.5 (interior higher by 1.5 unit) and a V of –117 mV (interior negative). Along with H+ ions, beta-galactosides are cotransported in response to the total \"proton motive force.\" How much energy (in kcal/mol) is made available by the above pH and V? Be sure to include the sign of G in your answer. The temperature is 37 °C, F = 23.1 kcal/V·mol. Report your answer to the nearest hundredth of a unit.

Solution

Ans. Free energy change of a proton gradient, when proton moves from its higher to lower concetration, is given by-

            dG = -2.303 RT (dpH) + nF(dV)              - equation 1

            where,

R = (0.001987 kcal mol^-1K^-1 or 0.008315 kJ mol^-1 K^-1)

                        T = 37.0⁰C = 300.15 K

                        (dpH) = (pH _siteH⁺_{moves from}) – (pH _siteH⁺_{moves to}) = 1.5

                        (dV) = (V _siteH⁺_{moves from}) – (pH _siteH⁺_{moves to}) = -117 mV = -0.117V

Putting the values in equation 1-

dG = [-2.303 (0.001987 kcal mol^-1K^-1 x 300.15 K) x 1.5] +

[1 x 23.1 kcal V^-1 mol^-1 x (-0.117V)]

Or, dG = (-2.0603 kcal/ mol) + (-2.7027 kcal/ mol)

Hence, dG = -4.76 kcal/ mol