What is the value of the equilibrium constant of ATP hydrolysis at 37 0C [ADP] [Pi ] Calculate the free enthalpy change ∆G at the ratio ATP/ADP = 100:1
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What is the value of the equilibrium constant of ATP hydrolysis at 37 0C [ADP] [Pi ] Calculate the free enthalpy change ∆G at the ratio ATP/ADP = 100:1
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Hydrolysis Synthesis ∆G = ∆G0 + ln ([ADP][P i]/[ATP]) = -13 7 kcal/mol ~1/500 ATP hydrolysis shifts the equilibria of coupled reactions Coupled reaction:
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Calculations in Bioenergetics
Basic Relationships:
Redox potential and standard redox potential (Nernst-Peters equation): E h´ redox potential at pH 7 (V)
E 0 ´ standard redox potential (both [oxid.] & [red.] are 1 mol/l), at pH 7 (V)R universal gas constant, R = 8.3143 J K -1
mol -1T temperature (K)
n number of electrons transferredF Faraday (Faraday's charge), F = 96 487 J V
-1 mol -1 = 96 487 C mol -1 ln natural logarithm, ln = 2.303 log [oxid.] concentration of the substance in oxidised form (mol/l) [red.] concentration of the substance in reduced form (mol/l)Free enthalpy change and equilibrium constant:
ΔG free enthalpy change (J mol -1
ΔG 0 standard free enthalpy change (concentrations of all reactants & products are 1 mol/l) (J mol -1R universal gas constant, R = 8.3143 J K
-1 mol -1T temperature in (K)
Keq equilibrium constant ln natural logarithm, ln = 2.303 log[A], [B], and [C],[D] ...actual concentrations of the reactants and products, respectively (mol/l)
[A] eq , [B] eq , and [C] eq , [D] eq ...equilibrium concentrations of the reactants and products, respectively (mol/l)RT [oxid.]
E h´ = E
0´ + - - - - ln - - - -
n F [red.]A + B C + D
[C]eq [D] eq K eq [A] eq [B] eq [C] [D]ΔG = - RT ln K
eq + RT ln - - - - [A] [B] [C] [D] ΔG = ΔG 0 + RT ln - - - - [A] [B] ΔG 0 = - RT ln K eq2Free enthalpy change and redox potential:
ΔG´ free enthalpy change at pH 7 (J mol
-1 ΔG 0 ´ standard free enthalpy change (concentrations of all reactants are 1 mol/l) at pH 7 (J mol -1 ΔE h ´ difference in redox potentials between two redox systems, at pH 7 (V) ΔE 0´ difference in standard redox potentials (all reactants are at conc. 1 mol/l) between two redox systems,
at pH 7 (V) n number of electrons transferredF Faraday (Faraday's charge), F = 96 487 J V
-1 mol -1 = 96 487 C mol -1Osmotic work:
A osmotic work (J mol
-1n amount of protons transported against the concentration gradient (numerically equivalent to number of
moles)R universal gas constant, R = 8.3143 J K
-1 mol -1T temperature (K)
ln natural logarithm, ln = 2.303 log c 1 concentration of the particles at the original side of the membrane c 2 concentration of the particles at the other side of the membrane E membrane potential difference resulting from uneven distribution of protons (V)F Faraday (Faraday's charge), F = 96 487 J V
-1 mol -1 = 96 487 C mol -1Examples:
TASK 1
What is the redox potential E
h´ of the system NAD / NADH against hydrogen electrode, if the standard redox potential E 0´ is - 0.32 V and ratio NAD
/NADH is 10:1? -1 mol -1 , F = 96 487 J V -1 mol -1Solution:
Use the Nernst-Peters equation
and take into account that NAD transfers two electrons.8.3143 x 298.15
E h´ = - 0.32 + - - - - - - - - x ln 10 =2 x 96 487
= - 0.32 + 0.0128458 x 2.3026 = = - 0.32 + 0.0296 = ≡ - 0.29 VΔG´ = - n F ΔE
h ΔG 0´ = - n F ΔE
0 c 2A = n RT ln - -
c 1 AE = - -
FR T [NAD
E h´ = E
0´ + - - - - ln - - - -
n F [NADH] 3TASK 2
What is the value of the equilibrium constant of ATP hydrolysis at 37 0 C [ADP] [P i K eq [ATP] [H 2 O] if ΔG 0´ = -35 kJ . mol
-1 ? (R = 8.3143 J K -1 mol -1Solution:
From this equation ln K
eq = ΔG 0 ´/ - RT = - 35 000 / (- 8.3143 x 310.15) = 13.5732 K eq = e13.5732
≡ 7.8 x 10 5Or: ln K
eq = 13.5732 log K eq = 13.5732 /2.303 = 5.893 K eq = 10 5.893 ≡ 7.8 x 10 5TASK 3
ΔG 0 = -35 kJ . mol -1 . Calculate the free enthalpy change ΔG at the ratio ATP/ADP = 100:1. (Temperature 37 0C, R = 8.3143 J K
-1 mol -1 . Concentrations of water and inorganic phosphate are to be omitted from the equilibrium equation, assuming that they do not change significantly)Solution:
ATP + H
2O ADP + P
i100 1
1 ΔG = - 35 000 + 8.3143 x 310.15 x ln - - - = 100= - 35 000 - 11 875.26 = = - 46 875.26 = ≡ - 46.9 kJ mol -1 ΔG 0 = - RT ln K eq [ADP]