How many protons per ATP?

How many protons per ATP? Each complete revolution yields 3 ATP If there are 10 c subunits it requires 10 protons per complete 360o turn of the rotor. and 10 protons yield 10 / 3 = 3.3 H+ / ATP. Round down to 3. In addition require 1 H+ to translocate 1 Pi into mitochondria via H+ / Pi symport Therefore: 4 H+ move into matrix for each ATP that is synthesized and 10 H+ yield 10 / 4 = 2.5 ATP Each pair of e- from NADH translocates 10 protons therefore each pair of e- from NADH accounts for the synthesis of 2.5 ATP and the consumption of of ½ O2 And the ATP / O = 2.5 = P / O

With succinate as electron source: Each pair of e- translocates 6 H+ from matrix to intermembrane space. 4 H+ required to make ATP And 6 H+ = 6 / 4 = 1.5 ATP Therefore 1.5 ATP / 2 e- = P /O ratio from succinate

Peter D. Mitchell The Nobel Prize in Chemistry 1978 "for his contribution to the understanding of biological energy transfer through the formulation of the chemiosmotic theory" b. 1920d. 1992

Chemiosmotic Hypothesis - The “Mitchell Hypothesis” (see Horton p 418 – 421) • In mitochondria proton gradient is across the inner mitochondrial membrane – • high [H+] (low pH) in the inter membrane space • more positive outside Proton motif force: energy stored in a proton concentration gradient across a membrane • 2 components contribute to proton motif force: • chemical gradient due to difference in H+ concentration • across the membrane • 2. voltage gradient due to charge differential cross the membrane

·Chemical contribution to PMF due to proton concentration gradient DG = nRTln ([H+in]/[H+out] (R = 0.0083kJ / oKmol) = -2.303nRT(pHin – pHout) = -5.7 DpH (at 25oC) were n = number of protons translocated = 1

·Electrical contribution due to charge gradient –more positive outside than inside DG = zFDψ where z = charge of transported molecule = 1 for H+ F = Faradays constant = 96.48 kJ / V mol Dψ = membrane potential = difference in charge across the membrane = ψin - ψout membrane is more positive outside than inside, therefore Dψ is negative

1.DG = -2.303nRT(pHin – pHout) 2. DG = zFDψ ·Overall DG for transport of 1 proton from the cytosolic side to the matrix DG = zFDψ - 2.303nRT(pHin – pHout) Since z = 1 = n DG = nFDψ - 2.303nRT(pHin – pHout) ·Proton motif force (PMF) = Dp = DG / nF = Dψ - (2.303RT / F) (pHin – pHout) at 25oC (2.303nRT) / F = 0.059V Therefore Dp = Dψ - 0.059V(DpH) NB: Dp has units of volts

Example: ·In liver mitochondria pH gradient is typically about 0.5 pH units, more acidic outside than inside. eg pH 6.9 out, 7.4 in and Dψ = -0.17V Therefore: (pHin – pHout) = 0.5 and DG due to pH gradient = -2.303nRT(pHin – pHout) = -5.7 x 0.5 = -2.85 kJ/mol and DG due to membrane potential = zFDψ = 96.5 x (-0.17) = -16.4 kJ/mol and overall DG = -16.4 + (-2.85) = -19.25 kJ/mol for the translocation of 1 proton Dp = DG / nF Dp = -19.25 / 1 x 96.5 = -0.2 V

ALTERNATIVELY ·Dp = -0.17 - 0.059(0.5) = -0.20V and DG = nFDp = -0.20 x 96.5 = -19kJ/mol

[B] DG = DGo’ + RTln [A] RT nF Free energychange DGo’ = -RTlnKeq Redox reactions DGo’ = -nFDEo’ DE = DEo’ - ln Q Proton motif force DG = -2.303nRT(pHin – pHout) = -5.7 DpH (at 25oC) DG = zFDψ DG = zFDψ - 2.303nRT(pHin – pHout) Dp = DG / nF Dp = Dψ - 0.059V(DpH)

How many protons per ATP?