If the outer membrane of the mitochondria is very permeable, how do mitochondria maintain a proton gradient by pumping protons into the intermembrane space? Wouldn't they just diffuse into the cytosol?
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$\begingroup$ The build up/increase of H+ ions in the intermembrane space establishes the electrochemical gradient (proton gradient). And no, after that the protons return to the matrix via ATP synthase $\endgroup$– EbbinghausApr 20, 2016 at 19:08
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$\begingroup$ So, what is preventing the protons from diffusing out of the outer membrane? $\endgroup$– Ryan WardApr 20, 2016 at 19:10
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$\begingroup$ depends, there can be some "proton leak", which could occur during proton pumping across the inner membrane, which might be due to when the pairing between ATP synthase and the oxidation of substrate isn't fully complete, which would result in the protons being able to travel independently without ATP synthase to the mitochondrial matrix, also note that the proton leak acts/behaves in a non-ohmic way. $\endgroup$– EbbinghausApr 20, 2016 at 19:17
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2$\begingroup$ also note that chemiosmosis/oxidative phosphorylation occurs in the cristae of the mitochondria $\endgroup$– EbbinghausApr 20, 2016 at 19:20
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$\begingroup$ In addition to the long and complete answer above, I want to point out something extra that is missing in the explanation: The proton gradient works both ways (like all gradients). Lowering the external pH is not the only way to create a gradient, increasing the internal pH also works perfectly fine. $\endgroup$– VonBecheApr 21, 2016 at 10:48
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Diffusion, is by definition (Ficks Law) describing movement along or against some gradient (here its concentration) even if the mechanism of transport differ: active, passive, facilitated. The setup of the electrochemical gradient across membrane, like any thermodynamic process is not perfect, there are always entropy losses. In this case, this manifests as the the diffusion of protons away from the membrane (one source, there are others). Note the connection between entropy of system (Mitochondria) and diffusion (the inefficient process) in this positive feedback process. I think its interesting as someone learning about this stuff to make these connections.
Recalling protons are being delivered freely into the environment (inter membrane space) by Electron Transport Chain. Some protons will diffuse away from membrane surface before they can be pumped back in since these highly charged species cannot passively diffuse back in. The chemiosmosis process, which is sustained by the energy input to drive ATP synthase, depends on maintaining a strong concentration gradient (separation) of H+ on either side of membrane. Since the outer membrane of the mitochondria is porous, it means the protons are free to diffuse out, and will do so because it is entropically favorable. This relationship is best described by $\ce{\Delta G = RTln(K)}$. Where $\ce{K=\cfrac{[B]}{[A]}}$ for a process $\ce{A \rightleftharpoons B}$
Where A= Protons near membrane, B= protons diffused out. Having established that thermodynamically they (protons) will diffuse out[3]. It begs the question will they actually reach the outer membrane in a reasonable time.
Of course over long enough time they will. But over some meaningful scale like 1 second, the proton pump rate of ATP synthase, 100s-1 [5], how far can a proton get ideally?. Back at the envelope calculation (ignoring any resistance effects from solvent, path, etc.) and using some approximate values (for yeast proteins and mitochondria):
From Fick's Rate Law, R, $ \sqrt[3]{R} = \sqrt[3]{ D A \cfrac{[H^+]_c - [H^+]_m}{d}} = 14 \mu m $
So in 1 s an average proton ideally can diffuse 14 micrometers from the inner membrane, driven by difference in pH between membrane and cytosol. I think i maybe be fair to presume that based on this the mitochondria is leaking protons into into its near surroundings constantly. (for scale the mitochondria is about 100nm).
Hope that was helpful
VALUES:
Thickness of mitochondria,$d$, equal 0.014 $\mu m $ [4]
$\ce{[H^+]_m }$ at membrane = $\ce{-log[H+] = 10^(-6.8), [H+] = 10^(-6.8)}$ [6]
$\ce{[H^+]_c }$ at in cytosol = $\ce{[H+] = 10^(-7.40)}$
Diffusion coefficient of H+ in aqueous media $D$ = 7000 $\mu m^2$ [2]
A (surface area from which diffusion is taking place) I set to 0.025 $\mu m^2$ (guess from average unit cell of crystallized structure of ETC Complex II in yeast).
REFERENCES:
- D. Nelson & Cox (2012). Lehninger, Principles of Biochemistry, 6th Ed
- https://esc.fnwi.uva.nl/thesis/centraal/files/f1163457446.pdf
- http://www.ncbi.nlm.nih.gov/books/NBKhttp://www.atpsynthase.info/FAQ.html
- http://www.ncbi.nlm.nih.gov/pubmed/9245766
- http://www.atpsynthase.info/FAQ.html
- http://jgp.rupress.org/content/139/6/415.full
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$\begingroup$ Yes absolutely helpful. I'm glad you've come to the same conclusion about mitochondria leaking protons! $\endgroup$ Apr 21, 2016 at 2:27
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$\begingroup$ hooray!! thanks Cayetano Gonçalves that boosts my reputation and morale. Even better it was helpful $\endgroup$– SciEntApr 21, 2016 at 2:34
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$\begingroup$ You are forgetting an important factor, the mitochondrial membrane potential (ΔΨm). See Nernst potential (en.wikipedia.org/wiki/Nernst_equation). Basically, the concentration difference will be balanced by the voltage difference. Given ΔΨm is usually around -150mV (cytosolic space is ground), there is a drive to keep the protons close to the inner membrane surface. $\endgroup$– bmillareJun 14, 2018 at 19:22
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$\begingroup$ In fact, the proton-motive force is primarily composed of the electric component, over the pH gradient. The opposite is the case in chloroplasts from the movement of Cl- ions (en.wikipedia.org/wiki/Chemiosmosis). $\endgroup$– bmillareJun 14, 2018 at 19:32