How many protons are pumped out per pair of electrons from NADH in oxidative phosphorylation?

I have searched the web and found that 10 protons are suppose to get pumped out during the electron cycle, but i'm a bit confused.

I'm trying to count, for every complex(1/3/4), the number of protons that are reduced in the matrix versus the number of protons added to the intermembrane space. The numbers don't add up.

my calculations:

• complex 1: 4 protons reduced, 4 protons added.
• complex 3: 2 protons reduced, 4 protons added.
• complex 4: 2 protons reduced(not counting the ones that condens to H2O), 2 protons added.

It seems like the mistake is in complex III. Look at this image from here:

It clearly shows the number of protons reduced in (and taken from) matrix and number of protons pumped into inter-membrane space. So the data becomes:

Complex I:

matrix: 2H+ reduced (from NADH + H+) + 2H+ pumped out

IMS: 4H+ pumped in

Complex II:

matrix: 2H+ reduced (from succinate)

IMS: 0H+ pumped in

Complex III:

matrix: 2H+ pumped out (when not considering complex II, you'd count 4H+ here)

IMS: 4H+ pumped in (2 from complex II)

Complex IV:

matrix: 2H+ reduced (to H2O, we won't consider it as you said) + 2H+ pumped out

IMS: 2H+ pumped in

TOTAL:

matrix: 10H+ subtracted/pumped out (with 2H+ to water, total 12H+)

IMS: 10H+ pumped in

This satisfies your statement that "10 protons are supposed to get pumped out during the electron cycle". I Hope this helps ;)

IMS = inter-membrane space

I just want to add a slight clarifying point to the previous member's already great answer. Keep in mind that these 10 protons that are pumped into the intermembrane space by the end are per one molecule of NADH. So each molecule of NADH will result in 10 protons being transported into the intermembrane space (as previously stated). For each molecule of FADH2, however, only 6 protons are pumped into the intermembrane space. This is because FADH2 skips Complex I (it feeds its electrons to ubiquinone "Q" through Complex II).