Does anyone know a real-world example of a cycle exactly like this:

or in other words, this:

$$\begin{array}{ccc} \ce{A + C1 -> C2}\\ \ce{X + C2 -> C3}\\ \ce{C3 -> B + C4}\\ \ce{C4 -> Y + C1}\\ \end{array} $$

where the reaction $\ce{A -> B}$ is exergonic (i.e., involves a decrease in free energy) while $\ce{X -> Y}$ is endergonic (i.e., involves a free energy increase)?

The idea is that the above cycle, presumably catalyzed so that all the reactions go fairly fast under normal conditions, 'couples' the exergonic reaction to the endergonic reaction, thus driving the endergonic one.

I would love an example from biochemistry.

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    $\begingroup$ Isn't this just the Krebs cycle? $\endgroup$ – Zhe Jun 26 '18 at 20:22
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    $\begingroup$ @Zhe - no, the Krebs cycle is much more complicated! $\endgroup$ – John Baez Jun 27 '18 at 18:45
  • $\begingroup$ You didn't set any stipulations on complexity. Maybe state that up front? $\endgroup$ – Zhe Jun 27 '18 at 22:31
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    $\begingroup$ I want the reaction cycle to be just like the one I showed! Four species cycling around, two inputs, two outputs! I'll say "exactly like this". $\endgroup$ – John Baez Jun 28 '18 at 2:12

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