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This diagram describes energy coupling between a nonspontaneous reaction (the formation of glutamine from glutamic acid and ammonia) and a spontaneous reaction (the hydrolysis of ATP). I can see that if you add reaction 1 ($\ce{Glu + NH3->Glutamine}$) and reaction 2 (ATP hydrolysis), then the overall ∆G will be negative, and this reaction will be spontaneous.

My question is this: why can’t you add the reverse of reaction 1, which would on its own be spontaneous, to reaction 2? Would that not make an overall ∆G that is even more negative (more spontaneous)? This would be even more favorable than what we got from the energy coupling shown in the diagram. Yet it seems that energy coupling can produce the reaction presented in the diagram. How does the universe know to add the nonspontaneous reaction to the spontaneous reaction rather than the spontaneous reaction to another spontaneous reaction? It seems to me that the latter would be more probable.

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Points to bear in mind

  1. That the biological coupling of an energetically favourable and unfavourable reaction (I would avoid using the term spontaneous†) is done through a composite reaction involving all the components of the two separate reactions. The reactants and products are the same as in the sum of the separate reactions — so it is valid to calculate the overall free energy change from the separate reactions — but we are talking about a different reaction or serious of reactions that occur on the enzyme. For example in the glutamate synthetase reaction that you mention there are the two reactions shown below. Gamma-glutamyl phosphate can be considered as an activated intermediate to which the free energy of hydrolysis of ATP has been transferred, rather than dissipated in heat, as would occur in the isolated reaction with inorganic phosphate as the product.

Glutamate Synthetase

  1. Such coupled reactions are no different from non-coupleld thermodynamically favourable reactions in a cell in that they require an enzyme to catalyse them. They do not proceed spontaneously† because there is an activation energy barrier. If you regard this as “forcing” a reaction, then the answer to the question you pose in your comment to @VonBeche is ‘yes’. However I would describe it as an enzyme having evolved to ‘permit’ or ‘facilitate’ a reaction. It does this by providing binding sites for the substrates and (often) a different reaction pathway that involves a lower activation energy.

So why no reaction Gln + ATP ➞ Glu + NH3 + ADP + Pi ?

This can be regarded in two ways.
(1) Why hasn’t an enzyme evolved to do this sort of thing?
Either there is no selective pressure on an organism for an unneccesary enzyme to evolve, or (in this case) if the organism needs an enzyme to deaminate glutamine one evolves, but this enzyme (glutaminase) doesn’t need to involve ATP as the reaction is already thermodynamically favourable.

(2) Why doesn’t the glutamate synthetase enzyme catalyse this reaction
From your comment, this seems to be your concern. There are three binding sites on the enzyme, one for glutamate, one for ATP and one for ammonia; and I presume you are thinking why can’t glutamine bind to the glutamate site (after all it leaves from there) and react with ATP to form γ-glutamyl phosphate. The answer to this is the chemistry of the reactions shown above. The mechanism of the glutamate synthetase reaction is complex, but at the simplest level the first stage is the nucleophilic attack of the negative acid oxygen (yellow) of glutamate on the γ-phosphate of ATP: Glu nucleophilic attack on ATP In glutamine there is an amino group instead of the negative oxygen, so the reaction will not occur.

Furthermore, you should be aware that the enzyme is an active participant in the reaction, and the various substrates and products are oriented specifically in relation to residues at the active site of the enzyme to allow the reaction to proceed. To give a flavour of this I reproduce a portion of the summary of a paper by Liaw and Eisenberg on the mechanism of action of glutamine synthetase. I don’t expect you (or anyone else) to digest this — it merely serves to illustrate that enzymes are highly sophisticated machines in which many components participate in producing a specific product.

Abstract of paper on mechanism of action of glutamine synthetase

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  • $\begingroup$ I still don’t understand how an enzyme can specifically couple two reactions in those fixed directions—the nonspontaneous with the spontaneous ATP hydrolysis. What is it about the enzyme that doesn’t couple the spontaneous reaction with the ATP hydrolysis? Enzymes can recognize both the reactants of a reaction and the products, so what gives it their specificity to couple the formation of γ-glutamyl phosphate from glutamate with the conversion of ATP to ADP, rather than the formation of glutamate from γ-glutamyl phosphate with the conversion of ATP to ADP? $\endgroup$ – lightweaver Jun 19 '16 at 12:39
  • $\begingroup$ @lightweaver — I've now modified my answer to try to deal with the question you ask in your comment. I didn't include a 3D model of the active site as the answer is already rather long, but I can add one if it will help. $\endgroup$ – David Jun 19 '16 at 18:00
  • $\begingroup$ Interesting. I’ve learnt that enzymes can always catalyze reactions in both directions. Sucrase can break down sucrose into glucose and fructose or it can build sucrose from those two. It is a catalyst, after all, and catalysts usually speed up both forward and reverse reactions so as to not alter the equilibrium position of the reaction. Is my conception wrong, then? Your answer seems to indicate that enzymes catalyze only the forward reaction. $\endgroup$ – lightweaver Jun 20 '16 at 11:13
  • $\begingroup$ @lightweaver Not at all. Enzymes do catalyse reactions in both directions. But what you are proposing is not the reverse reaction. The reverse reaction is Gln + ADP + Pi ➞ Glu + ATP + NH3, whereas you are asking why Gln + ATP ➞ Glu + NH3 + ADP + Pi does not occur. That is a quite different reaction! (And of course the reason that the true reverse reaction does not occur is thermodynamics — the coupling will ensure that the reverse reaction has a positive deltaG.) $\endgroup$ – David Jun 20 '16 at 12:40
  • $\begingroup$ Ahh. I think that was my main source of confusion. Thanks for clearing it up! $\endgroup$ – lightweaver Jun 20 '16 at 12:54
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Keep in mind that there needs to be an enzyme present to "couple" two reactions. You can imagine it like the energy from the ATP hydrolysis pushing the enzyme to a high energy state, and from that high energy state the enzyme can push the secondary reaction against the equilibrium.

You could do this, and there might even be examples (maybe for some reactions that are just barely exothermic), it's just that enzymes coupling two spontaneous reactions did not evolve that often as there's not much pressure to do that. A spontaneous reaction could just be sped up by a single enzyme, no need to build a big coupling enzyme for that. Coupling this to ATP hydrolysis would just lead to useless energy consumption and extinction.

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  • $\begingroup$ So it is the enzyme that forces a reaction to occur the way it does? $\endgroup$ – lightweaver Jun 17 '16 at 13:22

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