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This is a question that's been bugging me, and I haven't been able to find a definite answer anywhere.

We know there are thousands of enzymes (proteins, let's ignore catalytic RNA for now) that catalyze many different reactions, and they do this because they have the correct shape to fit the substrates.

Theoretically, given some reaction, can an enzyme be created to catalyze that reaction? Or is there some reaction that it's not possible to catalyze with an enzyme? Can any given shape be created out of polypeptide chains? If not, what determines the shapes that it's possible to create?

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    $\begingroup$ (+1). I think there is a great principle here: an enzyme can only catalyze a thermodynamically favorable reaction. If a reaction is at equilibrium, for example, an enzyme cannot change that. $\endgroup$ – user1136 Nov 9 '16 at 14:03
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This will probably be a difficult question to answer definitively without some hand-waving or redefining the question; I can't imagine proving the negative result that no enzyme is possible for a given reaction, except for some cases where the reaction is just thermodynamically impossible outside of incredible conditions (for an extreme example, what about hydrogen fusion: the reaction exists, but the conditions necessary are outside the tolerance of protein-based catalysts).

As @tomd pointed out in a comment, enzymes do not change equilibrium, so enzymes are only possible for reactions that are thermodynamically favorable. However, some enzymes couple reactions that are thermodynamically unfavorable with highly favorable reactions to produce a net thermodynamically favorable reaction, which greatly increases the number of reactions that can theoretically be catalyzed.

As for whether any shape can be created out of polypeptides: given the diversity of amino acids and the structural effects of the tertiary structure of proteins, there is a near limitless array of combinations which exceeds human comprehension, but not a truly mathematically infinite number. There are interesting projects such as this one that seek to harnessed underutilized computing power to iterate all of these possibilities to search for useful drugs and explain the causes of disease.

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Are there enzymes for every reaction? The short answer is, "No" - there are reactions that occur within the human biology that do not require enzymes. One example of this is the formation of advanced glycation end products (also known as "AGEs"). These are biological molecules like lipids or proteins that become glycated through exposure to high glucose concentrations, like those observed in diabetes or insulin resistance. The high concentrations of glucose allow non-enzymatic mediated covalent attachment of glucose molecules to the macromolecule. See this review for a more in depth discussion of AGEs as well as other references that discuss them.

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The question "Can any given shape be created out of polypeptide chains" is rather tricky, but let's unpack it. A protein has a fold - or topology - that determines its overall shape, but can be considered as a framework on which to hang active residues.

There are 'only' 1,200-1,400 known folds, depending on the classification scheme (CATH, SCOP) which seems quite limited. However, if we take just one of those folds - the TIM barrel - and alter the loops you can get a diverse set of structures. That paper does not discuss enzymatic function, of course.

So for small molecules, it's difficult to see any reason why you can't arrange active sites any way you like. The only theoretical difficulty is that you have to fold proteins before they can be active. It might be possible that some complicated arrangement of active site residues would prevent the whole protein from folding - although that's just speculation.

More complicated might be reactions on macromolecules. For example, there are enzymes that bind to DNA, polysaccharides, and other proteins. These longer molecules are still possible for enzymes to bind to - it generally just requires a long surface. Some of the more complex actions include that performed by topoisomerases or chaperones or whatever vaults do.

By moving from tertiary to quaternary structure, it seems like enzymes can do nearly anything that's chemically possible.

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