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Quoting Wikipedia: "Some enzymes operate with kinetics which are faster than diffusion rates, which would seem to be impossible." Which are those enzymes and how can they be so fast?

One example is catalase in which peroxide is catalyzed faster than the diffusion rate of peroxide allows. Lionel Milgrom discusses this case in Water Journal no. 7.

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    $\begingroup$ It doesn't work faster than diffusion. It's diffusion-limited. However, if diffusion rates were faster, the enzyme would also work faster. The bottom line is that you are rate-limited by diffusion in solution. $\endgroup$ – Zhe Jul 29 '19 at 0:43
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The conceptually easiest case is that of a positively charged active site with a negatively charged substrate. The substrate (i.e. reactant) enters the active site with kinetics that are faster than diffusion because there is a long-range electrostatic interaction.

Catalase works near the diffusion limit. The document the OP cites is a hypothesis, without experimental data. It suggests that catalase acts at a distance to catalyze reactions outside of its active site. I would not worry about this hypothesis until there is some experimental evidence supporting it.

Wikipedia has a list of 9 examples of diffusion limited enzymes:

Acetylcholinesterase

β-lactamase

Catalase

Carbonic anhydrase

Carbon monoxide dehydrogenase

Cytochrome c peroxidase

Fumarase

Superoxide dismutase

Triosephosphate isomerase

Some of them have neutral substrates, so the electrostatic attraction would not apply to them. There are other hypothetical mechanisms, though, like weak binding sites on the surface of the enzyme that increase the local concentration of substrate, for example.

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    $\begingroup$ Can you list any such enzyme and their reactants? $\endgroup$ – David Jonsson Jul 28 '19 at 23:58
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    $\begingroup$ I think enzyme kinetics in the case of the OP would refer to overall turnover rate, not just to binding rate. So whatever the mechanism of association, what's fast is the combination of binding, reaction in the active site, and release. $\endgroup$ – Buck Thorn Jul 29 '19 at 6:23
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    $\begingroup$ @BuckThorn If it is diffusion-limited, the binding step is limiting. If it is faster than the theoretical diffusion limit, the puzzling thing is how it can bind faster than that limit. It is amazing in any case that practically every binding event leads to a reaction, very different from what happens in the absence of a catalyst. $\endgroup$ – Karsten Theis Jul 29 '19 at 10:52

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