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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.
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.
