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Is it true that in an enzyme-catalyzed reaction, the rate of reaction does not vary with varying osmotic pressure?

Instead of just a true or false answer, why does it, or why does it not vary with osmotic pressure?

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This paper is a compelling example of an effect of osmotic pressure on enzyme function. Restriction enzymes are normally very selective in the base sequences of sites at which they cut DNA, but in some conditions they show cutting at off-target sites, called "star activity." "Star activity" increased for some restriction enzymes almost linearly with osmotic pressure generated by a range of non-ionic solutes. Supporting the idea that the higher osmotic pressure was directly responsible, increased hydrostatic pressure reversed the effect of increased osmotic pressure.

Increasing the osmotic pressure is essentially decreasing the chemical activity of the water in the system. So it's not surprising that any enzyme reaction might be affected, particularly if the structures of active sites of enzymes are altered as suggested by the authors of the paper cited above.

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In order to achieve initiation of DNA replication in vitro at the E. coli chromosomal origin of replication, Arthur Kornberg's lab had to include polyethylene glycol (PEG) in their reactions. The proposed mechanism for this enhancement was termed "molecular crowding" which was thought to increase the local concentration of the substrates.

A similar effect has been seen in reactions with T4 DNA ligase. Blunt-ended ligations are more efficient in buffers containing PEG.

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