Can I change the first sentence to the following sentence?

1) The cells were treated with enzyme A. -> The enzyme A was treated to the cells.

2) The protein was adsorbed to the nanoparticle. -> The nanoparticle was adsorbed with the protein.

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    @Tory see my comment below re "adsorbed" and "absorbed" – D. Nelson Dec 7 '16 at 19:06

The original sentences are correct, you should use those.

"treat to" means to give something as a gift or pay for something on someone else's behalf, e.g. "I'll treat you to dinner tonight". So "The enzyme A was treated to the cells" makes it sound like someone bought enzyme A some cells as a present.

"adsorb" means "to cause a substance, usually a gas, to form a very thin layer on the surface of another substance". So on, to or onto are the prepositions you could use. "adsorbed with" doesn't make any sense.

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    Per this NGram, the most common preposition after adsorbed is actually on. But to sounds fine to me anyway (and I quite agree that with doesn't cut the mustard here). – FumbleFingers Reinstate Monica Dec 7 '16 at 14:38
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    Good spot, I'll edit my answer to include "on" – D. Nelson Dec 7 '16 at 14:41
  • @FumbleFingers I'll raise your NGram with another NGram, "absorbed by" and "absorbed into" for a passive voice. – Tory Dec 7 '16 at 18:40
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    @Tory: Good point. But I'll see your "passive" and raise you an explicitly active voice chart by searching for which adsorbed xxx - if I'm not mistaken, that should screen out all passive usages (which unsurprisingly tend to favour by). – FumbleFingers Reinstate Monica Dec 7 '16 at 18:48
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    @Tory I think you've got "absorbed" and "adsorbed" confused :) – D. Nelson Dec 7 '16 at 19:05

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