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I read the following sentence in Nature:

The second test of cocaine seeking was a cue-induced reinstatement test conducted 5 min after the last of the extinction sessions.

Would it be correct to add the preposition at before the "5 min" bit? In the Journal of Nuclear Medicine, I've seen another sentence that did just that:

The amount of intact [111In-DOTA-Ala1]SS14 detected in the mouse circulation at 5 min after the injection of PA increased impressively—from less than 2% to 86%

And there are many similar sentences that sometimes use an at, and sometimes not:

  • Tonic formalin pain is substantially reduced by brief spinal anesthesia given 5 min before, but not 5 min after the formalin injection

  • The amount of intact [111In-DOTA-Ala1]SS14 detected in the mouse circulation at 5 min after the injection of PA increased

I am really confused when to use or omit at with time specifications.

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    Short story: at identifies a specific moment in time when an event occurred, whereas before and after frame the moment as a threshold. In other words, at names an instant, as opposed to other turns of phrase which deal with durations.
    – Dan Bron
    Apr 20 '15 at 11:18
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    BTW, you asked a clear question and provided helpful examples and references with attribution. I'd welcome many more questions like these. That said, the initial revision you posted came off at first blush like an impenetrable wall of text. So if you want to ask further questions, I'd encourage you to get familiar with the formatting and typesetting tools StackExchange provides. You can use this [now edited] question as an example to jump off from.
    – Dan Bron
    Apr 20 '15 at 11:20
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There is nothing wrong with omitting "at" in the example you cited. "5 min after" sufficiently defines the time. Also, the report obviously uses an abbreviated style; orherwise it would have spelled out "minutes" ( or at least "mins").

Anyway, In AmE, we tend to reserve the "at" in time references for instances where we cite a specific time on the clock:

  • The meeting will resume at ten after two.

When speaking of relative time (elapsed time between two events, without reference to the clock) we typically do not use "at", and in many cases it would strike us odd to hear it that way.

  • He fell asleep ten minutes after he got here.

not

  • He fell asleep at ten minutes after he got here.

However, in your sample, the experimenters are figuratively "starting a clock" (a virtual stopwatch") counting off the minutes. So although "at" is not needed, it doesn't sound strange to leave it in, in that specific context.

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"at" is used only for specific points in time. So we do not say "at some time after" or "at just after" or "at next week". But that does not mean that omitting "at" is invalid for specific points in time, since that depends on the type of time specification. "5 min after X" is already specific enough and leaves no doubt that it means "exactly 5 min after X". Likewise for phrases like "the day after" or "the week before".

That said, there is a tendency to say "at 5 min after" when describing that specific point of time, especially when it is something that the experiment is designed to find. In contrast your first example has "conducted 5 min after", where the time here is just part of the experimental procedure.

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"At 5 pm" indicates a snapshot/instant in time.

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  • And 5 minutes before suggests some leeway.
    – Huey
    Apr 20 '15 at 12:34

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