Experimental design for a 96 well plate I am designing an experiment that will include an assay on a 96 well plate and could use some advice on the optimal layout.
In our experiment we have 12 biological replicates, and each replicate has been given each of two treatments.  We are measuring our primary outcome on a single plate with 4 technical replicates for each measurement (12x2x4=96).
I suspect (and have some evidence) for row and column effects for this assay, and so row and column balance seems important.
My thought was to alias biological replicates with columns as blocks, since the comparison is being made within biological replicates, and then apply either a complete randomised block design (shuffling the eight technical replicates within the block) or to restrict the permutations using something like an extended Latin square so that the treatment was perfectly balanced across both rows and columns.
Option 1: Each column is a biological replicate, four treatment A technical reps and four treatment B technical reps shuffled within each column.  This I think is easy to analyse, but possibly unbalanced across rows.




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Option 2 - as before but with the restriction that treatments are balanced across rows (something like this - but built on Latin squares rather than just shuffled columns and rows as I've done it here).  This option is balanced but I think harder to analyse.




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So my question are whether these designs make sense at all, whether the first or second approach would be better (and possibly whether I'm overthinking the whole thing).

I have some experience with a problem like this, but not sure if I can provide a correct "answer". Rather I will outline some thoughts, observations, and comments with the hope that they will be helpful for you with figuring out what to do next.
Row and Column effects
I've noticed these two with some of the biological data I've worked with. Primarily I saw row effects while the column effects were weaker. But the general pattern was a gradient which started from the middle of the plate and formed a "wave" pattern towards the edges. Imagine it as a drop falling into water at the middle of the plate creating a round ripple across the plate. So in that regard the first and last rows were more similar to each other compared to, say, the first and middle rows. And the same was true for columns.
At that time, after discussing with "wet-lab" team, our understanding of the cause was a temperature gradient. Even thou each well had a separate controlled heater, we imagined that the temperature was somewhat higher near the middle, because of the proximity to other wells, wheres the edges had fewer neighbours and cooled down. But we were not 100% convinced on this interpretation.
Anyways, effect was there.
The size of the effect
Another thing we noticed is that the magnitude of this effect was not drastic and was quite low. For example - we would detect it when looking specifically for it and we would also see it on first principal components in cases where the samples put on the plate were very very similar to each other. However, if we had things like samples from very different donors (different sexes, different ages, etc) - these things had a lot bigger effect sizes and the gradient effect of the plate was dwarfed by them.
Our way of dealing with the problem
After noticing this effect we concluded that the main problem comes from the outer edges - first and last rows, first and last columns. Thus in the future experiments we did the following:

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*We used as many different plates as we had technical replicates (in your case - 4). So one plate would only contain biological replicates (in your case - 24)

*We left the outers of the plate empty and only used innermost wells.

*The position of each biological sample on the plate was randomised and this randomisation was performed separately for each set of technical replicates (each plate).

This way we avoided the biggest effects, and the rest were randomised. And on top of that we had as many sets of randomisations as there were technical replicates.
Another way of dealing with the problem
In your case I assume you will mainly be looking at differences between treatments. And, if I understood correctly, those differences are paired, i.e. biological sample 1 will have treatments A and B, biological sample 2 will also have treatments A and B, etc, same for all the biological samples. If this is correct you can try to place the pairs as close to each other as possible.
This way, when comparing treatments you would do a paired comparison (taking the differences of treatment A minus treatment B, for each sample separately, and testing if the mean of those differences is equal to zero). Thus, if sample 1 treatment A is on well position A1, and sample 1 treatment B is on well position B1, then after taking the difference the column effect is subtracted and should disappear.
You will have 4 replicates, so just repeat the same for other replicates across different places of the plate, but always make sure that the samples that will be subtracted from one another are neighbours.

Just ideas from someone who is a little familiar with the problem, do not take it as an authoritative answer.
