Here is my answer... although it may not be the only one:
Just to be clear (and apologies for any redundant diatribe here): one GOI's amplification characteristics
cannot be mathematically reconciled with a different GOI's amplification characteristics due to the differing
geometries and kinetics afoot...
That is to say: you can only compare plate 1 inter-plate calibrator's GOIx to plate 2 (3, 4, 5 etc)
inter-plate calibrator's run for the same GOIx. You cannot infer kinetic things from
inter-plate calibrator GOIy and super-impose that reality on another inter-plate kinetics
for GOIx. If you could, then, that would mean that you are using the exact same
primers (and/or probe) for all targets on every plate (which we know, is fantasy).
In order for an inter-plate calibrator to be assessed/addressed correctly - it first, must be
for the same GOI or (a "GOI" also includes the reference gene as a "GOI" of course).
The question you are ultimately asking is how to reconcile any GOIx's efficiency of amplification
at time 1 (on plate 1) with that same GOIx's efficiency of amplifcation at time 2, 3, 4 or 5 etc.
(on plate 2, 3, 4 or 5 etc.) ...
If this is a correct assumption, then you must have time 1 and time 2 (3, 4, 5 etc.) measurements of Cq
of amplification for inter-plate calibrator for GOIx at different times (on subsequent plates 2 or 3 or 4 or
5 etc., accepting the possibility/reality that a different efficiency of amplification for GOIx is indeed possible
each time; on each different plate)...
i.e. If indeed you have Cq measured for GOIx at different times (and most probably, at different efficiencies each time
- due to slightly different mastermix prep., different day, different coffee amount etc.), and if GOIr (reference gene or gene(s)
has/have already been measured reliably once - which is needed only once for the entire study if you are confident
in having reliably measured it/them and its/their efficiency of amplification adequately the first time that is), then, the
logical mathematical way to reconcile run 1 for GOIx with run 2 (3, 4, 5 etc.) for the same GOIx by analysis of the
inter-plate calibrator for GOIx is by the following rationale:
First: you must know the amplification efficiency for GOIx on the first run (if you trust run 1, that is).
(Efficiency of amplification is obtained either by a standard curve; e.g. dilution series of an appropriate
representative sample or sample mixture qPCR'd for GOIx; or by the Cyo method on a single 'trustworthy'
amplification curve run at the same dilution as the final measured samples for GOIx, etc.).
Second: if the Cq value for run 1 for the inter-plate calibrator for GOIx was 23.3 (e.g. at 92.37% efficiency)
and plate 2's (time 2's) run for the exact same sample inter-plate calibrator Cq value was 23.9, then the
following math should apply (in theory); to apprehend efficiency of amplification for run 2 for GOIx:
A Cq of (run 1) of 23.3 at (i.e.) 92.37% efficiency, to be interpreted in the same Cq language for the same
sample (inter-plate calibrator) for the same GOIx of 23.9 (from run 2; time 2) would mean that run 2 for
the inter-plate calibrator for GOIx went off at 89.2361875% efficiency because (for the same GOIx in the
same inter-plate calibrator in run 2):
EAMP2 = EAMP1^(Cq1/Cq2)
e.g.: EAMP2 - 1.9237^(23.3/23.9) = 1.892361875
Thus: EAMP2 for GOIx (e.g. on plate 2/time 2) was: 1.892361875 (in other words: 89.2361875% efficiency)
So: To apply this knowledge to all of your Cq values for GOIx (and only GOIx) on plate 2 you must use the following
transformation (using plate 1 as 'truth'):
Your Cq (Cq2) adjusted values on plate 2 for GOIx, when expressed in the same kinetic language as the Cq values for GOIx (and only GOIx) on plate 1 would be:
Cq2 adjusted = Ct1*LOG1.892361875(1.9237)
That should do it. You can express then, all Cq values for GOIx (and only GOIx) from plate 2 (3, 4, 5 etc.) in the same 'kinetic language' of plate 1 for GOIx
(and only GOIx) and compare all Cq values (for both plates) for GOIx (and only GOIx) on the same 'kinetic playing field.' Therefore, to apprehend what you are ultimately after, you need to have run the inter-plate calibrators for every different target on each different plate). And, according to e.g. Super Array Biosciences procedure, you only have to perform these in singlet if indeed each singlet reaction is assembled/performed with excellence and with the utmost presence of mind and best coordination/technical prowess possible.
Note: Never forget that sample and reagent aging, and sample freeze-thawing, is the red-eyed predator of every qPCR endeavor you undertake. Nothing is as pristine as the day it was born. Including 'scientifically sound' isolated DNA, RNA and reverse-transcribed cDNA. The sooner you can run your qPCR after sample isolations, the better: Always. Better yet, proof of sample integrity before any qPCR (e.g. Bioanalyzer 2100 analysis, i.e. for RIN of RNA) is a very good idea. Crucial.