Linearity question

[AnaChem1983]

Hi all,

I have a question pertaining to the demonstration of the linearity of a method when you don't actually have a reference material for the analyte in question. I have an decent idea of what I'm going to do (which will inevitably involve a few trips to the QA department!) but always useful to ask for advice.

Some background. The method development is needed to monitor a reaction that proceeds from one compound to another (stage 1 to stage 2) via 2 intermediates. In order for successful production there must be negligible intermediate 2 in the stage 2 compound (<= 0.5%). The reference method used at the moment to monitor this is a TLC method that can be quite hit and miss and therefore we need a more accurate means of monitoring intermediate 2 to ensure that the next stage of the reaction does not proceed until we are confident int. 2 has been reduced to acceptable limits.

The challenge comes in that we don't actually have any reference material for the 2nd intermediate. Therefore my proposal is simply to obtain a sample from the reaction vessel at the point when intermediate 2 is going to be at its highest (the nature of the reaction means that there is a point in the scheme where this can be assumed) and assign this a nominal concentration of 100%. A series of dilutions can then be prepared in order to demonstrate linearity.

QA may well have some additional concerns but I thought I'd run this general idea past people on here to see if anyone has encountered this issue before and if so what they did. If not is there anything else that might improve matters.

[Chromavore]

Hi AnaChem

I assume you are looking to develop a LC-UV method?
if input material and the intermediate are structurally similar and share chromophores you could assume a relative response factor of 1:1 (1mg/mL of material would give you a peak height or area of equal size for both molecules)

you can then assess linearity of the method against input material and use input material as a reference standard

If the end molecule is structurally closer to the intermediate in question and you can obtain a pure enough sample this would also be appropriate.

obtaining a pure sample of the intermediate would be best practice to confirm the relative response factors or just to use as the calibration/reference standard for the assay.

the more crude option would be to just use % relative area, e.g. inject your reaction solution and integrate all peaks, identify the intermediate and the desired end molecule and integrate these peaks, when intermediate peak <0.5% total area you are good to proceed. (this again assumes a response factor of 1:1 and will be subject to error if you have a lot of solvent peaks)

your suggestion of using an assumed maximum concentration and assigning a nominal value of 100% is workable for assessing the linearity but does not really help you quantify the concentration of intermediate molecule in a given solution.

hope this helped

[Hollow]

Agree with Chromavore especially the last sections.

With serial dilutions you can assess linearity of your detector.
But for the main goal it won't help you too much.

I would probably analyse several samples from different time points during production and monitor your intermediate with both methods, TLC and your new LC.

Then you can compare the peak ratio of your intermediate and target compound for that sample, that would be in spec by TLC.
Then, you can even adjust that ratio to add a safety margin for successful production.
(Make sure the peak of your main component is still ok and no detector overload occurs, otherwise the peak ratio will be wrong)

[Peter Apps]

Dilutions will work for linearity, but not for quantitation unless you can quantitate by another method and assign that value to one of your linearity levels.

Unless you need to establish lineariy over a wide range, it is better not to do serial dilutions, because errors in the first steps propagate nto subsequent steps.

Peter

[AnaChem1983]

Excellent advice so far everyone. Thanks a lot.

The assessment of moving forward to the next stage upon removal of all int. 2 is purely down to a modified area % calculation involving only the product/reactant compounds i.e. contributions from solvent are ignored. Therefore quantification in terms of, say, mg/L is not really needed.

Therefore my reasoning is that if we can get a sample in which int. 2 is likely to be at its highest we can say that the detector is never going to see a quantity higher than what is generated here. Therefore a series of samples, be it serial dilution or indiviudally prepared dilutions, should illustrate that the detector gives a linear response all the way down to the level that we are trying to focus in on. We would then proceed to demonstrate accuracy and precision at this level, as best we can.

Thanks again for the help, folks. Much appreciated.

[lmh]

Late to the party, but just in case anyone is still watching. If you are absolutely certain that the starting material can only be converted, stoichiometrically, to some mix between the two intermediates and the final product, and the sum of concentrations of starting material, end material and both intermediates is therefore constant, then you can of course find the relative extinction coefficients of all four materials, provided you have samples taken at four different time-points with four different sets of proportions. It's just a matter of solving the simultaneous equations (mathematically: draw out a matrix of data for each peak in each sample, invert the matrix, multiply it by a vector of the four expected total concentrations in the four samples, and the resulting vector is the inverses of the four extinction coefficients). But in this case the whole thing runs a risk of getting a bit circular: if you make assumptions about what was going on in the reaction vessel to set up your analytical method, and then use the analytical method to find out what was going on in the reaction vessel, then if anything weird happened (a third intermediate that no one guessed existed, or whatever) then it all falls apart. It just gives you a choice of a different assumption on which to fail, instead of having to make the assumption that the intermediates have an extinction coefficient close to something different that happens to be available in pure form.