Please help with the calculation of the concentration

[thaliaz]

I have two chromatography systems, one is affinity and another is size exclusion.

I have sample A, 0.32 ml dissolved in 5 ml of the solvent (0.32 ml sample A + 4.68 ml binding buffer). Then I inject 1 ml of that diluted sample A to the affinity column. When I wash the column with the elution buffer, the eluate (let's name it eluate A) comes out as a small band (0.5 ml). I also collect 5 ml of unbound portion that flows through the column. Then these samples I inject to the size exclusion column. So, what I inject to the SEC column include:

1. Eluate A 0.5 ml

2. Unbound portion 1 ml

3. Sample A 0.32 ml

 

Then I measure the concentration of the sample using colorimetric assay. However, when I process the data I got from the assay, I think there is something wrong with my calculation. From the SEC results, I know that there are 3 peaks coming from sample A in which one of these peaks I want to separate using the affinity column. The separation is successful since I only have that peak in my eluate A, and this peak does not appear in the unbound portion so it should all be bound to the eluate A.

 

However, when I compare the concentration results from the assay of sample A and eluate A, it does not make sense because it seems that concentration of that peak I want in sample A is much more than the one I got from eluate A. Then I realize that it might be wrong to compare the data from sample A 0.1 ml and eluate A right away because it should be calculated in a way that sample A is diluted which means that the data I got from sample A should be 15.625x less since it is dissolved in 5 ml before injecting to the first column. If I process the data this way, it does not really make sence because eluate peak will be 2x higher than the sample A peak. But then again, if I think about the content wise, sample A 0.32 ml injected to the SEC right away and sample A diluted in 5 ml contain the same amount of sample A (0.32 ml); therefore, this should be always comparable to eluate A right away without doing any dilution.

 

I have asked my supervisor and he said that I should do the dilution correction by dividing the sample A 0.32 ml with 5 then multiply with 500/320 so that I can compare with eluate A result. This works perfectly actually, and I get a very nice fit, but if I use different amount of sample A, this does not work anymore. Moreover, another suggestion is that I should try to inject the diluted sample A 0.5 ml to the SEC column so the result is comparable.

 

Moreover, I am certain that both columns do not cause the major loss as I calculate % recovery before and after I inject my sample to the SEC while there is nothing anymore washed out after the eluate is collected for affinity column.

 

Any idea and suggestion how I should process the data? I need to calculate % recovery for the first column.

[CharonY]

Just to clarify, you used affinity purification and got two fractions (target and unbound). And on the SEC you did three independent injections (total sample, target fraction and unbound fraction)? And if so, what is the injection volume in each case (did you use an autosampler or manual injection)?

[thaliaz]

Hi,

 

Thank you very much for the post! Please see my clarification below:

 

Just to clarify, you used affinity purification and got two fractions (target and unbound). - That's right.

And on the SEC you did three independent injections (total sample, target fraction and unbound fraction)? - Yes. All were independently injected.

And if so, what is the injection volume in each case (did you use an autosampler or manual injection)? - The machine is quite old so I had to do manual injection. The volume of each sample is as follows:

1. Eluate A 0.5 ml (so that was all the eluate from the affinity column)

2. Unbound portion 1 ml (I initially collected 5 ml of the unbound portion but I could only inject 1 ml max. to SEC column)

3. Sample A 0.32 ml (the same amount of sample injected to the affinity column but before dilution)

[CharonY]

I assume you are just not taking all dilutions into account. From what I read you are doing a colorimetric assay after capturing the respective fractions. What dilution did you use there (note that you have to take the elution volume into account) ? If you take those into account as well as the initial dilution (and assuming no loss) the calculations should be quite simple. It is easier if you actually calculate with final concentrations than just with ratios.

 

From your description it is also not quite clear to me at which step you actually do the quantitation and which values you compare to each other. Originally I assumed that you used the traces of the chromatographic runs, and missed that you measured the eluates.

[thaliaz]

Hi Charon,

 

Sorry for the confusion. You are right. I actually do the colorimetric assay after SEC for every fractionated sample I have. The dilution for the assay should not be a problem since all samples were done in the exact same manner. The quantification step is the assay step. The assay that I do is the cholesterol assay so after I got the concentration calculated by the plate reader machine e.g. 0.5 mg/ml for the original sample, I know amount of the sample (in mg) by the calculation based on the actual amount I initially injected to SEC which is 0.5 mg/ml*0.32 ml. From that I will get the amount of the cholesterol present in mg. In addition, I also did the same thing with the eluate, so it is the concentration measured multiplied with 0.5 ml which is the sample volume I inject to SEC.

 

However, the only confusing point is that when I compared the amount in mg of original sample with the eluate, what I got was that that certain peak of eluate had 2x less chol amount compared with the original sample. This does not make sense since we all know from the experiment that there is nothing coming out in the flow through for that peak, which means that everything was actually captured by my first affinity column. We have also considered that it might be lost elsewhere in the system or the elution solution was not strong enough to elute everything, however, we did get similar peak area of eluate from many repetition of the experiments, and the capturing capacity of the column was not decreased. Therefore, now we assume that there is something wrong with the calculation.

 

When we look at the calculation, one thing we have to consider is that we inject the diluted sample 320µl in 5 ml to affinity column. From that, if I want to know if my affinity column captures something, I have to inject 320µl of sample to the SEC column to compare with my eluate from the affinity column. Again, it seems that the data can be directly compared since they are both the same amount of sample injected although the concentrations are different, just that the first one it is diluted to 5 ml, but everything is injected to the system. So, basically everything is injected. And since SEC separates particles based on their sizes, and the colorimetric assay also works based on the amount of sample presents (more particles, more bonds for the enzyme to react with), the data should be directly comparable.

 

Is it correct in your opinion to compare the data from both system directly without having to do any dilution since the same amount was injected?

Edited February 28, 2017 by thaliaz

[CharonY]

Please clarify this to me. In order to measure recovery do you have quantified (beware, did it in a rush and may get numbers wrong):

 

A) Original concentration (without separation). Assuming you started with the 0.32 ml , your concentration would be Xmg/ml and multiplying it with 0.32 ml the original concentration is 0.32X mg total (X being 0.5 in your example)

 

B) After diluting it in a final volume of 5 ml you therefore start with 0.32/5=0.064X mg/ml (as you have 1 ml injection). Effectively you concentrate the sample to double the concentration, if you captured everything (final volume 0.5 ml) resulting in 0.128 Xmg/ml as concentration, assuming you used the same volume of your eluate to run the assay as in A). However, since you only have 0.5 ml total, you still only got 0.064 total load.

 

C) Now you load that amount on the second column. Here you should also take into account what final volume your eluate is now (which I cannot find in your posts) prior to running the assay. E.g. if your eluate is again 0.5ml you should yield the same amount (again, assuming no loss). Any other volume would increase or decrease the concentration accordingly.

 

D) Now if you run your original sample undiluted and loaded the whole 0.32ml you start off with five times the amount (with an 1 ml injection), assuming you got the same elution volume. If you do not get that, there is a chance that you may overloaded your column, especially as other components in your sample can interfere with the analysis. Diluting the original sample and run a SEC alone is a possibility, though a dilution series could help in assessing whether you are actually still in the dynamic range of the separation method.

[thaliaz]

Hi Charon,

 

First of all, thank you very very much for your help. I really appreciated that. I realize that it might be better to clarify the experimental portion since it is very complicated. I have drawn some figures, and uploaded it to this link: https://we.tl/kDRAPVHYKz. Unfortunately, I could not find a way to upload the media here. If you don't want to download from there, I can try to explain more or you may be able to advise me how to upload the photo/pdf file here. In addition, please find my clarification to your latest post below:

 

Please clarify this to me. In order to measure recovery do you have quantified (beware, did it in a rush and may get numbers wrong):

A) Original concentration (without separation). Assuming you started with the 0.32 ml , your concentration would be Xmg/ml and multiplying it with 0.32 ml the original concentration is 0.32X mg total (X being 0.5 in your example) - It was quantified yes.

B) After diluting it in a final volume of 5 ml you therefore start with 0.32/5=0.064X mg/ml (as you have 1 ml injection). - The injection to the first column was 5 ml, not 1 ml. (0.32 ml + 4.68 ml solvent) (I'm sorry I might confuse you with the injection of flow through which I collected 5 ml but injected 1 ml) Therefore, everything that was diluted was also injected to the first column. To see how much was actually injected to the first column, I injected 0.32 ml of sample without solvent to SEC since I cannot inject 5 ml. Effectively you concentrate the sample to double the concentration, if you captured everything (final volume 0.5 ml) resulting in 0.128 Xmg/ml as concentration, assuming you used the same volume of your eluate to run the assay as in A). However, since you only have 0.5 ml total, you still only got 0.064 total load. The eluate only contains a part of the original sample since the first column only captures specifically the particles I want. However, from SEC chromatogram, that part is all captured by my first column.

C) Now you load that amount on the second column. Here you should also take into account what final volume your eluate is now (which I cannot find in your posts) prior to running the assay.- From SEC, eluates were collected into 37 fractions (0.5 ml each). I take 0.05 ml of each fraction to do the assay in a 96-well plate. All samples were eluated in the same manner from SEC column. E.g. if your eluate is again 0.5ml you should yield the same amount (again, assuming no loss). Any other volume would increase or decrease the concentration accordingly.

D) Now if you run your original sample undiluted and loaded the whole 0.32ml you start off with five times the amount (with an 1 ml injection), assuming you got the same elution volume. I think answer to question 1 clarifies this. The total of 5 ml was injected. The reason for dilution was that we want the sample to be less viscous so it is better distributed in the solvent. If you do not get that, there is a chance that you may overloaded your column, especially as other components in your sample can interfere with the analysis. Diluting the original sample and run a SEC alone is a possibility, though a dilution series could help in assessing whether you are actually still in the dynamic range of the separation method. That might also be possible since the elution condition was quite harsh therefore the sample might be affected.

Edited March 2, 2017 by thaliaz