the Ultimate Deconvolution Experience

a true story

In May 2008 a letter arrived with the subject “iNMR suggestions”:

My name is Craig Robertson, a Ph.D student from the University of St Andrews. I work for Douglas Philp and he suggested I should get in contact to offer some suggestions which I feel would improve some of your software.

As you may guess I do a lot of NMR experiments, typically observing a reaction by 1H or 19F NMR for 16 h by recording a spectrum every 15/30 minutes. At the end of the day I have between 30-50 NMRs to deconvolute and typically look at 7-10 signals in each. To say it is tiresome is an understatement! Within our group we have different preferences on how to do this, I like using 1D WinNMR, (rather old) and others in my group use Topspin (A program I personally do not really get on with). We all use iNMR everyday for all our NMR needs except deconvolution, but with your introduction of the tool a little while back, we have had a look into it. There are a couple of things I would love to see before I can dump 1D WinNmr (And windows PC's altogether!) .

[note: Deconvolution had been introduced in October 2006 and Craig was probably the first customer to write about it, almost 2 years later. The letter went on with several suggestions which mostly demonstrated that Craig had never found the manual page describing the deconvolution module, something he soon admitted. That's curious, because that module sports a question mark icon labelled “Help”. It's also revealing: it looks like we stubbornly keep writing boring manuals that no user is ever going to read. Not to mention atypical articles like this one.] The letter finished with the following wish:

The holy grail for a deconvolution tool would be one which could watch a peak evolve over many spectra. ie a sort of automatic deconvolution tool. I don't know if this sort of thing is possible however I thought I might mention it just in case. : )

At the time of the above email, iNMR was already able to perform almost everything that Craig needed. The trick was as simple as copy & paste. It was indeed possible to copy the whole list of parameters from the deconvolution module, edit it into any text-editor (for example: adding or deleting lines) and pasting the list back into the same or a different deconvolution module. Yes, they are non-modal windows, you can create how many of them you like and they can even survive detached from their respective experimental spectrum. What wasn't possible yet was the “automatic deconvolution” tool, but it didn't take long...

There were two problems: the module had never been tested by the public (the so called beta testing). The solution, in this case, is simply to keep working on the details. The big problem was, as the reader has already realized, that Craig had thousands of peak to process! iNMR already had the technology to handle the situation, because it's a scriptable program, yet the deconvolution module had never been connected with the built-in Lua interpreter. There were also other chemical and spectroscopic issues, but they are outside the scope of iNMR. If you want to argue if deconvolution is really better than trivial integration, then our answer is that, in this particular case, it is. Here is a representation of the first experiment we received from Craig. For clearness, only the peaks increasing during the reaction are shown, (those decreasing are important as well). You can download the spectra in iNMR format from here if you want to recreate the ultimate deconvolution experience for yourself...

kinetic experiment console

After a single working day we had already created a communication door between the Lua interpreter and the deconvolution module, which had become fully scriptable in this way. The same day our first script was also ready to run. The whole “work” required to process the desired 160 signals consisted into the pushing of a single button.

The results were saved in tabular form as a text file:

point	ppm	area	ppm	area	ppm	area	ppm	area	ppm	area

01	3.710	158.981	3.927	1.120	5.665	0.000	5.008	10.222	3.775	6.660	
02	3.710	156.606	3.926	1.294	5.641	2.275	5.008	1.785	3.725	17.781	
03	3.710	154.335	3.925	1.133	5.665	2.194	5.017	2.212	3.735	15.102	
04	3.710	152.229	3.924	2.634	5.669	3.756	5.014	3.490	3.749	10.079	
05	3.711	147.785	3.919	8.495	5.671	5.686	5.011	5.136	3.753	12.886	
06	3.711	144.402	3.920	9.880	5.672	7.793	5.009	7.181	3.755	17.001	
07	3.711	139.776	3.918	13.994	5.673	10.168	5.007	9.103	3.757	20.275	
08	3.711	135.007	3.919	16.619	5.674	12.742	5.006	11.519	3.758	24.961	
09	3.711	129.215	3.918	20.249	5.674	15.181	5.005	13.960	3.759	29.479	
10	3.711	124.476	3.918	24.391	5.675	18.184	5.004	16.737	3.759	34.418	
11	3.711	118.477	3.918	26.400	5.675	20.961	5.003	19.377	3.760	40.019	
12	3.711	113.019	3.917	31.753	5.675	23.793	5.002	21.912	3.760	46.052	
13	3.711	107.711	3.917	35.634	5.675	26.979	5.001	24.823	3.760	51.704	
14	3.711	101.458	3.917	38.670	5.675	29.406	5.000	27.455	3.760	56.673	
15	3.711	96.096	3.916	41.935	5.675	32.424	5.000	29.934	3.760	61.986	
16	3.711	90.981	3.916	46.517	5.675	35.176	4.999	32.905	3.760	67.574	
17	3.711	85.938	3.916	50.616	5.675	37.724	4.998	35.648	3.760	72.676	
18	3.711	80.728	3.916	52.905	5.675	39.995	4.998	37.794	3.759	77.344	
19	3.711	75.670	3.916	56.149	5.675	42.612	4.997	40.455	3.759	82.661	
20	3.711	70.732	3.915	58.468	5.675	44.740	4.997	42.319	3.759	86.801	
21	3.711	66.532	3.915	61.093	5.674	47.021	4.996	44.713	3.759	90.900	
22	3.711	62.266	3.915	63.992	5.674	49.090	4.996	46.455	3.759	95.325	
23	3.711	58.436	3.915	66.910	5.674	51.181	4.995	48.559	3.758	99.654	
24	3.711	54.914	3.915	68.394	5.674	53.240	4.995	50.574	3.758	103.199	
25	3.711	51.620	3.915	71.398	5.674	55.086	4.994	52.366	3.758	107.380	
26	3.711	48.574	3.914	72.650	5.674	56.493	4.994	53.913	3.758	110.269	
27	3.711	45.332	3.914	74.438	5.674	57.942	4.994	55.334	3.758	113.179	
28	3.711	42.629	3.914	75.678	5.673	59.555	4.994	56.913	3.757	115.742	
29	3.711	40.732	3.914	77.763	5.673	61.135	4.993	58.331	3.757	118.953	
30	3.711	37.836	3.914	79.841	5.673	62.104	4.993	59.270	3.757	121.244	
31	3.711	35.633	3.914	81.420	5.673	63.317	4.993	60.662	3.757	123.958	
32	3.712	33.316	3.914	81.753	5.673	64.431	4.993	61.836	3.757	125.846

are the numbers meaningful?

The table above has been compiled from 160 different deconvolution modules, each one employing a (potentially) different unit to measure areas. The unit for frequencies is reported (ppm) but not the unit for the areas. How can we compare the 160 values? All we can do is to compare the values on the same row (same 1-D spectrum). From these values we can calculate the percentage of each compound at different times. Only the percentage values (not shown) can be used to monitor the kinetic of a reaction.

The areas expressed by iNMR are normalized either internally or externally. Normal integrals, those measured directly on the spectrum, can also be normalized or not (in the latter case the normalization factor is 1). The normalization factor can change from page to page. Each deconvolution module, when created, inherits the normalization factor in use at the moment, but only if it's different from 1. In the latter case, the modules are normalized internally, instead, in order to make their total area = 100. If we want to compare the areas evaluated by different modules, as in the case described, we must ensure ourselves that the normalization factor is the same for the peaks on the same row. It doesn't mind, instead, if it changes from spectrum to spectrum, because we can (and should) compare the variations in percentage and not variations in area among the spectra. In conclusion, we need not to compare areas between different spectra, but we that:

Our 1-D spectra are extracted from a 2D matrix just before using them and a new page is created by the extraction mechanism. The normalization factor of any new page is 1, exactly the value we must avoid. It is necessary, therefore, to normalize the integrals before starting the first deconvolution. All iNMR users know how to pick the integrator tool, double click an integral and enter the desired value into the dialog that appears. The command “intreg()” can perform the equivalent operation inside a script (macro). We must be sure, of course, that an integral already exists. Another way to normalize the integrals is to create the first integral, because it's automatically normalized. This alternative trick assumes that no integral exists. Our program adopts the latter alternative and, to be sure that there are no integrals, we explicitly delete them:


delint()		-- this command deletes all integrals
region( 2.4, 2.6 )	-- any region internal to the spectrum is good
press 'i'		-- creates the first integral, automatically normalized

-- we have finished doing the necessary things 
-- now we add something unnecessary:

intreg( 1, 300 )	-- we set our integral = 300

The unnecessary last line of the script adopts a meaningful scale for the areas. We have intentionally selected a region comprising the methyl signals of both the starting material and the product, and set its value = 300. In this way, any integral, divided by the number of underlying nuclei, already corresponds to the percentage concentration of the compound it belongs to, IF THERE ARE NO ERRORS. This particular normalization simplifies the visual inspection of the table of results, but it's not correct to assume that the integrals correspond to the percentages. If the methyl signals move (as they slightly do) or if an impurity appears during the reaction, the calculated values don't correspond to the percentages anymore.

how can we trust this script?

It's immediately evident that the value 10.222 (third from the right in the first row of our table) is wrong. It should be near to zero, because it measures the product of the reaction and the first spectrum contains almost no product. It is necessary to repeat the deconvolution manually or to ignore this value. In our opinion, at the early stages of the reaction, when the product is almost invisible, only the methyl singlets can be used to monitor the increase in concentration. Another prudential rule, at all advancement stages, is to avoid signals with severe overlap, if more resolved signals are available. That is to say that it's not necessary to always use the same method to estimate the percentage concentrations.

A problem still remains: how do we know what's happening during the script? Can we be sure that the optimal operations are performed each time? The solution is to modify the script and allow the user to suspend the run, change the parameters and the operations, to select with the mouse the regions that are fed into the deconvolution modules and to restart the run. We have actually split the original script into two new ones: An initialization script that is called only once and a step forward script that is called twice for each signal. After the initialization, the program shows the first peak. The user selects the portion of the spectrum to process, then clicks on the button associated to the step forward script.

The second script creates the deconvolution module and fills it with the appropriate parameters, then exits. Now the program shows the deconvolution window with the tentative parameters for the peaks. The user clicks the “FIT” button. If he likes the fit, he clicks the step forward button again. This time the script stores the values, closes the module, then jumps to the next peak. The cycle continues until all the peaks of all the spectra have been processed. The scripts take care of the book-keeping: extracting all the 1-D spectra from the 2-D matrix, zooming into the regions of interest, summing up the individual intensities to obtain the area of each multiplet, storing the results into a file. The user acts as a supervisor, while all the boring bureaucratic activities are delegated to the scripts. Each agent (the user and the computer) takes care of what it's more good at.

While the scripts are only valid for this specific spectrum, they can be easily adapted to many similar cases. It's enough to redefine the parameters. They are conveniently listed (and commented) at the beginning of the initialization script. The only other statement that may require a change is the optional normalization we have already seen:
intreg( 1, 300 )
but it can also be left there without harm. What's important, in all cases, is that you don't measure the kinetic directly from the areas, but from the percentage concentrations derived from those areas.

conclusion

The deconvolution module is based on a graphic interface. Built over this basis, a purely textual approach is also available. On top of both approaches, everything can be programmed by a skilled user, in full or in part. If he can't write the script, like in the case of Craig, we do it for free. It's even possible to add more buttons (inside the console) to adapt the interface to the individual needs and tastes.
In this article we have seen how a long-standing problem was elegantly solved in a few working days. For a more in depth analysis the curious reader is invited to study the lua scripts (see links above). More introductory articles on the same subjects are:

acknowledgments

We thank Craig Robertson for the initial input, the helpful discussions and his testing activity. We also thank Prof. Douglas Philp for letting us publish their spectra here.


 
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