NMR Analysis, Processing and Prediction

The bumpy road towards ASV

2011-07-26T09:45:00.000-07:00

Figure: Photo taken during our bike climbing to Galibier (Lautaret) in the Tour de France 2011

One of the most exciting and complex challenges in NMR software for small molecules at present is the ability to verify a proposed chemical structure from its NMR spectrum automatically, a process commonly known as Automatic Structure Verification (ASV). Nowadays, it is possible to acquire spectra automatically on large numbers of compounds, but the interpretation of all of this data constitutes a key bottleneck [1]. As John Hollerton wrote in Stan’s blog

So now I come to the purpose of ASV. I don't know of many (any) companies employing people to look at 50 spectra a day (except for specific, one-off projects)

We at Mestrelab have been working for several years already to provide the most powerful and usable ASV software package.

It was not an easy job, and in some ways, resembles the stages of the Tour de France that Santi, some friends and I made a few days ago. We had to suffer, curve by curve, ramp by ramp to reach the top of the mythical Cols of the Alps (Galibier, Alpe D'Huez, Croix de Fer, Telegraph, Les 2 Alpes, etc), but we've made it :-)

Similarly, the road to ASV has also been very steep and tough, but we think now that we have a truly sophisticated and successful system that delivers very good results.

Of course, there's always room for improvement (as with the Alps, which we could climb much faster if we had been riding on road bikes instead of BTTs:-)), but either way, we are very satisfied with the current state of our ASV.

From here I would like to take this opportunity to thank Stan Sykora for his superb work

References:
[1] S.A. Richards, J.C. Hollerton, Essential Practical NMR for Organic Chemistry, John Wiley & Sons, Ltd, 2011.

Intelligent Peak Picking of 1D NMR Spectra

2011-05-16T01:26:00.000-07:00

In case you hadn´t noticed, version 7 of Mnova was released just a few days ago.

Whilst this new version presents a number of significant improvements in the software, in this post I would like to focus on a new peak picking concept which, to the best of my knowledge, is novel and in some way, revolutionary. I will try to keep this as short and clear as possible, just to illustrate the very basic ideas that motivated this new approach to peak picking. In the next posts I will elaborate further on some of the new points introduced here.

Traditional Peak Picking

First up, to lay the groundwork for this article, let’s revisit the way in which peak picking algorithms usually work in all NMR software packages, including the former versions of Mnova: Essentially, in this procedure, all peaks maxima (and/or minima) in a spectrum are determined and their values are either stored in a tabular form (i.e. in a peak table) or displayed graphically over the spectrum (Figure 1).

Figure 1: Illustration of traditional peak picking

Each NMR application might offer different levels of sophistication in the peak picking algorithms. For example, some can resolve overlapped peaks better than others (http://nmr-analysis.blogspot.com/2009/06/fighting-against-peak-overlap.html ), others operate more efficiently with spectra with low SNR, etc.), but the important element I would like to highlight here is the fact that the output of any peak picking algorithm is just a plain list of significant points in a spectrum.

So far, so good. The question is: What is the purpose of applying peak picking? Well, there is no definitive answer and it depends upon the particular application. Nonetheless, if we restrict the context to that of the simple analysis of small molecules for their characterization, peak picking is usually applied to the calculation of coupling constants and chemical shifts, (in other words determination of the spin system(s) in the spectrum). Whenever practicable, this should be done as automatically as possible by the NMR Software.

Historically, this automatic analysis was based on Quantum Mechanical (QM) methods [1]. They are certainly the most rigorous yet complex methods, although interestingly, the most popular approaches even more than 40 years ago [2-4] when computer power was much more limited than today.

Another approach, which incidentally has attracted significant interest in recent years, despite being computationally much less demanding, is based on the same technique typically used by organic chemists, i.e. the use of the popular first-order analysis rules [5-7]. Of course, this approach is only valid in weakly coupled systems and, thus, has a more limited scope when compared to QM methods, but is useful for a rapid spectrum analysis.

In any event, regardless of the method employed, the main obstacle to achieving a successful automatic analysis of 1H NMR spectra with minimal user intervention lies in the fact that NMR spectra do not consist only of peaks arising from the transitions of the studied spin system, but also many others, such as, solvent and impurity peaks, spinning sidebands, reference peaks (e.g. TMS), satellite peaks, etc. Continuing the previous example, if the vertical intensities are expanded a little bit more, we can appreciate (see Figure 2) that peak picking finds not only the main transitions, but also many other peaks like small impurities, 13C satellites, etc.

Figure 2: Expanded view of Figure 1. It can be seen that small peaks, including 13C satellites and impurities are detected, but they lack any kind of classification.

This is certainly good as those peaks are real and it is important to detect them. However, the problem is that, in general, those peaks are not labeled or marked according to their type (compound, solvent, 13C satellite, impurity, etc): They are just peaks, they do not have a semantic context and do not present any further characterization. This has some important consequences when automatic analysis is required. For example, solvent peaks should be marked appropriately so that they are not used during the actual analysis. Same applies to impurities, 13C peaks, etc.

Intelligent Peak Picking

By Intelligent I mean a Peak Picking algorithm equipped with the ability to classify and mark a peak according to their type. Of course, the identification of any obvious impurity or solvents is a task an experienced chemist is very familiar with and can do very efficiently, and for this reason, it is very important that any software provides the user the ability to manually classify a peak. Of course, automation is very important, but this kind of analysis is extremely difficult for a computer program. Impurity or solvent peaks can overlap with compound resonances, making some simple strategies based on the definition of ‘solvent’ regions ineffective.

Just to give you a first impression on how an Intelligent Peak Picking looks like in Mnova, take a look at Figure 3:

Figure 3

This is the result of a fully automatic Peak Picking. Some points are worth noting:

As you can see, now the peak labels have different colors. They are color coded according to their classification (i.e. compound peak, impurity, solvent, etc) as per the legend shown in the figure. Once again, this classification has been done fully automatically by Mnova, but manual intervention is always possible.

Typically, peak picking algorithms use to include the so-called threshold parameter used to filter out small peaks in a spectrum. This is not very convenient, for many reasons, including:

a. It is very difficult to find a threshold parameter that works well under all spectral conditions. Even though this parameter can be used relatively to the noise level in a spectrum, very often it has to be tuned manually in order to get good results.

b. As this threshold parameter usually works globally across the spectrum, if it is set too high to filter small noisy or impurity peaks, we run into the risk of losing small compound peaks, for example, the small peaks in both sides of a heptaplet.

c. It is also very sensitive to baseline imperfections.

All the drawbacks outlined above are strongly alleviated (if not fully resolved) by the intelligent peak picking included in Mnova 7.0. Why and how will be the subject of my future posts.

Conclusions

Unlike traditional peak picking algorithms, the intelligent version presented for the first time in Mnova 7.0 adds an extra dimension: every peak is automatically classified according to different descriptors, ranging from peak compound, impurities, 13C satellites, solvent, etc. The automation of this classification is possible thanks to a fuzzy logic expert system developed in Mnova and which I will describe shortly in future posts.

In my opinion, this peaks classification opens new avenues in the automatic analysis of 1H NMR spectra of small molecules. For example, multiplet analysis using first order rules is much more efficient, especially in cases of sever signal overlap or multiplets contaminated with solvent peaks. For example, Figure 4 shows the result of analyzing the spectrum of Santonin fully automatically (i.e. with one button click).

Figure 4

In my upcoming posts I will describe in more detail this new approach to NMR peak picking and 1H NMR analysis, including automatic solvent detection, multiplet analysis and automatic determination of the number of protons in a spectrum. Stay tuned!

References:

P. Diehl, S. Sykora and J. Vogt, J. Magn. Reson. 19, 67 (1975).
J.D. Swalen and C.A. Reilly, J. Chem. Phys. 37, 21 (1962).
S. Castellano and A.A. Bothner-By, J. Chem. Phys. 41, 3863 (1964).
D.S. Stephenson and G. Binsch, J. Magn. Reson. 37, 395 (1980).
T.R. Hoye and H. Zhao, J. Org. Chem. 67, 4014–4016 (2002).
C. Cobas, V. Constantino-Castillo, M. Martín-Pastor and F. del Río-Portilla, Magn. Reson. Chem. 43, 843–848 (2005).
S. Bourg, J.-M. Nuzillard, J. Chim. Phys. 95, 18 (1998).

Hexacyclinol - NMR spectra vs plain images

2011-03-18T02:40:00.000-07:00

I’m sure that many of you are aware of the infamous controversy over the total synthesis of Hexacyclinol . There are a plethora of arguments, from the purely synthetic chemical point of view to the spectroscopist perspective, which both put in doubt the veracity of aforementioned total synthesis. You can find, at the end of this post, a list of references that may be of interest on this subject. In this particular post, I would like to comment on several interesting aspects from an NMR standpoint.

In the original article’s “supporting information”, one can find the spectra of Hexacyclinol and derived compounds. I believe that the key to the controversy here lies in the fact that these spectra are found solely as plain images, that is, all the relevant spectral information that could have provided more conclusive proof over the authenticity or not of the total synthesis of this compound is lost.

Let’s consider for example, the image of the Hexacyclinol spectrum:

I have cut the central vertical area of the image in order to visualize the highest intensities as well as the smallest ones together. The objective is to simply appreciate with clarity the level of 13C satellites intensities in the case of the CHCI3 signal. The level is indicated by the red horizontal line which would correspond, approximately to an intensity of 32, that is, a ~0.55% of the intensity of the CHCI3 signal.

At first glance, one cannot observe such signals from the 13C satellite. Is this a conclusive reason to assume that this spectrum is really a fake, that is, a spectrum that was created synthetically? Of course, I’d say it is not conclusive but it could be an indication.

In principal, I would say that the SNR of this spectrum seems good enough for the 13C signals to be observed; not only in the CHCI3 area but rather that they cannot be observed in any part of the spectrum. I can only come up with two reasons that justify the absence of those signals:

On the one hand, the author could have acquired the spectrum using a pulse sequence that removes the 13C signals (e.g. 13C GARP broadband decoupling). I’d say this is highly improbable given that, if this was so, it would seem reasonable that the author would have specified in the article the use of such decoupling technique. In any case, if the complete “raw data” acquired were available, then the pulse sequence could be analyzed. Of course, this would not be a conclusive proof either since the pulse sequence is generally found in a text file which could be manipulated easily by any editor (unless it is digitally signed).
On the other hand, the fact that the 13C signals are not observable may be due to the acquisition settings, more specifically gain settings in the case of very strong spectra. The problem lies in when there is not enough noise to fill at least ~6 ADC steps, you start rapidly losing small peaks and, of course, the noise starts looking weird, kind of binary, which can be actually perceived in this case. In any case, I don’t think this would really justify the absence of the 13C signals. If this is what happened during the acquisition, it would never be so perfectly void of satellites or have a perfect baseline and phase, according to my opinion.

Therefore I insist, if the raw data were available, more effective analysis could be carried out. For example, one could analyze the line widths of isolated signals. If all of them were the same, this would put us on that track that the spectrum was synthesized given that in real life, this is something very difficult to occur.

In summary, it is very difficult to reach conclusive results working with plain images. Once the spectra have been acquired, transforming them into images only result in an irreversible loss of important information. I believe that publishers should oblige authors to submit spectra/original FID’s (including all the files with additional metadata) to avoid any type of loss of relevant information.

References:

Micropost: Pulse Sequence Blues!

2011-02-23T04:24:00.000-08:00

Now that ENC is practically around the corner, here is a link that shows how far this conference encourages the participants’ creativity:

Pulse Sequence Blues!

NMR can also be fun :-)

Alignment of NMR spectra – Part VI: Reaction Monitoring (II)

2011-02-10T11:29:00.001-08:00

Previous posts on this series:

Crossing over of peaks is a very common event in Reaction Monitoring (RM) experiments. When this happens, the automatic alignment algorithm discussed in previous posts (here and here) might not work properly. To illustrate this issue, as I did not have a real experiment at hand, I simulated using Mnova a very simple data set comprised by a triplet and a singlet in such a way that the chemical shift of the triplet moves from 1.4 ppm to 0.7 ppm and having an exponential decay from spectrum to spectrum. This is depicted in the figure below, both as a stacked and a bitmap plot.

Now let’s say you are interested in extracting the intensities of the triplet as the reaction progresses. There is actually no need to pre-align the spectra algorithmically; it is much simpler to have some kind of graphical tool to instruct the software which peaks (or multiplets) need to be used for the reaction monitoring analysis. Let me show you how this works in Mnova:

First of all, in the Data Analysis module you select the region to be analyzed. As a starting point, the region will have a rectangular shape (green rectangle in the figure below):

It can be noted that the graph shows an exponential decay, but the actual values must obviously be wrong as the values calculated, using the green rectangle as a boundary for the integration, include peaks from both the triplet and singlet, and we are interested in the analysis of the triplet resonances only. Now let’s change this…

The selection rectangle has a number of handlers (small green boxes). You can drag and move them freely so that you can adjust the selection feature to follow the triplet (BTW, the number of handlers can be adjusted. In this case, there are 6 handlers, but higher numbers are also permitted). In the figure below, the result of adjusting the handlers to follow the triplet is shown:

Now you can see that there is an outlier in the exponential curve which, obviously is caused by the singlet which overlaps with the triplet (spectrum number 6 which corresponds to data point #5, as in the graph the numbering starts from zero). Figure below shows that particular spectrum showing the singlet overlapping with the triplet:

At this stage, there are several approaches. The simplest one is to just discard that point for the analysis, for example, by right clicking on that point in the graph and disabling it:

As soon as that point is deleted / disabled, Mnova will update the graph automatically. This is the new result:

Another approach would involve using GSD to eliminate the singlet from the triplet so that it would not be necessary to discard the information from that particular spectrum. However, this is something I will blog about in a future post.

Alignment of NMR spectra – Part V: Reaction Monitoring (I)

2011-02-08T09:13:00.000-08:00

Previous posts on this series:
1. Alignment of NMR spectra – Part I: The problem
2. Alignment of NMR spectra – Part II: Binning / Bucketing
3. Alignment of NMR spectra – Part III: Global Alignment
4. Alignment of NMR spectra – Part IV: Advanced Alignment

Following the progression of chemical reactions by NMR is becoming more and more popular. Quoting Michael A. Bernstein et al. (Magn. Reson. Chem. 2007; 45: 564–571)

(…)The technique is rich in structural information, and can uniquely provide subtle information on speciation, protonation sites, and intermediate compound production. NMR measurements can be made under quantitative conditions, and one can be confident that all organic species will be observed. These factors combine to make NMR a very attractive tool for these analyses, and address many of the shortcomings in traditional spectroscopic measurements (…)

Typically, as a reaction proceeds, it’s very common to observe very significant chemical shift fluctuations of a given resonance due to, for example, changes in pH or protonation of the starting material, just to mention a few. These changes in chemical shift can be so large that extracting relevant information from those spectra (e.g. intensities/integrals across the data set) can be difficult, so aligning those spectra can be helpful. Let me illustrate this with an example exhibiting clear nonlinear misalignments: peaks at about ca 11.6 ppm do not move whilst the peaks at higher field move very significantly:

Instead of displaying the data set as a stacked plot as above, it might be more convenient to display it as an intensity or bitmap plot because this plotting mode highlights more clearly the alignment /misalignment profiles:

It’s evident that correcting the data using a single reference peak (or a global shift) is not sufficient. In order to align this data set, we can follow two different strategies:

Strategy 1:

Starting with raw spectrum (1), it is possible to perform a full-spectrum correction (global alignment) before the single intervals are aligned:

It can be appreciated that after applying the global alignment, most of the peaks in (2) are now properly aligned, except the peaks at the left which were previously aligned but after this operation get misaligned. This problem will be covered in the next step.
After the spectra have been aligned ‘globally’, the user just needs to select the interval which comprises the peaks left to be aligned as depicted in (1). (2) shows the final result once both the global and local alignment have been applied:

Strategy 2:

A different, although analogous strategy, would consist in aligning two different spectral intervals separately without resorting to a global alignment as shown in (1) below. Note that the peaks in the interval in the left are already well aligned (so selecting this region is optional; if there were some minor misalignment, the algorithm would optimize such residual misalignment).

(2) shows the final result after the two intervals have been aligned. It’s completely equivalent to the result obtained with Strategy 1

Conclusion
In this post I showed how the automatic alignment algorithm can be used to align RM data sets prior to any further analysis. However, there is a better way to extract NMR descriptors from Reaction Monitoring experiments that does not require any prior pre-processing alignment. In fact, I believe that this method, which I will present in my next post, has several advantages (in the context of reaction monitoring), especially in those cases where the chemical shift ordering of some peaks changes during the reaction, situations in which automatic alignment algorithms usually have great trouble dealing with. An example of a reaction monitoring data set showing peaks crossing over is shown below, in bitmap mode (it’s a simulated data set)

Therefore in my next post, I will show how to analyze RM data sets with important peak fluctuations and crossing over

Alignment of NMR spectra – Part IV: Advanced Alignment

2011-02-07T08:33:00.000-08:00

Previous posts on this series:

As I mentioned in my previous post, simple alignment based on shifting or referencing the whole spectrum is not enough in cases where there are different local chemical shift fluctuations.
Resorting back to the synthetic data set used in the previous posts, let me introduce a semi-automatic method designed specifically to align spectra having local chemical shift variations. From a practical point of view, the User needs to select the spectral regions to be aligned and then the program will automatically align those regions separately by using the same technique showed in my last post, that is, maximization of the cross-correlation function. The picture below shows the spectrum before alignment and the two selected regions (top) and the result obtained after applying the alignment algorithm (bottom).

Before going into the details of the automatic alignment algorithm, there is a point I think is worth mentioning: when you have several spectra to be aligned, it is necessary to specify the spectrum which will act as the reference (alignment target). Our implementation provides the capability to use as a reference any spectrum in the data set or the average spectrum.

Automatic Alignment: What is under the hood

Assuming that the spectral segments to be aligned are represented by two vectors g and h, a new vector f can then be generated by cross-correlation:

where * indicates the complex conjugate.
The cross-correlation implemented in Mnova is computed using the fast Fourier transform (FFT), which is a fast O(N log2[N]) process. Briefly, the strategy is to perform an FFT on each of the two vectors, invert the sign of the imaginary part of one Fourier domain representation of one of the vectors, multiply the two Fourier domain functions, and transform the result back using the inverse FFT. By simply calculating the index corresponding to the maximum of f(n) one can find the number of points in which vector g has to be shifted in order to get the highest cross-correlation with respect to h.
This is not, of course, the first time that cross-correlation has been applied for the alignment of two (or more) vectors. Actually, it has been extensively used for alignment purposes in many different contexts, including:

Chromatography (Anal. Chem. 2005, 77, 5655-5661)
NMR (J. Magn. Reson. 2010, 202, 190-202)
DNA Sequence Alignment (J. Biomol. Tech. 2005, 16, 453–458)

The first article was the one that inspired me to include this method in Mnova and in fact, it was implemented several years ago as a method for the automatic alignment of 1D and 2D spectra (see this).
Very recently, we have improved the traditional cross-correlation algorithm by working on the first derivative domain calculated using an improved Savtizky-Golay routine in which the order of the smoothing polynomial is automatically calculated. The idea is to minimize potential problems caused by baseline distortions or very broad peaks.

We have found this method to be very useful not only in the context of metabonomics, but also in the alignment of Reaction Monitoring data sets. However, I better leave this topic for my next post …

Alignment of NMR spectra – Part III: Global Alignment

2011-02-03T01:49:00.000-08:00

Previous posts on this series:

We have seen that binning helps in minimizing, for example, the effect of pH-induced fluctuations in chemical shift so that, in the field of NMR-based metabonomics studies, ensuring that signals for a given metabolite appear at the same location in all spectra. One evident disadvantage of binning is that it greatly reduces the spectral resolution (e.g. in a 500 MHz instrument, a typical 64 Kb NMR spectrum with SW = 12 ppm, would be reduced to 300 points (bins) if a bin width of 0.04 ppm [20 Hz = ~218 points] is used).
This loss of resolution is not desirable and considering that today’s powerful computers can handle large data matrices, there is now an increasing tendency to perform multivariate analysis at the maximum spectral resolution possible. Alternatives to binning typically involve some form of peak alignment procedure and in this post I will cover the simplest one, global alignment. The purpose of this post is to simply illustrate the concept of alignment, but it is important to note that this method is not generally applicable to the misalignment problems found in metabonomics NMR data sets, although it might be useful in many other contexts.

The idea of global alignment is very simple and corresponds to the well-known chemical shift referencing method in which the user sets the internal reference peak (e.g. TMS, DSS, TSP, etc) of each spectrum to e.g. 0 ppm. In order to cope with small fluctuations in chemical shifts, this method seeks for the highest peak within a narrow (user-defined, auto-tuning option in Mnova) interval, as depicted in the figure below:

Clearly, this method will not work properly in those data sets with local misalignments, that is, when signals of one metabolite fluctuates in one direction whilst the peaks of a different metabolite move differently). As an example, let’s consider again the simulated data set of Taurine used in my previous post and which I copy below for convenience:

Remember that this data set has been generated by randomly changing the chemical shifts of the two CH2 groups. Now, let’s apply the global alignment procedure using as chemical shift reference at a value of 3.25 ppm as shown in the picture below:

As expected, all peaks corresponding to the triplet at 3.25 get perfectly aligned, but the other multiplet remains misaligned (see below).

One could devise an extension to this global alignment procedure in which the same procedure is applied to different segments of the spectrum. In this particular case, one could select two different windows, one for each triplet and apply the same algorithm locally to each segment. However, having to manually select the chemical shift reference for each segment is not very practical and, in addition, relying only on the simple search of the maximum peak within each segment is not a very robust method for automatic alignment. In my next post, I will present a much more powerful automatic alignment method in which the user will not need to define the reference chemical shift value for each segment / window, but before that, and as an introduction to that post, let me show you another global automatic alignment method.
Let’s assume that we have several spectra which we want to align automatically in such a way that we first manually reference the chemical shift of one of these spectra (e.g. the first one in the series) and then ask the software (e.g. Mnova) to automatically align all the other spectra using this one as a reference spectrum. The idea for such algorithm is to figure out which is the optimal value that a spectrum has to be shifted (left or right) so that the difference between this spectrum and the reference one is minimal.

Such alternative ‘global method’ has been implemented in Mnova several years ago already and is based on the maximization of the cross-correlation between the reference spectrum and the spectrum/spectra to be aligned. This procedure is the essential foundation for the advanced alignment method which I will present in my next post.

Alignment of NMR spectra – Part II: Binning / Bucketing

2011-01-30T15:20:00.000-08:00

In my last post, I wrote that spectra of biological samples are usually poorly aligned due to wide changes in chemical shift arising from small variations in pH or other sample conditions such as ionic strength or temperature.

The most widely used method of addressing this chemical shift variability across spectra is by means of the so-called binning (or bucketing), procedure that consists in segmenting a spectrum into small areas (bins / buckets) and taking the area under the spectrum for each segment. Preferably, the size of the bins should be large enough so that a given peak remains in its bin despite small spectral shifts across the spectra, but not so large as to include peaks belonging to multiple compounds within a single bin.
As a simple example to illustrate how binning works, let’s consider the spectrum of Taurine (Fig. 1)

Fig. 1: 1H-NMR spectrum of Taurine synthesized with Mnova NMRPredict. Only the spectral region corresponding to the methylene protons is shown.

Taking the spectrum shown in Fig. 1 which has been predicted using Mnova NMRPredict, seven additional spectra were created by changing the chemical shift of the CH2 protons randomly in an effort to simulate the chemical shift variability observed in real life biofluid NMR spectra.

Fig. 2: Synthesized data set comprised by 8 simulated spectra of Taurine with random chemical shifts for the CH2 protons and displayed in superimposed mode in Mnova.

These spectra have been synthesized using 32768 data points and a spectral width of 6001.6 Hz with a spectrometer frequency of 500.13 MHz. If the size of each bin is set to 0.02 ppm (represented by the vertical grid lines in Fig. 2), this will result in the generation of 6001.6 / (0.02 x 500.13) = 600 bins.

When the binning command is issued in Mnova, a new spectrum with 600 data points in which every point is the sum of all the points within each bin is produced. The result of this binning or bucketing operation applied to one single spectrum of the synthetic Taurine data set is depicted in fig. 3, where the circles correspond to the area of each bucket in the original spectrum. Fig. 4 shows the result applied to all spectra in superimposed mode. Digital resolution of the resulting binned spectrum is 10 Hz/point

Fig. 3: Methylene region of one synthetic 1H-NMR spectrum of Taurine after data reduction by uniform binning

Fig. 4: Result of applying data reduction by uniform binning to the 8 1H-NMR spectra of Taurine

Once the spectra have been binned, they are ready to be exported in a convenient format (e.g. ASCII) for further statistical analysis (e.g. PCA).
It can be noticed that binning greatly minimizes the effects from variations in peak positions (in this case, all peaks get perfectly aligned). Additionally, binning reduces the data size for multivariate statistical analyses, although today’s computers and optimized linear algebra algorithms are able to handle large data volumes very efficiently.

The major drawback of this procedure is the loss of a considerable amount of information enclosed in the original spectra. In this particular case, the fine structure of the two triplets is totally lost (the coupling constant is 6.6 Hz whilst the digital resolution is 10 Hz), precluding the direct interpretation of multivariate models. In addition, peaks moving on borders between bins might cause artifacts. Another source of loss of information occurs, for example,when peaks belonging to several compouns are included within a single bin.

There exist several better alternatives to binning, typically involving some form of peak alignment without data reduction. But this will be the subject of my next post …

Alignment of NMR spectra – The problem: Part I

2011-01-27T11:21:00.000-08:00

The chemical shift is of great importance for NMR spectroscopy because it reflects the chemical environment of the nuclides under observation providing detailed information about the structure of a molecule.

Although the chemical shift of a nucleus in a molecule is generally assumed to be fairly stable, there are a number of experimental factors (pH, ionic strength, solvent, field inhomogeneity –bad shimming, temperature, etc) which might produce slight or even quite significant variations in chemical shifts.
This is particularly important in metabonomics/metabolomics where shifts of NMR peaks due to differences in pH and other physico-chemical interactions are quite common in NMR spectra of biological samples. For example, some important metabolites, such as citrate or taurine, have peaks whose chemical shifts fluctuate in an uncontrolled way from sample to sample. These variations can cause spurious grouping of samples in chemometric models.

Example of peak position variation in the citrate region (simulated data)

Whilst it is critical to setup the experimental conditions in the best way to minimize these chemical shift fluctuations (for example by using an appropriate buffer; BTW, there exists a standard protocol for biofluid [urine, serum/plasma] and tissue sample collection and preparation as described by Beckonert et al. [1]), spectral misalignments may still occur and special post-processing methods have to be employed.
Another example in which variation in the chemical shift is important occurs in the context of kinetics or reaction monitoring experiments by NMR. For example, consider the following reaction monitoring example [2]:

Reaction monitoring data set for the solution of phenylethylamine and 2-methoxyphenyl acetate in D2O, with every 35th spectrum from the first (bottom) to the last (top) shown (see [2])

It can be appreciated that during the course of the reaction, the chemical shifts of several signals change as a result of the change in pH (in this case, as a hydrolysis proceeds)
Although characterizing these chemical shifts fluctuations can be sometimes important (pH or drug binding-induced chemical shifts, for example) in general they obscure the process of pattern recognition (metabonomics) and impede the performance of data analysis (e.g. selection of the peaks whose intensities/heights need to be monitored becomes more difficult).

In my next posts, I will cover different ways to deal with the peak misalignment problem, first in the field of metabonomics and then in reaction monitoring.

References:
[1] O. Beckonert, H.C. Keun, T.M. Ebbels, J. Bundy, E. Holmes, J.C. Lindon, J.K. Nicholson, Metabolic profiling, metabolomic and metabonomic procedures for NMR spectroscopy of urine, plasma, serum and tissue extracts, Nat. Protoc. 2 (2007) 2692–2703

[2] M. Khajeh, M. A. Bernsteinb, G. A. Morrisa, Magn. Reson. Chem. 2010, 48, 516–522

Here I am again!

2011-01-26T04:51:00.000-08:00

As you've undoubtedly noticed there has been little activity on my blog lately, which contrasts with the high activity I'm having in my real life, with a plethora of exciting (and challenging) new projects going on in my company, Mestrelab Research.

One particular area in which we have been working on quite intensively for the last few months belongs to the broad subject of the alignment of NMR spectra. This appears to be a very important topic for those scientists working, amongst others, on fields like metabonomics/metabolomics and reaction monitoring by NMR. Starting from today, I will start blogging about this issue, firstly covering some very basic concepts and then moving on to some more advanced techniques for the efficient alignment of NMR spectra.

So stay tuned!

Conformational analysis of cyclic compounds using Mspin and RDCs

2010-10-23T13:38:00.000-07:00

On the occasion of the release of a new version of Mspin (BTW, this is the very first multiplatform version of Mspin: it works now in Windows, Mac OS X and Linux), I would like to bring into your attention one of the many applications where this software plays an instrumental role: The application of Mspin to the study of seven-membered rings compounds by NMR.

The NMR study of seven-membered ring compounds is a classical problem in conformational analysis. They are commonly studied by means of NOE-based experiments or 3J coupling analysis using Karplus-Altona relationships. In a recent work, recently published in Chemical Communications, [ Chem. Commun. , 2010, 46, 5879–5881 ]from the groups of Roberto Gil (Carnegie Mellon University) and Navarro-Vázquez ( Universidade de Vigo ) have demonstrated that the conformation of a 3-benzazepine compound can be completely determined by using 1DCH residual dipolar couplings (RDCs). These RDCs were easily obtained by performing HSQC experiments coupled in the direct dimension using a polydimethylsiloxane gel as oriented medium

Conformational search indicated the presence of 11 possible conformations for this molecule. In agreement with computed DFT energies for these conformers, as well as observed 3J couplings, chemical shifts, and NOE's RDC analysis shows the preference of the system for a crown-chair conformation with equatorial disposition of the substituents.

Here you can download the rdc data file ( click here ) in the MSpin format and a multiconformer XYZ file with the DFT optimized conformations (click here) . Load them into the RDC module of Mspin, select the singular value decomposition method (SVD), just click the calculate button and see how convenient is to perform the RDC analysis with Mspin

New Fast NMR technique

2010-07-30T04:27:00.000-07:00

Instrument time is precious and a plethora of different fast NMR experiments are continuously being proposed in order to reduce the time required to record an NMR spectrum. Actually, money is not the only reason, there are many other factors which motivate the development of techniques to increase the speed of data collection. For example, if one wants to make real-time studies of kinetic processes or protein folding, it’s pivotal to speed up the acquisition of NMR data, in particular multidimensional spectra.
On this issue, we have just put our bit into this field and published an article which describes the use of localized spectroscopy for parallel multidimensional NMR data acquisition. The key idea is to interleave the data acquisition at a variety of localized bands within a given interscan repetition time.

In other words, the method is based on MRI-type slice selection techniques (e.g. spinecho multislice and gradient echo multislice) where nuclear spins in different parts of the tube are excited and detected during subsequent transients while the previously used spins have time to relax towards equilibrium before being excited again, hence achieving a considerable timesaving in the overall acquisition.

We believe that this method; named PALSY, is a very powerful yet simple and general technique to reduce experimental time. Of course, there is a sensitivity penalty approximately proportional to the number of slices chosen, but the good thing is that the achievable resolution in any dimension is not compromised in any way.

Another point of interest is that it does not require any fancy data processing, just a simple data shuffling operation needed to extract the different sub-spectra contained into the acquired raw data matrix. This operation has been implemented into the Mnova Alpha version and will be available in the next official release. Meanwhile, as always, should anyone be interested in evaluating this alpha version, just drop a comment here and I will get in touch to provide an executable.

The article can be accessed here:

Fast multidimensional localized parallel NMR spectroscopy for the analysis of samples

I would like to take this opportunity to acknowledge and congratulate my friend Manolo for this work. He is the intellectual father of this pulse sequence and is currently extending this idea further to cover other NMR experiments.

Riding up the peaks …

2010-07-27T03:57:00.000-07:00

… around the Pyrenees. NMR peaks are not the only ones that interest us in Mestrelab, we also love the Cols in the Tour de France, and I have some proof :-) :

Quoting a friend of mine: I had never seen the Yellow Jersey before. It is a bit surprising that the competitors would fight so hard for the right to wear it :-)

Even though I’m not a great fan of Lance Armstrong, I reckon he has incredibly popularized cycling in the US. The guy in the photo has been following him for several years already in the Tour de France, running by the riders. It looks easier than it actually is, as the riders go faster than 20 Km/h (i.e. 3 min/Km) in fairly hefty slopes, so you have to be in a pretty good shape to keep up with them for 200 m (that is approximately the distance he is doing with them).

Well, enough for this off topic post. I will follow up later on tonight with some real NMR stuff.

Fermentanomics

2010-07-02T06:43:00.000-07:00

We are now in an era in which a plethora of domains of sciencific investigations are combined with the suffix ‘omics’. These include neologisms such as genomics, proteomics, metabonomics, pharmacogenomics, nutrigenomics and many others.

Scientists at Lilly have now established the basis of a new –omics related discipline which they have dubbed Fermentanomics and consists in a new rapid and robust NMR method for monitoring mammalian cell cultures.
This work has been published as a JACS communication and I’m delighted to see that they have used our Global Spectral Deconvolution (GSD) technique available in Mnova for the extraction of the concentrations of the components from the NMR spectra of the spent media of mammalian cell culture

Bruker Smiles

2010-05-21T11:24:00.000-07:00

The above title is not aimed to mislead and it does not refer to Bruker’s state of mind: Quite simply, the purpose of this post is merely technical and the relation between Bruker and its smiles will be apparent in a moment… Just keep reading…

Because it wouldn't make sense otherwise, NMR instruments use receiver systems equipped with digital filters since a relatively long time ago. The advantages of such digital filters (generally designed as low-pass filters and applied together with oversampling and decimation methods) are many fold, ranging from higher quality spectral baselines to SNR and effective dynamic range improvements, enhanced reduction of potential sources of folded signals, etc

It´s not all about advantages though … I’m sure most of you are already very well aware of the pesky problem that is infamously known as group-delay artifact in Bruker (and Jeol) data which has plagued the NMR community since these companies switched to digital receivers. In short, the FID resulting from the digital filter does not start at time = 0 but only after a long and slowly rising oscillation of length G (G = Group Delay).

Some empirical procedures to correct it were presented on the internet but they are palliative and do not resolve the problem completely, particularly when apodization is applied.
Typically and depending on how the FID is processed, the spectrum might exhibit smiles (baseline artifacts pointing up) or frowns (baseline artifacts pointing down) at the outer regions of the spectrum as depicted below:

The ultimate solution
These small artifacts are in general not a big problem as one could use a spectral width large enough so that the peaks of interest in the spectrum will not be affected by these artifacts (although some processing algorithms such as backward Linear Prediction could be somewhat problematic with the Group Delay). In any case, we did not feel very comfortable with present solutions to this problem. A few months ago, I went for dinner with Stan and right after it, the power of the red wine and above all, the Galician octopus inspired Stan in such a way that he managed to understand the engineering drawback and proposed a new correction algorithm which we implemented together in Mnova just a few minutes later (whilst still under the influence of the wine :-) ).
Basically we have now a new pre-processing algorithm that corrects in a totally automatic way any Bruker FID corrupted by the group-delay artifact, producing a normal and physically correct FID so that the smiles will not be seen in the f-domain spectrum. The performance of the new algorithm is illustrated in the figure below:

This enhanced correction is available in Mnova since version 6.1.1 onwards, although it is not the default processing method for the moment. In order to activate it, it is necessary to select it via Processing/Group Delay menu command.

I guess the take home from the story is never underestimate the power of red wine and Galician octopus :-)

Back in the blogosphere

2010-05-20T03:46:00.000-07:00

After a 3 month-long hiatus, I'm back in the blogosphere. I’ve been travelling and working very hard on several exciting projects, but my entries have consequently suffered.

Although my workload has not decreased, I am not planning to travel for the next few weeks. Hopefully I will manage to blog on a more regular basis from now on, especially now that there are many things we have been working on lately that I hope will be of interest to the NMR community.

For now, I’d just like to point out a very interesting blog entry written by my friend Stan on his well-known NMR blog. One of the tools in Mnova for which we are most proud of is GSD (Global Spectral Deconvolution) which, as any other fitting process, requires the definition of a line shape model. GSD uses a Lorentzian model and some of the reasons for this choice have been elegantly exposed on his blog.

Why spectral lines are Lorentzian

Learning NMR with Deep Purple

2010-02-04T09:26:00.000-08:00

It’s not that I’ve gone crazy (well, I hope not :-) ) or that Deep Purple has moved from Hard Rock to Science (or at least I‘m not aware of this), but after my last post about the acoustic reproduction of NMR FIDS, I thought that it would be fun to compose a simple song and, at the same time, create some stuff which can serve as an educational tool for some very basic NMR.

I won’t actually compose anything original, but rather make an NMR cover of the famous Smoke on the Water riff by Deep Purple. It’s very simple with a central theme consisting in a four-note "blues scale" melody. If you don’t know this song, you can watch and listen here:

These are the notes for the central theme I learnt by ear. I know it’s not 100% accurate, but for the purpose of the exercise this should do just fine:

DFG DFAG DFG FD

You can play this riff with the virtual piano below, just click on the picture and click the notes above. It’s fun!

NMRing Smoke on the water

Before any further ado, these are the instructions to listen to the NMR version of Smoke on the Water:

First you will need Mnova. If you don’t own a license, you can download a free, fully functional demo from our web site.
Download this NMR document (SmokeOnTheWater.mnova)
Download this script (playArray.qs)
Finally, put on your earphones or amplify the volume on your computer speakers, open SmokeOnTheWater.mnova file with Mnova and run the script.

If everything works as I hope, you should be listening to 12 different pings pretending to be the melody of Smoke on the Water riff. I hope you won’t get too disappointed and more importantly, I hope that Deep Purple won’t detest me for ruining their song :)

Behind the scenes

As Dr. Walter Bauer explained on his web site, the most convenient way to create melodies with NMR is by means of pulse programmers to define the appropriate frequencies and delays. I’m taking a much simpler approach which, of course, cannot be used to create complex harmonies.

The basic idea is to synthesize NMR FIDs in such a way that each FID will represent a note of the song. For example, in this particular case I have simulated 4 FIDS with frequencies corresponding to A, D,F, and G. Next I stacked these 4 FIDs to create a new stacked item with 12 FIDs formed by the combination of the 4 main FIDs (main tones) and sorted to yield DFG DFAG DFG FD. The result is illustrated in the figure below.

As you can see, not all the FIDs have the same length. This is, of course, because some notes have to last longer than others. For example, we can consider the first FID (D) as the quarter note (crotchet), the third FID a half note (minim) and the sixth FID an eighth note (quaver). Next, I will comment on how the duration of the FIDs are controlled.

Some points of interest

At first sight, it may seem that in order to create the NMR version of Smoke on the Water one simply has to create the 4 FIDs with the ‘real’ frequencies corresponding to A, D, F and G notes and then organize them accordingly. For example, using the A220 pitch, the frequencies for the different notes should be:


A = 220 Hz
D = 146.83
F = 174.61
G = 196 Hz

However, if these notes are used in this way, the resulting song will be totally different than expected! The reason for that is very simple: NMR FIDs are expected to be in the so-called Quadrature Detection mode, that is, zero frequency in the center of the spectral width. Thus, it becomes necessary to translate the original frequencies into the NMR quadrature frame. The equation for such transformation is very simple:

NMR Note Frequency = Note Frequency + SpectralWidth/2

For example, in this case, as I have used a spectral width of 3000 Hz, the NMR frequencies for the 4 notes will be:


A = 220 + 3000/2 = 1720 Hz
D = 146.83

+ 3000/2

= 1646.83 Hz
F = 174.61

+ 3000/2

= 1674.61 Hz
G = 196

+ 3000/2

 = 1696 Hz

Another point worth mentioning concerns the way to modulate the duration of the different FIDs to create crotchets, quavers, etc. In NMR terms, this is equivalent to the acquisition time (AT) which is defined as:

AT = N / SW

Where N is the number of points and SW is the spectral width. We can modify any of these two values to change the duration of the note (= FID acquisition time). In this example, I have kept the spectral width constant and modified the number of points.

Finally …

In this example I have created pure tone notes (e.g. one single frequency for each note) but it could also be possible to create some kind of guitar chords (e.g. power chords) to make the song more realistic by simply combining the root tone and a fifth. This can be easily done by using the Spin Simulation toolkit available in Mnova.

If you haven’t had enough of Deep Purple yet, you can watch a Jazz version of Smoke in the Water in the video below. Enjoy!

Please note that if you are using Mnova under Windows 7 or Linux, you may not be able to play the song as described earlier on. I am currently investigating the reason for this, as tests carried out on other Windows and Mac versions went smoothly. Should you experience these difficulties, you can listen to the song as a .WAV file here.

Listening to NMR FIDs

2010-01-18T09:55:00.000-08:00

About ten years ago I implemented a command in MestReC for the acoustic reproduction of an NMR FID. This was motivated by the suggestion of Javier Sardina and also after I found the Web page by Walter Bauer (an excellent musician by the way).

This feature was missing in Mnova which I think is a shame as in my opinion it is a very valuable educational tool. For example, it’s a beautiful way to show that measured NMR frequencies lie in the audio frequency region.
So I have decided to write a script to fill this gap in Mnova. If I remember well, MestReC command played just the real part of the FID. As a minor improvement, I have added stereo capabilities now, basically by using the real and imaginary components of the FID as the two stereo sound channels. Another enhancement is that the sampling rate used to reproduce the FID corresponds to the actual acquired spectral width.

Download the script

Anyone interested in this feature can download the script from this link
As always, your feedback will be very welcome

On integrating overlapped peaks

2010-01-14T04:10:00.000-08:00

Following up from the integration problem raised in my previous post and before I delve into Line Fitting, I would like to give you a quick update on some progress we have recently done in Mnova to facilitate the accurate integration of peaks in those cases in which a multiplet is contaminated by one or several extraneous peaks (e.g. a solvent peak).
Consider the following spectrum predicted using NMRPredict Desktop

As expected (this is a perfect synthetic spectrum and therefore noise-free with no phase or baseline distortions and enough separation between the 3 multiplets) the relative integrals are in agreement with the structure, 1:2:1.

I will now modify this spectrum by adding an extra peak in the H-5multiplet

As a result, the multiplet corresponding to H-5 will show a relative integral of 2 instead of 1. This problem can be tackled by using, for example, some signal suppression algorithm to get rid of this extra peak or by deconvolving the multiplet and then summing up the individual deconvolved peaks without the extra peak.
The aim of this post is to let you know that we have just automated all this process via the powerful GSD algorithm (more about this in a later post) so that dealing with this kind of problems has become much easier than before. As I will describe in depth once the new version with this functionality is released, the user just has to select which peak or group of peaks needs to be excluded for the integration and the program will do the rest. This is illustrated in the figure below where the extra peak (in red) is not used for the integral calculation

Even though this new functionality is not available in the current official release of Mnova, it’s already fully operative in our internal version (alpha). Anyone interested in trying this new feature out is more than welcome. Just drop me a line (support at mestrelab.com ) and I will give more detail.

Basis on qNMR: Integration Rudiments (Part II)

2010-01-11T09:54:00.000-08:00

My last post was a basic survey on different measurement strategies for peak areas. Manual methods such as counting squares or cutting and weighing, known as ‘boundary methods’ were introduced for historical reasons. These methods were first used by engineers, cartographers, etc, end then quickly adopted by spectroscopists and chromatographers.

In the digital era, most common peak area measurement involves the calculation of the running sum of all points within the peak(s) boundaries or by other quadrature method (e.g. Trapezoid, Simpson, etc [1]). Obviously, the digital resolution, i.e. the number of discrete points that defines a peak is a very important factor in minimizing the integration error. Intuitively, it’s easy to understand that the higher the number of acquired data points, the lower the integration error. It’s therefore very important to avoid any under-digitalization when an FID is acquired, a problem which is unfortunately more common than many chemists realize.

As described by F. Malz and H. Jancke [2], at least five data points must appear above the half width for each resonance for a precise and reliable subsequent integration. What does this mean in practical terms? Typically, acquisition parameters are defined according to the Nyquist condition: the spectral width (SW) and the number of data points (N, total number of complex points) determine the total acquisition time AQ:

AQ = N/SW

And the digital resolution (DR) is proportional to the inverse of the acquisition time, the latter being the product of the dwell time (DW) and the number of increments:

DR = SW/N = DW x TD = 1 / AQ

If we consider a typical 500 MHz 1H-NMR spectrum with a line width at half height of 0.4 Hz (this is a common manufacturer specification) and a spectral width of 10 ppm (5000 Hz), the minimum number of acquired data points required to satisfy the five points rule should be:
5 pt x 5000 Hz / 0.4 Hz = 62500 complex points.

This number is not suitable for the FFT algorithm which requires, generally, a length equal to a power of two. This is done by zero padding the FID with zeroes until the closest upper power of two, in this case 65536 (64 Kb).

Furthermore, in order to get the most out of the acquired data points, zero filling once (adding as many zeros as acquired data points) has been found (see [3]) to incorporate information from the dispersive component into the absorptive component, and hence it is useful to zero fill at least once (which is exactly what Mnova does).. For example, as S. Bourg and J. M. Nuzillard have shown [4], even though zero-filling does not participate in the improvement of the spectral signal to-noise ratio, it may increase the integral precision by a factor up to 2^(1/2) when the time-domain noise is not correlated.

Regardless of the quadrature method, they all share the same systematic problem: in order to integrate one or several peaks it’s necessary to specify the integration limits. In qNMR assays, this is an evaluation parameter whose effect can be estimated using the theoretical line shape of an NMR signal. To a good approximation (assuming proper shimming), the shape of an NMR line can be expressed as a Lorentzian function:

Where w is the peak width at half height and H is its height value. When L(x) is integrated between +/- infinite, the total integrated area becomes:

Obviously, it’s it is unreasonable to integrate digitally from –infinite to +infinite so an approximation must be made by choosing limits. This has been studied by Griffiths and Irving [5] who have showed that for a maximum error of 1%, integration limits of 25 times the line width in both directions must be employed. If errors less than 0.1 % are desired, the integral width has to be +/-76 times the peak width. For example, in a 500 MHz NMR spectrum with a peak width of 1 Hz, the integrated region should be 152 Hz (~0.30 ppm), as illustrated in the image below

But in general, peaks are not so well separated and for example, when studying complex mixtures or impurities related to the main compound, wide integrals cannot be used. In general, integration by direct summation is not adapted to partially overlapping peaks.

For example, just consider the simple case of peak overlapping where, for instance, one peak of the double doublet overlaps within a triplet:

The theoretical relative integrals for the two multiplets should be 1:1. However, the area of the triplet calculated via the standard running sum method will be overvalued because of the contamination caused by one of the peaks of the double doublet which in turn will be underestimated. This is illustrated in the figure below where the green lines corresponds to the triplet, the blue lines to the double doublet and the red line is the actual spectrum (sum of all individual peaks)

The question is: how to overcome this problem? The answer is, of course, Line Fitting (Deconvolution) which will be the subject of my next post.

References:

[1] Jeffrey C. Hoch and Alan S. Stern, NMR Data Processing, Wiley-Liss, New York (1996)

[2] F. Malz, H. Jancke, J. Pharmaceut. Biomed. 38, 813-823 (2005)

[3] E. Bartholdi and R. R. Ernst, "Fourier spectroscopy and the causality principle", J. Magn. Reson. 11, 9-19 (1973)
doi:10.1016/0022-2364(73)90076-0

[4] S. Bourg, J. M. Nuzillard, "Influence of Noise on Peak Integrals Obatined by irect Summation", J. Magn. Reson. 134, 184-188 (1988)
doi:10.1006/jmre.1998.1500

[4] Lee Griffiths and Alan M. Irving, "Assay by nuclear magnetic resonance spectroscopy: quantification limits", Analyst 123 (5), 1061–1068 (1998)

Basis on qNMR: Integration Rudiments (Part I)

2009-11-30T08:01:00.000-08:00

First a quick recap. In my last post I put forward the idea that integration of NMR peaks is the basis of quantitative analysis. Before going any further, I would like to mention that, alternatively, peak heights can also be used for quantitation, but unless some special pre-processing is employed (see for example P. A. Haysa, R. A. Thompson, Magn. Reson. Chem., 2009, 47, 819 – 824, doi) measurement of peak areas is generally the recommended method for qNMR assays.

In this post I will cover some very basic rudiments of NMR peak areas measurements, without going into depth into complicated math , as my objective is just to set the basis for oncoming, more advanced posts.

NMR Integration basic Rudiments

Peak areas may be determined in various ways. While I was still at school I learnt a very simple peak area calculation method which just required a good analytical balance and scissors. This was the so-called ‘cut & weigh method’ and is illustrated in the figure below.

By simply cutting out a rectangle of known value, for example, known ppm or Hz on x-axis and known intensities on the y-axis, a calibration standard is obtained (in this case, 8 units of area). After cutting and weighing this standard, the area of any peak can be determined by cutting and weighing the peak(s) from the chart, weighing the paper and using this equation:

Area of Peak(s) = Area of standard * Weight of peak / Weight of standard

Yet, despite its primitiveness, this technique was remarkably precise for the purpose for which it was intended (obviously, not for accurate NMR peak areas measurement :-) ) but, of course, it assumed that the density of the paper was homogenous.

There are other classical methods such as counting squares, planimeters or mechanical integrators but in general they were subject to large errors. In the analogic era, it was more convenient to measure the integral as a function of time, using an electronic integrator to sum the output voltage of the detector over the time of passage through the signals. In those old days, as described in [2], before the FT NMR epoch, the plotter was set to integral mode and the pen was swept through the peak or group of peaks as the pen level rose with the integrated intensity.

Enough about archaic methods, we are in the 21st century now and all NMR spectra are digitalized, processed and analyzed by computers. As Richard Ernst wrote once [1], Without Computers – no modern NMR. How are NMR integrals measured? From a user point of view, it’s very straightforward: the user selects the left and right limits of the peaks to be integrated and the software reports the area (most NMR software packages have automated routines to automatically select the spectral segments to be integrated). For example, the figure below shows how this is done with our NMR software, Mnova.

Integration: What’s under the hood

But the question is: how is the computer actually calculating NMR peak areas? In order to answer this, let’s revisit some very simple integration concepts.

From basic calculus we all learnt in school, we know that in order to compute the area of a function (e.g. f(x)) we simply need to calculate the integral of that function over a given interval (e.g. [a,b]).

If the function to be integrated (integrand) f(x) is known, we can analytically calculate the value of the area. For example, if the function has the simple quadratic expression

and we want to calculate the area under the curve over the interval [1,3], we just need to apply the well known Fundamental Theorem of Calculus so that the resulting area will be:

Unfortunately, real life is always more complex. Where NMR is concerned, function f(x) is, in general, not known so it cannot be integrated as done before using the Calculus fundamental theorem. I wrote ‘in general’ because theory tells us the analytical expression for an NMR signal (i.e. we know that, at a good approximation, NMR signals can be modeled as Lorentzian functions) but, for the moment, let’s consider the more general case in which the NMR signal has an unknown lineshape.

Furthermore, up until now we have assumed that f(x) is a continuous function. Obviously, this is not the case for computer generated NMR signals as they are discrete points as a result of the analog to digital conversion. Basically, the digitizer in the spectrometer samples the FID voltage, usually at regular time intervals and assigns a number to the intensity. As a result, a tabulated list of numbers is stored in the computer. This is the so-called FID which, after a discrete Fourier Transform yields the frequency domain spectrum. So how can a tabular set of data points (the discrete spectrum) can be integrated?

A very naive method (yet as we will see shortly, very efficient) is to use very simple approximations for the area: Basically the integral is approximated by dividing the area into thin vertical blocks, as shown in the image below.

This method is called the Riemann Integral after its inventor, Bernhard Riemann.

Intuitively we can observe that the approximation gets better if we increase the number of rectangles (more on this in a moment). In practice, the number of rectangles is defined by the number of discrete points (digital resolution) in such a way that every point in the region of the spectrum to be integrated defines a rectangle.

For example, let’s consider the NMR peak shown in the figure below which I simulated using the spin simulation module of Mnova. It consists of a single Lorentzian peak with a line width at half height of 0.8531 points and a height of 100. With all this information we can know in advance the expected exact area calculated as follows:

In the spectrum shown in the image below we can see the individual digital points as crosses and the continuous trace which have been constructed by connecting the crosses by straight lines (usually only these lines are shown in most NMR software packages. The capability of showing both the discrete points and the continuous curve is a special feature of Mnova.

If the simple Riemann method is applied, we obtain an area = 146, which represents an error of ca 21% with respect to the true area value (184.12). It’s worth mentioning that the true value is calculated by integrating the function from minus infinite to plus infinite whilst in the example above the integration interval is very narrow.

As mentioned above, the approximate area should get better if we increase the number of rectangles. This is very easy to achieve if we use some kind of interpolation to, for example, double the number of discrete points. We could use some basic linear interpolation directly in the frequency domain, although in NMR we know that a better approach is to extend the FID with zeroes via the so-called zero filling operation.

So if we double the number of digital points and thus the number of rectangles used for the area calculation we obtain a value of 258 (see image below). In this case, as the digital resolution is higher, the line width at half height is also higher, 1.7146 (in other words, we have more digital points per peak) so the true integral value will be 269.32:

Now the error we are committing is just as little as 4%. As a general rule it can be said that the better the digital resolution, the better the integration accuracy.

Mathematically, Riemann method can be formulated as:

Considering that in almost all NMR experiments, we are interested in relative areas, the spacing between data points, Δx , is a common factor and can be dropped from the formulas with no loss of generality.

This is exactly the method of choice of most NMR software packages for peak area calculations: NMR integrals are calculated by determining the running sum of all points in the integration segment.

Other numeric integration methods

One important conclusion from the previous section is that in order to get more accurate areas we should increase the number of integration rectangles, something which is equivalent to increasing the number of digital points (e.g. by acquiring more points or using zero filling).

Instead of using the running sum of the simple individual rectangles, we can use some kind of polynomial interpolation between the limits defining each rectangle. The simplest method uses linear interpolation so that instead of rectangles we use trapezoids. This is the well known trapezoid rule which is formulated as:

If instead of linear interpolation we use parabolic interpolation, the method receives the name of Simpson as it’s formulated as [3]:

It is limited to situations where there are an even number of segments and thus, odd number of points. These 3 methods are summarized graphically in the figure below.

Other more sophisticated methods such as Romberg, Gaussian quadrature, etc, are beyond the scope of this post and can be found elsewhere.

Which integration method is more suitable for NMR?

This question will remain unanswered for now, open for discussion. Of the 3 integration methods discussed in this post, at first glance Simpson should be the most accurate. However, as explained in [3], this method is more sensitive to the integral limits (e.g. left and right boundaries) in such a way that if the limits are shifted one point to the left or to the right, the integral value will change significantly, while the other two approaches are more robust and the values are less affected.

In my experience, the difference between the simple sum and trapezoid method is small compared to other sources of errors (e.g. systematic and random errors, to be discussed in my next post) so using one approach or the other should not make any relevant difference.

Naturally, if very precise integral values are required, then more advanced methods based on deconvolution should be used. Of course, if you have any input, you’re more than welcome to leave your comments here.

Conclusions

There's a great deal more to NMR Integrals than reviewed here: I have simply scratched the surface. In my next post, I will follow up with the limits and drawbacks of standard NMR integration, introducing better approaches such as Line Fitting or Deconvolution.

References

[1] Ernst Richard R., Without computers - no modern NMR, in Computational Aspects of the Study of Biological Macromolecules by Nuclear Magnetic Resonance Spectroscopy, Edited by J.C.Hoch et al. Plenum Press 1991, pages 1-25

[2] Neil E. Jacobsen, NMR Spectroscopy Explained: Simplified Theory, Applications and Examples for Organic Chemistry and Structural Biology, N.J. : Wiley-Interscience, 2007

[3] Jeffrey C. Hoch and Alan S. Stern, NMR Data Processing, Wiley-Liss, New York (1996)

Basis on qNMR: Intramolecular vs Mixtures qNMR

2009-11-22T10:07:00.000-08:00

A bit of historical background

NMR has won its reputation as a powerful tool for structure determination of organic molecules. In addition to the information provided by chemical shifts and coupling constants, the quantitative relationships existing between the peaks (or groups of peaks - multiplets) arising from the various nuclides in the sample has proven pivotal for the assignment and interpretation of NMR spectra.

Despite the fact that the concept of quantitative NMR (qNMR) has been coupled to NMR since the early 1950, shortly after the technique's inception, it seems as NMR, as an analytical tool for quantitative analysis was firstly mentioned in 1963 by Jungnickel and Forbes [Anal. Chem., 1963, 35 (8), pp 938–942] who determined the intramolecular proton ratios in 26 pure organic substances and Hollis [Anal. Chem., 1963, 35 (11), pp 1682–1684] who analyzed the amount fractions of aspirin, phenacetine and caffeine in respective mixtures.

From those pioneer works, many and varied studies on qNMR arose. As pointed out in J. Agric. Food Chem. 2002, 50, 3366-3374, qNMR is particularly suitable for the simultaneous determination of the percentage of active compounds and impurities in organic chemicals such as pharmaceuticals, agrochemicals and natural products, as well as vegetable oils, fuels and solvents, process monitoring, determination of enantiomeric excess, etc.

In what follows, I will use the term qNMR to refer to any quantitative measurement of NMR signals, regardless of whether the technique is employed as an analytical method (e.g. determination of the relative amounts of the components in a mixture) or as tool for structure determination or conformational analysis.

What’s the deal with qNMR?

The basic principle of qNMR assays is that, ideally, the integral of the set of all peaks which can be assigned to a particular nucleus is proportional to the molar concentration of that nucleus in the sample. Theoretically, this holds quite well, though there are deviations from the rule in strongly coupled systems. An important point to keep in mind is the word “ideally”; this includes, for example, perfectly relaxed samples.
Even so there remain a number of problems which can be first of all divided into two categories:

Sources of statistical assessment errors (scatter)
Sources of systematic assessment deviations (bias)

I will cover these points in detail in separate posts.

Intramolecular vs Intermolecular (mixtures) qNMR

The most important fundamental concept of qNMR is based on the fact that, the absorption coefficient for the absorption of electromagnetic energy is the same for all nuclides of the same species, regardless whether they belong to one or several molecules (e.g mixture). As a result, the NMR signal response (more precisely the integrated signal area) is directly proportional to the number of nuclides contributing to the signal.

For example, all organic chemists are very familiar with integrating the multiples of a 1H spectrum to elucidate or confirm a particular molecular structure (see figure below)

This application can be classified as Intramolecular qNMR. NOE spectra, where the intensity is related to the distance between spins and represents the main basis for NMR as a tool in structural molecular biology, is another application of Intramolecular qNMR (Note: In this context I’m not including Transfer-NOE used e.g. to study the structure of a ligand in a complex under conditions of fast exchange)

Let’s consider now another example, Intermolecular qNMR:
Purity determination of a compound using an internal standard (is) with known purity and assuming instrumental parameters properly set is given by the equation below (see for example, 10.1002/mrc.2464):

% purity by weight = W(is)/W(s) * A(s)/A(is)*MW(s)/MW(is)*H(is)/H(s)

where W(s) and W(is) are the weights of the sample and ISTD, A(s) and A(is) are the integrals (areas) of the sample and ISTD peaks, MW(s) and MW(is) are the molecular weights of the sample and ISTD, and H(s) and H(is) are the number of hydrogens represented by the integral for the sample and ISTD, respectively.

As a simple application, see Q-NMR for purity determination of macrolide antibiotic reference standards: Comparison with the mass balance method

Common to all qNMR studies is the calculation of NMR integrals. In my next post, I will cover the basic principles on NMR integration.

Basis on qNMR: Rudiments

2009-11-21T09:58:00.000-08:00

When I started playing drums, so many years ago, I kept hearing about so-called "Drum Rudiments". By that time, I was too young to realize how important they were and to me, they appear just as boring and repetitive exercises. However, rudiments (basic building blocks or "vocabulary" of drumming) are absolutely essential to master drums (something I have to admit I never achieved :-) )

In the last few years I’ve had the opportunity to meet and interact with many chemists who are using our NMR software. Some of them are NMR specialists with an outstanding knowledge from whom I have learnt a lot. On the other hand, other chemists use NMR on daily basis simply to confirm the structure(s) they have just synthesized but do not have a deep grasp of the inner details of NMR theory and signal data processing. Whilst I understand that in general this is fine, I have noticed recently that many of these less-experienced NMR scientists are now getting involved in more advanced NMR studies and, in my humble opinion, the lack of some important rudiments can lead to an improper interpretation of the NMR data.

One interesting example is quantitative NMR (qNMR), a field which is being used increasingly in the pharmaceutical industry, for instance, to quantify impurity levels, but it’s also very important in the field of natural products (see for example J. Nat. Prod. 2007, 70, 589-595) and for the calibration of other quantitative techniques such as HPLC. Typically, qNMR is based on obtaining quantitative information through integral-based calculations so in principle, it might seem as this is something trivial which does not require any additional effort. Whilst this is generally true, there are some very important rudiments which I think are worth pointing out.
The rudiments I will present in this series of articles will range from basic concepts on NMR Integration to more advanced deconvolution techniques, including our newly developed Global Spectral Deconvolution algorithm, GSD.
So if you have any interest in qNMR, watch this space. I promise to post these qNMR rudiments on a regular basis.

Micropost [OT]: NMR meets Football

2009-11-19T02:33:00.000-08:00

Relaxation plays a major role in NMR spectroscopy – What’s better than playing sports to chill out and forget about everyday problems?

I reckon this is not the best football team you might find but at least I guarantee they are fun people (sponsored by a great company :-) ) with whom you can have a good time (and get a free t-shirt!) :-)

Mestrelab World of Sports - Free Mnova t-shirt quiz

Windows 7

2009-11-03T06:49:00.000-08:00

Windows 7 was released last week marking, in the opinion of many analysts, the beginning of the end of Windows Vista. Microsoft expects that Windows 7 will woo users who have resisted Vista by offering higher performance and compatibility as well as extra features. In fact, Windows 7 has been the biggest pre-order item in the history of Amazon UK.
If you are interested in making the switch, our preliminary tests indicate that Mnova 6.0.2 runs smoothly under Windows 7. Either way, we cannot exclude any incompatibility as our tests on Windows 7 have not been as comprehensive as we would have liked (still working on it though).

So if you are running Windows 7 and find any problem with Mnova, we would really appreciate it if you could let us know

NOTE: Some users have reported problems with version 5.2.5 Lite on Windows 7, although we have not been able to reproduce them in our computers. Rest assured that we are currently investigating this further

Binning and NMR Data Analysis

2009-10-21T16:07:00.000-07:00

Yesterday I mentioned that many NMR arrayed experiments suffer from unwanted chemical shift variations due to fluctuations in experimental conditions such as sample temperature, pH, ionic strength, etc. This phenomenon is very common in NMR spectra of e.g. biofluids (metabonomics/metabolomics) but also exists in many other experiments such us Relaxation, Kinetics and PFG NMR spectra (diffusion).

This problem negatively affects the reliability of quantitation using, for instance, peak heights, and for this reason integration is, in general, a more robust procedure as these spectral variations are mitigated by averaging data points over the integral segment. In this post, I just want to show you one simple trick which helps to understand, in a pictorial way, why integration is useful to remove the major part of chemical shift scattering.

First, consider the following experiment depicted in the figure below. It shows a triplet and as you can see, some minor peaks shifts are present from spectrum to spectrum

If peak heights are determined at a fixed position, this might introduce appreciable errors in the posteriori quantitative analysis (e.g. exponential fitting). As described in my former post, this could be circumvented in some extent by using parabolic interpolation or peak searching of the maximum in a predefined box.
Nevertheless, integration is a very simple solution as can be appreciated in the figure below. Instead of using the Peak Integrals tool in the Data Analysis module, I will show now a complementary procedure. Basically, what I have applied to all spectra is the well-known binning operation which consists of dividing each spectrum in equally sized (e.g. 0.01 ppm in this case) bins, so that integral (area) of each bin represents a new point in the binned spectrum

As seen in the figure above, binning clearly removes the effect of chemical shift changes but of course, at the cost of a significant reduction in data resolution.

Basics on Arrayed-NMR Data Analysis (Part IV)

2009-10-21T04:16:00.000-07:00

Next up in my survey on analysis of arrayed NMR experiments ( View Parts 1, 2, 3 ) takes me to a quick overview of the different methods of data evaluation, such as the determination of peak heights and peak areas from arrayed experiments. Here you go...

Of the different existing methods for the extraction of peak intensities from arrayed NMR spectra (see [1] ), Mnova provides the following ones:

(1) Peak area integration

This is the default method in Mnova Data Analysis module (see figure below)

This method consists of a standard numeric integration over the whole peak. Basically, the program is summing up all the points within the selected area of interest) as illustrated in the figure below:

This figure has been created as follow: two identical Lorentzian lines (green & red) were simulated and then noise was added. The noise level is the same in both spectra but obviously, the actual numbers are different (more technically, noise in both spectra was calculated using a different seed in the random number generator).

This peak area method for data extraction is quite robust to noise (provided that the noise level is more or less constant across the different spectra in the arrayed experiment) and more importantly, insensitive to chemical shift fluctuations from trace to trace in the experiment, a situation which is more frequent than generally realized. For these reasons, and for its simplicity of use, this is method of choice for well-resolved peaks.

If the peaks of interest exhibit some degree of overlap, this method is not very reliable and some of the next methods will be more convenient

(2) Peak Height Measurement

This is the second method for data extraction (see figure below) and it finds the peak height at a given chemical shift across all the spectra in the arrayed experiment.

By default, the program will find the peak intensity at the position indicated by the user (using a vertical cursor) and then it will perform a parabolic interpolation in order to refine the value. In addition, the user can specify an interval in such a way that the program will find the maximum peak within that region. This can be done in 2 different ways:

i) If you click in the Options button, you can define whether you want to use Parabolic and the interval in which the maximum should be found (in ppm

(ii) Alternatively, once a peak has been selected, you can change the interval by direct editing of the peak selection model. In the figure below, I’m showing how the peak selection model is PeakIntensity. The first number (6.001 in the figure) corresponds to the central chemical shift whereas the second number (0.100 in the figure) represents the interval for the peak maximum search.

Parabolic interpolation is useful because it minimizes the problems caused by the random noise. For example, let’s assume that Parabolic interpolation is not used so that peak heights extraction will be done always at the same fixed chemical shift position (see figure below). As described in reference [1] and illustrated in the figure below, when this method is used the values are seen to be quite different in the two cases: here the precision of the measurement will depend strongly on the noise.

Parabolic interpolation and/or measurement of the intensity as the maximum height within a fixed box around the peak will help to minimize the effects of movements on the chemical shift position of the peaks due to, for example, temperature instability, pH changes, etc.

For convenience, Mnova includes the so-called Pick Max. Peak method which is totally equivalent to the previous one but it allows the graphical selection of the left and right boundaries in which the maximum peak will be searched for.

In a nutshell, peak height measurement can be used in those cases in which peak overlap might represent a problem. However, it should be noted that if for some reasons the line widths of the peaks under analysis change from trace to trace, peak heights will not represent a reliable measurement and peak integrals should be used instead.

In general, I would recommend peak integrals as the most general-purpose method for quantitation of peak intensities in arrayed experiments.

In the next post of these series I will address the problem of exponential fitting useful in relaxation and diffusion experiments.

References:

[1] Viles JH, Duggan BM, Zaborowski E, Schwarzinger S, Huntley JJA, Kroon GJA, Dyson HJ, Wright PE. 2001. Potential bias in NMR relaxation data introduced by peak intensity analysis and curve fitting methods. J Biomol NMR 21:1–9 (link)

Basics on Arrayed-NMR Data Analysis (Part III): Extracting and calculating useful NMR related molecular information

2009-10-14T03:02:00.000-07:00

After the basic introductory posts on arrayed NMR experiments, it’s now time to get some action and see how to extract relevant information from these experiments and calculate useful NMR related parameters such as diffusion, relaxation times, kinetics constants, etc.

Actually, in this post I will cover the first case, that is, the analysis of PFG experiments to calculate diffusion coefficients. The reason for this is twofold: (1) I have a nice PFG data set whilst the quality of the relaxation experiments I currently have access to is quite poor (if any of you have any good relaxation data and can send them over, I would be very grateful) (2) The current version of Mnova has been optimized to handle PFG experiments fully automatically whilst some simple manual intervention is needed when working with other arrayed-like NMR experiments. However, I would like to emphasize that, for example, relaxation experiments are already fully supported in the current version of Mnova, although it is necessary to enter the time delays manually in the program (this is very simple, btw). Automation of relaxation experiments is already possible with alpha versions of Mnova.

This is how a PFG experiment can be analyzed with Mnova with the Data Analysis module (for your information, Mnova includes a DOSY-like processing algorithm based on a Bayesian Algorithm. See this http://mestrelab.com/dosy.html and this http://nmr-analysis.blogspot.com/2008/09/baydosy-whats-under-hood.html for more information):

Once the arrayed spectra has been loaded into Mnova, issue menu command Analysis/Data Analysis. The so-called Data Analysis widget will popup. This will be the central control panel (see figure below) for anything related to the analysis of arrayed experiments.

Its operation is very simple. The first thing you have to do is click on the New button. As a result, Mnova will populate the X-Y Table with some initial values (as described in a moment) and create a new item, the so-called Data Analysis Plot. This new item will display the values from the X-Y Table which in general are the values extracted from the arrayed spectra, both experimental (Y) and fitted (Y’).

The X-Y Table

This table is composed by one X column, X(I), one or several Y-columns (Y, Y1, Y2, etc) to hold the experimental values extracted from the arrayed spectra and one or several Y’-columns which hold the fitted values of their Y counterpart columns.

X-Column

When the table is initialized, in the case of PFG experiments the X-column is populated with the Z values from the Diffusion table, that is, the gradient strengths scaled by taking into account the constants from the selected Tanner-Stejskal model. In the case of a relaxation experiment, the X column will contain the time delays. Of course, it is possible to change the contents of the X-column by following any of these methods:

Manual editing of the individual cells

Copy & paste from a text file. For example, you can put the values for the X-column into a text (ASCII) file and then paste its contents into the table. To do that, just right click on the first cell you want the paste action to start from.

Enter a formula into the Model cell. Double click on the X(I) model cell (1) and then enter the appropriate equation to populate the X column (2). For example, if you simply enter I, the X column will be filled in with numbers 1, 2,3, etc. If you enter a formula like 10+25*I, the X column will be filled with numbers 35,60, 85, etc.

Y-Column

In all cases, when the table is initialized, the Y-column is automatically filled in with values 1,2,3, etc. The purpose of this column is to hold the experimental values from the arrayed experiment. For example, in the case of a PFG experiment, it may contain how the intensity (or integral) of a given peak (or set of peaks) evolves as the applied pulse field gradient changes. Likewise, in the case of T1/T2 experiments, this column will show the relaxation profile of a given resonance (or set of resonances). So the question is: how to populate the Y-column with actual information from the spectra?

This is again very easy. There is a graphical way (mouse driven) and a manual one. Let’s start with the graphical method:

Graphical Selection: Click on the ‘Interactive Y Filling’ button (see red-highlighted button in the image below). After doing this, the cursor will change into an integral shaped cursor expecting you to select the region from where you want the integrals to be extracted across all the subspectra in the arrayed item. After the selection is done (see figure below), all the integrals will be placed in the Y column and those values will be displayed in the X-Y plot as green crosses (note: the shape, color, etc of these crosses can be customized from the X-Y plot properties).

Manual selection: if you take a closer look at the Data Analysis table in the figure above, you can appreciate that once the integral region has been selected, the program shows the following text: Integral(4.752, 4.907). This means that we have selected an integral covering that range. This value can be edited manually so that you can specify the limits by simply editing that cell.

Y’-Column

The Y’ column is reserved for the fitted values assuming a particular theoretical model (e.g. a exponential decay). In this particular case, as we are dealing with PFG experiments, we will be interested in the calculation of the Diffusion coefficients and thus, our fitting model could be a mono-exponential decay (multi-exponential decays can also be handled with this module, but I will not address this problem in this post). The process is very simple:

First click on the Y’(X) cell and then on the small button with 3 points as indicated in the figure below.

This will launch a dialog box with powerful fitting capabilities.

This dialog provides two predefined functions useful for fitting mono-exponential data (such as PFG and Relaxation NMR experiments) using either a 2- or a 3-parameter fit. Furthermore, this dialog offers the possibility to enter user customized functions. As this post is already taking too much space, I will leave the details on data fitting for the next post. For the time being, suffice to say that if your problem regards mono-exponential functions, just select any of the 2 predefined functions in the dialog box and click on the Calculate button. Mnova will immediately compute the optimal values, returning these optimal values as well as the fitting error) and the probability that the acquired series follows the chosen monoexponential model.

Finally, after closing the dialog, it will populate the Y’ column and the X-Y will be updated with the fitted curve (Red line in the figure below).

One nice feature of the Data Analysis module is its ability to handle multiple series. For example, it’s possible to analyze the decay of several resonances within the same experiment. In order to do that, just click on the (+) button to add a new series and repeat the same process to select the desired resonance range and fit the values. For example, in the figure below I’m showing two curves with different decay rates.

In my next post I will cover some more details about the different methods available to select the intensities/integrals from the spectra and some basic points on the fitting algorithm.
BTW, you can download the full PFG data set used in this post

Basics on Arrayed-NMR Data Analysis (Part II): Practical hints

2009-10-09T07:24:00.000-07:00

Further to my previous post, I will cover today some more basic tools available in Mnova for the analysis of NMR arrayed experiments. In particular, I will touch on the following points:

How to use different display modes for 1D arrayed spectra
How to navigate throughout the different subspectra in the arrayed item
How to process individual spectra separately

When an arrayed experiment has been detected, all subspectra are grouped together and plotted in the stacked display mode in Mnova (see figure below). Several points are worth mentioning:

(A). Take a look at the green box in the figure below: it shows the so-called ‘active spectrum’. What does this mean?

The concept of active spectrum is easier to illustrate with the following example: as I wrote in my previous post, in general all the spectra in an arrayed item are processed exactly with the same processing operations. For example, same level of zero filling, same apodization function, same FT type, same phase correction, etc. However, it i’s possible that some particular spectra require a slightly different processing, independently from the others. In order to do that, it i’s necessary to deactivate the ‘Apply Processing to All spectra in Stack’ option.

So if that option is off, any processing operation will be applied only to the active spectrum in the stack.

The question is: how can we change the active spectrum? There are 3 different ways:

Just click on the spectrum you want to be active. This is probably the most intuitive way.
Use SHIFT + Mouse Wheel to navigate throughout all the spectra in the stack, one after the other.
Use SHIFT + Up/Down arrow keys. This is analogous to point 2)

(B). If the number of subspectra (traces) is large (e.g. > 10), working in the stack mode might not be very practical. Quite often, working only with the active spectrum on the screen will be a much better option. This mode can be activated as shown in the image below.

While working on this mode, you will see on the screen just the active spectrum. Should you want to move to another spectrum without resorting to the stack mode, just use methods 2) and 3) described above (Shift+Mouse Wheel or Shift + Up/Down keys).

IMPORTANT: Remember that even if only the active spectrum is visible, unless the “Apply Processing to All spectra in Stack” option is off, all spectra in the stack will also be processed.

(C) Another useful display mode consists of superimposing all subspectra (see figure below). This method is very useful, for example, when you want to check whether some peaks shift their position (for instance, due to differences in pH, temperature, etc., as is common in biofluids spectra).

Finally, there is an additional display mode, the so called whitewashed stacked plot. The whitewashing effect means that the spectra at the front of the display hide the spectra behind them from view, as depicted in the figure below.

This plotting mode can be useful to create nice reports, but it’s important to emphasize that drawing time will be significantly higher than with the other plotting modes, so it is not recommended when processing the spectra in real time (e.g. interactive phase correction).

In my next post I will show how to extract useful information from arrayed spectra.

Basics on Arrayed-NMR Data Analysis (part I)

2009-10-06T04:08:00.000-07:00

In this post I will cover some basic concepts on the analysis of a very important class of NMR experiments, the so-called Arrayed NMR spectra. The concept is very simple: an arrayed experiment is basically a set of individual spectra acquired sequentially and related to each other through the variation of one or more parameters and finally grouped together to constitute a composite experiment. These experiments are also known as ‘pseudo-2D’. For example, in the case of Bruker spectra they have the same file name as 2D spectra, that is ser files (ser = serial spectra) . In the case of Varian, the file name is fid (Varian uses the same name for 1D, 2D, 3D, … and arrayed spectra). However, unlike with actual 2D spectra, arrayed spectra are only transformed along the F2 –horizontal or direct- dimension (assuming 1D arrayed spectra only).

The modus operandi is better explained with an example: let’s suppose it is necessary to acquire a pulse field gradient (PFG) experiment. Instead of acquiring independent spectra, it is more convenient to create an array with increasing PFG amplitudes. All resulting spectra are now treated as a single experiment. This grouping greatly facilitates processing as, in general, all subspectra require the same processing operations (apart from some occasional minor adjustments of one or several spectra). More about this in a moment.

Well known examples of NMR arrayed experiments are, among others:

Relaxation (T1, T2)
PFG experiments (DOSY)
Kinetics and reaction monitoring by NMR

Any good NMR processing software should be able to automatically recognize when an NMR spectrum is an arrayed experiment and will setup all processing operations accordingly. For example, the figure below illustrates the results obtained when a Bruker arrayed folder is dragged and dropped into Mnova:

What has happened here are basically 2 things:

First, Mnova detects that the dropped folder contains an arrayed experiment
With that knowledge in hand, Mnova proceeds to process all the individual spectra, one after the other and of course, along the only valid dimension (F2). So for every spectrum, Mnova applies appropriate weighting, zero filling, FT, phase correction, etc and stacks all the spectra as shown in the picture above

As a result, all individual spectra grouped within one composite item (i.e. arrayed item) have been processed in the same way. However, it’s very common that some subspectra might require independent tuning. For example, many PFG NMR experiments present gradient dependent phase shift so that it becomes necessary to adjust the phase of some individual spectra separately. This is very easy to accomplish with Mnova and it will be the subject of my next post.

Mnova 6.0, at last! GSD, Line Fitting, Data Analysis, handling of LC/GC/MS data and much more!

2009-09-16T01:24:00.000-07:00

It's been over 6 weeks since my last post on this blog but don’t worry, I haven’t been idle. On the contrary, I have a very good excuse for this lack of posts: We all at Mestrelab have been working very hard trying to get version 6.0 of Mnova finished. Now I’m delighted to announce that we have done it and version 6.0 is finally available for download from our Web site. This is certainly a major upgrade of the software in which we have put a lot of work and passion. It brings a number of enhancements and bug fixes but most significantly are the following new developments:

Mnova MS

Yes, Mnova speaks a new language now, not just NMR. Since its conception, Mnova was Multi-document, Multi-Page, Multi-Platform and designed to become Multi-Technique, which it has now done

GSD (Global Spectral Deconvolution)

I have already blogged about it, but now GSD is finally available so that you all can try it and play with it. We are confident that this new powerful analysis tool will open new avenues in many NMR fields

NMR Line Fitting (Deconvolution)

Even though GSD is a fully automatic spectral deconvolution algorithm, a general purpose line fitting (deconvolution) module is always useful. In an effort to maximize user experience, we have developed a powerful, yet easy to use Graphical User Interface which makes possible both the manual and automatic adjustment of any peaks parameters (i.e. peaks positions, heights, line widths, shapes). I will talk more about it in a new post in a few days

NMR Data Analysis Module

Designed for the analysis of arrayed NMR experiments such as DOSY, Relaxation (T1, T2), kinetics, metabonomics, reaction monitoring, etc. This new module includes, among other features, the capability to apply reliable and fast non linear fitting (including specialized mono-exponential fitting), plotting of the experimental and fitted data, etc

Well, this list is not a fair account of all the number of new things implemented in this version. For a detailed list you could check out the ‘What’s new in 6.0'.

From here I encourage you to try this new version and experiment with the new tools. You can download an evaluation version from our website (at www.mestrelab.com). If for some reason your license has already expired, please do not hesitate to get in touch with us at Mestrelab, we will be delighted to supply a license for the software. In the meantime, I can only add that in the next few days I will be creating new posts where I will be revealing in detail each and every new tool of this brand new version as well as some innovative and interesting applications

Agilent Technologies to Acquire Varian

2009-07-28T00:03:00.000-07:00

This morning I got up with this shocking news:
Agilent Technologies to Acquire Varian, Inc. for $1.5 Billion
http://www.agilent.com/about/newsroom/presrel/2009/27jul-gp09016.html

Note:
Just to clarify, the word shocking was used in the sense of surprising, and with no negative connotations meant. Not being privy to the detail of the deal or to Agilent's plans, I can of course not foresee how this may affect Varian's position in the NMR marketplace or how it may affect the NMR community, although having a big company with a big interest in R&D like Agilent in our market could well be very positive

Fighting against peak overlap – Introducing Global Spectral Deconvolution (GSD)

2009-06-05T03:17:00.001-07:00

1H NMR is for sure the most powerful technique for structure elucidation, especially for small organic molecules. Typically, an organic chemist uses the chemical shift, coupling constants and integration information contained in an 1H-NMR spectrum to either verify or elucidate an unknown compound. Of course, it’s quite common that a simple 1H-NMR spectrum is not enough to unambiguously confirm a structure and thus other NMR experiments (e.g. 13C-NMR, HSQC, COSY, etc) are used to get more structural information.

Nevertheless, I have often found that many organic chemists do not always try to get the most out of 1H-NMR spectra (which is the cheapest experiment), in particular when some multiplets are complex to interpret (strong coupling) or when peaks overlap prevents valuable information to be detected in some multiplets. Overlapping peaks and new ways to get around it will be the subject of this post.

As it is well known, there are two principal factors limiting the resolution power in a spectrum. First, we have the natural line width limitation imposed by the T2 (spin-spin relaxation). For example, if T2 is about 1 second, the peak linewidth at half height cannot be less than 0.32 Hz (remember, line width at half height = 1 / (pi * T2) = 1 / 3.1415 = 0.32) no matter how powerful is our NMR instrument or the field homogeneity. On the other hand, there are instrumental shortcomings (e.g. spatial uniformity of the applied magnetic field, etc).
Nonetheless, there is an additional limiting factor, and whose importance is generally underestimated which has to do with the generally large number of transitions in 1H-NMR spectra. In short, the peaks we can observe in a 1H-NMR are just a small fraction of the actual transition resonances which are not observable because of the limited digital resolution. In fact, every peak in an 1H-NMR spectrum is basically an envelope of a large number of transitions and its shape is dominated by the coupling pattern of the spin system. Even in molecules of modest size the number of distinct peaks is tens to thousands times smaller than that of quantum transitions. As a very simple example, consider an A3B2 spin system. Depending on the second order interaction and on the available digital resolution, we might observe the expected triplet / quadruplet multiplet patterns. This is illustrated in the figure below.

However, if we use Mnova capabilities to display all main transitions of any coupled spin system by simply hovering with the mouse over the particle of interest, we can appreciate the additional number of resonances (see below):

Furthermore, I can easily increase the digital resolution of the A3B2 spectrum above by just reducing the line width used in the spin simulation module of Mnova. As a result, it’s now possible to observe more resonances in this particular A3B2 spin system (although not all of them, of course):

Of course, this way of increasing the digital resolution is only possible with synthetic spectra and cannot be applied to experimental data. Obviously there are many resolution enhancement techniques being Resolution Booster one of the most powerful ones. As a nice example of the application of this technique, let me tell you this story:
A couple of weeks ago, a very good friend of mine, a professor of organic chemist, came to me with an interesting structural problem. His research group had carried out a reaction which resulted in one single product whose 1H-NMR spectrum was, in principle, compatible with two potential structures. In order to ambiguously find the right structure, they acquired more NMR spectra (DEPT, HSQC, HMBC, COSY) which allowed them to find the correct molecule However, while discussing the problem having a few beers at a bar in Santiago, we found that just the 1H spectrum was more than enough in order to discard one of the two structures and completely assign the correct one without the necessity to acquire any other NMR experiment. The key was the ability to resolve a long range coupling (homo-allylic) with the assistance of Resolution Booster. Basically, the 1H-NMR showed a clean double doublet which was compatible with both structures (I’m sorry, but I cannot reveal those structures). This multiplet is shown below:

After appling Resolution Booster, we could clearly appreciate a further splitting which we could assign to the expected homo-allylic coupling with a value of 1.76 Hz. This coupling was also found in its corresponding multiplet partner confirming the structure:

At this point, it’s worth mentioning that Resolution Booster is a very powerful method to resolve overlapped peaks, but it cannot be used for integration as the area of the peaks get distorted by this process. The good news is that we have developed a new method which in addition to taking advantage of the power of resolution booster, it yields accurate integrals.

This method has been named as Global Spectral Deconvolution (GSD) and as its name says, it automatically deconvolves all the peaks in a spectrum. In short, this method first recognizes all significant peaks in a spectrum, then assigns a realistic a-priori bounds to all peak parameters (chemical shift, heights, line widths, etc) and finally fits all these parameters in a very reasonable time.
Following with the example above, if we apply GSD, we get a multiplet with all the individual peaks clearly resolved and this time, with accurate integrals.

It’s important to mention that we haven’t just fitted the multiplet above, but we have actually fitted the whole spectrum!

We are confident that GSD will open new avenues in NMR data interpretation and quantitative analysis (qNMR). I will blog about these points in future posts.

Mspin, RDC’s and efficient use of freely rotating groups

2009-05-19T04:19:00.000-07:00

In the last ten years, Residual Dipolar Couplings (RDC) have come to occupy a very important place in the structure determination of proteins, nucleic acids and carbohydrates in liquid state. Although RDCs were originally discovered and theoretically explained for small molecules in liquid crystal solvents by A. Saupe in 1968 (Angew. Chem. Int. Ed. Engl. 1968, 7, 97) the spectra were too complex for a practical use in structure determination. The discovering of weak orienting media in water led to an explosion in the application of RDCs for biomolecule structure determination. However, those aligning media used for biomolecules were not applicable to most of the small molecules. Fortunately, recent research results considerably extended the applications of RDCs to small molecules as new alignment media for organic solvents, either liquid crystal type as poly-?-benzyl-L-glutamate (PBLG), or mechanically stretched cross-linked polymer gels such as poly(methyl methacrylate) gel (PMMA) or polydimethylsiloxane (PDMS) are available. If you are interested in RDCs you should certainly check the very didactic introduction in the theory by Kramer et al. Applications and practical considerations are nicely reviewed in the recent reviews by Cristina Thiele ( See this and this) and Burkhard Luy ( see this).

The use of RDCs in small molecule structural determination is typically based on the determination of the alignment tensor, a 3x3 matrix, which contains the information about the probability of the molecule pointing in a particular direction of the space. This matrix can be determined by least squares fitting to the experimental RDCs.
However, there exists a further potential problem on the application of RDC to the structure determination of small molecules: the lack of enough independent RDCs, i.e, those coming from non parallel vectors, since in most cases only 1DCH RDCs are available from F1 ( see this) or F2 coupled (see this ) HSQC type experiments, thus making the fitting problem underdetermined. Armando Navarro et al. have recently proposed an elegant approach to get the most out of the experimental data by incorporating into the calculations two of the most common freely rotating groups, namely the methyl and phenyl groups (using 2-fold and 3-fold jump models).

The authors have automated this averaging of RDCs from freely rotating groups in version 1.03 of our program Mspin which we hope will facilitate the use of RDC among a broader community of users interested in solving structural questions of small molecules

New Mestrelab Blog

2009-04-26T07:02:00.000-07:00

I’m happy to announce our new blog on Mestrelab. As Santi wrote, the purpose of this blog is “to report on company progress and ideas, to tell stories about our trips and conferences, and to highlight aspects of our products which we may think our users may be interested in reading, or hearing, about”
A lot of people seemed to be very interested in what we're doing in Mestrelab so we thought that it would be helpful to create this blog so as to keep you all up to date on what’s going on with our commercial initiatives, trips (including photo sets from those trips) etc.
So if you feel curious about Mestrelab activities, please visit our new blog. We look forward to hearing from you.

Mestrelab's blog: http://blog.mestrec.com

NMR Spectroscopy Explained

2009-04-21T14:16:00.001-07:00

When I initiated the development of MestReC back in 1995 (15 years ago!), my knowledge of NMR was fairly elementary and limited to basic theoretical rudiments (quantum mechanics description of NMR phenomenon, vector model, etc) and some experience in the practical interpretation of NMR spectra gained primarily whilst working as an organic chemist at Leicester University.

That said, during that first phase of development, I wish I had enjoyed the opportunity to have access to the book ‘NMR Spectroscopy Explained: Simplified Theory, Applications and Examples for Organic Chemistry and Structural Biology' by Neil Jacobson, I’m sure that my productivity would have been boosted very significantly by it. For example, there is an unmissable section devoted to practical NMR aspects and, in particular, NMR data acquisition and processing. It’s clear from this section that the book was written from the perspective of a spectroscopist who works with NMR on a day-to-day basis (Neil Jacobsen is the NMR Facility Manager at the University of Arizona). Concepts such as oversampling and digital filtering are presented in more detail than that found in standard introductory texts. I bought this book about 6 months ago and I have to say that it is a shame that it wasn’t available much earlier when I started my work on NMR.

Nothing is ever perfect and if I had to point out something missing in the book it would be a chapter devoted to DOSY, which I think would make a nice addition.

Overall, I believe that this is a great book which I warmly recommend to all of you who wish to deepen your understanding of NMR both from a practical and theoretical standpoint. Enjoy, and let me have your thoughts!

Mnova reviewed by Tim Claridge at JCIM

2009-04-10T08:56:00.000-07:00

High-Resolution NMR Techniques in Organic Chemistry is one of the most popular books on NMR which is now used at many universities as a foundation for graduate-level courses on NMR techniques. It has been written by Tim Claridge who is the Director of NMR Spectroscopy at the Organic Chemistry Department at Oxford University and has now written a very nice review on Mnova in the Journal of Chemistry Information and Modeling (JCIM). I'll just quote one of his conclusions because I'd rather let you read the full article:

Overall I was very impressed with the package, finding it not only very comfortable and intuitive to use so well suited to non-NMR specialist, but also well endowed with more advanced processing features for more experienced users

(Click here for the full article)

I would like to take this opportunity to thank all of you for your support, advice and contributions to our design and development, and also congratulate my team; it seems we are doing well at developing easy to use but powerful NMR software. But don’t worry, we are not going to get complacent because of reviews like this, on the contrary, they are just a spur to work harder and develop the software further

Article bookmark. Tim Claridge University of Oxford J. Chem. Inf. Model., Article ASAP DOI: 10.1021/ci900090d Publication Date (Web): March 30, 2009 http://pubs.acs.org/doi/abs/10.1021/ci900090d Copyright © 2009 American Chemical Society

Pre-ENC User Meeting Video

2009-03-13T10:04:00.000-07:00

As you may know, we are going to hold an user meeting prior to the 50th ENC Conference.
There, Mestrelab's team and some guests are going to present some new Mnova features, algorythms and new products.

You can check the meeting program and get registered here.
Whether you are planning to attend or not I also encourage you to watch this 5 minutes video.

Double-click to switch to full screen

Pre-ENC User Video from Dani Fraga on Vimeo.

NMR and the Chemist’s Illusion

2009-03-05T02:46:00.000-08:00

Stan has just posted a nice entry in which he uses the aromatic region of Strychnine to discourse about the different effects in the NMR spectrum (in terms of resolution and multiplicity) produced when the magnetic field frequency is changed. In particular, I like his description of the ‘Chemist’s Illusion’ and as a chemist, I would like to illustrate, just with a picture, what this illusion is all about.

In the picture below, I have synthesized the ABCD spin system corresponding to the aromatic region of Strychnine at different fields (we don’t own a 1500 MHz spectrometer and we don’t expect to get one for Mestrelab in the short- or mid-term :-) ). It can be appreciated that as we move to higher fields, the multiplets appear to be more separated (this is an illusion: their chemical shifts, in ppm, are exactly the same!) and get more resolved and more first-order like.

Below I’m showing an expansion of the right most multiplets:

Another interesting and well known example is represented by an AA’BB’ spin system (for example, o-diclhrobenzene) . Again, as we go to higher fields, the apparent multiplets separation looks larger, although the multiplet fine structure remains virtually unchanged. In other words, in these systems, second order effects will always exist regardless of the magnetic field. When the magnetic field is increased, it will be possible to get a larger chemical shift difference between the AA’ and the BB’ groups, but not between A and A’ or B and B’ (it’s always zero), so that the highest simplification one can achieve by increasing the magnetic field is to move from an AA’BB’ group to an AA’XX’ group which is a second order spin system too.

Peak Shapes in NMR Spectroscopy

2009-02-23T09:59:00.000-08:00

Routine analysis of NMR data involves peak picking and integration to get chemical shifts (and couplings) and quantitative information (e.g. number of protons). When the peaks are not well resolved, none of these parameters can be accurately estimated and nonlinear least squares fit (curve fitting or deconvolution) is often performed to extract the desired information. However, deconvolution presents, at least two important difficulties:

Problem #1

In general, line fitting is applied to some limited number of lines in a spectrum as a deconvolution of the full spectrum is very difficult to say the least. This implies a manual intervention of the User (choice of multiplet, specification of the number of lines and of their starting parameters).

Problem #2

Curve fitting requires the definition of an analytical model for the line shape and in particular, NMR lineshaphes have typically been assumed to be either Lorentzian, Gaussian, or a combination of both (e.g. Voight Profile). The problem is that Lorentzian deconvolutions are numerically ill defined because all complete sets of Lorentzian-shaped functions are approximately linearly dependent (in other words, a Lorentzian peak can be approximated very well by several Lorentzian lines). This problem is specially important in 1H-NMR spectra where peaks are really complicated envelopes of many unresolved transitions (for example, in a generic 10 spin system there are 5120 distinct main transitions, but one typically resolves less than 100 peaks).

These problems have been the motivation of the development of a brand new peak analysis algorithm, the so-called GSD (Global Spectral Deconvolution) which has been recently presented by Stan Sykora in a talk he gave at MMCE 2009 conference. In fact, GSD is now fully operative within MestReNova .

If you are interested in GSD and planning to visit ENC, we will be pleased to show you every detail at the user meeting we will keep on Sunday 29th March and at our exhibitor and hospitality suite (you do not need to be a MestReNova User to participate).

DOSY-shift reagents

2008-12-31T09:20:00.000-08:00

A well-known procedure to separate resonances that would otherwise overlap in crowded NMR spectra is by adding to the sample some paramagnetic substance, the so-called shift-reagent. The most commonly used shift reagents are complexes of paramagnetic lanthanide ions such as europium(III) for down field shifts and praseodymium(III) for upfield shifts.

A similar approach has been recently reported to resolve mixture components via DOSY-NMR. It’s not very uncommon that in some mixture analyses, 2 or more compounds have diffusion coefficients so similar that they cannot be resolved by any mathematical procedure. For example, the figure below shows a synthetic DOSY spectrum (based on Figure 2 of the original article) of a mixture of two peptides, Trp-Gly and Leu-Met having D values nearly identical

M. E. Zielinski and K. F. Morris proposed in their article to add perdeuterated surfactant micelles to the mixture. Analogous to the chemical offsets induced by shift reagents, the molecules in the mixture under analysis interact differentially with the micelles and thus have different Diffusion values.

Using perdeuterated surfactant micelles to resolve mixture components in diffusion-ordered NMR spectroscopy
Matthew E. Zielinski, Kevin F. Morris, Magnetic Resonance in Chemistry
Volume 47 Issue 1, Pages 53 - 56

Microreview on NMR structural elucidation

2008-12-21T14:00:00.000-08:00

A nice short review presenting practical strategies for the elucidation of small organic molecules with NMR spectroscopy has been published a few months ago. I highly recommend it as a reference for organic chemists engaged in structural elucidation tasks.

Eugene E. Kwan, Shaw G. Huang, Structural Elucidation with NMR Spectroscopy: Practical Strategies for Organic Chemists European Journal of Organic Chemistry, 2008 (16), 2671-2688

DOI: 10.1002/ejoc.200700966

Better NMR Processing and Analysis with Mnova 5.3.0

2008-12-18T09:26:00.000-08:00

I’m pleased to announce the release of the latest version of Mnova (version 5.3.0), our software for the efficient processing, analysis and prediction of NMR spectra.
With the unveiling of version 5.3.0 come a multitude of enhancements over previous releases . Here I’d just like to highlight some key new features which I’m very proud of as I think they represent a substantial enhancement in the software’s capabilities and, in some cases, new breakthroughs in the world of NMR software:

Bayesian DOSY Processing
Whitening algorithm for 2D automatic Phase Correction
Prediction of X-Nuclides spectra
Spin Simulation module with support for scalar, dipolar and quadrupolar interactions and its unique classification of transitions feature
Covariance NMR: Direct, Indirect and Unsymmetrical by means of the Advanced Arithmetic Module
Multipoint (manual) Baseline Correction

We have also greatly improved some algorithms such as peak picking, automatic noise estimation, resolution booster, integration, etc.
It’s also worth mentioning that most of the new dialog boxes in the program are modeless. For example, now while phase correcting a spectrum, you can zoom in to a particular spectral region without having to quit the phase correction dialog.
There are many other new features in this new version, and many more to come shortly in forthcoming updates. I will be featuring some of them in future posts.
I would like to take this opportunity to congratulate our development team on the fantastic work they have done. Big thanks, guys!

Note. This version will be available for download from our web site Friday 19th

Quantitation of Pharmaceutical Compounds

2008-11-28T07:33:00.001-08:00

This is probably something that you weren’t expecting, but I think it’s a fun way to end the week

Intelligent NMR Clipboard

2008-11-24T02:33:00.001-08:00

The clipboard is for sure one of the most useful features in any modern Operating System and it is used for short-term data storage and/or data transfer between documents or applications, via copy and paste operations. Any modern application should support clipboard operations and, of course, Mnova is no exception. However, Mnova goes one step further compared to other applications as I will try to show in this post.

Following the same principles as standard Office applications, with Mnova it’s possible to copy any object (e.g. spectra, molecules, etc) into the clipboard and paste it either in Mnova (for example in a different page) or in any other application such as MS Office. The peculiar thing is that once a spectrum has been transferred to the clipboard (via Ctrl+C), it is possible to ‘paste’ it into another spectrum. Two simple examples will illustrate this new feature.

Example #1

You have processed a spectrum and integrated carefully in order to quantify some signals of interest. Next you realize that you also want to integrate a different spectrum but using exactly the same integral regions as those in the first spectrum. There are several ways to do that in Mnova, but a very simple one involves copying the first spectrum into the clipboard and then selecting ‘Paste Integrals’ from the Edit menu. You can paste these integrals either to a single spectrum or to a bunch of selected spectra (or pages).

Example #2

You have customized the graphical properties of a spectrum (e.g. fonts, colors, grid, etc) and you find that you want to rapidly apply the same graphical settings to another spectrum. Once more, this is very easy with the clipboard: copy the first spectrum (Ctrl+C) and then select the target spectrum and issue command ‘Paste NMR Properties’.

NMR Arithmetics

2008-11-22T05:33:00.000-08:00

2D NMR spectra are simply 2D matrices (Note: these matrices can be real, complex or hypercomplex, but for the sake of simplicity, we will consider real matrices only) which can be subject to standard matrix algebra operations. I have presented in previous posts how Indirect and Direct Covariance NMR can be applied by proper matrix algebra. These methods are incorporated in Mnova as a dedicated module which also makes the filtering of spurious resonances possible . In order to show you that Covariance NMR actually involves these matrix operations, you can use Mnova’s powerful Arithmetic module which we have recently completed. This module has been designed in such a way that it operates as a simple spectral calculator. You enter the equation which the program parses and produces the expected result. For example, if we have a HSQC-TOCSY spectrum (A), we can enter the Indirect Covariance formula like this:

Where A corresponds to the real part of the original spectrum and TRANS indicates the transpose operation. This operation will produce the (unnormalized) Covariance NMR spectrum, in this case the 13C-13C correlation spectrum. Of course, in order to better approximate the covariance spectrum to the corresponding standard 2D FT counterpart, it’s necessary to calculate the square-root using, once more, matrix algebra. This is again very simple with our arithmetic module by just adding the square root operation (SQRT) into the equation:

This arithmetic module is not restricted to matrix operations within a single spectrum. We can freely combine as many spectra as we want. For instance, if we have, in the one hand a COSY spectrum and in the other a HSQC spectrum, we can combine both in an analogous way so that the indirect covariance NMR spectrum yields a HSQC-COSY 2D spectrum. More about this in a future post …

Removal of artifacts in direct Covariance NMR

2008-11-20T03:54:00.000-08:00

I have previously blogged about direct Covariance NMR as a technique to increase the digital resolution of the indirect dimension in 2D homonuclear experiments. As is always the case, there is some price to pay: Covariance NMR introduces some unexpected resonances, in special when the number of t1 increments is small making the covariance exhibit poor statistics (JACS, 2006, 128, 15564–15565). Some of these extra resonances are true spurious peaks whilst others correspond to multistep or RCOSY-type correlations (see MRC, 2008, 46, 997-1002)

The picture below shows the regular 2D FFT spectrum of Strychnine:

And this is its standard direct Covariance counterpart where I have highlighted some of the extra resonances.

While some of these additional resonances can be beneficial because they provide kind of TOCSY correlations, others are just pure artifacts which make the analysis of these experiments unreliable (it’s difficult to know in advance whether a peak is a real correlation or just an artifact).

We have recently incorporated into Mnova a new filter which eliminates these artifacts very efficiently. For example, this is the result obtained after automatic filtering of the Covariance NMR spectrum:

It can be observed that extra peaks have been eliminated without giving up the resolution advantage.

All these new processing capabilities will be available in the next version of Mnova (5.3.0, to be released in a few days), although we have a pre-release candidate available to anyone interested. Just contact me and I’ll be happy to send it out.

MestReS: A Virtual NMR Spectrometer

2008-11-10T03:49:00.000-08:00

Aircraft pilots use cockpit flight simulators since they are considerably less expensive to operate than actual aircraft and provide an opportunity to practice crisis problem solving without putting real people or aircraft at risk. Following the same principle, MestReS is a virtual NMR simulator package intended to allow students to learn and practice the NMR instrumental techniques while saving rather expensive spectrometer time and avoiding equipment damage due to improper use. MestReS provides real-time simulation of the processes of field locking, shimming and acquisition. Both continuous-wave (Bruker spectrometers) and FT (Varian spectrometers) deuterium channel simulation are included. Most common physical properties (e.g. sweep rate variation, spinning sidebands, etc) can also be simulated. The program provides basic 1D processing and includes the tools needed to effortlessly create 1H and 13C NMR databases from synthetic FID’s

You can download it from the link below:

Download MestReS at the Mestrelab Research Chemistry Software Product Page

MestReS can emulate locking and shimming effects in real time. Both continuous-wave (Bruker spectrometers) and FT (Varian spectrometers) deuterium channel simulation are included. Emulation of most commonly used shimming coils (Z,Z2..X,Y) is also provided. Most common physical properties are also simulated (sweep rate variation, spinning sidebands, etc) giving to the student a very realistic feeling.

While we offer MestReS as a totally free program, we are not longer developing it further or offering technical support for its use. Nevertheless, should you have any comment on the program, feel free to let me know.

I would particularly like to thank Armando Navarro, of the University of Santiago de Compostela, for his work in developing MestReS and making it available to our user community. It was a pleasure to collaborate with him on this project while I was working at the University

EXSYCALC: A free software for NMR analysis of molecular systems undergoing chemical exchange

2008-11-04T15:02:00.000-08:00

EXSYCALC is a free program intended for the study by NMR of molecular systems undergoing chemical exchange. It does a quantitative analysis of the experimental intensities of the NMR peaks obtained in EXSY experiments to calculate the magnetization exchange rates k' of the exchange equilibrium (related with the reaction rate constants k ). The program allows the calculation of systems with an arbitrary number of exchange sites, spins, populations and arbitrary longitudinal relaxation rates. The calculations are done according to a full relaxation matrix analysis of the intensities. The range of applicability of the approach used requires that the signal of each different species in the exchange process is conveniently separated from the others in the NMR spectrum (i.e. slow chemical exchange in the chemical shift time scale)

You can download it from this link:

Download EXSYCalc at the Mestrelab Research Chemistry Software Product Page

For the calculation of rate constants, the program requires that the user supplies the experimental amplitudes of certain NMR peaks obtained in two different EXSY experiments, one is an EXSY experiment acquired at a certain mixing time (tm), and the other is an EXSY experiment acquired at 0 or very short mixing time (reference experiment). In the former experiment the mixing time (tm) need to be large enough for the magnetization exchange process to take place. In this experiment the amplitudes (intensities) of those signals in exchange, A(tm), have to be quantified for both diagonal and cross peaks. In the other EXSY experiment, the EXSY reference experiment, no cross peaks due to magnetization exchange should be observed (thermal equilibrium) and the amplitudes of just the diagonal peaks of those signals in exchange, A(0), have to be measured. It is important to mention that both experiments must be acquired and processed under identical conditions, temperature, number of scans etc.

Enjoy it!

Indirect Covariance NMR – Fast Square Rooting

2008-11-02T11:55:00.000-08:00

In my previous post I wrote about Direct Covariance NMR as a powerful processing tool to improve the resolution along the indirect dimension of a 2D homonuclear spectrum. Using a naïve explanation, we can understand this as a resolution transfer from the direct dimension to the indirect one. Mathematically this is done by simply multiplying the transpose of the real part of the spectrum by itself:

Cdirect = (F'.F)^(1/2)

Interestingly, if we have a heteronuclear spectrum, it‘s possible to transfer the correlation information from the indirect dimension to the direct one by simply changing the order in which the multiplication is carried out:

Cindirect = (F.F')^(1/2)

For example, the spectrum below shows the HSQC-TOCSY spectrum of sucrose (left) and its resulting indirect covariance counterpart (right) which contains essentially the same spin-connectivity information as a 13C-13C TOCSY with direct 13C detection (more information here).

The advantage is obvious: Indirect Covariance NMR yields a 13C-13C TOCSY correlation without having to detect the 13C nucleus. In other words, it brings in a sensitivity increase of 8 over a 13C detected experiment. Of course, in indirect covariance NMR spectroscopy, the spectral resolution along both frequency axes is determined by the sampling along the evolution t1 time.
The first time I implemented Indirect Covariance NMR in MestReC, I found that the computational effort required was quite high. The computation of the covariance matrix requires O(N1N2^2/2) floating point operations, whereas the square-root operation based on diagonalization of C requires O(N2^3) floating point operations (see this for more details).
For example, calculation of the indirect covariance NMR spectrum (including square root computation) of the HSQC-TOCSY spectrum showed above (1024x1024 data points) took about 60 seconds in my laptop (Sony VAIO, Intel Core, Duo Processor, 2.40 GHz, 2 GB RAM) in MestReC. The new implementation of Covariance NMR in Mnova is much more efficient and for this particular example, full calculation of the Indirect Covariance spectrum takes less than 3 seconds in the same computer.
The very high performance of Mnova makes Covariance NMR computationally affordable and open to a wide range of routine applications.

Introduction to Covariance NMR

2008-10-20T00:02:00.000-07:00

Resolution and sensitivity are two key factors in NMR spectroscopy. In the case of 2D NMR, the resolution of the direct dimension (f2) depends, among other things, on the number of acquired complex points, whilst the resolution of the indirect dimension (f1) is directly proportional to the number of increments (or number of acquired FIDs). In general, it could be said that the resolution along the direct dimension comes for free in the sense that increasing the number of data points does not augment the acquisition time of the experiment significantly. However, increasing the number of t1 data points (increments) has a direct impact in the length of the experiment as can be seen from the Total acquisition time for a 2D NMR spectrum:

T = n*N1*Tav

Where n is the number of scans per t1 increment, N1 is the number of T1 increments and Tav is the average length of one scan. This usually means the resolution of the indirect dimension f1 is kept lower than that of f2.

For example, let’s consider a COSY spectrum (magnitude mode) of Strychnine which has been acquired with 1024 data points along the direct dimension and with 128 t1 increments. It’s clearly appreciated that resolution along F2 is much higher than along F1. For example, doublets corresponding to protons H20a and H23 are resolved in F2 but not in F1.

How could this be improved? We could try to extrapolate the FID (somehow) along the columns (F1) to a higher number of points (e.g. 1024). A well known and very simple technique is simply to add zeros, a process called zero-filling, which basically is equivalent to a kind of interpolation in the frequency domain. For example, in this particular case we could try to extrapolate the FID (along t1) from 128 to 1024 points in order to match the number of points along f2. The figure below shows the results:

It can be observed now that the resolution along f1 is slightly higher than in the previous case but we still cannot distinguish the inner structure of the multiplets (e.g. H20a and H23). Zero Filling is certainly a good technique to improve resolution but, of course, it cannot invent new information from where it does not exist. In this case we have zero filled from 128 to 1024 data points (e.g. 4 fold). In theory, zero filling by at least a factor of two is highly recommended because it enforces causality but beyond that, the gain in resolution is purely cosmetic. We might get more data points per hertz, but no new information is achieved as it’s shown in the figure above.

Is there a better way to extrapolate the FID? Yes, and the answer is very evident: Linear Prediction. In a few words, Forward Linear Prediction uses the information contained in the acquired FID to predict new data points so that we are artificially extending the FID in a more natural way than with Zero Filling. Of course, we cannot create new information with this process but the resulting spectrum will look better. This is illustrated in the next figure:

In this case, we have extended the t1-FID from 128 to 512 data points and then zero-filled up to 1024. Now we can see that the f1-lines are narrower but the couplings cannot be resolved yet.

In recent years there has been great interest in the development of new methods for the time-efficient processing of 2D (nD in general) NMR data. One of the more exciting methods is the so-called Covariance NMR, a technique developed by Brüschweiler at al. In fact, there are several types of Covariance NMR: Direct, Indirect Covariance NMR (there is a third method, Unsymmetrical Indirect Covariance which can be considered as a subtype of Indirect Covariance NMR). In this post I will cover only the first type, Direct Covariance NMR leaving, the other 2 types for future posts.

Before going any further with Covariance NMR, let’s see the results of applying this technique to the same spectrum. This is what we get:

At first glance, this result looks like a kind of magic: Now the splitting corresponding to H20a and H23 are clearly resolved in both dimensions. Actually, the resolution along F1 is virtually analogous to that of the F2 dimension. How did we arrive to such a good result? From an intuitive stand point, what we have attained here was a transfer of the resolution of F2 to the F1 dimension. In other words, we have applied a mathematical process which takes advantage of the higher spectral resolution in the F2 dimension to transfer it to the F1 one.

Mathematically, direct Covariance NMR is extremely straightforward as defined by the following equation:

C = (F'F) (1)

Where C is the symmetric covariance matrix, F is the real part of the regular 2D FT spectrum and F' its transpose (NOTE: direct covariance NMR can also be applied in the mixed frequency-time domain, i.e., when the spectrum has been transformed along F2. In this case, a second FT will not be required – nor apodization nor phase correction along the indirect dimension).

In order to approximate the intensities of the covariance spectrum to those of the idealized 2D FT spectrum, the square root of C should be taken. Root squaring may also suppress false correlations which may be present in F'F due to resonance overlaps. Taking the square root of C matrix is in practice done using standard linear algebra methods (in short, diagonalizing the matrix and then reconstructing C^(1/2) using eigenvectors and the square roots of eigenvalues).

So direct Covariance NMR allows us to produce a 2D spectrum in which the resolution in both dimensions is determined by the resolution of the spectrum along the direct dimension. I have created a stacked plot representation with the 1D projections obtained from the different processing methods described in this post (Zero-Filling, Linear Prediction and Direct Covariance NMR). I think that this plot shows the power of the Covariance NMR method.

There is nothing magic about Covariance NMR. It’s a process with a strong mathematical background based on the well-known Parserval’s theorem. An elaborate discussion of this method is beyond the scope of this post (at least for the time being), but it has been nicely described in the following articles by Brüschweiler et al.

[1] R. Bruschweiler and F. Zhang, J. Chem. Phys., 120, 5253 (2004)
[2] F. Zhang and R. Bruschweiler, Chem Phys Chem, 5, 794 (2004)
[3] R Bruschweiler, J. Chem Phys., 121, 409 (2004).
[4] N. Trbovic, S. Smirnov, F. Zhang, and R. Bruschweiler, J. Magn Reson, 171, 277 (2004).
[5] F. Zhang, N. Trbovic, J Wang, and R. Bruschweiler, J. Magn. Reson., 174, 219, 2005).
[6] Y CHen, F. Zhang, W. Bermel and R Bruschweiler, JACS, 128, 15564 (2006)
[7] F Zhang and R Bruschweiler, Angew Chem., Intl. Ed., Engl., 46, 2639 (2007)
[8] Y. Chen, F. Zhang, D. Snyder, Z Gan, L. Bruschweiler-Li, and R. Bruschweiler, J. Biomol. NMR, 38, 73 (2007)

If you still feel skeptical about Covariance NMR, just try it out. We have recently implemented this technique in Mnova. This version is still in alpha stage but if you want to try it, just send me an email (my email is carlos followed by ‘at’ and mestrelab.com) and I will give you a link to download this alpha version of Mnova.

BTW, I’m proud to say that MestReC was the first NMR software package (apart from the in-house algorithms developed by Brüschweiler group) which offered Covariance NMR processing (here is the proof). Now we have ported and greatly enhanced MestReC old implementation in Mnova. Now Covariance NMR is not only much faster than it was in MestReC; it’s also easier to use and more versatile. I hope you will enjoy it!.

Before I finish, I’d like to acknowledge Dr. Fengli Zhang for his support while implementing Covariance NMR into MestReC.

MestReJ: A free tool for the prediction of vicinal proton-proton 3J(HH) coupling constants

2008-10-10T04:11:00.000-07:00

Scalar coupling constants are sensitive to the geometrical features of a molecule and therefore, their magnitude provides a direct insight into the geometry and electronic structure of a molecule. For example, the Karplus equation [J. Chem. Phys., 30, 11 (1959), J. Am. Chem. Soc., 85, 2870 (1963)] describes the relationship between the 3J coupling constant and the dihedral angle between vicinal hydrogens.

After the pioneering work of Karplus, several other generalized Karplus equations have been proposed for the mutual dependence of J and the dihedral angle. Among these, Haasnoot-de Leeuw-Altona (HLA) are by far the most widely used. Applications including other generalized Karplus equations are scarce which hinder their general use for the common organic chemist. Such is the case of the more recent and precise Díez-Altona-Donders (DAD) equations, developed by Altona’s group.

A few years ago, we developed an easy to use J pocket calculator MestReJ which you can now download directly from the link below and use for free with no strings attached.

Download MestReJ at the Mestrelab Research Chemistry Software Product Page

MestReJ is a very easy little application to work with: it uses a Newman projection of the fragment under observation and a plot of the J values against the torsion angle HCC’H’. It implements the two kinds of generalized Karplus equations developed by the Altona’s group: the classical Haasnoot-de Leeuw-Altona equations and the more recent and precise Díez-Altona-Donders equations. The Colucci-Jungk-Gandour, the Barfield-Smith and the Karplus equations are also implemented in the program. For further information, see this article:

A Graphical Tool for the Prediction of Vicinal Proton-Proton ³J_HH Coupling Constants

Navarro-Vazquez, A.; Cobas, J. C.; Sardina, F. J.; Casanueva, J.; Diez, E.
J. Chem. Inf. Comput. Sci.; 2004; 44(5); 1680-1685. DOI: 10.1021/ci049913t

I hope you will find this application useful in your research

A very graphical display of the value of promotional literature

2008-10-01T04:54:00.000-07:00

Is promotional literature a valuable investment for a company like ours and an appreciated resource by our customers, or just a way of killing trees for no gain?. In the photo below you can see the take of some conference attendees on this question, which is taking Mestrelab to reevaluate whether we should be making this effort to produce the literature

BayDOSY: What’s under the Hood

2008-09-18T06:21:00.000-07:00

I have already posted about our efforts towards the evaluation of diffusion NMR experiments by means of a new Bayesian-based approach, the so-called bayDOSY.
Recently Stan Sykora has given a talk at GIDRM conference covering some background of this technique for NMR DOSY analysis, including its basic math principles and advantages over other techniques. Also, the limitations of this new data evaluation scheme are noted, as well as potential extensions designed to address some of these limitations.
This talk is available in PDF format from the web page below:

http://www.ebyte.it/stan/Talk_GIDRM_2008.html

As I have already offered, should you be interested in testing bayDOSY, just drop me a line and I will give you a special version of Mnova

2D Phase Correction

2008-09-05T02:15:00.000-07:00

‘Understanding NMR Spectroscopy’ by James Keeler is one of my favorites NMR books which I highly recommend to anyone seriously interested in NMR spectroscopy. All NMR concepts, ranging from quantum mechanics to product operator formalism and data processing are very elegantly and clearly exposed.
These days I’m working on several points regarding 2D phase correction and while consulting this book, I found a phrase which immediately caught my attention. In page 240, you can read this:

(…) However, phasing a two-dimensional spectrum is not quite so straightforward as phasing in one dimension, as it is not feasible to recompute the whole spectrum after each trial phase correction is applied – to do so would simply be too time consuming. (…)

Indeed this is true, to the best of my knowledge, with most existing NMR software packages but not with Mnova or iNMR, in which the recommended way to iteratively adjust the phase of a 2D spectrum is by real time operations (drag & drop) on the full 2D hypercomplex matrix, in just the same way as you do it with 1D spectra. In fact, I believe that this way is much more convenient than the traditional, old fashioned way of extracting some selected traces (cross-sections) parallel to one of the dimensions, calculating the phase on them, and then applying the correction to the full 2D spectrum.
Obviously, real time 2D phase correction was not possible at early times of 2D NMR development (eighties), when computers were not fast enough to make this task possible, so that the 1D cross-sections approach was the only feasible way. However, since the late nineties, advances in computer technology made real time processing of 2D NMR possible, not only regarding phase correction but any other iterative process such as weighting. For example, it is now possible to iteratively adjust the weighting functions in a 2D spectrum and see, in real time, the results in the processed full 2D spectrum.

SPECTRa

2008-08-16T09:26:00.000-07:00

During the flight to Stockholm (where I’m having a great time btw), I read with great interest this article:

SPECTRa: The Deposition and Validation of Primary Chemistry Research Data in Digital Repositories
DOI: 10.1021/ci7004737

In my opinion, the project presented in this article is a great initiative which I can only applaud and support. There is, however, a point which I would like to comment on because it’s not fully clear to me which regards to the way in which NMR spectra are stored in the repository.

The authors have decided to use JCAMP as the format for file input to their repositories. They do not specify which actual data is being saved in these JCAMP files, the processed spectrum or the FID (or both). I hope that they are saving the original FID and not only the processed spectrum, otherwise data preservation will be broken. I think this is a very important point which deserves some further clarification. This is how I see it:

The most important piece of information in an NMR experiment is, for sure, the acquired FID, not the processed spectrum. A chemist could have processed an FID to produce a spectrum in such a way that some spectral features are lost. For example, he/she could have applied a very large line broadening function which will make the analysis of the finer structure of some multiplets impossible. If the original FID has not been kept, the option to re-process the spectrum to calculate those lost couplings will not be viable (in some cases, Inverse Fourier Transform and/or some resolution enhancements procedures could help, but only in a very limited extent). In fact, there are many processing operations which could alter, irreversibly, either the qualitative or quantitative information present in the NMR experiment.

In short, I’m strongly convinced that any system aimed at preserving all information contained in NMR experiments should keep the original acquired data points, the FID. This is something I have learnt during the many years of development of both MestReC and Mnova: Mnova keeps, in addition to the processed spectrum, all the original files as they were acquired in the spectrometer. And I know that iNMR does the same thing, though in a different way (Mnova packs all the files within a single binary file, whereas iNMR keeps all the files separately and a processing log file so that the processed spectrum does not need to be saved. From my point of view, both approaches are equivalent and perfectly valid).

Bayesian DOSY: a New Approach to Diffusion Data Processing

2008-07-22T07:51:00.001-07:00

Yesterday I blogged about basic concepts on DOSY NMR. From an experimental stand point, the pulse sequences are not very complex, being the Pulse Field Gradient Stimulated Echo (PFGSE) experiment proposed by Tanner one of the basic pulse sequences used to determine diffusion by NMR. This pulse sequence can be considered as a building block for a number of extended pulse sequences designed to minimize some sources of artefacts caused by thermal convection currents in the sample, background gradients, radiation damping, zero order coherences in strongly coupled spin systems, etc. Other effects such as J-modulation and Cross-Relaxation have also been considered.

The tricky part comes in the mathematical DOSY transformation. As I mentioned earlier, there exists different approaches, each of them with their own strengths and weaknesses. Today I would like to introduce a new method for DOSY transformation based on Bayesian Theory which has been implemented in our software Mnova as a result of our collaboration with Stan Sykora. We call this new algorithm BDT (Bayesian DOSY Transform)

A formal description of the Bayesian theory and its particular implementation for DOSY transformation is beyond this blog entry, but we are currently writing an article which will give all the details of the method as implemented in Mnova.
In short, this Bayesian approach assigns an a-priori probability (this is the key word in Bayesian context) to the elements in a space defined by the entities to be estimated. In this context, an entity is the pair (f,d) where f is frequency and d is a mono-diffusion coefficient. Actually, it should be (f,d,w) where w is a weight (intensity), but this weight is factored out by finding its optimal value (since the dependence is linear, this can be done explicitly). So we are actually finding the a-posteriori probability for the sentence there is a component - no matter how intense - at f that has such and such d. Next, a final normalization process modifies the probability still further (composite probability) by looking at the intensity in the spectrum at location f (this would be real probability if the spectrum were normalized to 1).

Stan Sykora will be presenting the mathematical background and physical insights necessary to understand this new method as well as some real life examples processed with Mnova in the GIDRM conference to be held in Bressanone (Brixen) next September.

So how does the algorithm perform? We first tested the algorithm by simulating with Matlab a diffusion experiment with 2 synthetic peaks with frequencies of 100 and 200 Hz and diffusion coefficients of 1 and 0.01 (dimensionless).

Application of BDT yields the following DOSY spectrum:

The synthetic DOSY spectrum was changed in order to include artificial noise and different degrees of peak overlap and diffusion distances. We’ve found the performance of the algorithm to be excellent in all the cases analyzed.

Next we implemented the algorithm in Mnova and we applied it with a sample of an aqueous solution of potassium N-methyl-N-oleoltaurate (a surfactant) with TSP at 23 C (The original Varian FID file has been obtained from the VARIAN NMR USER GROUP LIBRARY which was submitted by Brian Antalek as a sample for this DECRA algorithm). This is the original raw data after automatic Fourier Transform, phase and baseline correction in Mnova:

After applying BDT, we obtain a DOSY spectrum in which the three components are clearly well resolved in the diffusion dimension and the absolute values are in accordance with the expected values

Below you can see the DOSY spectrum of a mixture of Caffeine + 2-EthoxyEthanol + Water acquired in a Bruker instrument by my friend Andy Soper.

Main properties of the algorithm

Compared to other approaches, we believe that this Bayesian method implemented in Mnova appears extremely promising. It automatically avoids having exact, unnatural zeros anywhere in the resulting DOSY map since every point of the 2D map has a well defined value of statistical congruence with the data. Moreover, the BDT maps show ‘normal’ line widths in the f-direction, correctly positioned and resolved peaks in the d-direction and quantitatively correct horizontal and vertical projections – a combination difficult to achieve by any other means.
The approach can be easily extended to non-exponential cases arising from overlapping lines and, like all Bayesian methods, incorporate additional information available from other sources (a-priori knowledge). Likewise, it is possible to place a statistical premium on alignment of spectral peaks along horizontal lines in the [f,d] plot.

Do you want to try it out yourself?

The algorithm is readily available in the alpha stage in Mnova. From this post, I would like to offer this special version to anyone interested in trying the BDT algorithm with his own data sets. I will very much appreciate any feedback from you.
Just write to me at the email address below and I will give you the instructions on how to get the software.

DOSY NMR

2008-07-20T23:49:00.000-07:00

NMR diffusion experiments provide a way to separate the different compounds in a mixture based on the differing translation diffusion coefficients (and therefore differences in the size and shape of the molecule, as well as physical properties of the surrounding environment such as viscosity, temperature, etc) of each chemical species in solution. In a certain way, it can be regarded as a special chromatographic method for physical component separation, but unlike those techniques, it does not require any particular sample preparation or chromatographic method optimization and maintains the innate chemical environment of the sample during analysis.

The measurement of diffusion is carried out by observing the attenuation of the NMR signals during a pulsed field gradient experiment. The degree of attenuation is a function of the magnetic gradient pulse amplitude (G) and occurs at a rate proportional to the diffusion coefficient (D) of the molecule. Assuming that a line at a given (fixed) chemical shift f belongs to a single sample component A with a diffusion constant D_A, we have

(1) S(f,z) = S_A(f) exp(-D_AZ)

where SA(f) is the spectral intensity of component A in zero gradient (‘normal’ spectrum of A), DA is its diffusion coefficient and Z encodes de different gradient amplitudes used in the experiment.

Depending on the type of experiment, there are various formulae for Z in terms of the amplitude G of the applied gradient and one or more timing parameters such as Δ (time between two pulse gradients, related to echo time) and δ (gradient pulse width). In the original Tanner-Stejskal method using two rectangular gradient pulses, for example,

(2) Z =γ²G²δ²(Δ-δ/3)

Eq. (2) holds strictly for simple PFG-NMR experiments, and is modified slightly to accommodate more complicated pulse sequences.

In practice, a series of NMR diffusion spectra are acquired as a function of the gradient strength. For example, the figure below shows the results of a series of 1H-NMR diffusion experiments for a mixture containing caffeine, 2-Ethoxyethanol and water.

It can be observed that the intensities of the resonances follow an exponential decay. The slope of this decay is proportional to the diffusion coefficient according to equation (1). All signals corresponding to the same molecular species will decay at the same rate. For example, peaks corresponding to water decay faster than the peaks of caffeine and 2-Ethoxyethanol

The DOSY transformation

As far as data processing of raw PFG-NMR spectra is concerned, the goal is to transform the NxM data matrix S into an NxR matrix (2D DOSY spectrum) as follows:

The horizontal axis of the DOSY map D is identical to that of S and encodes the chemical shift of the nucleus observed (general 1H). The vertical dimension, however, encodes the diffusion constant D. This is termed Diffusion Ordered Spectroscopy (DOSY) NMR. In the ideal case of non-overlapping component lines and no chemical exchange, the 2D peaks align themselves along horizontal lines, each corresponding to one sample component (molecule).

The horizontal cut along such a line should show that component’s ‘normal’ spectrum. Vertical cuts show the diffusion peaks at positions defining the corresponding diffusion constants.

The mapping S=>D will be henceforth called the DOSY transformation. This transformation is, unfortunately, far from straightforward. Practical implementations include mono and biexponential fitting, Maximum Entropy, and multivariate methods such as DECRA.

Recently, Mathias Nilsson and Gareth A. Morris have proposed the so-called ‘Speedy Component Resolution’ (Anal. Chem., 2008, 80, 3777–3782) as an improved variation of the Component Resolved (CORE) method (J. Phys. Chem, 1996, 100, 8180). This is a multivariate-based method and the examples used in the article show an excellent performance of the algorithm.

Following a different approach, we have recently developed a brand new method for DOSY processing which has been included in Mnova. I will leave the details (and how to get the program to try it out) for the next post. In the meantime, should you be interested, just drop me a line.

Sensitivity Enhancement for free?

2008-07-01T13:43:00.000-07:00

In my previous post I discussed about NMR FID/spectra having two channels, the Real and Imaginary parts and that in general, only the Real part is displayed. In fact, we could use the term Stereo-FID in the same fashion as we use Stereo-Sound (remember that NMR spectra span audio frequencies).
If we think about these stereo signals as coming from two receiver coils in quadrature and assuming simultaneous detection, we could formulate the following scenario:

It’s a common practise to acquire several (hundred or thousand) FIDs which are then added together (signal averaging). Because NMR responses build up in proportion to the number of signals recorded, N, whilst the noise varies randomly from one measurement to the next and thus, adds up more slowly, as sqrt(N), there is an overall improvement in sensitivity of sqrt(N).
If the noise in the Real and Imaginary channels were totally independent, it should be possible to add to the Real channel the Imaginary channel (after a 90º phase shift to make it phase coherent with regard to the Real part) so that we could achieve a further improvement of sensitive of sqrt(2)!. Would this be possible? This will be the subject of this post.

Of course, this ‘trick’ would only work if the noise in the two channels were totally independent. In the NMR field it is assumed that the experimental noise is stationary and white (i.e. the correlation between two consecutive points is zero). But what about the correlation between the noise in the two different channels? Are they correlated? This is very easy to analyze experimentally with Mnova by writing a very simple script which calculates the Correlation Coefficient (Pearson). For example, consider the spectrum below. We could use this script to calculate the Pearson Correlation Coefficient using the points between 5000 & 10000 which is a signal free region

As shown in the figure below, the correlation coefficient between the noise in both channels is almost zero. You can repeat this operation with different spectra and you will arrive to similar results

So it appears as if the noise in both channels is statistically uncorrelated, something which should be intuitively expected as the 2 acquisition channels are orthogonal. Does this mean that the noise in both channels is independent?
We can make a very simple experiment: We could phase a spectrum in order to make the real part perfectly in phase and then change the phase of the imaginary part in such a way that the peaks in both channels become perfectly phase-coherent. Next, both channels can be added so that the signals will increase 2 fold. On the other hand, if the noise in both channels were phase-incoherent, it will increase more slowly and therefore the overall S/N should increase by sqrt(2).

We can carry out this experiment very easily by applying a 90º phase shift into the imaginary channel and then summing up both channels. This is done with the following script:

Before applying this script, we need to calculate the SNR of the original spectrum. We can use the central peak of the Chloroform multiplet as a reference peak to estimate the SNR as depicted in the figure below:

Next, we can apply the script above (sumReImPhased) to apply a 90º phase shift to the imaginary part followed by the addition of the imaginary channel to the real one. If the SNR of this new spectrum is calculated we get the following result:

We can appreciate that the Chloroform peak is now twice the height, but the standard deviation has also increased two-fold, so the SNR remains constant. What a disappointment!

Conclusions:

We have first found out that the noise in the Real and Imaginary channels is statistically uncorrelated. However, this does not mean that they are independent. Just as sin(x) and cos(x) functions are orthogonal "uncorrelated", but not independent (sin^2(x) = 1 – cos^2(x)).
And we have shown that noise in the Re and Im channels is certainly not independent: the SNR does not improve at all.
The essence is that if the spectrometer has just one coil (which is, to the best of my knowledge, always the case in spectroscopy), then the noise in the two orthogonal channels would not be independent and thus the sqrt(2) sensitivity enhancement is not possible. It will be necessary to have two separate coils (and two receivers) in quadrature to have uncorrelated real and imaginary noise. Why is this not possible? I don’t really know, most likely because of lack of space …

References:

Experimental Noise in Data Acquisition and Evaluation III. Exponential Multiplication, Discrete Sampling, and Truncation Effects in FT Spectroscopy. Dr. S. Sýkora.

Real NMR

2008-06-20T01:54:00.000-07:00

We often forget that NMR spectra are complex entities. By complex I don’t mean complicated or difficult to understand (which is, unfortunately, a very common thing too), but by the numbers in the complex space, that is, formed by real and imaginary numbers. One reason that can justify why NMR spectra are barely considered as formed by complex numbers is that NMR software, in general, only displays the real part. However, the imaginary part is present in the background (unless discarded e.g. to save memory) and it’s actually very important. The imaginary part makes it possible to correct the phase of the spectra in such a way that we can get nice absorptive lines (e.g. Lorentzian / Gaussian lines) which provide higher resolution than out-of-phase spectra (e.g. combination of absorptive and dispersive lines. See figure below).

NMR spectra, being of complex nature, can also be displayed in magnitude mode which makes the spectra phase insensitive. This can be advantageous in those cases in which phase correction is difficult, but at the expense of poorer resolution (though in the case of 13C NMR, magnitude mode can facilitate automatic processing, as I have blogged before). In addition, phase information can be very useful in some cases (e.g. DEPT, NOESY, edited NMR experiments, etc).

Acquisition of NMR spectra as complex numbers is also important (in addition to making phase correction possible) to distinguish positive from negative frequencies (quadrature detection. See this link for more information).

Mnova does not have a built-in function to show the imaginary part of the spectrum, but in the case you really need to see it, I will offer here two solutions:

1. One obvious way is by realizing that that the Re and Im channels differ by a phase shift of 90º. Thus, if we apply a (zero order) phase correction of +/-90º, the real part displayed in the software becomes analogous or equivalent to the imaginary counterpart.

2. There is a second alternative: it’s possible to write a very simple script which swaps the real with the imaginary part of the spectrum. This is the script:

function swapRI()
 
{
 
var w = new DocumentWindow(mainWindow.activeWindow());
 
//get active spectrum
 
var spectrum = nmr.activeSpectrum();
 
if (!spectrum.isValid() || spectrum.isReal)
 
return;
 
if (spectrum.dimCount > 1)
 
return; //1D only
 
var dCount = spectrum.dimCount;
 
var npts = spectrum.count(1);
 
//To print the value of one of the spectral points
 
for (var i=0; i<npts; i++)
 
{
 
var tmp = spectrum.real(i);
 
spectrum.setReal(i, spectrum.imag(i));
 
spectrum.setImag(i, tmp);
 
}
 
spectrum.update();
 
w.update();
 
}
 
}

Having said that NMR spectra are of complex nature and why this is important, then, how is it possible, from a hardware point of view, to get real and imaginary numbers? After all, NMR detectors are just measuring ‘real’ values (i.e. induced oscillating voltage in a resonant RF coil). When we say Re and Im numbers in this context, we could have said X and Y values, or u and v values, etc. What matters here is that we are using 2 (orthogonal) detectors to measure (generally simultaneously) the magnetization along X and Y axis. We know that the Re and Im components in the complex space are related by a phase angle of 90º, analogous to the X and Y axis. Thus, the values recorded by the detector placed along the X axis can be considered as the real part of the spectrum (or the cosine component), whereas the values measured in the detector placed in the Y axis will correspond to the imaginary part (or sine component) of the spectrum.

What I would like to highlight here is that the Re and Im, in principle, could appear as 2 INDEPENDENT physical measures, even though they are (generally) recorded simultaneously. In other words, the Re and Im channels are UNCORRELATED. However, this is not completely true. I have already mentioned that the dispersive and absorptive lines (corresponding to Real and Im components of a phased spectrum) are related by a phase shift of 90º. More strictly speaking, the Re and Im components are connected by the well known Kramers–Kronig relation being the Hilbert Transform the mathematical bridge connecting both components. This transform makes it possible to obtain the imaginary part from the real one and the other way round. How about the noise? Is the noise in the imaginary and real parts uncorrelated? In that case, theoretically, it should be possible to achieve a further sqrt(2) gain in sensitivity when quadrature detection is used. This issue will be the subject of my next post.

References
Quadrature versus linear detection, and where do complex MR data come from
Nothing is better

Automatic chemical shift calibration of 2D NMR spectra

2008-05-16T00:41:00.000-07:00

Accurate calibration of the chemical shift scales of NMR spectra is very important for both reproducibility and the correlation of the chemical shift with structural properties. Usually, this task is very easy in 1D NMR and in general, it is carried out graphically by simply selecting with the mouse cursor a reference signal (e.g. TMS or a residual solvent peak).

In the case of 2D NMR, this operation is more tedious as it has to be applied to both dimensions. In addition, the low digital resolution typically obtained in 2D NMR (nD in general) spectra makes calibration more sensitive to the actual position of the reference peak selected for referencing.

Wouldn’t it be possible to use the calibration information from the 1D spectra (where the digital resolution is usually >20 times higher than in a 2D spectrum) to automatically reference 2D spectra? In theory, this should be possible (at least with several 2D experiments), but I was surprised when I found that none of the NMR software applications I’m aware of incorporates such capability (if anyone knows a software with this feature, please let me know).

Most of the NMR software packages I know include facilities to manually align the 2D and 1D spectra, that is, to correlate signals of 2D and 1D spectra. However, I was interested in a fully automatic procedure to take advantage of the higher digital resolution of the 1D spectrum to calibrate the 2D spectrum.

After studying this issue in depth, we came out with a new algorithm which works exactly as I wanted: Once the 1D spectrum is properly referenced, the 2D spectrum is automatically calibrated with the information contained in the 1D spectrum.

As always, a picture is worth a thousand words. Consider the following 2D COSY spectrum:

And compare it with the corresponding high resolution 1H-NMR counterpart:

It can be observed that the chemical shift scales of both spectra differ by about 1.5 ppm. If the 1D spectrum is attached to the 2D COSY as an external projection, the result would look something like this:

Application of the newly developed autoalignment algorithm will yield the following result (please note that there is not need to enter any user-defined parameter: it's fully automatic):

The scales of the 2D spectrum have been calibrated by using the information contained in the high resolution 1H spectrum.

It’s important to mention that at present, this algorithm does not work with all 2D spectra. Basically, it works fine in those spectra in which internal projections are compatible, in terms of number of resonances, with the external 1D traces. This would be the case of 2D homonuclear experiments and the proton dimension of HSQC and related spectra, but it will not work in the 13C dimension in these experiments.

This new algorithm has been incorporated into the latest version of Mnova (Mnova 5.2.2). Should you be interested in testing it, just download Mnova and play with it. Any comments, suggestions, bug reports, etc, will be very welcome.

Metabonomics databases

2008-04-30T00:17:00.000-07:00

Having access to NMR databases of most common metabolites is very important if you’re interested or involved in NMR-based metabonomomics/metabolomics studies. Here are two good sites worth checking out:

For a more comprehensive review, see this article

13C Chemical Shift prediction: Typos and NMR misinterpretations

2008-03-26T04:58:00.000-07:00

It is well known that 13C Chemical Shifts are essential for structure verification and elucidation of organic molecules by NMR. For example, in the field of structure verification, one can compare the observed 13C chemical shifts with the calculated (predicted) values in such a way that the structure hypotheses can be assessed by means on some numerical matching factor.
What is less evident is the great potential that 13C chemical shift prediction has in order to reveal typos and misinterpretations of NMR data that often (much more than expected, I’m afraid) appear in the experimental sections of scientific literature.

Wolfgan Robien has recently created a very interesting Web page in which he shows how his famous CSEARCH program for 13C –NMR prediction can be used for automatic data-checking. According to his personal opinion, there are at least 3 scenarios in which such checks should be done:

Daily routine during generation and interpretation of NMR-data
Check again during preparation of a manuscript
Check again during the peer-reviewing process ('robot-referee')

Mnova is honoured to include Wolfgang Robien’s CSEARCH algorithm within its NMRPredict Desktop plugin and includes simple yet very useful verification tools which can be used to easily identify errors in 13C-NMR data assignments.

Basic Misinterpretations, Typos and other Sad Events in NMR-Spectroscopy

Wavelet-based filtering applied to the diagonal suppression of 2D NMR data sets

2008-02-25T13:40:00.000-08:00

Published in Stan's Library
Click here to read the full article
Permalink via DOI: 10.3247/SL2Nmr08.002

Why aren’t Bruker FIDs time corrected?

2008-02-22T09:07:00.000-08:00

Most of NMR has finally gone totally digital and is now routinely resorting to high-frequency ADC sampling at rates of several tens of MHz, with a tendency to ever higher sampling frequencies. Such a drastic oversampling has clear advantages in simplifying the front-end electronics. It has also many side benefits due to the fact that the subsequent down-conversion to low frequency range is done digitally and therefore theoretically artefact free. This includes perfect, calibration-free quadrature detection and drastic reduction of quantization noise. By the way, such techniques are routine in other areas of electronics (military, astronomy, audio, …); NMR is just a latecomer to this world.

High-frequency (HF) oversampling, however, has also some problems of its own. The digital decimation from the HF range to the audio range and the contextual digital filtering (a combination of CIC and FIR filters) need to be properly implemented in the hardware in order to be completely transparent to the User.

However, in the case of Bruker spectra a death time or group delay can be observed in the FID: it starts with very small values and then, after some points (usually between 60-80 points) the normal FID starts.

If a plain FT is applied to this FID, we will get a spectrum with a lot of wiggles in the baseline analogous to the convolution with a sinc function centred in the middle of the spectral window. This can be explained by recalling the time shift theorem of the Fourier Transform which says that if the time domain signal is shifted by n points, the frequency domain spectrum corresponds to the standard spectrum (when the FID has not been shifted) multiplied by exp(-i2*pi*w*n). In other words, we have introduced a very large first order phase correction in the spectrum. For example, if the FID is right shifted by 60 points (death time = 60 points), f-spectrum will exhibit a first order phase distortion of 60 * 360 = 21600 degrees.

In order to work around this problem, most NMR software packages read the decimation factor (and the DSP firmware version) from Bruker files and calculate the required phase correction. So far, so good.
However, the fact remains that Bruker FID’s are not time corrected. Evidently, Varian also uses oversampling and digital filtering and their FIDs are time corrected, that is, they start at time = 0. If the digital filter is known in advance, which is always the case, the group delay should be compensated in the spectrometer, therefore, in my opinion, this death time or group delay is a bug in the spectrometer. For this reason, and going back to the title of this article, any input given as to why Bruker FID’s are not time corrected, would be greatly appreciated.

Mspin and Diasterotopic 1H NMR Assignment using 3J and RDCs

2008-01-22T02:39:00.001-08:00

Scalar coupling constants, in particular vicinal (3J) couplings, are widely used in NMR for the determination of relative stereochemistry and preferred conformation of molecules. A number of different empiric equations to correlate the dihedral angle with the 3J values have been proposed, the Karplus equation being the most famous. The NOE (nuclear Overhauser effect) experiment is also extensively used, primarily, to define the stereochemistry within a molecule. Unlike scalar couplings, its mode of operation relies on the direct, through-space interaction between nuclei, and is independent of the presence of through-bond couplings.

However, both NOE and scalar coupling have limitations for measuring the structure information between atoms which are far apart. In addition, there are cases in which the 3J or NOE values of different stereoisomeric compounds are very similar so unambiguous assignment is not possible.

On the other hand, residual dipolar coupling (RDC) is able to provide global orientations between remote internuclear vectors, and thus gives a potential solution to these limitations. RDC’s have been widely used for the analysis of proteins and nucleic acids, but to a lesser extent in the small molecules area. Roberto Gil et al. have just published an article in which they propose the use of PMMA as a novel alignment media and discuss in a very nice way the unambiguous stereochemistry and assignment determination of the diastereotopic protons of Ludartin.

Stretched Poly(methyl methacrylate) Gel Aligns Small Organic Molecules in Chloroform. Stereochemical Analysis and Diastereotopic Proton NMR Assignment in Ludartin Using Residual Dipolar Couplings and 3J Coupling Constant Analysis
Gil, R. R.; Gayathri, C.; Tsarevsky, N. V.; Matyjaszewski, K.
J. Org. Chem.; (Article); 2008; ASAP Article; DOI: 10.1021/jo701871g

Roberto Gil and collaborators have used Mspin to calculate RDCs and 3J coupling constants for Ludartin. Below is an excerpt from the original article:

[...] The Mspin package includes modules for the calculations of 3J coupling constants, RDCs, and NOEs from 3D structures. Its usage is straightforward, and it can run on multiple platforms. For non-NMR experts, solving the structure using RDCs would be no longer a difficult task

Should you be involved in NMR structure elucidation, I believe you will find Mspin a very valuable tool, and we would very much appreciate your feedback on this application, which is currently in alpha version. It is available for download from here.

Induced Coupling & Chirality

2008-01-14T01:37:00.000-08:00

As a sequel to my last entry, I’m glad to post here a letter from my colleague and friend Stan Sykora about induced chilarity and coupling.

_______________________________________

Dear Carlos,
I wonder whether you could put this as an entry on your blog. Originally, it ought to be a comment on your last entry, but then it grew …

Concerning the chains of CH2 groups with convergent chemical shifts, I would like to point out another mechanism which has similar NMR consequences and leads inevitably to strong couplings even at the highest fields (present and future):

Consider a chain of the -(CH2)n-R attached to a chiral carbon:

(S1S2S3)C-CHaHb-R
(S1S2S3)C-CHaHb-CHcHd-R
(S1S2S3)C-CHaHb-CHcHd-CHeHf-R

etc.,

with the substituents S1,S2 and S3 all distinct. The chirality of the first carbon is explicit, so I will say that it is first-order. Now, when R is not a proton, Ha and Hb have different chemical shifts. But this means that the two protons are not equivalent and therefore the second carbon is also chiral (let us call this the induced chirality of second-order). Which means that the protons Hc and Hd in the second formula are also chemically distinct, etc. This logic carries on iteratively, leading to induced chiralities of ever higher orders.

Naturally, the chemical shifts Ha-Hb, Hc-Hd, He-Hf, etc. decrease rapidly with induced chirality order, while their geminal couplings stay more or less fixed at about -20 Hz (geminal J's are always negative and quite large). Consequently, even in a relatively short chain of methylenes attached to a chiral carbon, the protons in the first one will be non-equivalent and well resolved (maybe even first order), but the shifts of the protons in the subsequent methylenes will be much closer (hence leading to strong coupling patterns), and finally each CH2 will approximate an equivalent A2 spin group. Again, moving to a higher field may help a bit, but not too much - at best it might push up by one the limit of induced chirality treatable by first-order approach.

This also brings to my mind another problem: the predictions of the chemical shifts due to the above cases of chirality. I have noticed that the Modgraph and ACD softwares both do some physically funny things there, so I do not trust them. ACD apparently just drops-in a fixed value (like 0.01 ppm) every time there is any chance of induced chirality, while Modgraph, more appropriately, makes the shifts 0 whenever they don't know better. Since I have a cute idea about what could/should be done, could you tell me (or ask an expert like Erno Pretsch) what is the current state-of-the art on this point? As often happens with my cute ideas, it might be well known since 50 years (in which case, I will keep my mouth shut). But if it is not, it might be a thesis assignment for a student.

BTW, I wonder whether the adjective "induced" might not be more proper also in the context of virtual coupling you were writing about in your last entry. Maybe "induced coupling" would be a bit less controversial. Though I am not sure. You could propose it for an e-poll.
Ciao, Stan

1H NMR Analysis: Common Myths and Misconceptions

2008-01-11T07:34:00.000-08:00

The analysis of NMR spectra, in particular 1H-NMR, is certainly an exciting and challenging area of research and considerable effort has been made in the past 50 years or so to overcome many of the difficulties that this analysis faces. Actually, most of the work on this subject was done in the early 50’s and computer programs for the analysis of complex spin systems appeared in the 60’s and 70’s (see for example, references [1-4]). However, even though the analysis of 1H NMR spectra is for sure one of the most frequent tasks carried out by chemists, almost on a daily basis, I have found that there are several very popular misconceptions and fallacies amongst chemists which I would like to bring to your attention. In fact, some of these incorrect explanations can be found in books and articles. By doing this, I could run into the risk of introducing some inaccuracies in my comments (which is very likely). I’d like to take advantage of the interactive nature of this blog so, if you see any errors, please, just post them as a comment below.

This post will be somewhat lengthy, I tried to cover these points with all the detail I could think of, including illustrative figures and potential pitfalls, so grab your favourite caffeinated drink before you start reading!

Myth #1 All NMR signals are symmetric

When a chemist is first introduced into 1H NMR analysis, he/she is trained with the basis of the simple and well known first order multiplet patterns which, by definition, are always symmetric. It would be nice if all multiplets would behave following these simple rules. However, lines in any real-life spectrum are highly composite (more on this below), so no experimental line is "pure"; generally, experimental lines are a superposition of a large number of transitions. For example, let’s take the very simple case of the NMR spectrum of ethanol at 500 MHz:

The multiplets in this synthetic spectrum show indeed a large degree of symmetry and, in principle, as expected from the first order rules, we observe 4 lines for the CH2 group (triplet) and 3 lines for the CH3 group (assuming that coupling with OH does not occur).
This is certainly what one would observe in a modern high field spectrometer, but the truth is that there are 12 distinct main transitions in the CH2 group and 13 in the CH3 group, but all of them are never resolved. However, this more complex than expected structure of the CH3 and CH2 groups can be appreciated if the spectrum is recorded at lower field as illustrated in the CW experimental spectrum (from reference [2]).

This does not mean that all the 12+13 transitions only exist at low field. It’s just that the distance between the different transitions depends on the magnetic field in such a way that at higher fields they are too close to be observed and several transitions often contribute to the same peak. For example, in the following two figures, all these transitions are displayed as sticks superimposed on the observed multiplets which, apparently, look like a first order quadruplet and triplet respectively. As you can see, the inner structure is much more complex.

By the way, do not take too lightly the powerful capability of Mnova to classify and display graphically all the transitions corresponding to a given nucleus. If only first order rules were used, this would be a trivial task, however, when a rigorous quantum mechanics treatment is carried out to calculate all the transitions, this classification is far from being trivial. Combination lines, that is, transitions which correspond to the simultaneous change of spin of several nuclei, are particularly challenging on this classification system. They are forbidden in the first order limit but will have a small, non-zero intensity in the general case. These lines, when their intensity is large enough, are also taken into account in the classification system of Mnova. To the best of my knowledge, this capability is available in Mnova only, but if you know any other application which allows you to select one proton with the mouse and display the entire individual transitions corresponding to that nucleus (and the other way round, that is, selecting one transition in the spectrum and highlighting the nucleus causing such transition), please let me know.

Well, you may argue that even though the fine structure of the ethanol spectrum is somewhat complex, the truth is that the multiplets look symmetric and first order compliant (please note however that even in the simulated 500 MHz spectrum, the multiplets are STILL not symmetric, look at the sticks: The asymmetry is about 15% which is not little!) . But let us take, as a new example, a spectrum comprising an ABX spin system (as per Pople notation) with the couplings depicted in this figure:

In this spectrum we can observe the expected doublet for the X nucleus as a result of its coupling with B. However, if the chemical shift difference between A and B is reduced, the splitting pattern will become more complex. For example let’s now take a look at the same spin system when |A-B| = 15 Hz.

Interestingly, the X nucleus appears as a double doublet (disregarding the two small combination lines) even though it’s only coupled to nucleus B (JAX = 0). This kind of situation, where a nucleus appears to be coupled to another nucleus, even though the actual coupling constant is zero, is called Virtual Coupling. In general, if one nucleus is coupled to another nucleus which forms part of a strongly coupled group, the former nucleus will behave as if it were coupled to all the members of the spin system.
Do you still believe that 1H NMR spectra are always symmetric? Let’s make the chemical shift difference between A and B even smaller (5 Hz).

Clearly, an analysis of the X nucleus based on first order rules will yield incorrect values for the coupling constants. Obviously, the AB spin system can only by interpreted by means of a rigorous quantum mechanics treatment. From a symmetry standpoint, the X nucleus is symmetric (which could mislead one to assume it is a first order multiplet) but the AB multiplet is not.
Typical examples of ABX systems are pro-R and pro-S protons of methylenes in pro-chiral molecules.

So as a conclusion, in general multiplets are never really perfectly symmetrical, even disregarding the fact that they often overlap. In addition, relaxation effects in coupled systems are nontrivial and affect each transition in a different way, and there are often other effects such as exchange processes, co-presence of isomeric forms, impurities, etc.

Myth #2 High magnetic fields make the analysis of 1H NMR spectra by means of first order rules possible

Well, this is not completely wrong as it’s true that by increasing the spectrometer frequency, most of the 1H spin systems may become suitable for First-Order Analysis at least as a rough or grosso modo approach. For example, if we were to go back to the previous ABX spin system, and increase the magnetic field, the chemical shifts between A and B will become larger in such a way that we can arrive to a point in which the 3 individual multiplets can be perfectly handled with simple first order rules (see figure below).

However, there are many situations in which higher magnetic fields will be of little or no help. Let me present just a couple of examples:

Saturated fatty acids
AA’BB’ spin system

Consider the 1H NMR spectra of fatty acids with long saturated chains. In the figure below I have simulated the 1H NMR spectra of 3 fatty acids of different lengths. The first thing to notice is that the CH3 does not appear as a simple triplet. This is because it is (weakly) coupled to a CH2 group which is strongly coupled to the next CH2 group in the chain, leading the CH3 resonance to show virtual coupling with the CH2 protons in the chain. Even at higher fields, the pack of CH2 groups is very strongly coupled, though such higher fields may make it possible to resolve the resonances of some of the CH2 groups. However, as the number of methylene groups increases, the "newly resolved" methylenes will have quite small relative chemical shifts and they will always couple to their neighbors by J's of the same order of magnitude. So, whilst the CH2s at the extremes of the chain become 1st order when increasing the magnetic field, there are always others which are strongly coupled, and still others which are insufficiently resolved.

Another, more striking example, occurs in spin systems of the type AA’XX’ (or AA’BB’ if the chemical shifts are close) as is the case, for example, in spectra of o-dichlorobenzene (ODCB). This compound is often used to calibrate instrument resolution.
In an AA’BB’/AA’XX’ system there are 2 pairs of magnetically non-equivalent protons with the same chemical shift, that is, they are chemically equivalent. In general, when groups of chemically equivalent nuclei exist, second order effects are expected. As the chemical shift difference separating the nuclei in the molecule is always zero because of the symmetry, second order phenomena will always exist regardless of the magnetic field applied. If the magnetic field is increased, it will be possible to get a larger chemical shift difference between the AA’ and the BB’ groups, but not between A and A’ or B and B’, so that the highest simplification one can achieve by increasing the magnetic field is to move from an AA’BB’ group to an AA’XX’ group which is a second order spin system too.
There are a total of 12 transitions for each spin (the AA’ part or the BB’ part).
As an example, the figure below depicts the spectrum of ODCB at two magnetic field strengths, 60 MHz and 400 MHz.. At 60 MHz the inner lines are more intense than the outer lines and there is an evident lack of symmetry. These peculiarities are easily recognizable as second order effects and they are caused by the small chemical shift difference between AA’ and BB’. If the spectrometer field strength is increased (e.g. 400 MHz), these effects are reduced as the chemical shift difference between the two groups is now larger and we can now see two more symmetric multiplets. However, each multiplet does not follow the first order rules (e.g. they are not simple doublets of doublets of doublets) because A and A’ and B and B’ will always be strongly coupled regardless of the magnetic field strength. Once again, the only way to accurately analyze these systems is by means of quantum mechanics calculations.

Myth #3 Protons within a CH3 group do not couple with each other

I have found very frequently that chemists assume that CH3 protons are not coupled because only a singlet is observed in the spectrum. This is simply not true! The correct explanation is that couplings within a magnetically equivalent group such as a methyl group do not affect the spectrum appearance, but coupling definitely exists (it is known that geminal couplings are usually large and negative). In other words, if we synthesize a spectrum with and without couplings within a magnetically equivalent group, the spectrum will look exactly the same, so for calculation purposes, these couplings can be neglected.

That is all for now I hope you find these comments of some use and/or interest and if there are any points where I have failed to make myself dear, please do not hesitate to post a comment here. I’d also like to thank Stan Sykora for several useful discussion about this work.

References

[1] Pople J.A., Schneider W.G., Bernstein H.J., High-resolution Nuclear Magnetic Resonance, McGraw-Hill, New York 1959
[2] Roberts J.D., Nuclear Magnetic Resonance: Applications to Organic Chemistry, McGraw-Hill, New York 1959
[3] Early History of Nuclear Magnetic Resonance
[4] Automatic Analysis of NMR Spectra: An Alternative Approach Diehl P., Sykora S., Vogt J., J.Magn.Reson. 19, 67-82 (1975) [click here]

Proctor, Yu and Dickinson

2008-01-03T12:13:00.000-08:00

NMR is by far the most powerful and widely used tool for the determination of organic structures by chemists. Of the wealth of information that this technique provides, the chemical shift is what makes NMR so attractive to chemists as it allows them to distinguish among the different protons within a molecule.

However, despite the fact that chemical shift is what makes NMR useful in chemistry, I’m amazed about how little is known in the chemistry community about their discoverers. I have run a quick survey among 10 chemists colleagues of mine and none of them was able to cite one single name! Maybe the words of M.E. Packard had a higher impact than what he expected when he said "chemists got the point very
quickly, thanked the physicists, and took over"
I think that all chemists are in debt with the pioneering work carried out by W.G.Proctor, F.C.Yu and W.C.Dickinson and I would like to take advantage of my blog to give more recognition to these scientists. Now that we live in a world in which self-promotion and ‘rock star’ popularity are so valued, I find it necessary to acknowledge the value of what they have contributed to humankind in such a quiet way.
For a recent, worth reading, post about Chemical Shift and W. G. Proctor, do not miss Stan’s blog and Reminiscences of the Early Days of Nuclear Magnetic Resonance at Stanford University

Glenn Facey’s blog

2007-12-18T02:58:00.000-08:00

In case you’re interested in experimental aspects of NMR, do not miss Glenn Facey’s blog at University of Ottawa. Whether you are an NMR facility manager or a scientist using NMR routinely, I’m sure you will find it a very useful resource.

http://u-of-o-nmr-facility.blogspot.com/

Introducing 2D Resolution Booster ™ (RB)

2007-12-14T05:00:00.000-08:00

In recent entries I presented Resolution Booster as a simple but robust method to obtain highly resolved NMR spectra and showed some of its properties. Today I want to show the preliminary results we are getting by applying an extension of this method to 2D NMR spectra.

In order to illustrate the performance of the algorithm I have simulated a 2D spectrum of an A2B3 spin system with the following parameters:

Spectrometer Frequency = 500 MHz
Shift A = 4 ppm (2000 Hz)
Shift B = 8 ppm (4000 Hz)
JAB = 30 Hz
Line Width = 30 Hz
Data points = 2048 x 2048

As the coupling constant is very close to the line width (they are actually exactly the same, 30 Hz), the multiplets are not resolved (2D spectrum at the left). After applying 2D RB, the spectrum achieved has a higher resolution along both dimensions, where all multiplets are now clearly well resolved.

We are still working on this method but the results we are currently getting are certainly very promising and we are confident that it will soon become a very valuable tool for automated 2D NMR processing. It is not available in the current version of Mnova but it will be included in the new release scheduled for the end of January 2008. Together with my friend Stan Sykora, we will be presenting a poster on RB in ENC 2008 at Asilomar. Should you be attending ENC, please stop by to see us. We will be delighted to discuss this (or any other) topic with you.