Sunday, 2 November 2008

Indirect Covariance NMR – Fast Square Rooting

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.


old swan said...

This application is much more intriguing that the first one you showed (the homo-nuclear case, I mean). Unfortunately the link to the PDF article is broken... If the article is not available on the net, it may be useful to publish the literature reference. What's the first version of Mnova that includes your new algorithm?
Great work!

Carlos Cobas said...

This is the original reference:

J. Am. Chem. Soc., 126 (41), 13180 -13181, 2004

The first version of Mnova which includes this algorithm is still in alpha stage (we plan to release an official version by the end of this monty). Should you want to try it out, just drop me a line and I will send it to you

Carlos Cobas said...

BTW, the broken link on Indirect Covariance has now beeen corrected

ChemSpiderMan said...

In terms of indirect covariance NMR you might want to look at the work of Gary Martin from Schering Plough. He led the development of indirect covariance applications and has over a dozen publications out already. He did the work with myself and Kirill Blinov from ACD/Labs. A search on indirect covariance on Google will point you to a pile of resources.

Gary said...

First, anyone using indirect covariance processing to calculate 13C-13C correlation spectra should be aware of the propensity of this method to generate two types of artifact responses. They are mentioned only in a footnote by Bruschweiler and co-workers in the 2004 JACS communication. Artifacts in indirect covariance processed GHSQC-TOCSY spectra have been analyzed in the work that we've published.

It is also possible to forecast where those artifacts will be observed by calculated by covariance processing of GHSQC data. This work has also been published.

Readers of this blog may also want to take a look at the work that we've done in the development of unsymmetrical indirect covariance processing, which allows a spectroscopist to calculate spectra such as GHSQC-COSY from the component COSY and GHSQC spectra:

Blinov KA, Larin NI, Williams AJ, Mills KA, Martin GE. J.
Heterocycl. Chem. 2006; 43: 163

or a 13C-15N long-range correlation spectrum from 1H-13C GHSQC and a long-range 1H-15N GHMBC specta.

In my opinion at least, unsymmetrical indirect covariance processing capabilities are far more interesting and potentially useful than simply indirect covariance processing itself. There are a myriad of potential applications of unsymmetrical indirect covariance processing, e.g. the calculation of HSQC-NOESY spectra, etc.