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Rapid Communication
Received: 9 January 2008 Revised: 23 April 2008 Accepted: 25 April 2008 Published online in Wiley Interscience: 17 September 2008
(www.interscience.com) DOI 10.1002/mrc.2260
Multistep correlations via covariance
processing of COSY/GCOSY
spectra: opportunities and artifacts
Gary E. Martin,a∗ Bruce D. Hilton,a Kirill A. Blinovb and Antony J. Williamsc
Long-range homonuclear coupling pathways can be observed in COSY or GCOSY spectra by the acquisition of spectra with
larger numbers of increments of the evolution period, t1, than would normally be used. Alternatively, covariance processing of
COSY-type spectra acquired with modest numbers of t1 increments, allows the observation of multistage correlations. In this
work results obtained from covariance-processed GCOSY spectra are fully analyzed and compared to normally processed COSY
and 80 ms TOCSY spectra. Multistage or ‘RCOSY-type’ correlations are observed when remote protons both exhibit correlations
to the same coupling partner e.g. A→ B and B→ C gives rise to an A→ C correlation. In the strict sense, RCOSY-type responses
are artifacts albeit providing useful information. Nonbeneficial artifact correlations are observed when protons couple to other
protons that overlap or partially overlap. The origin of artifact responses is also analyzed. Copyright c© 2008 John Wiley & Sons,
Ltd.
Keywords: covariance processing; RCOSY-type responses; artifact; COSY; GCOSY
We have recently reported the use of unsymmetrical indirect
covariance NMR-processing methods to provide convenient ac-
cess to hyphenated 2D NMR correlation data[1 – 3] and access to
experimentally inaccessible 13C–15N heteronuclear shift correla-
tion plots.[4 – 7] It is important to recall, however, that covariance
NMR-processing methods can also be advantageously applied
to individual 2D NMR spectra.[8,9] Bru¨schweiler et al. have demon-
strated the acquisition of 2D NMR spectra with minimal datasets[10]
as well as the use of covariance processing methods with
TOCSY spectra to extract individual component spectra from a
mixture.[11,12] We now report the application of covariance NMR-
processing methods to observe multistep long-range correlations
in COSY spectra acquired with modest numbers of increments of
the evolution period, t1. Generally, the observation of small, long-
range homonuclear couplings in a COSY spectrum requires either
the acquisition of a spectrum with large numbers of increments
of the evolution period or by delaying the start of the evolution
period. Covariance processing of COSY or GCOSY spectra with
more modest numbers of increments of the evolution period,
t1, however, provides spectra with resolution in both dimensions
defined by the resolution in the directly acquired F2 frequency
domain.[13] In those cases where remote protons are both coupled
to a common partner, multistep or RCOSY-type correlations are
observed linking the remote protons, e.g. A → B and B → C
giving rise to an A → C correlation. In the strict sense, RCOSY-type
responses are artifacts, albeit useful. When protons of different
spin systems are coupled to resonances with overlapping proton
multiplets, undesired artifact responses can also be observed, al-
though this facet of covariance processing has not been discussed
in the previous reports of Bru¨schweiler et al.[11,12]
Covariance processing of a 2D FT NMR spectrum represented by
the real N1 ×N2 matrix, F, affords a symmetric matrix, C, according
to Eqn (1):
C = FTF (1)
1
14
13
12
8
N
11
15
16
N
17
18
20
O
H
H
H
22
23
O
H
H
where the FT refers to the transposed matrix. It should also be
noted that the resolution in both dimensions is determined by the
resolution of matrix F in the F2 dimension[8,13] Thus, subjecting
the GCOSY spectrum of strychnine (1) shown in Fig. 1(A) (1 K
number of points in F2 after the first FT; 128 increments of t1 linear
predicted to 256 points and then zero-filled to 1 K points prior to
the second FT processing step) to covariance processing affords
the result shown in Fig. 1(B).[16] Even by casual comparison of the
two contour plots it is obvious that there is improved resolution in
the F1 frequency domain as well as a significant difference in the
∗ Correspondence to: Gary E. Martin, Rapid Structure Characterization Labora-
tory, Pharmaceutical Sciences, Schering-Plough Research Institute, Summit, NJ
07901, USA. E-mail: lighthouse@gmail.com
a Rapid Structure Characterization Laboratory, Pharmaceutical Sciences,
Schering-Plough Research Institute, Summit, NJ 07901, USA
b Advanced Chemistry Development, Moscow Department, Moscow 117 513,
Russian Federation, Russia
c ChemZoo, Inc., Wake Forest, NC 27587, USA
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G. E. Martin et al.
A
B
Figure 1. (A) GCOSY spectrum of a 2 mg sample of strychnine dissolved in ∼200 µl CDCl3 recorded as 128 × 2 K points in approximately 30 min.[14] The
data were linear predicted to 256 points and zero-filled to 1 K points in F1 prior to the second Fourier transform. (B) Result obtained from covariance
processing of the GCOSY spectrum shown in (A). Comparison of the two spectra reveals that there are considerably more responses contained in
the covariance-processed spectrum. Analysis of the covariance-processed spectrum reveals numerous multistep correlation responses (black-boxed
responses) as well as a similar number of undesired artifact responses (grey-boxed responses) that arise due to resonance overlap. Responses with no
labeling correspond to responses that would normally appear in the GCOSY spectrum.
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RCOSY-type responses from covariance-processed COSY/GCOSY spectra
Figure 2. (A) 1H reference spectrum of strychnine recorded at 600 MHz. (B) F1 slice taken through the GCOSY spectrum shown in Fig. 1(A) at the 1H shift
of the H15a resonance. (C) F1 slice taken through the GCOSY spectrum shown in Fig. 1(A) at the 1H shift of H12. As will be noted from the black-hatched
boxed region, both the H15a and H12 resonances have H14 as a common coupling partner. This commonality in their coupling pathways gives rise to
the multistep or RCOSY-type correlation response between H15a and H12 (A → C) that is observed in the H15a F1 slice from the covariance-processed
spectrum shown in Fig. 1(B). (D) F1 slice at the 1H shift of H15a in the covariance-processed spectrum shown in Fig. 1(B). The artifact response is labeled
in red and boxed; the multistep correlation response is black-boxed; normal COSY correlation responses are labeled in black.
information content after covariance processing relative to the
conventionally processed COSY spectrum. The threshold levels of
both plots are identical.
There are numerous responses identified by black or red boxes
in Fig. 1(B). These responses are two types of ‘artifacts’ from
the covariance processing to which the data were subjected.
The analysis of the responses in the covariance-processed data
warrants comment. Superposition of the COSY and the covariance-
processed spectrum allows the facile determination of which are
new responses based on the absence of overlap in the two
spectra. Once a given response has been identified as ‘new’ in
the covariance-processed data, F1 slices can be extracted from the
conventional GCOSY spectra at the 1H shifts of the two resonances
involved. For example, the covariance-processed spectrum has
a prominent response at the chemical shift of H12 (4.26 ppm)
when the F1 slice at the 1H shift of H15a (2.36 ppm) is examined.
The 600 MHz 1H reference spectrum is shown in Fig. 2(A). The
extracted F1 slices from the conventionally processed GCOSY
spectrum at the 1H chemical shifts of H15a and H12 are shown
as traces B and C, respectively, in Fig. 2. The F1 slice from the
covariance-processed GCOSY spectrum at the 1H shift of H15a is
shown in trace D. Multistep (RCOSY-type) responses are denoted
with black-boxed assignments; artifact responses are denoted
by red-boxed assignments. Note that both resonances have a
common coupling partner in H14 (black-hatched box) in traces
B and C. The common coupling partner in this case gives rise
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G. E. Martin et al.
Figure 3. (A) 1H reference spectrum of strychnine recorded at 600 MHz. (B) F1 slice taken through the COSY spectrum shown in Fig. 1(A) at the 1H shift of
the H18b resonance. (C) F1 slice taken through the COSY spectrum shown in Fig. 1(A) at the 1H shift of H13. As will be noted from the grey hatched boxed
region, the H18b resonance has a correlation to H18a and H13 shows a correlation to the H11a resonance. The responses to H18a and H11a are partially
overlapped, which gives rise to the artifact response to H18b at the 1H chemical shift of H13 in the covariance-processed spectrum shown in Fig. 1(B).
(D) F1 slice at the 1H shift of H13 in the covariance-processed spectrum shown in Fig. 1(B). Artifact responses are labeled in grey and boxed; multistep or
RCOSY-type correlation responses (A → C) are black boxed; normal COSY responses are labeled in black.
to the response at the H12 chemical shift affording a multistep
correlation or RCOSY-type response in the covariance-processed
spectrum shown in Fig. 1(B) (black-boxed response) and trace 2D.
All of the black-boxed responses shown in Fig. 1(B) correspond to
multistep correlation responses that arise when the two protons
in question have a common coupling partner in the conventional
COSY or GCOSY spectrum.
In contrast, other types of response overlap during covariance
processing are nonbeneficial giving rise to the artifact responses
that are boxed in red. As an example, the H13 resonance (1.27 ppm)
exhibits a cross-peak at the 1H chemical shift of the H18b resonance
(2.86 ppm). Once again extractingF1 slices from the conventionally
processed COSY spectrum affords the traces shown in panels B
and C, respectively, in Fig. 3. In this case, there is a partial overlap of
the H18a and H11a resonances in the two traces. The H18a/H11a
overlap leads to the artifact correlation observed at the 1 H chemical
shift of H18b in the F1 slice corresponding to H13 shown in trace
D. In similar fashion, other responses shown in Fig. 1(B) that are
boxed in red have been identified as artifact responses.
While some of the unsymmetrical indirect covariance-processed
spectra studied thus far are amenable to artifact identification via
algorithmic analysis through the use of covariance spectra of one
of the co-processed spectra[7,14] or by other methods[15] at present
this is not possible for covariance-processed COSY spectra. We are
exploring the possibility of algorithmic artifact identification for
COSY-type spectra but these efforts have thus far not yielded a
viable method.
Figure 4 shows extracted F2 slices for the H13 resonances from
the conventionally processed GCOSY spectra with the number
of increments in the second frequency domain set to 128 and
1024 in traces 4A and 4B, respectively. The corresponding F2
slice of the covariance-processed spectrum shown in Fig. 1(B) is
presented as trace 4C; the corresponding trace from a TOCSY
spectrum acquired with an 80 ms mixing time is shown in
trace 4D; and finally, a segment of the 600 MHz high resolution
reference spectrum of strychnine is shown in trace 4E. All of
the correlations observed in the conventionally processed COSY
spectrum are observed following covariance processing as well as
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RCOSY-type responses from covariance-processed COSY/GCOSY spectra
Figure 4. (A) F2 slice taken at the 1H shift of the H13 resonance from the conventionally processed GCOSY spectrum of strychnine (1) shown in Fig. 1(A).
(B) F2 slice taken at the 1H shift of the H13 resonance of a GCOSY spectrum (not shown) acquired with 1024 increments of the evolution time, t1. (C) F2
slice taken at the 1H shift of the H13 resonance from the covariance-processed GCOSY spectrum shown in Fig. 1(B). (D) F2 slice taken at the 1H shift of the
H13 resonance of a ZTOCSY spectrum (not shown) of strychnine (1) acquired with an 80 ms mixing time. (E) Segment of the 600 MHz reference spectrum
of strychnine shown for comparison.
Magn. Reson. Chem. 2008, 46, 997–1002 Copyright c© 2008 John Wiley & Sons, Ltd. www.interscience.wiley.com/journal/mrc

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G. E. Martin et al.
several multistep correlation responses that are not observed in
the conventionally processed spectrum. Several undesired artifact
responses are also observed (trace 4C response labels boxed in red).
Multistep correlations observed in the covariance-processed data
compare favorably with the correlations observed in the F1 slice
taken from the TOCSY spectrum acquired with an 80 ms mixing
time and shown in trace 4D except that most of the correlation
responses in the F1 trace from the covariance-processed data are
observed with higher response intensity than the corresponding
responses in the trace from the ZTOCSY spectrum.
Covariance processing of COSY or GCOSY spectra affords
access to multistep or RCOSY-type correlations as illustrated using
strychnine (1) as a model compound (Scheme 1).
The covariance processing algorithm, unfortunately, can also
give rise to artifact responses as illustrated and discussed with
reference to Figs 2 and 3 when protons are coupled to remote
protons with overlapping responses. While covariance processing
of a COSY or GCOSY spectrum will not replace the acquisition
of long-range homonuclear correlation spectra, this approach can
provide access to multistep or RCOSY-type correlation responses if
care is taken to ascertain, as shown in Figs 2 and 3, that the observed
responses are not artifacts arising due to unfortuitous overlap.
When both COSY and TOCSY spectra are available, covariance
processing of the former provides the means of ascertaining
the validity of weak responses in the latter. We are working to
develop an algorithmic method to identify artifact responses that
would make the process less subject to human bias. Hopefully a
method for the algorithmic identification of artifact responses will
make covariance processing of COSY and GCOSY spectra a more
useful means of accessing multistep or RCOSY-type correlation
information.
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[16] All NMR data shown were recorded using a sample of 2 mg
of strychnine dissolved in ∼200 µLCDCl3 (Cambridge Isotope
Laboratories) in a 3 mm NMR tube (Wilmad). Data were acquired
using a Varian three channel NMR spectrometer operating at a
1H observation frequency of 599.75 MHz and equipped with a
5 mm cold probe operating at an rf coil temperature of 20 K. The
sample temperature was regulated at 26 ◦C. GCOSY data for the
spectrum shown in Fig. 1A were acquired as 128 × 2K points
with 16 transients/t1 increment in 30 min to insure a completely
flat noise floor in the 2D spectrum. The data were processed by
linear prediction to 256 points and zero-filling to 1 K points prior
to the second Fourier transform. The GCOSY spectrum acquired
with 1024 increments of the evolution period that provided trace
B in Fig. 4 was acquired with 16 transients/t1 increment in 6 h. The
80 ms zTOCSY data used for comparison purposes were acquired as
512 × 2K points with 16 transients/t1 increment in 3 h. The zTOCSY
data were processed by linear prediction in the second frequency
domain to 1024 points prior to Fourier transformation.
www.interscience.wiley.com/journal/mrc Copyright c© 2008 John Wiley & Sons, Ltd. Magn. Reson. Chem. 2008, 46, 997–1002