Structural assignment of 2,6- and 2,7-disubstituted naphthalenes and prediction of 13C nuclear magnetic resonance chemical shifts: Applications of topology and two-dimensional NMR spectroscopy

Article abstract of DOI:10.1016/S0960-894X(02)00556-5

Unambiguous assignments of monocarboxymethylnapthalenes isolated as oxidation products of dimethylnaphthalenes by Pseudomonas putida, a bacterial strain, were made using two-dimensional nuclear Overhauser enhancement correlation spectroscopy (NOESEY). The two-dimensional long-range heteronuclear correlation NMR technique was also utilized for the assignment of quaternary carbons in the naphthalene system. In addition, we describe methods for prediction of ¹³C NMR chemical shifts of 2,6- and 2,7-disubstituted naphthalenes using topological approach. The method involves computation of molecular descriptors from topological representation of molecule, namely Wiener (W) and Szeged (Sz) indices. The results have shown that W and Sz indices can be successfully used for predicting ¹³C NMR chemical shifts and that Σ¹³Cn can be used as a molecular property which in turn can be modeled by both W and Sz indices successfully.

Full text of DOI:10.1016/S0960-894X(02)00556-5

Bioorganic & Medicinal Chemistry Letters 12 (2002) 2673–2680
Structural Assignment of 2,6- and 2,7-Disubstituted Naphthalenes
13
and Prediction of C Nuclear Magnetic Resonance Chemical
Shifts: Applications of Topology and Two-Dimensional
NMR Spectroscopy
a,
b
c
Padmakar V. Khadikar, * Sadanand V. Pathre and Anjali Shrivastava
aResearch Division, Laxmi Fumigation & Pest Control Pvt. Ltd., 3 Khatipura Indore 452007, India
bCorporate Research Laboratory, 3M Company, 3M Centre, 201-BS-05, St. Paul, MN 55144, USA
cDepartment of Chemistry, Government Autonomous and Model Holkar College, Indore 452 001, India
Received 5 June 2002; accepted 13 July 2002
Abstract—Unambiguous assignments of monocarboxymethylnapthalenes isolated as oxidation products of dimethylnaphthalenes
by Pseudomonas putida, a bacterial strain, were made using two-dimensional nuclear Overhauser enhancement correlation spec-
troscopy (NOESEY). The two-dimensional long-range heteronuclear correlation NMR technique was also utilized for the assign-
1
3
ment of quaternary carbons in the naphthalene system. In addition, we describe methods for prediction of C NMR chemical shifts
of 2,6- and 2,7-disubstituted naphthalenes using topological approach. The method involves computation of molecular descriptors
from topological representation of molecule, namely Wiener (W) and Szeged (Sz) indices. The results have shown that W and Sz
1
3
13
indices can be successfully used for predicting C NMR chemical shifts and that ꢀ Cn can be used as a molecular property which
in turn can be modeled by both W and Sz indices successfully.
#
2002 Elsevier Science Ltd. All rights reserved.
Introduction
The assignment of the substitution position in disub-
stituted naphthalene is commonly made by proton
and/or carbon-13 NMR. However, such determination
is not always trivial when no reference compounds or
spectra are available. For instance, the mono-
carboxymethylnaphthalenes (1 and 2) isolated from the
cell cultures in very small amounts (>80 mg) could not
be distinguished from each other by their normal 1-D
Pseudomonas putida, a bacterial strain that carries a
1
naphthalene-degradative plasmid, NAH has been eval-
uated for oxidation of dimethylnaphthalenes (DMN).
Two derivatives were isolated from the cell cultures of
Pseudomonas putida 2,6- and 2,7-dimethylnaphthalenes.
These derivatives were readily identified as mono-
carboxymethylnapthalenes (MCN) by Gas Chromato-
graphy—Mass spectroscopy (GC–MS). Since no
reference standards were available, the substitution
position could not be determined by the latter.
Although the bacteria is not known to isomerizes the
DMN used, it was necessary to demonstrate that no
isomerization had occurred in the formation of MCN.
Therefore, unequivocal assignments of substitution of
the isolated MCNs were necessary.
1
H NMR spectra. Both yielded identical proton multi-
1
13
plets. The H or C NMR spectra of these derivatives
1
13
have not been reported. H and C chemical shifts of
several other disubstituted naphthalene’s have been
1
reported, but those would be of little use for unambig-
uous assignment of 1 and 2. The limited sample (<80
mg) availability also precluded the use of chemical
1
3
degradation or techniques involving C NMR. In this
communication we describe an application of two-
dimensional nuclear Overhauser enhancement corre-
5
lation spectroscopy (NOESY) for unambiguous
assignment of the monocarboxylated methylnaphtha-
lenes. In addition, we also describe topological model-
1
3
ling of C chemical shift using Wiener (W) and Szeged
(Sz) indices. Such a modelling of chemical shifts using
*Corresponding author. Tel.: +91-731-531906; fax: +91-731-531906;
e-mail: anjalee_shrivastava@rediffmail.com
0
960-894X/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved.
PII: S0960-894X(02)00556-5

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P. V. Khadikar et al. / Bioorg. Med. Chem. Lett. 12 (2002) 2673–2680
5
À7
topological indices may help in prediction of chemical
shifts directly from the structure (molecular graph) and
confirm experimental assignement. Furthermore, the
results, as discussed below, show the possibility of pre-
dicting of these compounds and application of these
methods, which seem to be helpful for many organic
chemists, thus establishing that the methods are of
timeliness.
associated with the molecular structure.
The Wiener
8
index (W) is the first, the oldest, and even today the
most widely used topological index. However, it is
applicable to acyclic (trees) graphs only and not to cyc-
lic graphs. Consequent to this, Gutman has intro-
duced a new index called Szeged index and abbreviated
9
,10
it as S . This new index is considered as the modification
z
of W to cyclic graphs. For acyclic graph (trees), W and
Sz coincide. Compared to the Wiener (W) index, little is
known about the applicability of S in predicting prop-
During the course of this work, several dimethyl-
naphthalenes were analyzed by NMR for unambiguous
characterization of the microbial conversion products.
z
erties as well as physiological activity of organic
1
1À17
Hence, as stated earlier, another
compounds.
objective of the present study is to investigate the
1
3
Assignment of C NMR spectra of 10 dimethyl-
naphthalenes have been reported by Wilson and
Stothers and summarized by Hansen.1 Most of the
assignments were made by the use of selective proton
decoupling; however, it is not amnable to distinguish
carbons when the long-range coupled protons have near
equivalent chemical shifts. In some instances quaternary
and methine carbons of these naphthalenes have to be
reassigned. Our assignment in most cases were in
agreement with those reported except in some cases
where chemical shifts are too close to be able to assign
using selective proton decoupling. Two-dimensional
1
3
potential of S in predicting C NMR chemical shifts of
z
dimethylsubstituted naphthalenes (Table 1) and to
compare the results with those obtained by using W.
The results as discussed below show that both these
indices (W and S ) have equal predicting potential in
z
that C NMR shifts (C ), sum of C NMR chemical
n
1
3
13
1
3
shifts (ꢀC ), and mean C NMR chemical shifts are
n
predicted successfully using W and Sz.
Results and Discussion.
2
homo (COSY) and heteronuclear chemical shift corre-
2
lation spectroscopy (HETCOR) provided unequivocal
assignment of those aromatic methines. The long-range
Monocarboxylated methylnaphthalenes
2
,3
hetronuclear 2D chemical shift correlation technique
was particularly found to be valuable for assignment of
the quaternary carbons.
These derivatives were isolated as their methyl esters (1
and 2). Proton NMR spectra of these esters show six
well separated aromatic protons, two pairs of ortho
protons and two isolated protons (the meta coupling is
not resolved).This pattern would be consistent for 2,6-
and 2,7-disubstituted naphthalenes. One of the isolated
protons in these spectra is observed significantly down-
field near d 8.5. This proton must be assigned to a peri
(a) proton ortho to the carboxy substituent. Therefore,
the carboxy substituent must be assigned to the b posi-
tion in both derivatives. The position of the other sub-
As is well known, 13C Nuclear Magnetic Resonance
(
study of the immediate atomic environment in a mole-
NMR) chemical shifts offer a powerful probe in the
1
3
cule. C NMR spectroscopy is thus increasingly gain-
ing importance for organic chemists. It was realized that
1
3
the C NMR chemical shift and the bonding between
carbons and other nuclei are strongly dependent on
even minor change of the geometrical and atomic
environment of the organic molecules. Therefore,
topology of the organic molecule plays a dominant role
stituent, ÀCH cannot be distinguished by chemical
3
shifts.
1
3
4
in the exhibition of C NMR chemical shifts. This is
true even for the series of dimethylnaphthalenes used in
the present study. Consequently, we can use topological
indices for modeling, monitoring, estimating, and pre-
Since these peri protons are in close proximity to each
other, they can be correlated by nuclear Overhauser
enhancement (NOE) effects. Indeed NOESY spectra
(Figs. 1 and 2) of 1 and 2, clearly show the NOE con-
nectivities. In 1 the peri proton at d 8.5 shows NOE
correlation to the 8 Hz doublet; therefore, it must be
2,6-disubstituted. The peri proton at d 8.5 in 2, however,
shows connectivity with the broad singlet at d 7.7, as
one would expect for the 2,7-disustituted naphthalene.
1
3
dicting C NMR chemical shifts in organic molecules.
A topological index is a graph-theoretical invariant
which codes quantitative information regarding the size,
shape, bonding type, heteroatom, and branching
Table 1. 13C Chemical shifts of dimethylnaphthalenes
Compd
Dimethyl
naphthalene
C-1
C-2
C-3
C-4
C-5
C-6
C-7
C-8
C-9
C-10
ꢀ13
C
n
1
2
3
4
5
6
7
1,2-
1,3-
1,4-
1,5-
1,6-
2,6-
2,7-
131.0
133.9
132.2
135.0
131.1
126.5
126.1
133.0
128.8
126.1
126.6
124.9
134.3
135.3
128.9
134.9
126.1
125.6
124.8
128.0
127.1
125.5
125.1
132.2
122.7
125.0
126.9
127.3
128.3
127.7
124.5
135.0
126.7
126.5
127.3
124.3
125.5
125.2
126.6
134.1
134.3
127.1
125.6
124.7
125.2
125.6
127.1
128.0
135.3
123.6
132.8
124.5
122.7
123.1
126.9
126.1
132.7
130.8
132.6
132.9
130.1
131.8
133.8
132.1
133.0
132.6
132.9
133.0
131.8
129.8
1285.0
1297.2
1281.2
1285.6
1279.9
1295.0
1295.2
ꢀ13 , summation of 13
C C where n varies from 1 to 10.
n n

P. V. Khadikar et al. / Bioorg. Med. Chem. Lett. 12 (2002) 2673–2680
2675
Figure 1.
Figure 2.

2676
P. V. Khadikar et al. / Bioorg. Med. Chem. Lett. 12 (2002) 2673–2680
Figure 3.
Figure 4.

P. V. Khadikar et al. / Bioorg. Med. Chem. Lett. 12 (2002) 2673–2680
2677
1
3
Hence,
methylnaphthalene, respectively.
1
and
2
are 2,6- and 2,7-carboxy-
C ¼ A TI þ B
ð1Þ
n
1
1
and
Dimethylnaphthalenes
13
ꢀ
C ¼ A TI þ B
ð2Þ
n
2
2
The normal high-resolution heteronuclear and long-
range heteronuclear 2D chemical shift correlation spec-
for sum of the 13C NMR chemical shifts of the dime-
thylnaphthalenes used in the present study. The calcu-
lated values for the coefficients A (i=1, 2) and B
i
(i=1,2) of the aforementioned equations as well as the
data showing the quality of the respective correlations
are given in Table 3.
n
1
3
tra provided C NMR assignment (Table 1). The tech-
nique is elucidated for 1,6-dimethylnaphthalene. The
proton spectrum of 1,6-dimethylnaphthalene is assigned
from a COSY experiment. The assignment of carbons
C-2, C-3, and C-4 was made from the HETCOR spec-
trum. These carbons and C-1 and C-10 have not been
i
2
assigned earlier due to resolution problem. The qua-
As seen from Tables 1 and 3, by means of eq 1 it is
1
3
ternary carbons C-1 and C-10 can be unambiguously
distinguished by along range heteronuclear correlation
spectrum (Figs. 3 and 4).The H-8 proton shows the
correlation with the quaternary carbon at d 133.0 and
C-1 carbon is correlated with the methyl protons at
possible to quite accurately estimate the C NMR
chemical shifts of the dimethylnaphthalenes, however,
poor results are obtained in case of C , C and C . It is
interesting to record that although individual chemical
shifts for different atoms have received wide attention, it
is somewhat surprising that there is hardly any study
devoted to the collection of chemical shifts in a mol-
ecule. However, the present study shows that sum of the
3
5
6
1
3
C-1. The assignment of 2,7-dimethylnaphthalene
spectrum was similarly made.
C
1
3
13
The proton spectrum of 1,3-dimethylnaphthalene can be
C NMR chemical shifts ꢀ C display regularity in
n
1
,2
assigned on the basis of chemical shifts. The singlets
of the isolated protons H-2 and H-4 and doublet of H-8
and H-5 are distinguished because the peri protons are
more desheilded. The assignment was confirmed by a
NOESY spectrum which showed NOE between H-5
and H-4. The long-range heteronuclear correlation
variations. The statistics presented in Table 3 show that
1
3
ꢀ C NMR chemical shifts of the dimethylnaphtha-
n
lenes act as a very good molecular property which can
be estimated successfully employing the above men-
tioned eq 2. The corresponding regression models are
found as under:
1
,2
spectrum in agreement with the earlier assignments of
carbons except for C-1 and C-10, which should be
reversed. Although the peaks due to C-4 and C-7 of 1,2-
dimethylnaphthalene are separated by less than 0.4
ppm, resolution was sufficient to make the unequivocal
assignment also indicated long-range C-H coupling of
C-2 with H-4 and C -CH , and of C-9 with H-5 and
1
3
ꢀ
ꢀ
Cn ¼ 1100:6465 þ 1:0425 W
ð3Þ
ð4Þ
13
C ¼ 1091:9475 þ 0:5254 Sz
n
2
3
C -CH to confirm the assignment of those carbons.
1
In order to confirm our findings, we have estimated
1
3
3
ꢀ
experimental values of ꢀ C . Such a comparison is
C from eqs 3 and 4 and compared them with the
n
1
3
Prediction of 13C NMR chemical shifts
n
shown in Table 2. The results show that using distance-
based topological indices W and S it is possible to infer
The data presented in Tables 1–3 show that 13C NMR
chemical shifts (C , n=1, 2, 3...0) and their sums
z
1
3
13
about the ꢀ C and that it (ꢀ C ) can be used as a
n n
n
1
3
(ꢀ C ) are linearly correlated with W and S indices.
Hence, if TI stands for one of the topological indices W
molecular property. The data also show that W and Sz
indices have practically the same predictive ability, W
being slightly better than S . This is obvious because S
n
z
and S , then the following approximation can be used
z
z
z
for 1 C (n=1, 2, 3,...10) NMR chemical shifts:
3
index is a modification of the W index for cyclic
n
Table 2. Wiener (W) and Szeged (Sz) indices of dimethylnaphthalenes used in the present investigation and estimated ꢀ13
C
using W and Sz indices
n
Compd
W
Sz
Sz/W
ꢀ13
C
n
ꢀ13
C W
n
Estimated from Sz
Est.
Res.
Est.
Res.
1
2
3
4
5
6
7
178
179
176
176
181
186
185
369
372
366
366
376
386
383
2.0730
2.0782
2.0796
2.0796
2.0774
2.0753
2.0703
1285.0
1297.2
1281.2
1285.6
1279.9
1295.0
1295.2
1286.22
1287.25
1284.13
1284.13
1289.34
1294.15
1293.51
À1.22
9.95
1285.82
1287.40
1283.77
1283.77
1289.50
1294.75
1293.18
À0.82
9.80
À2.93
À2.57
1.47
1.83
À9.44
0.45
1.69
À9.60
0.25
2.02
g=2.0757
Res, residue, that is difference between experimental and estimated ꢀ13
C of dimethylnaphthalenes.
n

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P. V. Khadikar et al. / Bioorg. Med. Chem. Lett. 12 (2002) 2673–2680
Table 3. Regression parameters and quality correlation for estimated13 chemical shift and ꢀ13
C of dimethylnaphthalenes used in the present
n
investigation
Correlation
A
i
(i=1,2)
B
i
(i=1,2)
Sx
Sy
R
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
ꢀ
ꢀ
1
1
2
–W
–Sz
–W
242.5728
À0.6202
6.6968
0.4997
0.2408
À0.1965
À0.0988
0.2702
0.1353
À0.1516
À0.0751
0.3041
0.1626
0.5327
0.2560
0.3087
0.1527
0.1390
0.0648
À0.1978
À0.6546
1.1026
0.5491
0.0901
0.0448
4.4615
8.9149
4.1173
8.9149
4.4615
8.9149
4.4615
8.9149
4.4615
8.9149
4.4615
8.9149
4.4615
8.9149
4.4615
8.9149
4.4615
8.9149
4.4615
8.9149
4.4615
8.9149
4.4615
8.9149
3.5220
6.0901
4.2751
4.2751
3.3860
3.3860
2.9678
2.9678
3.3131
3.3131
4.228
4.2284
3.6846
3.6927
1.5668
1.5668
1.2858
1.2858
1.2734
1.2734
6.3989
6.3989
0.5155
0.5155
0.7856
0.6213
0.4813
0.5022
À0.2530
À0.0988
0.4062
0.4064
À0.2041
À0.2020
0.3208
0.3428
0.6450
0.6179
0.8791
0.8688
0.4824
0.4493
À0.6932
À0.6546
0.7818
0.7685
0.7749
0.7755
À2330.6753
40.1933
39.9921
2ÀSz
3À
3ÀSz
4À
W
163.2337
164.7814
77.8242
W
4
–Sz
75.9030
5À
5ÀSz
–W
6ÀSz
W
155.2366
156.0137
73.5120
67.4795
31.6313
31.8326
68.9022
67.4082
107.1206
107.9206
167.8446
167.1742
1088.6842
1081.9385
91.0414
6
7À
W
7
–Sz
–W
8
8ÀSz
9
–W
–Sz
9
10–W
10–Sz
1
3
a
a
a
a
C
n
–W
–Sz
13C
n
1
3
Mean C–W
Mean C–Sz
13
90.5053
A
i
,B
i
, regression parameters; Sx, standard deviation in W or Sz; Sy, standard deviation in 13C chemical shift or ꢀ13
When compounds 2 and 5 are deleted being outliers the R values becomes as high as 0.9643 and 0.9622 when W and Sz are respectively used for
n
C ; R, correlation coefficient.
a
13
modelling ꢀ
n
C .
Under similar conditions R values for modelling Mean 13C changes to 0.9656 and 0.9641 respectively when W and Sz are used. The other statistics
reported herein are for modelling O 13Cn and Mean C when either of the two compounds 2 and 5 are deleted.
13
compounds and that the number of cycles remained the
same in all the dimethylnaphthalenes used. Hence, vari-
ations in S is due to tree-like substituent at different
positions for which coincidence of S with W is well
z
known.
naphthalenes and observed that there was no improve-
ment in the quality of correlations discussed above. This
is obvious because the normalization factor (number of
carbon atoms=12) remained the same in all the cases.
However, the regression expression changed to the
following:
z
The data presented in Table 2 show that difference in
1
3
the experimental and estimated values of ꢀ C NMR
n
Mean carbon-13 ¼ 91:6986 þ 0:0870 W
chemical shifts
ð5Þ
chemical shifts are much larger for compounds 2 and 5.
Thus, they can be considered as outliers. When treating
either of the two compounds as outliers we observed
that the correlation is increased dramatically to the
extent that the correlation coefficient increases from
Mean carbon-13 ¼ 90:9663 þ 0:0439 Sz
chemical shift
ð6Þ
0
S indices are respectively used for predicting ꢀ C
.5880 to 0.7818 and from 0.5856 to 0.7685 when W and
1
3
The corresponding statistical parameters are shown
in Table 3. Interestingly, Sy (standard deviation in
mean carbon-13 chemical shift) values for these
z
n
NMR chemical shifts. Furthermore, when both these
compounds, 2 and 5, are deleted the correlation in dra-
matically increased to 0.9643 and 0.9622, respectively,
1
3
expressions are found lower than those for ꢀ C NMR
n
1
3
when W and S are used for modelling ꢀ C .
z
chemical shifts indicating that mean carbon-13 chemical
1
n
3
shifts is a better molecular property than ꢀ C NMR
n
If the derived chemical shifts sums are normalized by
dividing the values with the number of carbon atoms in
the molecule one apparently derives an average or mean
carbon-13 chemical shifts for individual dimethyl-
naphthalenes. Because carbon-13 chemical shifts are
atomic property, it seems more agreeable to refer to the
composition when suitably normalized as a ‘mean
atomic’ property. An additional advantage of this use of
shifts.
Conclusions
From the aforementioned results and discussion, we
conclude that the two-dimensional long range hetero-
nuclear correlation NMR technique can be utilized for
the assignment of quaternary carbon for the naphtha-
lene systems. Also that, the W and Szeged Sz indices
provide inside into variation of sum as well as mean
carbon-13 chemical shifts and the same can be modeled
successfully. To a lesser extent the individual carbon-13
‘
mean carbon-13 chemical shifts’ over ‘chemical shifts
sums’ is that the former facilitates comparison between
molecules of different size. In view of this, we have nor-
malized the chemical shifts sum by dividing them by the
number of carbon atoms present in the dimethyl-

P. V. Khadikar et al. / Bioorg. Med. Chem. Lett. 12 (2002) 2673–2680
2679
chemical shifts are also modeled by both W and S indi-
z
obtained using the following acquisition parameters:
1
13
ces. Our results also show that sum of the carbon-13
chemical shifts as well as mean carbon-13 chemical
shifts are the excellent molecular properties. The case of
H
4000 Hz
C
20,000 Hz
Spectral width
Pulse width
Acquisition
ꢀ
ꢀ
5 ms (12 )
2.5 s
6 ms (40 )
0.75 s
1
3
C NMR shifts in dimethylnaphthalenes well illustrate
the difference between the statistical approaches such as
graph theoretical approach where one can identify the
critical structural parameters from observations rather
than from computer read-outs of statistical packages,
that at best give answers but cannot anticipate them.
The results obtained may be useful for pharmaceutical
and medicinal chemistry to better explain physiological
activity exhibited by disubstituted naphthalenes.
Two-dimensional spectra COSY and HETCOR were
recorded using standard pulse sequences and para-
meters available on the spectrometer system. The two-
dimensional NOE experiment (NOESY) consists of a
ꢀ
ꢀ
ꢀ
sequence of three non-selective 90 pulses: [90 Àt À90
1
ꢀ
atically as: mix + 0.1*t to diphase J correlations. The
Àt À90 ÀAT] . The mixing time t was varied system-
m
n
m
1
9
1
delay ‘mix’ was chosen to be between 1 T and 1.5 T .
1
1
The longitudinal relaxation time T for the protons of
1
interest were determined by nonselective inversion-
recovery experiment. The T of the aromatic protons of
Experimental
Chemicals
1
1 and 2 range from 3.5 to 4.6 s. The optimum mix was
selected to be 5 s. The pulse sequence was repeated with
a delay of 15 s, typically 32 transients were accumulated
for each of 128 increments. The chemical shifts are
reported in ppm downfield from tetramethylsilane.
All dimethylnaphthalenes except 1 and 2 were pur-
chased from Aldrich Chemical Company and used after
purification. Proton and carbon NMR spectra of these
compounds are consistent with the structural assign-
ment as discussed above. Compounds 1 and 2 were
analysed by mass spectra. All NMR spectra were
Topological indices
8
8
obtained on CDCl solution on a Varian XL-400 NMR
3
Wiener index (W). The Wiener index (W) is the oldest
and widely used topological index. It is based on the
vertex distance of the respective molecular graph. Let us
denote a molecular graph by G and having v , v , v ...v .
1
13
spectrometer ( H, 400 MHz; C,101 MHz) using a 5-
mm broad band probe. Two-dimensional spectra were
recorded using standard pulse sequence and software
available on the spectrometer system.
1
2
3
n
its verices. Let d(v ,v |G) stands for the distance between
i
j
the vertices v and v . Then the Wiener index (W) is
i
j
defined as:
Cultural conditions
n
n
XX
ꢀ
P. putida 1013, a strain that carries a naphthalene-
degradative plasmid, NAH cell were grown in basal
ꢀ
W ¼ WðGÞ ¼
dðv ; v GÞ
i
j
i¼1 j¼1
1
8
ꢀ
medium overnight in a 30 C shaker with the addition
of sodium acetate (0.1%) as the carbon source and 2-
aminobenzoate (0.005%) as the inducers. The cells were
washed with 0.5 M Tris–HCl buffer. A typical incu-
bation mixture contained: 1.4 mL of 0.05 M Tris–HCl,
pH=7.5, 0.01 mL of 0.1 M naphthalene substrates dis-
solved in N,N-dimethylformamide, 0.1 mL of 0.03 M
NADH solution, and 0.02 mL of the cell suspension.
Szeged index (Sz).9,10 Let e be an edge of the molecular
graph G. Let n (e|G) be the number of vertices of G
1
lying closer to one end of e; let n (e|G) be the number
2
of vertices of G lying closer to the other end of e. Then
the Szeged index (Sz) is defined as:
X
ꢀ
ꢀ
ꢀ
ꢀ
Sz ¼ SzðGÞ ¼
n1ðe GÞn2ðe GÞ
e
Isolation of 1 and 2
After 24 h, the culture supernant was filtered through a
0
with the summation going over all edges of G.
.22-m filter. The monocarboxylic acids were pre-
cipitated with concentrated HCl. The precipitate was
washed once with 70% aq ethanol. Metabolites were
separated by HPLC using a reverse-phase C18 column;
and subsequently derivatized with BF -CH OH (Pierce
In cyclic graphs, there are edges equidistant from both
the ends of edge e; by definition of Sz, such edges are
not taken into account. These calculations were made
using the Software provided by Professor Lukovits.
3
3
Chemical Co. Rockford, IL, USA) to convert carbon
metabolites into their methyl esters for analysis by GC–
MS. The fractions containing monocarboxymethylesters
were then analyzed by NMR.
Regression analysis.20 All the regression analyses20 were
carried out using the software provided by Professor
Lukovits, Hungarian Academy of Sciences, Budapest,
Hungary.
NMR experiments
NMR spectra were obtained in CDCl solutions on a
3
Acknowledgements
Varian XL-400 NMR spectrometer operating at 400 and
1
13
1
switchable probe. Normal 1-D H and C, NMR were
01 MHz for H and C, respectively. Using a 5-mm
1
The authors are thankful to Professor Ivan Gutman for
introducing them to the fascinating field of Chemical
13

2680
P. V. Khadikar et al. / Bioorg. Med. Chem. Lett. 12 (2002) 2673–2680
Topology and Graph Theory and to Prof. I. Lukovits
for providing software.
7. Todeschini, R.; Consonni, V. Handbook of Molecular
Descriptors; Wiley-VCH: Weinheim, 2000.
8. Wiener, H. J. Am. Chem. Soc. 1947, 69, 17.
9. Gutman, I. Graph Theory Notes New York 1994, 20, 9.
10. Khadikar, P. V.; Deshpandey, N. V.; Kale, P. P.; Dobry-
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