IJEB 52(6) 623-629

Indian Journal of Experimental Biology
Vol. 52, June 2014, pp. 623-629
Insulin secreting and α-glucosidase inhibitory activity of hexane extract of
Annona squamosa Linn. in streptozotocin (STZ) induced diabetic rats
Ranjana & Yamini B Tripathi*
Department of Medicinal Chemistry, Institute of Medical Sciences, Banaras Hindu University, Varanasi 221 005, India
Received 1 July 2013, revised 13 January 2014
The hexane extract of A. squamosa (ASHE) in 100 and 400 mg/kg body weight dose raised the insulin level when
compared with Glimepiride (1 mg/kg) and also inhibited α-glucosidase activity when compared with Acarbose (10 mg/kg)
in streptozotocin induced diabetic rats. The ASHE significantly reduced peak blood glucose (Gp30) and area under curve
(AUC) in diabetic rats in oral glucose (OGTT) and oral sucrose (OSTT) tolerance test, but there was more reduction of Gp30
value than AUC in OSTT. Thus, it can be suggested that the ASHE, has hypoglycemic role at 2 levels, i.e. it acts as
secretagogue and also inhibits the intestinal enzymes, responsible for glucose metabolism.
Keywords: α-glucosidase, Annona squamosa, Diabetes, Herbal, Postprandial hyperglycemia
Diabetes mellitus is characterized by hyperglycemia
together with biochemical alterations of glucose
and lipid metabolism1. Current drugs used for the
treatment of diabetes include a few groups of
chemical compounds such as the drug biguanide
(metformin), which although antihyperglycemic, does
not affect hypoglycemia in the normal subjects2 and
involves extra pancreatic mechanisms3,4. Then, there
are the sulfonylureas (glibenclamide, tolbutamide
etc.), which are insulin secretagogues, and lastly,
the new class of drugs known as thiazolidinedions
(rosiglitazone,
pioglitazone)
which
enhances
sensitivity to insulin in target tissues5. At present,
α-glucosidase inhibitors are the most common oral
agents used to decrease postprandial hyperglycemia.
It reduces the rate of digestion and absorption of
ingested carbohydrates. Drugs like acarbose and
miglitol are already in clinical use but they are
associated with side effects like abdominal distention,
flatulence, meteorism and possibly diarrhea6,7.
In addition, numerous studies have been carried out
to isolate effective and safe α-glucosidase
inhibitors from natural products, including plant
materials, as alternative hypoglycemic agents for
diabetes that can be used in addition to conventional
treatments8-10.
——————
*Correspondent author
Telephone: 0091-542-2366577, 6702171, 2307547
Fax: 0091-542-2366577, 2368174
E-mail: [email protected]; [email protected]
Therefore, search of newer agents is in demand. In
this process, standardized herbal extracts may be of
high benefit because it is a natural cocktail of many
secondary metabolites, which may be active at various
sites. Here, we propose to investigate the role of
herbal formulation, because of their natural cocktail of
variety of secondary metabolites and possibility of
multi-targeted mode of action. The Annona squamosa
Linn. (AS) is a shrub and cultivated by horticulturists
for its fruits, known as caster apple. Reports indicate
the hypoglycemic property in its leaves11-14 but the
mechanism of action is not very clear. Besides
hypoglycemic activity, its leaf extract also possesses
anti-oxidant11&15, anti-fertility, anti-tumor16,17, antihyperthyroidism18 and hepato-protective activities19
etc. The secondary metabolites of AS-leaf-extract
include variety of steroids, alkaloids, saponins,
terpenes, tannins, phenolic substances, volatile oil and
mucilage 20,21. The present communication reports the
hypoglycemic effect of leaf of AS on streptozotocin
(STZ) induced diabetic rats with especial reference to
inhibitory response on intestinal α-glucosidase activity.
Based on earlier observations, it was found that
non-polar hexane fraction was most active therefore its
inhibitory study was undertaken in detail by using
in vivo and in vitro experimental models.
Materials and Methods
Materials—Streptozotocin (STZ) (Sigma Chemical
Co (St. Louis, MO, USA). Acarbose and Glimepiride
624
INDIAN J EXP BIOL, JUNE 2014
(Bayer pharmaceuticals and Aventis Pharma
respectively), glucose assay kit (Accurex), maltose (E.
Merck Pvt. Ltd., Mumbai (India), glucose and sucrose
(Hi-Media Laboratories Pvt. Ltd., Mumbai (India)
were used. All other reagents were of analytical
grade. Rats of CF strain were purchased from the
central
animal
house
of
the
Institute.
The animals taken under this study were 8-10 weeks
old male 5, weighing 100-150 g body weight. The
experimental protocol was approved by Animal
Ethics Committee of the Institute. All animals were
kept on a 12 h dark and light schedule and fed
standard laboratory chow ad libtum.
Preparation of plant extract—The leaves of
Annona squamosa Linn. (AS) were purchased and
their authenticity was reconfirmed on pharmacognostical
parameters by Department of Dravyaguna, Faculty of
Ayurveda, BHU. The voucher specimen of leaves was
preserved in the department, wide reference no
MC/YBT/1-2009. These leaves were washed, air
dried under shade, and pulverized in a mechanical
grinder. The 3 extracts namely, hexane (ASHE),
methanol (ASME) and water decoctions (ASWD)
were separately prepared. The course powder was
separately extracted with hexane and methanol in
continuous soxhlet extractor for 20 h. The solvent free
extracts were prepared by distillation and desiccated
until constant weight was attained. The water extract
was prepared by boiling weighed amount of dried
leaves in distilled water (16 times, w/v) and when the
water volume was reduced to ¼, it was filtered and
dried at 40 °C in hot air oven.
Induction of diabetes by streptozotocin (STZ)—The
overnight fasting rats were given intra-peritoneal
injection of STZ (50mg/kg, dissolved in chilled citrate
buffer (pH 4.5) and after 3 days, blood glucose was
measured. The rats having blood glucose, higher than
200 mg/dL, were considered as diabetic for
experiments22.
The blood was collected from tail of each rat in
anesthetic condition. Blood glucose was measured
using a GOD/POD method and serum insulin was
measured by Immulite 1000 (Siemens) solid-phase,
two-site chemiluminescent immunometric assay.
Assay of α-glucosidase—The tissue homogenate
prepared from small intestine of rats was used as
enzyme source. A small pieces (2-3 mm) of smallintestine was taken out in pre-cooled phosphate buffer
saline (PBS), thoroughly cleaned, dried on blotting
paper, weighed and then homogenized in glass Teflon
homogenizer. The homogenate was centrifuged at
5,000 g for 30 min and its supernatant was used as
enzyme source. Final volume of supernatant was
maintained to 20% (w/v).
Spectrophotometric assay method23 was used with
slight modification. Tissue homogenate (40 µL) was
mixed with 80 µL of test/standard/drug vector and
incubated for 15 min at 37 °C. Thereafter, 280 µL
maltose (37 mM) was added and further incubated for
30 min. Finally, the reaction was stopped by putting
the tubes in boiling water for 10 min. The tubes were
centrifuged and glucose concentration was assessed in
the supernatant by GOD/POD method based kit. The
change in activity was expressed as:
Inhibition (%) = (Absorbance Control - Absorbance
Test/ Absorbance Control) ×100
In vivo studies :
Hypoglycemic screening of different extracts of AS
leaves in STZ induced diabetic rats—Rats were
randomly divided into 6 groups of 6 rats in each. The
1st and 2nd groups were normal and experimental
control and treated with 20% Tween 20 @ 5 mL/kg
body weight. The 3rd, 4th and 5th groups were treated
with ASHE, ASME and ASWD at 200 mg/kg body
weight respectively. The 6th group was treated with
Glimepiride (1 mg/kg body weight). After 2 h of oral
administration of all extracts and standard drug, blood
glucose was measured by GOD/POD method.
The hypoglycemic activity of ASHE on 7 days
treatment in STZ induced diabetic rats was carried out
in different doses. Glimepiride and Acarbose were
used as positive control. After 7 days, blood insulin
and blood glucose were estimated in all grpous. The
designs of groups are given below:
Groups
Normal control
Experimental diabetic control
ASHE
ASHE
Glimepiride (sulphonyl urea group)
Acarbose (α-glucosidase inhibitor)
Treatment plan
20% Tween 20 @ 5mL/kg
body weight
20% Tween 20 @ 5mL/kg
body weight
100 mg/kg body weight
400 mg/kg body weight
1 mg/kg body weight
10 mg/kg body weight
The effect of ASHE on oral carbohydrate challenge
was carried out using glucose and sucrose
separately24,25. The animals were randomly divided
into different groups for various treatments and to
RANJANA & TRIPATHI : ANNONA SQUAMOSA & STREPTOTOCIN INDUCED DIABETES
each rat glucose/sucrose were orally given at 4 g/kg
dose. At time intervals of 30 min, blood glucose was
estimated up to 2 h. Peak glucose value was
ascertained at 30 min of glucose administration
(Gp30). The concentration verses blood glucose was
plotted against time. The formula for AUC
determination is as follows:
AUC (mg) = (BG0+BG30/2*30) + (BG30+BG60/2*30)
+ (BG60+BG120/2*60)
where BG0, BG30, BG60, BG120 represented the blood
glucose at 0, 30, 60 and 120 min. respectively.
Effect of ASHE on oral glucose tolerance test
(OGTT)—The rats were fasted overnight for 18 h but
had free access to water. The rats were divided into
following 6 groups of 6 rats each. Group 1, was
treated orally with 100 mg/kg body weight of ASHE
(R1), rats of treatment group 2 were treated with 400
mg/kg body weight ASHE (R2). The rats of group 3
were treated with Acarbose at 10 mg/kg body weight
(R3). In the normal and experimental control groups
(R4) only drug vector were orally given (20% Tween
20, 5 ml/kg. After 30 min, Glucose was orally given
to rats at 4 g/kg body weight and blood was collected
from tail vein at 0 min (before glucose administration)
and at 30, 60, and 120 min after glucose
administration and blood glucose was measured by
GOD/POD method.
The effect of ASHE on oral sucrose tolerance test
(OSTT) was carried out in the same manner as
described above in case of OGTT, but here sucrose
was given at the dose of 4 g/kg body weight in place
of glucose.
Effect of AS hexane fraction on intestinal αglucosidase activity—The effect of ASHE on αglucosidase activity under in vivo condition was
carried out in normal and diabetic rats. They were
625
randomly divided in to various groups of 6 each and
treated with ASHE/standard/drug-vector for 7 days.
Finally all animals were sacrificed under anesthesia to
collect small intestine for assay of α-glucosidase
activity as mentioned above.
In vitro study:
Inhibition profile of ASHE on semi-purified αglucosidase enzyme—For assessment of the specific
inhibitory activity of hexane fraction on α-glucosidase
activity, an in vitro study was performed. Tissue
homogenate was prepared from the rat intestine,
collected from normal rats. It was used as enzyme
source and incubated with different concentrations of
ASHE/acarbose/drug vehicle. Thereafter maltose
solution was added and activity of α glucosidase was
assessed as described above.
Statistical analysis—The data have been expressed
as mean±SD. Pearson’s correlation analysis (SPSS 16
for Windows, SPSS Inc.) was used to test for the
significance of the relationship between the
concentration and percentage inhibition. In order to
evaluate dose dependent effect of the extract,
compared with the experimental control was excluded
and data analyzed using 2- way analysis of variance
and post hoc multiple comparison (Bonferroni test).
Results
Hypoglycemic effect of different extracts of AS
leaves (2 h study)—All the 3 extracts (ASHE, ASME
and ASWD) showed significant hypoglycemic
activity in STZ induced diabetic rats at dose of
200 mg/kg body weight, but the hexane extract
(ASHE) showed the best potency (Table 1). The
lowering of raised blood glucose level was up to
14.49±3.80%, when compared with diabetic
experimental control group, which blood glucose was
295.16±3.98 mg/dL. However in similar conditions,
Table 1—Hypoglycemic activity of different extracts of AS leaves
[Values are mean±SD from 6 animals in each group]
Groups
Blood glucose (mg/dL)
Inhibition in blood glucose
level (mg/dL) (%)
0 min
2h
Normal rats (drug vector)
73.69±2.32
74.06±2.64
Diabetic rats (drug vector)
294.67±5.26
295.16±3.98
ASHE (200 mg/kg bw)
351.49±6.29
300.54±1.80
14.49±3.80
350.26±3.62
322.40±1.60
7.95±2.90
ASME (200 mg/kg bw)
ASWD (200 mg/kg bw)
287±2.45
257±3.60
10.45±3.62
Glimepiride (1 mg/kg bw)
246±4.60
208±2.76
15.44±4.18
ASHE = hexane extract of AS leaves; ASME = methanolic extract of AS leaves; ASWD = water decoction of AS leaves; P values are
significant at *< 0.05 and highly significant at **< 0.01
INDIAN J EXP BIOL, JUNE 2014
626
Glimepiride (1 mg/kg body weight) showed
hypoglycemic response in range of 15.44±4.18%.
Hypoglycemic response of ASHE in STZ induced
diabetic rats (7 days)—The ASHE treatment for 7
days showed significant rise in blood insulin along
with decrease in blood glucose level. In STZ treated
experimental control rats, the blood glucose level was
raised to 386.93±2.60 mg/dL when compared to
normal control value i.e. 115±3.54. The oral treatment
of ASHE showed dose dependent decline in
blood glucose. It was 41.18±2.46% at 100 mg/kg
and 78.10±1.57% with ASHE 400 mg/kg, when
compared experimental diabetic control group. The
standard drug Acarbose also showed the potent
reduction (61.66%) at 10 mg/kg in glucose level. On
the other hand, the serum insulin level declined to
8.56±1.42 µU/mL in experimental diabetic control
rats and it was found to be significantly raised in
ASHE treated rats to 11.58±1.80 at 100 mg/kg and
16.26 µU/mL in 400 mg/kg. In similar conditions,
Glimepiride showed 17.36 µU/mL of rise in insulin
level at dose of 1 mg/kg. In normal control
animals, the insulin value was 22.4 µU/mL (Table 2).
Oral glucose tolerance test (OGTT)/Oral sucrose
tolerance test (OSTT)—The earlier experiment
indicated the role of ASHE on insulin release in
diabetic rats, but its role on intestinal enzyme was not
clear. Thus is effect on OGTT and OSTT was
assessed. The results were expressed in terms of peak
glucose value at 30 min (Gp30) and AUC for blood
glucose change recorded up to 120 min of oral
glucose/sucrose administration. The Gp30 in normal
rats was 111.57±2.70 mg/dL and in experimental
diabetic control rats it was 368.10±1.31 mg/dL
(Table 3 and Fig. 1).
Effect of AS hexane fraction on intestinal αglucosidase activity—To further clarify the role of
ASHE on intestinal enzymes, responsible for
carbohydrate metabolism, the activity of α-glucosidase
was determined in small intestine of rats treated with
ASHE. At 100 mg dose, the reduction in activity was
57.06±1.44% and at 400 mg dose this reduction was
in range of 75.69±1.7%. The inhibitory response
was concentration dependent. In similar conditions
the
Acarbose
treatment
(1
mg/kg
body
weight) showed reduction of 53.60±1.45% (Table 4).
Table 2—Effect of ASHE on blood-glucose and blood-insulin level after 7 days of oral treatment to STZ induced diabetic rats
[Values are mean±SD from 6 animals in each group]
Groups
Glucose level (1st day) Glucose level (7th day) Glucose level (% inhibition)
Normal control
96.38±2.80
115±4.53
Diabetic control
342.44±3.70
386.93±2.67
ASHE(100 mg/kg bw)
289.06±3.60
170.00±1.80*
41.18±2.46**
ASHE (400 mg/kg bw)
361.73±1.70
79.41±1.56**
78.04±1.57**
Acarbose (10 mg/kg bw)
383.46±3.98
147.82±2.80**
61.45±1.52**
Glimepiride (1 mg/kg)
293.89±2.80
159.10±3.20**
45.86±2.52**
ASHE = hexane extract of AS leaves; P values are significant at *< 0.05 and highly significant at **< 0.01
Serum insulin (µU/mL)
22.46±2.45
8.56±1.42
11.58±1.80
16.26±1.20**
10.50±1.94
17.36±0.90**
Table 3—Effect of ASHE on peak glucose value at 30 min and AUC during OGTT and OSTT in STZ induced diabetic rats.
[Values are mean±SD from 6 animals in each group]
Groups
OGTT
Blood glucose at
0 min (mg/dL)
Blood glucose at 30
min (GP30) (mg/dL)
ASHE 100
260±2.30
389.72±4.34c,f
mg/kg (R1)
(49.90±1.03%)*
ASHE 400
262.78±2.84
367.10±3.24a,f
mg/kg (R2)
(38.33±0.92%)*
Acarbose 10
245.40±0.93
343.34±1.13c
mg/kg (R3)
(39.91±0.86%)*
Diabetic
222.48±0.722
368.10±1 .31
Control (R4)
(65.66±0 .3%)*
Normal
79.57±1.42
111.57±2.70
control
(39.74±1.30%)*
P values: a,d <0.05 ; b,e <0.01 ; c,f <0.001 a,b,c: compared
change after glucose loading in diabetic rats
OSTT
AUC(mg)
40216±104.00c,d
Blood glucose at Blood glucose at 30
0 min (mg/dL) min (GP30) (mg/dL)
AUC(mg)
393.30 ±2.46 c,f
38550±194.66 c,f
(21.80±0.14%)a
39151±193.41c,f
292.52±2.30
342.75 ±2.56 c,f
38411 ±262.98 a,f
(17.16±0.43%)*
38191±66.41a
282.45±2.05
317.46±1.94 c
36326 ±308.94 c
(12.38±0.29%)*
41901±110.20
223.35±2.45
357.92±2.39
44032 ±302.09
(60.26±0.88%)*
12582±184
82.53±2.54
118.71 ±2.58
14490±308.58
(43.85±1.38%)*
with the diabetic control; d,e,f : compared with the Acarbose group *% unit
322.86±2.24
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627
Table 5—Effect of ASHE on α- glucosidase activity under in vitro
condition in a semi-purified rat intestinal enzyme preparation
[Values are mean±SD from 6 animals in each group]
Concentration (mg/mL)
Inhibition (%)
1.0
12.40±1.1*
3.0
20.4±1.00*
5.0
27.50±0.59*
7.0
34.50±0.96**
10.0
64.35±0.84**
15.0
66.805±0.34**
ASHE: IC50
9.157 mg/mL
Acarbose: IC50
0.049 mg/mL
Results are expressed in terms of % inhibition in comparison
to experimental control (Pearson’s correlation analysis)
ASHE = hexane extract of AS leaves; P values are significant at
*
< 0.05 and highly significant at **< 0.01
Fig. 1—Effect of hexane extract of A. squamosa on oral glucose
tolerance test (a) and oral sucrose tolerance test (b) in diabetic rats
[R1=ASHE 100 mg/kg, R2=400 mg/kg, R3=Acarbose 10 mg/kg,
R4=diabetic control]
Table 4—Effect of ASHE activity on intestinal α-glucosidase
after oral treatment for 7 days in STZ induced diabetic rats
[Values are mean±SD from 6 animals in each group]
Concentration
(mg/kg)
Inhibition in intestinal
α-glucosidase (%)
ASHE (100)
ASHE (400)
Acarbose (10)
Glimepiride (1)
57.06±1.44**
75.69±1.7**
53.60±1.45**
22.18±1.24
Results are expressed in terms of % inhibition in comparison
to experimental control (Pearson’s correlation analysis)
ASHE = hexane extract of AS leaves; P values are significant at
*
< 0.05 and highly significant at **< 0.01
The role of ASHE on intestinal α- glucosidase
activity under in vitro condition—Finally, in order to
assess the director inhibitory role of ASHE on
intestinal α-glucosidase activity, an in vitro study
was carried out, by using semi purified enzyme
preparation from normal rat intestine. Both ASHE
and acarbose significantly inhibited the α-glucosidase
activity. The response was concentration (1.0 mg - 10
mg/mL) dependent, varied from 57.02–12.40%.
IC50 ASHE was 9.157 (mg/mL). In similar
conditions acarbose showed IC50 at 0.049 mg/mL
(Table 5).
Discussion
The highest activity of ASHE, followed with
ASWD and ASME, could be due to presence of more
active secondary metabolites in the non-polar region.
Higher activity in water decoction than methanol
extract may be due to higher concentration of nonpolar phytomolecules due to their low melting point.
Earlier reports have also indicated the hypoglycemic
response of methanolic and water extracts of AS
leaves11-14 but for the first time, present
communication reports α- glucosidase inhibition with
hexane fraction.
When ASHE was tested for 7 days treatment in
STZ induced diabetic rats, there was reduction in
blood glucose along with rise in blood insulin level.
This indicates towards its action as secretogague, by
targeting pancreas as it’s site of action. The response
was similar to Glimepiride as reported26,27. Various
other plant extracts have also shown similar
secretogague activity27.
The data related to OGTT and OSTT indicate that
in case of ASHE and Acarbose, the Gp30 value is
higher in OGTT as compared to OSTT. This
difference indicates that ASHE might be interfering
with the metabolism of sucrose, similar to Acarbose28.
It is known that sucrose, being a disaccharide, first
gets metabolized to monosaccharides by intestinal
hydrolases before absorption and α-glucosidase and
α-amylase are the important enzymes involved in the
digestion of carbohydrates 29.
Interestingly, the AUC data of OGTT and OSTT
showed different results than the corresponding
Gp30 values. In both the cases, the AUC did not show
significant differences as compared to differences in
628
INDIAN J EXP BIOL, JUNE 2014
GP30 in OGTT and OSTT. The AUC of OGTT and
OSTT showed significant change in ASHE treated
rats in comparison to diabetic control rats. However
the peak glucose value GP30 recorded after 30 min of
oral administration of glucose and sucrose showed
significant difference. In sucrose treatment, δ was
17.16±0.43% for ASHE 400 mg/kg where in glucose
fed rat it was 38.33±0.92% this indicate the ASHE is
delaying in attainment of glycemic peak value in
sucrose fed rats. It is indirectly suggesting the
inhibition of intestinal enzyme responsible for
digestion of starch (sucrase). This suggests the
additional property of ASHE towards hypoglycemic
property i.e its action as secretogague and also as
inhibitor of intestinal enzymes, responsible for
carbohydrate metabolism.
Other reports have also indicated such reduction in
AUC with reference to acarbose and other herbal
drugs28,30. This could be due to presence of
polyphenolic compounds in the extracts, which binds
to the protein and inhibits its activity.
When the activity of α-glucosidase in the intestinal
homogenate, isolated from the ASHE treated rats for
7 days in different doses of 100 and 400 mg/kg was
tested, a significant inhibition was noted in its
activity. Acarbose was used as positive control, which
also showed similar α-glucosidase inhibitory effect.
So the ASHE extract acting on 2 level i.e it raised the
insulin level (Table 2) in diabetic rats when compared
with Glimepiride. The Glimepiride is a drug of
sulphonyl urea group and raises the insulin level to
17.36±0.90 µU/mL, without any significant inhibition
of α-glucosidase activity. It was only in range of
22.18±1.24% while in similar conditions, Acarbose,
inhibited α-glucosidase activity to tune of
61.66±1.52%. Interestingly, acarbose did not raise the
insulin level and it remained at 10.50±1.94 µU/mL
(Table 2).
However, the hexane extract of Annona squamosa
leaves showed both properties together. It raised the
insulin level (11.58±1.80 at 100 and 16.26±1.20
µU/mL at 400 mg/kg dose respectively) and also
inhibited the activity of α-glucosidase (41.18±2.46%
at 100 and 78.10±1.57% at 400 mg/kg, respectively).
Thus it could be suggested that hypoglycemic
response of leaves of Annona squamosa has
additional property than the existing standard drugs
such as Glimepiride and Acarbose.
The in vitro studies further supported the inhibitory
role of ASHE on α-glucosidase activity. On incubation
of ASHE extract with enzyme preparation there was
concentration dependent inhibition in activity, which
could be due to the interaction of secondary
metabolites of ASHE with α-glucosidase protein.
Acarbose showed significant inhibitory effect also.
Therefore, the retardation and delay of carbohydrate
absorption with a plant-based α-glucosidase inhibitor
offers a prospective therapeutic approach for
the management of type 2 diabetes mellitus and
borderline patient.
Conclusion
The hexane fraction of AS leaves (ASHE) showed
hypoglycemic response better than its water decoction
or methanol extract. Its mechanism of action could be
through 2 mechanisms, i.e. by enhancing the insulin
level (as secretagogue) and also by inhibiting the
activity of intestinal α-glucosidase. Thus it can be
used as food supplement for the regulation of
postprandial hyperglycemia (PPH), which is one of
the major causes for diabetic complications.
Acknowledgement
Thanks are due to UGC for financial support, Parul
Pathology & Research Centre, Varanasi for insulin
assay and Dr. Girish Singh for help in statistical
analysis.
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