Journal of General Microbiology (1989), 135, 675-682.
Printed in Great Britain
675
Degradation of Fungal Cell Walls by Lytic Enzymes of
Trichoderma harzianum
By A L E X SIVAN*T A N D I L A N C H E T
Department of Plant Pathology and Microbiology, The Hebrew University of Jerusalem,
Faculty of Agriculture, Rehovot, 76100, Israel
(Received 18 May 1988; revised 12 October 1988; accepted 16 November 1988)
In in vitro tests, two strains of Trichoderma harzianum failed to parasitize colonies of Fusarium
oxysporurn f. sp. vasinfectum and F. oxysporum f. sp. melonis. However, these strains were
strongly mycoparasitic on Rhizoctonia solani and Pythium aphanidermatum. When grown in
liquid cultures containing laminarin, chitin or fungal cell walls as sole carbon sources, both
strains of T . harzianum released 1,3-P-glucanaseand chitinase into the medium. Higher levels of
these enzymes were induced in strain T-203 than in T-35 by hyphal cell walls of F. oxysporum.
When the lytic enzymes produced by T-35 were incubated with hyphal cell walls of the test fungi,
more glucose and N-acetyl-D-glucosamine was released from cell walls of R. solani and
Sclerotium rolfsii than from those of F . oxysporum. Treatment of F. oxysporum cell walls with
2 M-NaOH, protease or trypsin prior to their incubation with the lytic enzymes of T. harzianum
significantly increased the release of glucose and N-aCetyl-D-glUCoSamine. The effect of these
treatments on R . solani and S . rolfsii cell walls was much lower. These results suggest that
proteins in the cell walls of F. oxysporum may make these walls more resistant than those of
R . solani or S . rolfsii to degradation by extracellular enzymes of T . harzianum.
INTRODUCTION
The direct mycoparasitic activity of Trichoderma spp. is one of the major mechanisms
proposed to explain their antagonistic activity against soil-borne plant-pathogenic fungi
(Dennis & Webster, 1971;Elad et al., 1982; Lynch, 1987; Ridout et al., 1986). The lytic activity
of fungal, as well as of bacterial, antagonists is mainly due to the lytic enzymes 1,3-P-glucanase
and chitinase (Mitchell & Alexander, 1963; Henis & Chet, 1975). 1,3-P-Glucanase is a semiconstitutive enzyme (Bull & Chesters, 1966) which may be induced by several inducers such as
laminarin, starch, xylose, mannitol and glycerol (Reese & Mandels, 1959). However, in the
presence of laminarin the excretion of this enzyme increases (Elad et al., 1982). Chitinase is an
inducible enzyme excreted by many micro-organisns in cultures containing chitin or its
oligomers as sole carbon source (Monreal & Reese, 1969).
Different strains of Trichoderma harzianum effective in controlling Rhizoctonia solani
produced 1,3-P-glucanase and chitinase in cultures containing cell walls of this pathogen as a
sole carbon source (Elad et al., 1982; Hadar et al., 1979; Ridout et al., 1986). Similarly, Tokimoto
(1982) reported the production of these enzymes in dual cultures of T. harzianum and Lentinus
edodes. It has been suggested that the lytic activity of several strains of T . harzianum on cell walls
of Sclerotium rolfii, Rhizoctonia solani and Pythium aphanidermatum can be correlated with the
degree of biological control of those pathogens in vivo (Artigues & Davet, 1984; Elad et al., 1982).
f Present address : Department of Horticultural Sciences, Cornell University, New York State Agricultural
Experiment Station, Geneva, NY 14456, USA.
Abbreviations: S M , synthetic medium; YM, yeast-extract/glucose medium; PDA, potato dextrose agar;
GlcNAc, N-acetyl-D-glucosamine.
0001-4894 0 1989 SGM
676
A . S I V A N A N D I . CHET
The objective of the present study was to evaluate the possible role of mycoparasitism in the
biological control of Fusarium oxysporum obtained with a new strain of T. harzianum. This strain
is one of the very few strains effective in controlling this pathogen (Sivan & Chet, 1986; Sivan et
al., 1987).
METHODS
Fungal strains and growth media. Trichoderma harzianum strains were cultured at 30 "C on a synthetic medium
(SM; Okon et al., 1973) containing (g per litre of distilled water): glucose, 15; MgS04.7H,0, 0.2; KH2P04,0.9;
KC1, 0.2; NH,NO,, 1.0; Fez+,0-002; Zn2+,0.002; agar, 20 (in solid medium). The mycolytic activity of the
biocontrol agent ( T . harzianum strain T-35) against Fusarium oxysporum was compared with that of another
T. harzianum strain (T-203) isolated by Elad er al. (1980) and reported as an effective mycoparasite of Rhizoctonia
solani Kuhn and Sclerotium rolfsii Sacc. (Elad et al., 1982).F. oxysporum f. sp. melonis Snyd. & Hans. ( F . 0.melonis)
and F. oxysporum f. sp. vasinfectum (Atk.) Snyd. & Hans. ( F . 0.vasinfectum) were isolated from infected melon and
cotton plants, respectively (Sivan & Chet, 1986) and cultured at 27 "C on a yeast extract/glucose medium (YM)
containing (g per litre of distilled water): yeast extract (Difco), 5 ; peptone (Difco), 5 ; glucose, 10; agar, 20 (in solid
medium). R . solani, S . roysii and Pyrhium aphanidermatum were grown on SM at 30 "C.
Dual culture tests. Mycelial disks ( 5 mm in diameter) of F. 0. melonis, F. 0. vasinjectum, R . solani or
P. aphanidermatum were placed on one edge of a Petri dish containing PDA, while mycelial disks of T . harzianum
were placed on the opposite side of the plate. Because of the lower growth rate of F . oxysporum, in each test where
this fungus was used, the inoculation with mycelial disks of T . harzianum was performed 72 h after that of
F. oxysporum ; otherwise the inoculation with T. harzianum was performed simultaneously with that of the test
fungi. After the desired incubation time, at 27 "C, the overgrowth of colonies of the test fungi by the antagonist was
determined.
Survival of mycelium of F. oxysporum and S . rorfii was determined after exposure to conidia of T . harzianum.
Mycelial disks ( 5 mm in diameter) were removed from 72-h-old cultures of the tested fungi on water agar (20 g agar
per litre of distilled water). Disks were soaked for 30 s in a conidial suspension of T . harzianum ( lo6 conidia ml-I)
and incubated in Petri dishes, each containing four layers of wet Whatman no. 1 filter paper. Mycelial disks
treated with autoclaved distilled water and incubated as described above served as controls. After the desired
incubation time, mycelial disks of F. oxysporum were transferred to a Fusarium-selective medium (Nash & Snyder,
1962) containing 1 mg methyl l-(butylcarbamoyl)-2-benzimidazolecarbamate(Benomyl) l-', in order to inhibit
growth of T. harzianum (Elad & Chet, 1983). Similarly, mycelial disks of S . rolfsii were transferred to Shl plates
containing the same concentration of Benomyl. The results were expressed as the percentage of the mycelial disks
from where the test fungus grew.
Preparation of hyphal cell walls. Cell walls were obtained from F . 0. melonis, F. 0.vasinjectum, R . solani and
S . rovsii after culture at 27 "C for 5 d in 50 ml liquid YM. Flasks with cultures of R . solani or S . rolfsii were shaken
in a rotary shaker at 120r.p.m., while those of F. oxysporum were incubated without shaking, to reduce
conidiation. After incubation, mycelia were thoroughly washed with distilled autoclaved water and homogenized
on ice, with an Ultra Turax homogenizer (Ika-Werk, W. Germany) for 5 min at the highest speed. Mycelial
suspension was centrifuged at 30000 g for 20 min at 4 "C. The pellet was resuspended in distilled water and
sonicated on ice three times for 5 min each using a Heat Systems-Ultrasonics sonicator at full amplitude. The
suspension was centrifuged again at 800g for 10 min at 4 "C to precipitate the coarse particles. The supernatant
containing the remaining fine particles was washed by centrifugation and homogenized intermittently until no
residual glucose, protein or amino acids could be detected in the supernatant, as determined with glucose oxidase
(Sigma), Coomassie brilliant blue (Sedmak & Grossberg, 1977) or ninhydrin (Cocking & Yemm, 1954) reagents,
respectively. The precipitated walls were then deep-frozen, lyophilized and kept as powder in a sealed container
until use (Chet & Huttermann, 1980).
Induction of extracellular lytic enzymes in T. harzianum. Erlenmeyer flasks (250 ml) each containing 50 ml liquid
SM were inoculated with 1 ml of a conidial suspension ( 5 x lo7 conidia ml-l) of T. harzianum. The glucose in the
medium was substituted with one of the following carbon sources (each at 2 mg ml-') : laminarin (Sigma), colloidal
chitin (prepared according to Rodriguez-Kabana et al., 1983),or one of the fungal cell wall preparations. Cultures
were incubated at 28 "C in a rotary shaker at 120 r.p.m. for the desired time, then centrifuged at 15000 g at 4 "C for
10 min. The supernatant was dialysed against distilled water at 4 "C for 24 h to eliminate residual glucose or Nacetyl-D-glucosamine(GlcNAc). The dialysate was lyophilized or tested directly for enzyme activity. Filtrates
from chitin cultures also contained traces of 1,3$-glucanase, but those from laminarin cultures contained no
detectable chitinase.
Enzyme assays. The activity of extracellular lytic enzymes was tested according to Elad et al. (1982). 1,3-pGlucanase (exo-l,3-/3-D-glucosidase,
EC 3.2.1 . 5 8 ) was assayed by following the release of free glucose from
laminarin using the glucose oxidase reagent. Specific activity was expressed as pmol glucose h-I (mg protein)-'.
The reaction mixture, containing 1 ml crude 1,3-/3-glucanase,1 mlO.1 M-citrate buffer (pH 5.1) and 1-6mg soluble
Lytic activity of' Trichoderma harzianum
677
laminarin, was incubated at 38 "C for 1 h. The reaction was stopped by placing the reaction mixture in boiling
water.
EC 3.2.1 . 14) was assayed by following the release of
Chitinase (1,4-,4-poly-N-acetyl-~-gliicosaminidase,
GlcNAc from colloidal chitin (Reissig et al., 1959). Specific activity was expressed as pmol GlcNAc h-' (mg
protein)-'. The reaction mixture, containing 1 ml crude chitinase, 1 ml 0.1 M-citrate buffer (pH 5.1) and 1.6 mg
colloidal chitin, was incubated at 38 "C for 2 h and the reaction then stopped by boiling.
The release of monomers from fungal cell walls was also tested using lypophilized crude enzymes from cultures
containing chitin or laminarin as sole carbon sources and designated chitinase or 1,3-P-glucanase, respectively.
The reaction mixture (2 ml), containing 1.5 mg lyophilized enzyme and 1.6 mg cell walls ml-l was incubated at
38 "C for 24 h. Each test tube was amended with 10 p1 methylbenzene (toluene) to prevent contamination.
The activity of these enzymes on a living mycelium was tested by using mycelial mats of F. o. melonis grown in
liquid YM for 96 h. Each mycelial mat was washed with sterile citrate buffer (pH 5-1) and transferred to a 250 ml
Erlenmeyer flask containing 25 ml of the same buffer and lyophilized enzyme (1 mg ml-l) obtained from culture
filtrates of T . harzianum grown on laminarin or chitin as sole carbon source.
Modjfication of'hyphul cell walls. In some experiments, cell walls were treated prior to application of the lytic
enzymes. In all these treatments, 40 mg of cell walls were suspended and shaken for 1 h at 50 r.p.m. in 60 ml of (a)
2 M-NaOH at 25 "C, (h)chloroform/methanol(2 : 1, v/v) at 25 "C, (c) protease (Sigma type XXV) (300 yg ml-l in
0.1 M-phosphate buffer pH 7.0) at 37 "C or ( d )trypsin (100 yg ml-' in 0.1 M-phosphate buffer pH 7.0) at 37 "C. The
proteolytic activity was stopped by boiling for 10 min at 100 "C.
After each treatment the agent was removed and the hyphal walls were thoroughly washed by centrifugation
(I5000 g at 4 "C), suspended in flasks containing 20 ml 0.1 M-citrate buffer (pH 5.1) amended with lyophilized
crude 1,3-P-glucanase or chitinase, and incubated for 24 h at 38 "C.
Reproducibility. In all experiments, three replicates of each treatment were used. All experiments were
performed at least twice.
RESULTS
In vitro tests
Both strains of T. harzianurn failed to parasitize colonies of I;. 0. melonis and F. 0.vasinfectum
even after 160 h incubation. However, when cultured on PDA plates with R. solani, P.
aphanidermatum or S. roljiii, T. harzianum strain T-35 overgrew the test fungal colonies. In dual
culture plates of T-35 and P. aphanidermatum, after 120 h incubation the antagonist covered
most of the test colony, while the rate of colonization of R. solani and especially of S . rolfii was
lower (Table 1). Similar results were obtained when T . harzianum T-203 - the mycoparasite of
R. solani and S. rolfsii (Elad et al., 1980) - served as the antagonist.
Dual culture tests performed with other media - SM, YM and Malt-extract agar (Sigma) showed similar results.
After treatment of disks of F . 0. melonis and F . 0.vasinfectum with conidia of T-35 or T-203 and
incubation for up to 16 d, hyphae survived in 100 and 75% of the disks, respectively. However,
when S. roljsii was subjected to the same treatment for 7 d, no hyphae survived (Fig. 1).
4
8
12
Incubation time (d)
16
Fig. 1. Survival of mycelial disks of F. o. vusinfectum (O), F . o. melonis (A) and S . rolfsii (m) after
treatment with conidia of T . harzianum T-35 (lo6 conidia ml-I).
A . S I V A N A N D I . CHET
24
48
72
24
48
72
96
120
Incubation time (h)
Incubation time (h)
Fig. 2. Specific activity of (a) 1,3-fl-glucanase and (b)chitinase produced by T. harzianum T-35 ( 0 )and
T-203 ( 0 )during growth in liquid SM containing cell walls of F. 0.melonis (2 mg ml-l) as sole carbon
source.
Table 1. In vitro mycoparasitism of test fungi by T. harzianum T-35
The data represent the average extent of growth of hyphae of T-35 over mycelium of the test fungus.
F. 0.melonis and F. 0. vasinfectum were not overgrown by T. harzianum, even after 160 h incubation.
Overgrowth of fungal colonies
by T. harzianum (mm)
r
\
Incubation time (h):
Test fungus
72
96
120
S. rolfsii
R. solani
P. aphanidermatum
0
15.1
27.0
2.1
19.2
22.5
32.5
38-1
4.5
Activity of cell-wall-degrading enzymes in T . harzianum
When T. harzianum T-35 and T-203 were cultured in liquid medium containing laminarin as
sole carbon source, both strains produced high levels of 1,3-P-glucanase [ 165.5 and 210-3pmol
glucose h-I (mg protein)-' after 48 h incubation, respectively]. After growth on chitin as sole
carbon source for 48 h the level of chitinase released to the medium was similar in both strains
[5-3 and 5-5 pmol GlcNAc h-' (mg protein)-' in T-35 and T-203, respectively].
When the T. harzianum strains were grown in media amended with hyphal cell walls of F . 0.
melonis as sole carbon source (Fig. 2a, b), the levels of 1,3-fi-glucanaseand chitinase secreted by
T-203 were higher than those produced by T-35. In both strains, maximal induction of 1,3-/3glucanase was obtained after 48 h incubation (Fig. 2a). However, the maximal level of chitinase
was obtained after 72 h in T-203, but after 48 h in T-35 (Fig. 2b).
The specific activities of the extracellular lytic enzymes of T. harzianum T-35 were also tested
using cell walls of the four test fungi as the substrate (Fig. 3). The lytic activity of 1,3-/?-glucanase
was higher when incubated with cell walls of S . rolfsii or R. solani than with those of P. 0.
vasinjectum and F. 0.melonis. Similarly, when incubated with chitinase, the release of GlcNAc
from cell walls of S. rolfsii was the highest amongst the tested hyphal walls. On the other hand,
there was little or no difference between the specific activity of chitinase after incubation with
cell walls of R. solani and the fusaria (Fig. 3).
The release of monomers from a live mycelium of 1". 0.melonis after treatment with the crude
lytic enzymes of T-35 was minimal (Fig. 4).
Lytic activity u j Trichuderma harzianum
a
679
F. o. melonis
I
F. o. t'asinfecturn
R. soiani
W
c
.
'
b
7 100 * &O
S . rolfiii
a
u
ik
C
Fig. 3. Specific activity of (a) 1,3-P-glucanaseand (b)chitinase of T. harzianum T-35 incubated with cell
walls (1 mg ml-') of the four fungi indicated. Columns marked by the same letter are not significantly
different (P= 0.05) according to Duncan's multiple range test.
8
--
1.6
6
%
0.4
l?2
24
36
48
Incubation time (h)
60
Fig. 4. Release of glucose and GlcNAc from a live mycelium of F. oxysporum f . sp. melonis by,
respectively, 1,3-fl-glucanase(0)
and chitinase (m) of T. harzianum (T-35). The lytic enzymes were
incubated with mycelial mats of F . oxysporurn in a reaction mixture containing 1 mg lyophilized crude
enzyme ml-' and one 96-h-old mycelial mat in 25 ml citrate buffer (pH 5.1) amended with 0.5 ml
toluene.
The possible interference of a fusarial cell wall moiety in the mycoparasitic activity of T.
harzianum T-35 was tested by treating cell walls with alkali or organic solvent prior to incubation
with the lytic enzymes (Table 2). 1,3-P-Glucanase incubated with NaOH-treated cell walls of
both fusaria released more glucose (up to 135fold) compared with incubation with untreated
walls. Similarly, an improvement in chitinase activity was found with the NaOH-treated
Fusarium walls. In contrast, NaOH treatment had only a slight effect on the susceptibility of
walls of R.sulani and S . ruEfsii to attack by the two lytic enzymes (Table 2). Treatment with
chloroform/methanol did not increase the release of glucose or GlcNAc from walls of either
Fusariurn strain (Table 2).
The hypothesis that a protein or a protein-like constituent(s) is involved in the resistance of
fusarial cell walls to lytic enzymes was tested using proteolytic enzymes (Table 3). Protease or
trypsin treatment of walls of F. u. m e h i s or I;. u. vasinfectum before incubation with 1,3-pglucanase or chitinase increased the release of monomers, as compared with nontreated walls.
However, proteolytic treatments had little effect on cell walls of R. solani and S. rolfsii (Table 3).
680
A. SIVAN A N D I . CHET
Table 2. Eflect of’NaOH and chloroformlmethanol treatments on the release of monomers from
cell walls of F. oxysporum, R . solani and S . rolfsii by 1,3-P-glucanase and chitinase of
T . harzianum T-35
-
Release of monomers (pg ml-I) after treatment :
f
None
Cell walls of
w
Glucose
F. 0. melonis
F . 0. vasinfectum
R. solani
S. roljsii
14-5
12.0
76.0
63.0
Chloroform/
methanol (2 :1)
2 M-NaOH
Y
GlcNAc
Glucose
GlcNAc
42-5
32.3
22.0
193-0
152.5
162.5
102.5
82.0
241-4
246.1
74.0
125.5
Glucose
GlcNAc
6.0
44.0
30-5
31.2
250.8
9-0
74-0
73-0
Table 3. Efect ofproteolytic enzyme treatments on the release of monomers from cell walls of
F. oxysporum, R . solani and S . rolfii by 1,3-P-glucanase and chitinase of T. harzianum T-35
-
Release of monomers (pg ml-l) after treatment:
f
None
Cell walls of
F. 0. melonis
F . 0.vasinfectum
R. solani
S . rolfsii
r
>
Protease
Glucose
GlcNAc
11.8
7.4
88.2
122.1
41.2
42.0
43.2
153.2
Trypsin
Glucose
GlcNAc
Glucose
GlcNAc
37.2
44.7
81.9
109.7
59.6
78-8
30.2
121.0
44.1
48.9
86.3
131-5
79.8
86.0
41.0
152.8
DISCUSSION
The mycoparasitic potential of Trichoderma spp. is well established (Dennis & Webster, 1971;
Elad et al., 1982; Lynch, 1987). This trait has often been utilized as a means of in vitro screening
for biocontrol candidates (Elad et al., 1980; Hadar et al., 1979). In the present study, using the
same dual culture technique, neither of the tested T . harzianum strains showed a significant
mycoparasitic interaction with Fusarium oxysporum. T-35, however, parasitized mycelium of
Rhizoctonia solani, Pythium aphanidermatum and Sclerotium rolfsii. Moreover, the survival of
mycelium of F . oxysporum treated with conidia of T-35 was markedly higher than that of S .
rolfii. Similar results were also obtained with T-203, a mycoparasite of R . solani and S . rolfii
(Elad et al., 1982). This was the first indication of the higher resistance of I;.oxysporum to lysis.
Lynch (1987) demonstrated the overgrowth of Fusarium spp. by two Trichoderma strains. Thus,
it appears that the potential of Trichoderma spp. to parasitize Fusarium is strain dependent.
T . harzianum is, however, an effective biocontrol agent of F. oxysporum on several crops
(Sivan & Chet, 1986, 1987).The lack of mycoparasitic interaction between T . harzianum and F .
oxysporum indicates that this mechanism is unimportant in this specific system. Therefore, in
vitro dual culture tests appear not to be a sufficient screen for effective biocontrol agents against
F. oxysporum.
Two hypotheses for the ineffectiveness of mycoparasitism against F. oxysporum were
evaluated: (1) lytic enzymes of T . harzianum (e.g. 1,3-P-glucanase and chitinase) are not
excreted, or (2) lytic enzymes are produced and released but the cell walls of F . oxysporum are
more resistant to lysis than other fungal cell walls.
To test the first hypothesis we compared the induction and activity of lytic enzymes of T .
harzianum T-35 with,those of the mycoparasite T-203. When grown in liquid medium containing
laminarin or chitin as sole carbon source both strains secreted similar amounts of both enzymes.
On the other hand, when the strains were cultured on cell walls of F. oxysporum as sole carbon
source the release of chitinase (but not 1,3-P-glucanase)was 90% higher from T-203 than from
T-35. Similarly, chitinase produced by T-203 released more GlcNAc from cell walls of F. 0.
Lytic activity o j Trichoderma harzianum
68 1
melonis than did the chitinase of T-35. However, neither T-35 nor T-203 parasitizes fusaria; and
only T-35 is an effective biocontrol agent of fusarial wilt diseases. Thus, the level of lytic enzyme
production is unrelated to either mycoparasitism or biocontrol capability. Similar enzyme
preparations did, however, degrade hyphal walls of S . rolfsii and R. solani, which suggests that
fusarial cell walls are more resistant to lysis (hypothesis 2). These results were confirmed by the
inability of T-35 to degrade cell walls of live mycelium of F. oxysporum. Similarly, the
mycoparasite Pythium nunn was unable to degrade live mycelium of F . oxysporum f. sp.
cucumerinum (Elad et al., 1985).
Thus our second hypothesis, that cell walls of F. oxysporum are more resistant to
mycoparasitism, is probably correct. Treatment of hyphal walls of F. oxysporum with NaOH or
proteolytic enzymes increased their susceptibility to lysis by chitinase and 1,3-@-glucanaseof T.
harzianum T-35. Pretreatment of the same hyphal walls with an organic solvent had almost no
effect on their lysis. This suggests that fusarial cell walls contain a proteinaceous interfering
substance. However, neither the alkali nor the proteolytic pretreatment gave such an effect with
cell walls of R. solani or S . rolfsii. Elad et al. (1985) similarly found that lytic enzymes produced
by Pythium nunn also acted more effectively on trypsin-treated walls of P. oxysporum f. sp.
cucumerinum than on non-treated walls. They postulated the presence of a mucilaginous layer on
hyphae of fusaria that protects cell walls against degradation.
We have recently found that Fusarium oxysporum cell walls contain more protein than walls of
other fungi (unpublished results). Other fusaria also have high (7-28 %) protein contents (Barran
et al., 1975; Laborda et al., 1974; Schneider et al., 1977). Schneider et al. (1977) suggested that
the very high protein content of chlamydospores of F . suIfureum (21 %) may be responsible for
their ability to resist lysis in soil.
Our present study suggests that the lack of mycoparasitic interaction between T. harzianum
(T-35) and F. oxysporum may be a result of an outer layer of protein in the hyphal walls of the
latter, thus increasing their resistance to lysis. The significant biological control of F. oxysporum
obtained by this strain (Sivan & Chet, 1986; Sivan et af., 1987) may be due to other mechanisms
such as competition (Sivan & Chet, 1989) or antibiosis.
This study was supported in part by the National Council of Research and Development (Israel) and the GSF
Munchen, West Germany.
The authors gratefully acknowledge the critical review of the manuscript by Dr G. E. Harman, NY State
Agricultural Experiment Station Geneva, NY, USA, and the technical assistance of Mr J. Inbar.
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