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Soil Biology & Biochemistry 32 (2000) 815±823
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Interaction of catalase with montmorillonite homoionic to cations
with di€erent hydrophobicity: e€ect on enzymatic activity and
microbial utilization
L. Calamai a,*, I. Lozzi a, G. Stotzky b, P. Fusi a, G.G. Ristori c
a

Dipartimento di Scienza del Suolo e Nutrizione della Pianta, UniversitaÁ degli Studi, Piazzale Cascine 28, 50144 Firenze, Italy
b
Laboratory of Microbial Ecology, Department of Biology, New York University, New York, NY 10003, USA
c
Istituto per la Genesi e l'Ecologia del Suolo (IGES), CNR, Piazzale Cascine 28, 50144, Firenze Italy
Accepted 14 November 1999

Abstract
The exchange sites of montmorillonite (M) were made homoionic to calcium (Ca), hexadecyltrimethylammonium (HDTMA)
or pyridinium (PY) cations. The clays were used as adsorbents for the enzyme, catalase (CA). Equilibrium adsorption and
binding isotherms (i.e., after washing of the clay±CA complexes after adsorption at equilibrium until no CA was desorbed) were
of the L3-type and ®tted the Langmuir equation in the initial, but not in the later, portions of the isotherms. The amounts

adsorbed and bound at the plateau, as well as the anity, were higher for the hydrophobic clays (M±HDTMA and M±PY) as
indicated by the Langmuir parameter, Bmax and Keq. In all three systems, there was additional adsorption after the initial
plateau at higher concentrations of CA. In the case of M±Ca±CA this probably resulted from some penetration of CA into the
interlayer spaces of the clay, as shown by X-ray di€raction analysis. No penetration of the interlayers was observed in the M±
HDTMA±CA and M±PY±CA systems. The additional adsorption that occurred after the initial plateau in these systems may
have resulted from the formation of multilayers of CA or from a change in the orientation of CA on these clay-organic surfaces,
which may also have occurred in the M±Ca±CA system in addition to intercalation. Most of the CA adsorbed at equilibrium
was bound on the clays (85±90%). Fourier-transform infrared di€erence spectra showed a shift in the Amide I and Amide II
frequencies for only M±Ca±CA and M±PY±CA, which was consistent with the hypothesis of a conformational modi®cation of
the structure of CA on M±Ca and M±PY. The enzymatic activity of CA adsorbed at equilibrium on the three clays was lower
than that of free CA and decreased in the order of M±Ca±CA > M±PY±CA > M±HDTMA±CA. As shown by the values of
the overall ®rst-order rate constant, K1, there was a further reduction in activity when CA was bound on the clays, especially on
M±Ca. The pH optimum for the activity of CA remained essentially unchanged when adsorbed or bound on all clays. CA
bound on the clay systems, except on M±PY±CA, was poorly utilized in comparison with the free enzyme as a sole source of
carbon or nitrogen. 7 2000 Elsevier Science Ltd. All rights reserved.

1. Introduction
Interactions between clay minerals and organic polymers of biological interest (e.g., enzymes, other proteins, nucleic acids) are important in soil (Stotzky,
1986, 1989; Khanna and Stotzky, 1992; Gallori et al.,
1994; Tapp et al., 1994; Vettori et al., 1996, 1999; Kos-

* Fax: +39-055-333273.
E-mail address: calamai@iges.®.cnr.it (L. Calamai).

kella and Stotzky, 1997; Alvarez et al., 1998; Tapp and
Stotzky, 1998; Khanna et al., 1998). These organic
molecules di€er in their anity for clay surfaces,
which has been related to such physicochemical factors
as the types of cations on the clay exchange complex,
pH, origin and amount of the layer charge, surface
charge density, speci®c surface area, and structure of
the molecules (Theng, 1979; Stotzky, 1986; Fusi et al.,
1989).
The properties of smectites homoionic to long-chain

0038-0717/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved.
PII: S 0 0 3 8 - 0 7 1 7 ( 9 9 ) 0 0 2 1 1 - 4

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L. Calamai et al. / Soil Biology & Biochemistry 32 (2000) 815±823

alkylammonium cations, which are able to change the
nature of the clay surface from hydrophilic to hydrophobic, have been studied, especially in relation to the
adsorption of small organic and nonpolar molecules
(Boyd and Mortland, 1985, 1986, 1990; Lee et al.,
1990; Favre and Lagaly, 1991; Jaynes and Boyd,
1991a, 1991b). These studies have demonstrated that
the siloxane surfaces of smectites possess hydrophobic
characteristics at sites distant from isomorphous substitution and are able to adsorb such hydrophobic
molecules as hydrocarbons. However, the e€ect of
these hydrophobic sites is overshadowed by the preponderance of hydrophilic sites. When inorganic
charge-compensating cations on clays are replaced
with hydrophobic cations, e.g., trimethylphenylammonium
(TPMA),
hexadecyltrimethylammonium
(HDTMA), the hydrophobicity of the clay surfaces
increases. Moreover, when the hydrophobic organic
cations possess a long alkylammonium tail (e.g.,
HDTMA), the formation of a ``bulk'' hydrophobic

phase is postulated, and the adsorption of small nonpolar organics on the clay surfaces may be enhanced
(Favre and Lagaly, 1991). Smectites made homoionic
to alkylammonium cations are important not only in
the adsorption and subsequent deactivation of toxic
pollutants in soil, water and industrial wastes (Boyd et
al., 1988), but also in the adsorption of macromolecules of biological interest, including enzymes, with
possible subsequent modi®cation of their activity (Garwood et al., 1983; Boyd and Mortland, 1985, 1986,
1990). Depending on the type of organic cation on the
clay and the enzyme being studied, the enzymatic activity of the adsorbed enzyme may be either decreased
or enhanced (Boyd and Mortland, 1986).
Our purpose was to determine the e€ect of di€erent
hydrophobic and hydrophilic charge-compensating cations, i.e., HDTMA, pyridinium (PY), and calcium
(Ca2+), on the equilibrium adsorption and binding
and on the enzymatic activity and microbial utilization
of bound catalase (CA). These cations were chosen to
provide di€erent degrees of hydrophobicity (high for
HDTMA and low for Ca) of the clay surface.

2. Materials and methods
Montmorillonite (M) from Upton, WY, was

obtained from Ward's Natural Science Establishment
(Rochester, NY). The adsorbed CA > bound CA. Parallel analyses were performed using comparable amounts
of the clays only, to estimate the contribution of the
clays to the decomposition of H2O2. No detectable decomposition of H2O2 by the clays alone was observed
at the clay-to-H2O2 ratios used.
CA is partially inactivated by contact with high concentration of H2O2, e.g., in the range of the Michaelis±Menten constant (Km=1.1 M) where pseudosaturating kinetics are obtained unless the initial velocity is measured within a few seconds after mixing
(Ogura, 1955), which is incompatible with obtaining a
uniform mixture of H2O2 and suspensions of claybound CA. Therefore, an interval of 1 min and initial
concentrations that would not cause decomposition of
CA (3.94 to 81.7 mM H2O2) were used. At these concentrations, CA exhibits ®rst-order kinetics, and, therefore, the kinetic parameter calculated was the overall
®rst-order rate constant, K1 (in Mÿ1 sÿ1), for the
equation, V=K1x[H2O2]x[CA], where V = velocity of
decomposition of H2O2 (in M sÿ1), and [H2O2] and
[CA] are the concentrations of H2O2 and CA (both in
M), respectively. A plot of V over [H2O2]x[CA] yields
a straight line with slope=K1
The enzymatic activity of free and clay-bound CA
was also determined at pH 4±10 using 9.5 mM H2O2
and the following bu€ers (150 mM): citrate, pH 4±5;
KH2PO4/Na2HPO4, pH 5±8; and borate, pH 8±10.

The activity of CA is dependent on pH, but it is not
in¯uenced by the type or concentration of bu€er
(Ogura, 1955). Because H2O2 can decompose chemically at alkaline pH, parallel analyses were done in the
bu€er solutions alone, to estimate the amounts of
H2O2 decomposed chemically. There was no detectable
chemical decomposition of H2O2 at any pH.
The utilization of CA, either free or bound on the
di€erent clay systems, as a sole source of carbon or

817

nitrogen by a mixed community of microbes was evaluated by measuring, by FT-IR, CO2 evolution during
incubation of CA with a microbial inoculum derived
from soil. Free or bound CA (2 mg) suspended in
0.5 ml of ddH2O was mixed with 1 ml of modi®ed
Davis' minimal medium that did not contain nitrogen
(Dmin) (3  concentrated and sterilized) (Gerhard et al.,
1981) and 0.2 ml of soil inoculum (Si) (10 g of a nonsterile and unfertilized garden soil suspended in 25 ml
of tap water, ®ltered through a paper towel, centrifuged at 10,000 g, washed 3 times in ddH2O, and
resuspended in ddH2O, to a ®nal optical density at

500 nm of 0.8 to 1) in 100-ml Erlenmeyer ¯asks and
adjusted to a ®nal volume of 3 ml with sterile ddH2O.
The ¯asks were sealed with air-tight rubber stoppers
and maintained at 258C in the dark. CO2 evolution
was measured after 3 and 7 d by injecting 2 ml of air
from the head-space of each ¯ask with a syringe into a
micro gas cell (optical path=10 cm, total

Fig. 1. Equilibrium adsorption and binding isotherms of CA on
montmorillonite homoionic to HDTMA, PY, or Ca. Standard errors
of the means are within the dimensions of the symbols.

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L. Calamai et al. / Soil Biology & Biochemistry 32 (2000) 815±823

volume=8 ml), which was ¯ushed extensively with N2
before each analysis by FT-IR. Preliminary experiments showed that the best FT-IR scanning conditions for quantitative determination of CO2 were
two scans at a resolution of 32 cmÿ1 and peak integration of the spectra at absorbances between 2440
and 2100 cmÿ1. The areas of the integrated peaks were

compared with a calibration curve constructed with
pure CO2.
Free or bound clay±CA was incubated with: (i)
Dmin+Si; (ii) Dmin+Si+glucose; (iii) Dmin+Si+NH4NO3; or (iv) Dmin+Si+glucose+NH4NO3
(with the amounts of glucose and NH4NO3 being
equivalent to the carbon and nitrogen contents of 2 mg
of CA). Control experiments with (i), (ii), (iii), and iv
either alone or with the homoionic clay systems (i.e.,
without CA) or with only HTDMA chloride or PY
chloride (in amounts equivalent to those present on
the clays), were done to evaluate the inhibition by or
utilization of the organic cations, free or bound on the
clay, by soil microorganisms.

3. Results and discussion
The shapes of the binding isotherms were similar to
those of the equilibrium adsorption isotherms, and 85±
90% of CA adsorbed at equilibrium was bound
(Fig. 1). Both isotherms were of the L3-type, according
to the classi®cation system of Giles et al. (1960), and

showed a good ®t to the Langmuir equation at low
concentrations of CA (Table 1), suggesting the formation of a monolayer of CA on the external surface
of the clays. This was con®rmed by X-ray di€raction
analyses of the clay±CA complexes, which showed no
di€erences, neither after drying at room temperature,
nor at 1508C, in the basal d001 spacing from that of
the pure clays at these lower concentrations of protein
(Fig. 2). The amount of CA adsorbed at equilibrium
on M±Ca at the initial plateau (Bmax), and the value
of the equilibrium constant (Keq), calculated with the

Langmuir equation, were lower than those with M±
HTDMA and M±PY (Table 1), indicating that the
adsorption of CA di€ered with the degree of hydrophobicity of the clay surface. More adsorption at equilibrium was expected on M±HDTMA than on M±PY,
as M±HDTMA was more hydrophobic. However,
higher Bmax and Keq values were obtained with M±PY,
probably because of its greater external surface area
(Table 1).
The isotherms did not ®t the Langmuir equation
over the entire range of concentrations of CA at equilibrium. The additional adsorption and binding of CA

on M±Ca after the initial plateau was probably the
result of the penetration of the protein into the interlayer spaces of the clay, as the X-ray di€ractograms
after drying at room temperature (Fig. 2) and after
heating at 1508C (not shown) showed an expansion of
the interlayer spaces with the higher amounts of CA
bound. In contrast, the additional adsorption and
binding of CA on M±HDTMA and M±PY after the
plateau, albeit not as great as on M±Ca, cannot be
explained by an intercalation by CA, as the d001 spacings of M±HDTMA±CA and M±PY±CA remained
unchanged regardless of the amount of CA bound.
The second rise in the adsorption and binding isotherms in the M±HDTMA±CA and M±PY±CA systems may have resulted from the formation of
multilayers of CA on the external surfaces of the clay
or from changes in the orientation of CA on the surfaces. The formation of multilayers and changes in
orientation may have also occurred in the M±Ca±CA
system, in addition to the intercalation of CA.
The frequencies of the Amide I and Amide II bands
of free CA and of the clay±CA complexes in the FTIR spectra are shown in Table 2. The Amide I band of
the M±Ca±CA and M±PY±CA complexes shifted to a
higher frequency (1655 vs 1650 cmÿ1 for free CA),
whereas the Amide II band shifted to a lower frequency (1536 and 1534, respectively, vs 1545 cmÿ1 for

free CA). These di€erences were signi®cant, as the frequencies were the average of 128 repeated scans. The

Table 1
Values of Bmax and Keq, regression coecients for ®tting adsorption data to the Langmuir equation, and speci®c surface areas of and water
retention by the clay systems
System

Bmaxa 2SEMb (mmol gÿ1 clay)

Keqc 2SEM (mMÿ1)

r 2d

Surface areae (m2 gÿ1 clay)

H2O retentionf (ml gÿ1 clay)

M±HDTMA±CA
M±PY±CA
M±Ca±Ca

1.420.07
1.720.11
0.620.04

17.822.9
25.024.1
3.120.9

0.997
0.998
0.993

9.9
18.0
27.5

7.54
6.17
4.04

a

Bmax=Maximum adsorption at plateau calculated by the Langmuir equation; see text for details.
SEM=Standard error of means.
c
Keq=Anity coecient for adsorption of Ca on the surfaces; see text for details.
d
Regression coecient for ®tting adsorption data to the Langmuir equation at the ®rst plateau.
e
External surface area measured by N2 adsorption at 77 K.
f
Measured by weight loss at 1058C. See text for details.
b

L. Calamai et al. / Soil Biology & Biochemistry 32 (2000) 815±823

819

Fig. 2. X-ray di€raction spectra of bound M±HDTMA±CA, M±PY±CA, and M±Ca±CA complexes after air-drying at room temperature. The
amounts of CA bound are indicated. Similar results were obtained when the complexes were dried at 1508C.

changes may have resulted from a distortion of the
structure of CA caused by its binding on these clays.
Shifts of the Amide I band (C1O stretching band) to
higher wavenumbers and of the Amide II bands (NH
bending) to lower wavenumbers are diagnostic of an
increase in random or less-ordered portions of secondary structure (D'Esposito and Koenig, 1978). No
di€erences were observed in the Amide I and II bands
of M±HDTMA±CA in comparison with free CA, indicating that binding of CA on this clay did not cause
any signi®cant perturbation of the structure of the protein. These observations were consistent with the hypothesis of a weaker binding of CA by hydrophobic
interactions on M±HDTMA than by hydrophilic interactions on M±Ca, as also suggested by Garwood et al.
(1983) for glucose oxidase and by Boyd and Mortland
(1985, 1986, 1990) for urease.
The values for the kinetic parameter, K1, of the activity of free, adsorbed and bound CA on the di€erent
Table 2
Infrared frequencies (cmÿ1) of CA free or bound on M±Ca, M±
HDTMA, or M±PYa
Form of CA

Amide I

Amide II

Free CA
M±HDTMA±CA
M±PY±CA
M±Ca±CA

1650
1650
1655
1655

1545
1544
1536
1534

a

Di€erential FT-IR spectra; see text for details.

clays are reported in Table 3. The value for free CA
was higher than the values reported in the literature
for CA from beef liver (Ogura, 1955; Nichols and
Schombaum, 1963), but it was consistent with the K1
calculated from information provided by Sigma Co.
for type C40 CA. These di€erences in the K1 for free
CA probably resulted from di€erences in the preparation and purity of the enzyme. When CA was
adsorbed at equilibrium on M±Ca, the value for K1
was reduced by 80% (Table 3), whereas the reduction
was 90% for M±PY±CA and 95% for M±HDTMA±
CA. The value of K1 for CA bound on M±Ca was
reduced by more than two order of magnitude (99.3%)
in comparison with free CA. This di€erence between
the activities of CA adsorbed at equilibrium and
bound suggests that di€erent pools of CA with di€erent enzymatic activity existed in the equilibrium complex of the hydrophilic M±Ca±CA system, i.e., tightly
bound CA, loosely bound CA, and CA dissolved in
the water retained by the clay pellet. For M±HDTMA
and M±PY, the di€erences in K1 values between
bound and adsorbed CA were small.
To evaluate the contribution to the enzymatic activity of the unadsorbed CA dissolved in the water
retained by the clay pellets after the initial centrifugation for the determination of the amount of CA
adsorbed at equilibrium, the pellets were weighed after
drying at 1058C for 12 h. The amount of water
retained by the hydrophobic systems was greater than
by M±Ca±CA (Table 1), probably because the rapid

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L. Calamai et al. / Soil Biology & Biochemistry 32 (2000) 815±823

Table 3
Kinetic parameter, K1, after 1 min for the activity of CA free, adsorbed or bound on M±Ca, M±HDTMA, or M±PY
Form of CA

K1 (Mÿ1 sÿ1)

ra

Residual CA activityb (%)

Reduction in CA activityc (%)

Free CA
M±HDTMA±CA
Absorbed
Bound
M±PY±CA
Adsorbed
Bound
M±Ca±CA
Adsorbed
Bound

6.46  108

0.97

100

3.84  107
2.20  107

0.98
0.99

5.9
3.4

94.0
96.6

6.43  107
5.53  107

0.97
0.99

9.9
8.6

90.0
91.4

1.23  108
4.21  106

0.95
0.92

19.0
0.6

80.9
99.3

0

a

Regression coecient for the equation, V=K1  [E]  [S]. See text for details.
K1(adsorbed or bound clay±CA complex)/K1(free CA)  100.
c
100ÿK1(adsorbed or bound clay±CA complex)/K1(free CA)  100.

b

¯occulation that occurred in the hydrophobic systems
resulted in a random orientation of the quasi-crystals
and in the formation of large pores. In the hydrophilic
M±Ca system, the quasi-crystals remained dispersed
and a close-packing occurred during centrifugation,
which resulted in small pores. The amounts of CA dissolved in the water within the pores created by the
arrangement of the particles after centrifugation probably contributed to the apparent activity of adsorbed
CA, but this e€ect should have been more evident in
the M±PY±Ca and M±HDTMA systems, as more
water was retained by these systems than by M±Ca±
CA. As large di€erences between the enzymatic activity of adsorbed vs bound CA were observed only
with M±Ca, larger structural modi®cations of CA or
di€erences in steric hindrance in the binding of H2O2
may have occurred with bound CA than with CA
adsorbed at equilibrium on M±Ca.
The optimal pH for the activity of CA was not
a€ected by the adsorption or binding of CA on the
di€erent clays, regardless of the type of charge-compensating cation (Fig. 3). Garwood et al. (1983)
reported that the optimal pH for the activity of free
and ``immobilyzed'' glucose oxidase was the same for
hydrophobic and ionic modes of binding. The optimal
pH for the activity of several enzymes has been
reported to shift to higher values after adsorption of
the enzymes on clays homoionic to inorganic cations,
presumably as a result of the acidic character of the
clay surface (Hattori, 1973; Theng, 1979). Although
these authors did not di€erentiate between adsorption
at equilibrium and binding, the interaction of these
enzymes with clays homoionic to inorganic cations was
presumably mainly via ionic interactions, whereas our
present study, the adsorption and binding of CA
occurred in unbu€ered systems at pH values above the
pI of CA, suggesting that hydrogen bonding between
CA and M±Ca was primarily involved (Stotzky, 1986;
Fusi et al., 1989).

Soil microorganisms utilized free CA and glucose as
sole C sources to the same extent, as the amounts of
CO2 evolved almost doubled when an equal amount of
C as glucose was added to free CA (Fig. 4, experiment
(iii) vs experiment (i)). The N contained in CA
appeared to be adequate for growth of the microbes,
as supplementation with NH4NO3 did not increase
CO2 evolution (Fig. 4, experiment (ii) vs experiment
(i)). Also, in the CA+glucose and CA+glucose+NH4NO3 experiments (Fig. 4, experiments (iii) and
(iv)) no signi®cant di€erences in CO2 evolution were
observed. There were no signi®cant di€erences in CO2
evolution between the control (M±HDTMA) and M±
HDTMA±CA alone (Fig. 4, experiments (i) and (ii)).
This was not primarily the result of an inhibition of
microbial growth, as the addition of glucose, with or
without NH4NO3, to M±HDTMA or M±HDTMA±

Fig. 3. E€ect of pH on the enzymatic activity of CA free or bound
on M±HDTMA, M±PY, or M±Ca.

L. Calamai et al. / Soil Biology & Biochemistry 32 (2000) 815±823

821

Fig. 4. Evolution of CO2 from di€erent systems inoculated with a microbial community from soil after a 7 d incubation at 258C (mean2 standard errors of the means). See text for details.

CA (Fig. 4, experiments (iii) and (iv)) resulted in signi®cant CO2 evolution but, rather, to a reduced bioavailability of the bound CA. As expected for a
quaternary ammonium salt such as HDTMA, essentially complete inhibition of microbial growth occurred
with free HTDMA chloride in all treatments (Fig. 4,
experiments (i), (ii), (iii), and (iv)), but this inhibition
did not occur when HTDMA was present as the
charge-compensating cation on M.
In contrast, CA bound on M±PY was utilized by
microbes as a sole source of C and N to the same
extent as free CA, showing that the binding on M±PY
did not a€ect the bioavailability of CA. The control
treatments with only M±PY and PY chloride in
amounts corresponding to those present in M±PY
showed neither inhibition of microbial growth nor appreciable utilization of the PY as a source of C,
although it was utilized as a source of N, con®rming
that the CO2 evolution observed with M±PY±CA was
the result of the utilization of bound CA.
When CA was bound on M±Ca, CO2 evolution was
reduced by about 90% in comparison with free CA.
As also observed with M±HDTMA±CA and M±PY±
CA, the addition of glucose, without or with NH4NO3
(experiments (iii) and (iv)), resulted in increased respiration, con®rming that the reduced CO2 evolution from
M±Ca±CA was the result of reduced utilization of
bound CA and not of inhibition of microbial growth.
The results on microbial utilization indicate that CA is
poorly available as source of nutrients when bound on
M both by hydrophobic or ionic interactions. The M±
PY±CA bound represent a unique case. When present

on the clay as a charge-compensating cation, PY presented a rapid ¯occulation of the clay suspension, i.e.,
the di€use double layer surrounding the clay colloidal
particles was suppressed. Nevertheless, the anity for
nonpolar organic molecules, or ``organophilicity'', was
limited, as no hydrophobic tail was present. According
to Tanford (1991) the ability of organic amphiphylic
molecules, such as fatty acids, alcohols, amides, etc.,
to form micelles in bulk solution increases threefold
for each CH2 group added to the alkyl chain
(``Traube's rule''). For these reasons, the interactions
of CA with M±PY probably involved both weak
hydrogen bonding (as demonstrated by the shift in the
Amide I and Amide II bands observed by FT-IR) and
limited hydrophobic e€ect, which rendered CA available for the microbes.

4. Conclusions
Both hydrophobic and hydrophilic modes of interaction of montmorillonite with CA resulted in high
amounts of CA being adsorbed, in a reduction but not
complete elimination of the enzymatic activity, and in
reduced bioavailability of CA. However, the anity of
the hydrophobic surfaces for CA was higher and the
reduction in enzymatic activity less than that observed
on M±Ca, where ionic and hydrogen-bonding interactions are assumed, indicating that CA can probably
persist and function in soil when bound in clay-humic
complexes having a hydrophobic character. The spectroscopic data of CA bound on M±HDTMA and M±

822

L. Calamai et al. / Soil Biology & Biochemistry 32 (2000) 815±823

PY indicated that the structural modi®cations, detected
by FT±IR, may not be related to changes in the enzymatic activity or bioavailability of CA, and that more
information on the e€ect of clay on the active center
of CA is needed. For these reasons, further investigation on the structure of the active center of CA
bound on clay systems is needed.

Acknowledgements
This work was supported by the Italian Consiglio
Nazionale delle Ricerche (CNR) within a cooperative
program between the Dipartimento di Scienza del
Suolo e Nutrizione della Pianta UniversitaÁ di Firenze,
Italy, and the Laboratory of Microbial Ecology,
Department of Biology, at New York University. We
thank Mr Fabrizio Filindassi for his assistance in the
preparation of the graphs.

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