Electrochemical and computational studies, in protic medium, of Morita-Baylis-Hillman adducts and correlation with leishmanicidal activity

Article abstract of DOI:10.1016/j.electacta.2014.05.066

Enzymatic bioreduction of nitro groups plays an important role on the activity of biologically active nitroaromatic compounds. Electrochemical methods are useful tools to simulate in vivo metabolic processes. This work presents electrochemical studies, in

Full text of DOI:10.1016/j.electacta.2014.05.066

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Electrochimica Acta
journal homepage: www.elsevier.com/locate/electacta
Electrochemical and computational studies, in protic medium, of
Morita-Baylis-Hillman adducts and correlation with
leishmanicidal activity
Yen G. de Paivaa, Waldomiro Pinho Júniora, Antonio A. de Souzab, Cícero O. Costac,
Fábio P.L. Silvad, Cláudio G. Lima-Juniord, Mario L.A.A. Vasconcellosd,1
,
Marília O.F. Goularta,∗
a Instituto de Química e Biotecnologia, Universidade Federal de Alagoas, Maceió, AL, 57072-970, Brazil
b Instituto Federal de Educac¸ ão, Ciência e Tecnologia de Alagoas, IFAL, 57020-600 Maceió, AL, Brazil
c Instituto Federal de Educac¸ ão, Ciência e Tecnologia de Alagoas, IFAL, Satuba, AL, Brazil
d Departamento de Química, Universidade Federal da Paraíba, Campus I, 58059-900 João Pessoa-PB, Brazil
a r t i c l e i n f o
a b s t r a c t
Article history:
Enzymatic bioreduction of nitro groups plays an important role on the activity of biologically active
nitroaromatic compounds. Electrochemical methods are useful tools to simulate in vivo metabolic pro-
cesses. This work presents electrochemical studies, in protic media (EtOH + phosphate buffer 4:6), using
cyclic voltammetry (CV) of twelve Morita-Baylis-Hillman adducts (MBHA) with significant leishmanici-
dal activity. To facilitate the analysis, the molecules were grouped in four classes according to their side
chains. Cyclic voltammograms display, in all cases, only one cathodic wave related to the formation of
the correspondent hydroxylamines, which suffer further oxidation generating the nitroso derivatives in
a sequential cycle. Ortho compounds exhibit more negative reduction potentials compared to the other
isomers, in the same chemical class. This phenomenon could be related not only to structural effects
but also to the presence of solvation spheres during the electroreduction process and/or stabilization of
the resulting hydroxylamine. A proposal to explain the higher leishmanicidal activity of the ortho com-
pounds compared with the meta and para compounds was suggested based on theoretical calculations
(HF/6-31 + G */PCM, water, as a calculation level) that indicated lower thermodynamic stability for the
ortho, in comparison to the corresponding meta and para hydroxylamines, fact that may suggest the eas-
ier transformation of the electrogenerated compounds into reactive electrophilic intermediates or final
products, able to react with physiological important endobiotics.
Received 11 January 2014
Received in revised form 12 May 2014
Accepted 13 May 2014
Available online xxx
Keywords:
Morita-Baylis-Hillman adducts
electrochemical parameters
aromatic nitrocompounds
protic media
leishmanicidal activity
© 2014 Elsevier Ltd. All rights reserved.
1. Introduction
(CL) and visceral leishmaniasis (VL) (also known as black fever or
kalazar), a potentially lethal systemic infection. Approximately 0.2
Leishmaniasis is
a
poverty-related vector-borne disease
to 0.4 cases and 0.7 to 1.2 million VL and CL cases, respectively,
occur each year. More than 90% of global VL cases occur in six coun-
tries: India, Bangladesh, Sudan, South Sudan, Ethiopia and Brazil.
Cutaneous leishmaniasis (CL) is more widely distributed, with
about one-third of cases occurring in each of three epidemiological
regions, the Americas, the Mediterranean basin, and western Asia
from the Middle East to Central Asia, with a tentative estimate of
20,000 to 40,000 leishmaniasis-caused deaths per year [3]. Up to
now, no vaccine approved for human use is available [5], despite
several prototypes, in different states of product and clinical
development [6]. The current treatment is unsatisfactory due to its
high cost, toxic side effects and drug resistance of the parasite [7,8].
Thus, many efforts have been made for the development of new
endemic in 98 countries caused by parasite of the genus Leishma-
nia [1]. It represents a worldwide public health problem with 350
million people being at risk [2–4]. There are three different clinical
manifestations: cutaneous, the most common, mucocutaneous
∗
Corresponding author. Instituto de Química e Biotecnologia, Universidade Fed-
eral de Alagoas, 57072-970 Maceió, AL, Brazil, Tel.: +55 82 3214-1393;
fax: +55 19 3214-1393.
E-mail addresses: mlaav@quimica.ufpb.br (M.L.A.A. Vasconcellos),
mariliaofg@gmail.com (M.O.F. Goulart).
1
Departamento de Química, Universidade Federal da Paraíba, Campus I, 58059-
900 João Pessoa-PB, Brazil, Tel.: +55 83 32167589; fax: +55 83 32167433.
http://dx.doi.org/10.1016/j.electacta.2014.05.066
0013-4686/© 2014 Elsevier Ltd. All rights reserved.
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(MBHA) with significant leishmanicidal activity, to complement the
studies already published in aprotic medium [31]. A proposal for the
higher bioactivity of the compounds was suggested based on theo-
retical calculations (HF/6-31 + G */PCM, water) of the corresponding
hydroxylamines.
Fig. 1. General scheme for Morita-Baylis-Hillman (MBH) reactions.
2. Experimental
effective drugs for the treatment of this neglected disease, which
discovery is a pressing concern for global health programs. Some
nitrocompounds are still in investigation toward this disease,
using a hybrid approach, with a promising result [9].
The Morita-Baylis-Hillman (MBH) reaction is a carbon-carbon
bond-forming reaction. It has all interesting basic properties of
an efficient synthetic method – it is selective, atom economi-
cal, requires mild conditions and generates poly-functionalized
molecules [10,11]. It involves coupling of alkenes contain-
ing electron-withdrawing groups (EWG) with aldehydes, imines
or ketones, among other starting materials. Most of these
reactions are normally catalyzed by tertiary amines as 1,4-
diazabicyclo[2.2.2]octane (DABCO) [12,13] (Fig. 1).
Some MBH adducts (MBHA) are nitrocompounds of whose
biological activity is related to aromatic nitro group reduction gen-
erating ArNO2−• or more reduced intermediates [14,15], depending
on external conditions. As interesting biological electrophiles,
some studies have been reported, using these adducts, against
Biomphalaria glabrata [16], Plasmodium, Leishmania, Trypanosoma
[17–23], bacterias [23], fungi [24] and some human cancer cells
[14,15,24], displaying significant activity [25]. Concerning the bio-
transformation point of view, the bioactive metabolites (i.e. nitro
radical anion and/or hydroxylamine and/or nitroso derivatives)
formed through biological reactions, have several cell compo-
nents (for instance enzymes, DNA, membranes) as potential targets
[26–28]. The redox chemistry of different nitro compounds of bio-
logical significance is focused to understand how the reduction of
the nitro group can play an active role in several aspects, especially
in free radicals generation, in stability and reactivity [28]. As biore-
ductive prodrugs, they are designed to be activated by a metabolic
reaction of reduction in target tissues or organisms, with differ-
ent oxygen concentrations. Only organisms with an appropriate
redox machinery will produce the biologically active form of the
compound. In other words, cellular toxicity will depend first and
foremost on oxygen levels in the cells and the molecular mecha-
nism of action can vary accordingly [26].
2.1. Chemicals
According to the general procedures [13,21] already published,
we have synthesized 12 MBHA (Fig. 2). The purity of all the com-
pounds was assessed by gas chromatography and their structures
confirmed by usual physicochemical methods.
2.2. Apparatus and procedures
All experiments were performed at room temperature
(25 2 ◦C) and degassed by pure and inert gas (Argon). Cyclic
voltammetry (CV) experiments were performed with a conven-
tional three-electrode cell in an Autolab PGSTAT-30 potentiostat
(Echo Chemie, Utrecht, the Netherlands) coupled to a PC micro-
computer, using GPES 4.9 software. The working electrode was a
Metrohm GC electrode of 2 mm diameter, the counter electrode
was a platinum coil, and the reference electrode was Ag|AgCl, KCl
(0.1 mol L-1), all contained in an one-compartment electrochemi-
cal cell with a volumetric capacity of 10 mL, using a volume of 5 mL.
The glassy carbon electrode was previously polished with alumina
on a polishing felt until getting a mirror-like surface appearance.
All the reagents employed for the preparation of the buffer solution
(pH = 7.4) were of analytical grade. The phosphate buffer (pH 7.4)
(ionic strength of 0.2 mol L-1) was prepared as following: 0.434 g
of NaH2PO4 and 1.747 g of Na2HPO4 dissolved in milliQ water in
a volumetric flask of 200 mL.The pH value was monitored in a
pHmeter, previously calibrated. Stock solutions of each compound
in EtOH + buffer (4:6) were prepared. The aqueous solutions were
prepared by diluting the stock solution in order to obtain a final
substrate concentration of 1 x 10-3 mol L-1. Stock and working solu-
tions were handled and stored avoiding exposure to light during all
experiments. The solutions were purged with pure argon for five
minutes before the voltammetric runs and covered with a argon
blanket during the experiments.
2.3. Computational Details
Electrochemical techniques have been extensively used for pro-
viding important insights about the mechanisms of action of a
variety of drugs. This understanding may inspire the design of next-
generation more effective therapeutic compounds [28–30]. Redox
potentials are considered the main physicochemical parameter
that determines the effectiveness of nitrocompounds providing
information about the electron transfer (ET) process, with ther-
modynamic and kinetic informations [27–30]. However, to obtain
more information about the mechanisms of molecular action, it
is interesting to study not only the electronic properties of the
bioactive nitrocompounds, but also their molecular environment.
Changes of the intermolecular interactions (hydrogen-bond ability,
dipolar moment, etc.) are clearly capable of affecting the structures,
reactivity, biological activities, equilibria, reaction rate constants,
and a host of other aspects that are of central interest to chemistry
and biology. Thus, specific shifts in the redox potentials reflect the
extent of stabilization that the molecular ground and electrogen-
erated states experience due to their own nature as well as their
solvent-solute interactions.
Computational analyses of hydroxylamines Ia’–IVc’ were per-
formed using GAUSSIAN09W® package version for Linux [32].
Initially, relaxed potential energy surfaces scan (RPESS) was per-
formed in a semi-empirical PM6 level, considering the relevant
rotational degrees of freedom for the reduced compounds (sigma
bonds). Dihedral angles were frozen in steps of 10◦, while the
remaining portion of the molecule was optimized. At the end,
potential energy curves for each dihedral angle were obtained,
and the conformation of minimum energy for each compound was
selected. They were, then, subjected to calculation at HF/6-31G+(d)
level, considering a polarized continuum model (PCM) by intro-
ducing water dielectric constant (␧ = 78.39). HOMO, LUMO and N
values were obtained from the most stable conformations of the
hydroxylamines. The molecular hardness (N) was calculated from
N = [(LUMO - HOMO)]/2] equation.
3. Results and Discussion
The present work aims to investigate the electrochemical
studies in protic media (EtOH + phosphate buffer, 4:6), using
cyclic voltammetry (CV) of twelve Morita-Baylis-Hillman adducts
The nitrocompounds were classified into four classes (I, II,
III and IV) based on the side chain as nitrile, methyl acrylate,
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3
OH
OH
NO2 OH
O2N
R
R
R
O2N
Ic: R= CN
IIc: R= CO2CH3
IIIc: R= CO2CH2CH2OH
IVc: R= CO2CH2CH2CH3
Ia: R= CN
IIa: R= CO2CH3
IIIa: R= CO2CH2CH2OH
IVa: R= CO2CH2CH2CH3
Ib: R= CN
IIb: R= CO2CH3
IIIb: R= CO2CH2CH2OH
IVb: R= CO2CH2CH2CH3
Fig. 2. Structures of the experimentally studied nitro-substituted MBHA.
of the nitro group, turning its reduction more difficult, with few
exceptions.
OH
OH
4H+ + 4e-
- 2H+ - 2e-
CN
CN
CN
HOHN
ON
O2N
Ic
OH
The effect of the nitro substituent and its position in a series
of molecules can be correlated with electrochemical thermody-
namic and kinetic parameters [28,34,35]. The ortho substituent (in
Ia, IIa, IIIa, IVa) must be evaluated carefully due to position-specific
influence, such as hydrogen bonding, field and steric effects. This
phenomenon can be related not only to intrinsic structural effects
but also to solvation spheres during the reduction and stabilization
process of the electrogenerated groups. This knowledge is impor-
tant for a better understanding of the biological activity of certain
classes of compounds.
Ic'
OH
CN
HOHN
Ic'
Fig. 3. Reduction of compound Ib in EtOH + phosphate buffer 4:6 (pH = 7.4) (also
applied to the other studied MBHAs).
In the present work, the easier reduction of the para isomers
could be explained by the higher stability of the electroreduced
intermediates or final products, due mainly to solvation effects,
once the para hydroxylamines (Ic’, IIc’, IIIc’, IVc’) are not bulky and
consequently, easily accessed by solvents. Resonance stabilization
in respect to the phenyl ring is also possible, by the maintenance
of the coplanarity of the system. On the other hand, for ortho
derivatives (Ia’, IIa’, IIIa’, IVa’), the stabilization is precluded due
to the distortion of the coplanar arrangement of the generated
hydroxylamines, or less reduced intermediates, which decreases
the resonance with the aromatic system, with the additional pres-
ence of internal hydrogen bonding (IHB), allowing only a partial
solvation in protic medium, with a consequent decrease on stabil-
ity. These combined effects lead to more negative potentials in the
ortho-hydroxylamines derivatives (Ia’, IIa’, IIIa’, IVa’) compared to
other isomers.
Sturm and co-workers [34] and Nún˜ez-Vergara and co-workers
[35] noticed, in protic media, the nitro group influence, consider-
ing only intrinsic effects in different positions of benzoic ring in
1,4-dihydropyridines (1,4-DHP) series. The ortho-nitrophenyl-1,4-
DHPs derivatives were reduced at more negative potentials than
meta and para derivatives. Coplanarity distortions of the nitro group
in ortho position due to 1,4-DHP substituent diminishes the reso-
nance effect, with a consequent more negative reduction potential
compared to the others.
2-hydroxyethylacrylate and propyl acrylate (Fig. 2). The letters a,
b and c refer to ortho, meta and para substitution to the side chain
on the aromatic ring.
3.1. Electrochemical studies: protic media
The electrochemical reduction of the aromatic nitrocom-
pounds has been broadly investigated by organic electrochemists,
with considerable attention and reveals a very complex mech-
anism, strongly dependent on the nature of the reaction media
[14,26–31,33]. Most of these works involve aqueous solutions con-
taining or not co- solvents as necessary to aid the dissolution of
insoluble organic compounds. As typical aromatic nitrocompounds,
CV studies of all MBHAs show the expected reduction behavior
of this class of electroactive compounds involving a unique irre-
versible (Epc1 dependent on v) and diffusional (Ipc1 vs v1/2) wave
in the first cycle, in agreement with the generation of the derived
hydroxylamine, through a 4e−/4H+ process (Fig. 3) [14].
The stable hydroxylamines suffer oxidation at Epa2 generat-
ing the nitroso derivative which reduction could be observed in
a second cycle (Fig. 4),designed as Epc2.
Table 1 lists the main electrochemical parameters (Epc1, Epc2,
Epa2) for all the nitrocompounds studied.
The analysis of Table 1 allows to evincing that:
An inverse behavior was obtained for the same MBHA in aprotic
media [31]. Notice that in aprotic media, solvent influence is less
important, and intrinsic effects play the major role in the evalua-
tion of reactivity and stability. The ortho adducts present facilitated
reduction in comparison to the other isomers (meta and para), due
1) In all series, independent of the electrochemical method used:
c (para) reduces easier than b (meta) and than a (ortho);
2) There is a slight influence of the side chain, the ester group being
less effective than the nitrile in decreasing the electron density
Table 1
Reduction potentials vs. (Ag/AgCl/0.1 M KCl)/V of MBHA from the classes I, II, III and IV, a for ortho, b for meta and c for para-substitution, in protic media EtOH + phosphate
buffer 4:6, glassy carbon electrode, v= 0.100 V s−1
.
MBHA
Epc1/V
Epc2/V
Epa1/V
MBHA
Epc1/V
Epc2/V
Epa1/V
Ia
Ib
Ic
IIa
IIb
IIc
- 0.784
- 0.755
- 0.750
- 0.823
- 0.784
- 0.729
- 0.242
- 0.193
- 0.188
- 0.276
- 0.229
- 0.179
- 0.012
- 0.027
- 0.007
0.002
0.012
0.012
IIIa
IIIb
IIIc
IVa
IVb
IVc
- 0.818
- 0.789
- 0.777
- 0.804
- 0.765
- 0.760
- 0.301
- 0.247
- 0.240
*
- 0.203
- 0.203
0.075
0.051
0.046
0.007
- 0.003
- 0.003
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Fig. 4. Cyclic voltammetric behavior of MBHA (nitro group in para position) in protic media (EtOH + phosphate buffer 4:6), glassy carbon electrode, auxiliary: Pt, reference:
Ag/AgCl/0.1 M KCl. v= 0.100 V s-1. (—) in A, C, E, G represents the second cycle. (—) in B, D, F, H represents E after Epc1. The same electrochemical behavior could be observed
␭
for all other MBHA studied.
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5
Table 2
Calculated thermodynamic stabilities of hydroxylamines Ia’–IVc’ and their corresponding absolute hardness. HF/6-31G* using PCM to simulating water solvation.
*N = [ꢀ(LUMO-HOMO)/2]. ** IC50 values obtained values of the corresponding nitrocompounds Ia-IVc [19].
Comp.
␧+G◦ (Hartree)
ꢀ(␧ + G◦) kJ mol-1
E LUMO
E HOMO
ꢀ (LUMO
ŋ*
IC50 (␮mol L-1)**
–
HOMO)
Ia’
Ib’
Ic’
-642.898786
-642.900391
-642.901353
-777.766907
-777.770956
-777.770792
-855.784628
-855.788700
-855.787869
-891.596954
-891.598851
-891.602420
0.000
-4.2093
-6.7340
0.000
-10.6214
-10.1908
0.000
-10.6799
-8.5021
0.000
-4.9742
-14.3374
+0.062
+0.064
+0.063
+0.068
+0.067
+0.068
+0.068
+0.066
+0.067
+0.104
+0.110
+0.101
-0.314
-0.316
-0.317
-0.311
-0.313
-0.310
-0.311
-0.313
-0.309
-0.319
-0.307
-0.303
0.376
0.400
0.380
0.379
0.380
0.378
0.379
0.379
0.376
0.423
0.417
0.404
0.188
0.200
0.190
0.189
0.190
0.189
0.189
0.189
0.188
0.212
0.209
0.202
62.00
238.27
128.27
50.08
451.58
196.16
28.38
72.23
52.04
20.52
64.57
53.03
IIa’
IIb’
IIc’
IIIa’
IIIb’
IIIc’
IVa’
IVb’
IVc’
to internal hydrogen bond formation between the carbinolic–OH
and the nitro group, which stabilizes the reduction product (anion
radical nitro) more efficiently than the original compound [31].
medium (mimicking the hydrophylic cytoplasm) have shown that
the absolute hardness and also the atomic charges did not correlate
with the bioactivity. In this case, computational results show that
ortho-hydroxylamines (Ia’, IIa’, IIIa’, IVa’) are thermodynamically
the compounds with higher energy (less stable), which may suf-
fer degradation to form, preferentially at equilibrium (see Fig. 3),
highly reactive electrophiles (Ar-NO or ArNHOH), able to react with
physiologically important endobiotics. So the damage for the par-
asite could occur by a diverse mechanism, as largely discussed in
the literature, especially in hypoxic regions [28,37], or in anaero-
bic media, were the O2 concentration is lower, turning the aerobic
pathway (release of reactive oxygen species) secondary in impor-
tance.
3.2. Computational studies
In the theoretical published results for aprotic media, [31] both
the value of Epc1 and the calculation results indicated a good rela-
tionship between higher reactivity of ortho-nitro compounds (more
positive Epc1 values) to form [Ar-NO2]•-, with the corresponding
highest leishmanicidal activity (lower IC50 values). The parameters
of absolute hardness and atomic charge of the nitrocompounds
were also in accordance with the experimental electrochemical
results [31]. On the other hand, the present calculation, shown in
Table 2, made with the resulting hydroxylamines Ia’–IVc’, formed
after the complete reduction process of nitro compounds, (Ar-
NO2→ [Ar-NO2]•-→ Ar-NO→ Ar-NHOH), by simulation in protic
In the preferential ortho-hydroxylamines (Ia’, IIa’, IIIa’, IVa’)
conformations (Fig. 5), formation of one or more intramolecular
hydrogen bonds (IHBs) are observed [36], which could reduce the
solvating water stabilization (PCM is implicitly implemented in the
Fig. 5. Conformational minima of MBHA hydroxylamines Ia’-IVc’ calculated from HF/6-31+G(d)/PCM, on water simulations.
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program), making these ortho species less solvated and less stable
than the meta and para ones.
[4] D.G. Arias, V.E. Marquez, M.L. Chiribao, F.R. Gadelha, C. Robello, A.A. Iglesias,
S.A. Guerrero, Redox metabolism in Trypanosoma cruzi: Functional character-
ization of tryparedoxins revisited, Free Rad. Biol Med. 63 (2013) 65.
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Finally, we highlight here the difference between the aprotic
and protic media. In aprotic medium, the intrinsic effects are
most important due to the absence of the solvation sphere effect.
Thus, the intrinsic calculated parameters in aprotic media were
consistent with biological activity [31]. On the other hand, in
protic medium the intrinsic effects are less important than the
influence of solvation sphere [38] and therefore the lower solvating
effect of ortho compounds (Ia’, IIa’, IIIa’, IVa’) (due to the higher
number of IHB) in relation to the corresponding para and meta
hydroxylamines make ortho compounds less stable. Additionally,
in terms of drugs and mechanisms of biological action, it is worthy
mentioning, to exemplify the importance of the two chemother-
apeutical approaches concerning nitrocompounds [26–28,37],
that in the case of Chagas’disease, caused by Trypanosoma cruzi,
parasite phylogenetically related to Leishmania (they share many
similarities, but there are also significant differences between
them [39]), two drugs are available: nifurtimox (3-methyl-4-(5’-
nitrofurfurylideneamine)tetrahydro-4H-1,4-tiazine-1,1-dioxide)
and benznidazole (N-benzyl-2-nitroimidazole acetamide). The
first acts by reducing the nitro group to generate nitro-anions
that subsequently react with molecular oxygen to produce toxic
superoxide and peroxide radicals, while the second appears to
act differently, as it produces metabolites that react with macro-
molecules such as DNA, RNA, proteins, and possibly lipids [40].
Electrochemists should be aware of these pharmacological differ-
ences to be able to contribute in this fruitful interface between
electrochemistry and life sciences.
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ties, Clin Microbiol Infect 17 (2011) 1478.
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Rodrigues, Exper. Parasitol 135 (2013) 153.
[10] K. Morita, Z. Suzuki, H. Hirose, A tertiary phosphine-catalyzed reaction of acrylic
compounds with aldehydes, Bull. Chem. Soc. Jpn. 41 (1968) 2815.
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In a series of twelve (Ia-IVc) MBHA nitrocompounds, inde-
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than b (meta). The a (ortho) MBHA (Ia, IIa, IIIa, IVa) are the most
difficult to reduce. In agreement with the electrochemical exper-
imental parameters, theoretical calculations in protic simulation
(PCM) have indicated low stability for the electrogenerated ortho
hydroxylamines (Ia’, IIa’, IIIa’, IVa’), in comparison to the cor-
responding meta and para ones. In protic medium, the intrinsic
effects are less important than the influence of solvation sphere.
The ortho hydroxylamines (Ia’, IIa’, IIIa’, IVa’) are less solvated than
the meta and para isomeric compounds. Due to the existence of
more IHB, it might suffer hydrogen-bonding assisted fragmenta-
tion, leading to electrophilic intermediates [26], which are able to
react with physiological important endobiotics. This may be the
reason for the obtained inverse correlation between the calculated
thermodynamic stability of hydroxylamines (less stable) and the
leishmanicidal activity of the compounds presented in this work.
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Acknowledgements
synthesis and biological and optical properties of methylene-dinaphthyl bis-
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(2007) 8562.
This research was supported by grants from the Conselho
Nacional de Desenvolvimento Científico e Tecnológico (CNPq),
CAPES and Fundac¸ ão de Apoio à Pesquisa do Estado de Alagoas
(FAPEAL, PRONEX). Y.G.P. wishes to acknowledge her CNPq fellow-
ship and fruitful discussions with MSc. Cleylton B. Lopes.
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