molecules
Article
Theoretical Reactivity Study of Indol-4-Ones and
Their Correlation with Antifungal Activity
María de los Ángeles Zermeño-Macías 1 , Marco Martín González-Chávez 2, *,
Francisco Méndez 3, *, Rodolfo González-Chávez 2 and Arlette Richaud 3
1
2
3
*
Posgrado en Ciencias Farmacobiológicas, Universidad Autónoma de San Luis Potosí,
78210 San Luis Potosí, Mexico; [email protected]
Facultad de Ciencias Químicas, Universidad Autónoma de San Luis Potosí, Av. Dr. Manuel Nava No. 6
Zona Universitaria, 78210 San Luis Potosí, Mexico; [email protected]
Departamento de Química, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana,
Unidad Iztapalapa, 09340 Ciudad de México, Mexico; [email protected]
Correspondence: [email protected] (M.M.G.-C.); [email protected] (F.M.);
Tel.: +52-444-826-2300 (ext. 6471) (M.M.G.-C.); +52-555-804-6400 (ext. 3326) (F.M.)
Academic Editors: Luis R. Domingo and Alessandro Ponti
Received: 1 January 2017; Accepted: 2 March 2017; Published: 8 March 2017
Abstract: Chemical reactivity descriptors of indol-4-ones obtained via density functional theory
(DFT) and hard–soft acid–base (HSAB) principle were calculated to prove their contribution in
antifungal activity. Simple linear regression was made for global and local reactivity indexes. Results
with global descriptors showed a strong relationship between antifungal activity vs. softness (S)
(r = 0.98) for series I (6, 7a–g), and for series II (8a–g) vs. chemical potential (µ), electronegativity (χ)
and electrophilicity (ω) (r = 0.86), p < 0.05. Condensed reactivity descriptors sk + , ω k − for different
fragments had strong relationships for series I and II (r = 0.98 and r = 0.92). Multiple linear regression
was statistically significant for S (r = 0.98), η (r = 0.91), and µ/ω (r = 0.91) in series I. Molecular
electrostatic potential maps (MEP) showed negative charge accumulation around oxygen of carbonyl
group and positive accumulation around nitrogen. Fukui function isosurfaces showed that carbons
around nitrogen are susceptible to electrophilic attack, whereas the carbon atoms of the carbonyl
and phenyl groups are susceptible to nucleophilic attack for both series. The above suggest that
global softness in conjunction with softness and electrophilicity of molecular fragments in enaminone
systems and pyrrole rings contribute to antifungal activity of indol-4-ones.
Keywords: DFT; HSAB principle; indol-4-ones; Fukui function; MEP; antifungal activity; structure-activity
analysis
1. Introduction
Azole antifungal compounds have been used as therapeutic options for the treatment of systemic
fungal infections. Mostly triazoles (fluconazole, etc.) and imidazoles (ketoconazole, etc.) [1,2] are
used effectively against yeast and filamentous fungi. However, some etiologic agents have developed
resistance by different mechanisms; moreover, azole compounds also present toxicity or side effects [2–5].
Consequently, some studies to discover new antifungal agents have been done [3,6].
Recently, González et al. designed and synthesized a series of novel indol-4-one derivatives
with 1- and 2-(2,4-substituted phenyl) side chains (Figure 1). These compounds were tested in vitro
against eight human pathogenic filamentous fungus and yeast strains by determination of the minimal
inhibitory concentration (MIC); as MIC decreased, the antifungal activity increased. Based on their
results, they reported activity against Candida tropicalis, Candida guilliermondii and Candida parapsilosis
at MIC values of 0.0316 mM (8 µg·mL−1 ) for compounds 8a–g; and MIC values of 0.1014 mM
Molecules 2017, 22, 427; doi:10.3390/molecules22030427
www.mdpi.com/journal/molecules
Molecules 2017, 22, 427
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Molecules 2017, 22, 427
2 of 16
(31.25
·mL−1 ) against
Aspergillusfrom
fumigatus
(Table
1) for compounds
7a–g. Aactivity.
change in
of theµghalophenyl
regioisomers
N-1 to
C-2 increased
the antifungal
It the
wasposition
the first
ofreport
the halophenyl
regioisomers
from
N-1
to
C-2
increased
the
antifungal
activity.
It
was
the
first report
about antifungal activity for these indol-4-one derivatives.
about antifungal activity for these indol-4-one derivatives.
O
X
N
H
6
7a–g
Compound
a
b
c
d
e
f
g
X
H
2-F
4-F
2,4-diF
2-Cl
4-Cl
2,4-diCl
8a–g
Figure 1. Indol-4-ones 6, 7a–g and 8a–g designed, synthetized and tested by Gonzalez et al. [6].
Figure 1. Indol-4-ones 6, 7a–g and 8a–g designed, synthetized and tested by Gonzalez et al. [6].
Density
Densityfunctional
functionaltheory
theory(DFT)
(DFT)and
andthe
thehard–soft
hard–softacid–base
acid–baseprinciple
principle(HSAB)
(HSAB)have
havebeen
beenused
used
totostudy
studythe
thebiological
biologicalactivity
activityofofsome
somebiomolecules.
biomolecules.Fukui
Fukuifunctions
functionswere
wereused
usedfor
forunderstanding
understanding
the
of DNA
DNA and
and RNA
RNA[7,8];
[7,8];chemical
chemicalhardness
hardnesswas
was
used
study
thereactivity
reactivityof
ofnitrogenous
nitrogenous bases
bases of
used
to to
study
the
the
dopamine
drug–receptor
interactions
[9];
the
relationship
between
different
biological
activity
dopamine drug–receptor interactions [9]; the relationship between different biological activity and
and
chemical
reactivity
indices,
suchasaselectrophilicity,
electrophilicity,hardness,
hardness, and
and electronegativity
chemical
reactivity
indices,
such
electronegativity was
wasused
usedfor
for
testosterone
derivatives
and
their
biological
activity
[10,11];
the
dipolar
moment,
ionization
potential,
testosterone derivatives and their biological activity [10,11]; the dipolar moment, ionization potential,
electronic
electronicaffinity,
affinity,electronegativity,
electronegativity,electrophilicity,
electrophilicity,and
andothers
othersshowed
showedthe
theinhibitory
inhibitoryactivity
activityofof
carbonic
carbonicanhydrase
anhydrase[12];
[12];quantum
quantumchemical
chemicaldescriptors
descriptorswere
wereused
usedtotostudy
studyprotoporphyrinogen
protoporphyrinogen
oxidase
inhibitors
[13,14];
Fukui
functions,
softness,
and
electrostatic
potential
wereuseful
usefulforfor
oxidase inhibitors [13,14]; Fukui functions, softness, and electrostatic potential were
an
an
antituberculotic
drug
design
[15];
hardness,
electronegativity,
softness
electrophilicity
has
antituberculotic
drug
design
[15];
hardness,
electronegativity,
softness
andand
electrophilicity
has been
been
applied
to study
the toxicity
in specific
[16]; different
descriptors
were
used to
study
applied
to study
the toxicity
in specific
speciesspecies
[16]; different
descriptors
were used
to study
mosquito
mosquito
repellent
[17];
parameters
such
as
dipolar
moment
were
used
to
study
chemical
radioactivity
repellent [17]; parameters such as dipolar moment were used to study chemical radioactivity
protector
protector[18];
[18];ionization
ionizationpotential
potentialand
andcharge
chargewere
wereused
usedtotostudy
studyantioxidants
antioxidants[19];
[19];other
otheractivities
activities
and
chemical
reactivity
parameters
have
been
used
in
the
study
of
nonnucleoside
HIV-1
and chemical reactivity parameters have been used in the study of nonnucleoside HIV-1reverse
reverse
transcriptase
transcriptaseinhibitors
inhibitors[20],
[20],histone
histonedeacetylase
deacetylaseinhibitors
inhibitors[21],
[21],and
andanti-HIV-1
anti-HIV-1integrase
integrase[22];
[22];anti-HIV
anti-HIV
activity
activityvs.
vs.electronegativity,
electronegativity,hardness,
hardness,chemical
chemicalpower,
power,and
andelectrophilicity
electrophilicitywas
wasevaluated
evaluated[23,24];
[23,24];
and
others
[25,26].
Within
the
above
lies
the
importance
of
understanding
the
biological
and others[25,26]. Within the above lies the importance of understanding the biologicalactivity
activityinina a
particular
particularmolecular
molecularset
set[27]
[27]and
andtherefore
thereforefor
forrational
rationaldrug
drugdesign.
design.
InInthis
work
we
made
a
DFT-HSAB
reactivity
study
this work we made a DFT-HSAB reactivity studyofofthe
theindol-4-one
indol-4-onederivatives
derivatives6–8
6–8toto
understand
which
molecular
fragments
are
essential
for
antifungal
activity.
The
development
of
understand which molecular fragments are essential for antifungal activity. The development of new
new
antifungal
drugs
basedon
onobtaining
obtaining good
good relationships
antifungal
drugs
cancan
bebe
based
relationships between
between DFT-HSAB
DFT-HSABreactivity
reactivity
descriptors
and
antifungal
activity.
Based
on
the
biological
activity
results
reported
byGonzález
Gonzálezetetal.
descriptors and antifungal activity. Based on the biological activity results reported by
al.
[6],
classified
indol-4-one
derivatives
6–8two
intoseries
two according
series according
to the structure
and
[6],
wewe
classified
the the
indol-4-one
derivatives
6–8 into
to the structure
and biological
biological
activity.
Series I compounds
includes compounds
6 and
7a–g,
while
series IIcompounds
includes compounds
8a–g.
activity. Series
I includes
6 and 7a–g,
while
series
II includes
8a–g.
2. Theoretical Methods
2. Theoretical Methods
The geometries of the molecules 6, 7a–g and 8a–g (Figure 1) were fully optimized at the
The geometries of the molecules 6, 7a–g and 8a–g (Figure 1) were fully optimized at the B3LYP/6B3LYP/6-311+G (d,p) level of theory using the Gaussian 09 program package [28]. For all stationary
311+G (d,p) level of theory using the Gaussian 09 program package [28]. For all stationary points,
points, vibrational analyses were carried out. The ionization potential I = EN−1 − EN and the
vibrational analyses were carried out. The ionization potential I = EN−1 − EN and the electronic affinity
electronic affinity A = EN − EN + 1 were calculated at the geometry of the neutral species using
A = EN − EN + 1 were calculated at the geometry of the neutral species using the respective vertical
the respective vertical energies EN , EN + 1 , and EN − 1 of the systems with N, N + 1 and N − 1 electrons.
energies EN, EN + 1, and EN − 1 of the systems with N, N1+ 1 and N − 1 electrons. The global reactivity
The global reactivity indexes, chemical potential µ = − 2 ( I + A), electronegativity χ = −µ, hardness
indexes, chemical potential = − ( + ), electronegativity
= −μ, hardness = ( − ), softness
χ2
η = 12 ( I − A), softness S = 1/η and electrophilicity ω = 2η
[29–31], were calculated.
= 1/ and electrophilicity =
[29–31], were calculated.
Molecules 2017, 22, 427
Molecules 2017, 22, 427
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Table 1. MIC in vitro of 6, 7a–g and 8a–g against yeast and filamentous fungus.
Table 1. MIC in vitro of 6, 7a–g and 8a–g against yeast and filamentous fungus.
6
6
7a
7b
7c
7d
7e
7f
7g
8a
8b
8c
8d
8e
8f
8g
8a–g
C. albicans
C. glabrata
C. krusei
C. tropicalis
C. guilliermondii
C. parapsilosis
A. niger
A. fumigatus
C. albicans
C. glabrata
C. krusei
C. tropicalis
C. guilliermondii C. parapsilosis
A. niger
A. fumigatus
24 h 24 h 48 h48 h 24 h24 h 48 48
h h 2424
hh
48
24
48 hh
24hh
48hh
24 hh
48
24
4848hh
24 24
h h 48 h48 h 48h48h
h h 72 72
h h 48 48
h h
7272
hh
1.4105
2.8210
2.8210
5.6420
2.8210
5.6420
1.4105
5.6420
1.4105
2.8210
0.0451
0.3526
0.7052
1.4105
0.7052
1.4105
1.4105
2.8210
2.8210
5.6420
2.8210
5.6420
1.4105
5.6420
1.4105
2.8210
0.0451
0.3526
0.7052
1.4105
0.7052
1.4105
H 0.2467
0.24671.9736
1.97360.9868
0.9868 3.9473
3.9473 0.9868
0.9868 3.9473
3.9473 0.4934
0.4934 3.9473
H
3.9473 0.4934
0.4934 0.4934
0.4934 0.0316
0.0316 0.2467
0.2467 0.2467
0.2467 0.4934
0.4934 0.2467
0.2467 0.4934
0.4934
2-F 2-F 0.2304
3.6856 0.4607
0.4607 0.4607
0.4607 0.0590
0.0590 0.2304
0.2304 0.2304
0.2304 0.2304
0.2304 0.1152
0.1152 0.4607
0.4607
0.23041.8428
1.84280.4607
0.4607 3.6856
3.6856 0.9214
0.9214 3.6856
3.6856 0.4607
0.4607 3.6856
4-F 4-F 0.2304
3.6856 0.4607
0.4607 0.4607
0.4607 0.0590
0.0590 0.9214
0.9214 0.4607
0.4607 0.9214
0.9214 0.2304
0.2304 0.9214
0.9214
0.23041.8428
1.84280.4607
0.4607 3.6856
3.6856 0.9214
0.9214 3.6856
3.6856 0.4607
0.4607 3.6856
2,4-diF2,4-diF0.4321
0.4321 0.4321
0.4321 0.4321
0.4321 0.0553
0.0553 0.2160
0.2160 0.2160
0.2160 0.4321
0.4321 0.4321
0.4321 0.8641
0.8641
0.43210.8641
0.86410.8641
0.8641 3.4564
3.4564 0.4321
0.4321 0.8641
0.8641 0.2160
0.2160 0.4321
2-Cl 2-Cl 0.4344
0.4344 0.4344
0.4344 0.4344
0.4344 0.1086
0.1086 0.1086
0.1086 0.2172
0.2172 0.8687
0.8687 0.1086
0.1086 0.4344
0.4344
0.43440.8687
0.86870.8687
0.8687 3.4748
3.4748 0.4344
0.4344 0.8687
0.8687 0.2172
0.2172 0.4344
4-Cl 4-Cl 0.4344
0.8687
0.8687
3.4748
0.4344
0.8687
0.2172
0.4344
0.4344
0.4344
0.0556
0.2154
0.4344
>0.8687
0.4344
0.8687
0.4344 0.8687 0.8687 3.4748 0.4344 0.8687 0.2172 0.4344
0.4344
0.4344
0.0556 0.2154
0.4344
>0.8687
0.4344
0.8687
2,4-diCl
0.3879
0.3879 0.3879
0.3879 0.3879
0.3879 0.0970
0.0970 0.7758
0.7758>0.7758
>0.7758>0.7758
>0.7758 0.3879
0.3879 0.3879
0.3879
2,4-diCl
0.38790.7758
0.77580.7758
0.7758 3.1034
3.1034 0.3879
0.3879 0.7758
0.7758 0.1940
0.1940 0.3879
H
0.5223
1.0447
0.5223
4.1787
0.5223
1.0445
0.2612
0.5223
0.2612
0.5223
0.0669
1.0447 >1.0447 >1.0447 1.0447
1.0447
H
0.5223 1.0447 0.5223 4.1787 0.5223 1.0445 0.2612 0.5223
0.2612
0.5223
0.0669 1.0447 >1.0447 >1.0447
1.0447
1.0447
2-F
0.4858
0.9716
0.4858
0.9716
0.4858
0.9716
0.2429
0.4858
0.2429
0.2429
0.0622
0.2410 >0.9716 >0.9716 0.9716
0.9716
2-F
0.4858 0.9716 0.4858 0.9716 0.4858 0.9716 0.2429 0.4858
0.2429
0.2429
0.0622 0.2410 >0.9716 >0.9716
0.9716
0.9716
4-F
0.2429
0.9716
0.4858
0.9716
0.2429
0.4858
0.1214
0.2429
0.1214
0.2429
0.0622
0.2410 >0.9716 >0.9716 >0.9716 >0.9716
4-F
0.2429 0.9716 0.4858 0.9716 0.2429 0.4858 0.1214 0.2429
0.1214
0.2429
0.0622 0.2410 >0.9716 >0.9716 >0.9716 >0.9716
2,4-diF
0.2270
0.9081
0.4541
0.9081
0.2270
0.4541
0.1135
0.2270
0.1135
0.2270
0.0581
0.9081 >0.9081 >0.9081 >0.9081 >0.9081
2,4-diF
0.2270
0.9081
0.4541
0.9081
0.2270
0.4541
0.1135
0.2270
0.1135
0.2270
2-Cl
0.2283
0.9132
0.4566
0.9132
0.2283
0.4566
0.1142
0.2283
0.1142
0.1142 0.0581
0.1142 0.9081
0.9132>0.9081
>0.9132>0.9081
>0.9132>0.9081
>0.9132>0.9081
>0.9132
2-Cl
0.2283
0.9132
0.4566
0.9132
0.2283
0.4566
0.1142
0.2283
0.1142
0.1142
0.1142
0.9132
>0.9132
>0.9132
>0.9132
4-Cl
0.2283
0.9132
0.4566
0.9132
0.2283
0.4566
0.1142
0.2283
0.1142
0.1142
0.0584
0.2265 >0.9132 >0.9132 >0.9132>0.9132
>0.9132
0.22830.8112
0.91320.4056
0.4566 0.8112
0.9132 0.2028
0.2283 0.4056
0.4566 0.1014
0.1142 0.2283
2,4-diCl 4-Cl 0.2028
0.1014 0.1142
0.1014 0.1142
0.1014 0.0584
0.1014 0.2265
0.2012>0.9132
>0.8112>0.9132
>0.8112>0.9132
>0.8112>0.9132
>0.8112
2,4-diCl 0.2028 0.8112 0.4056 0.8112 0.2028 0.4056 0.1014 0.1014
0.1014
0.1014
0.1014 0.2012 −1>0.8112 >0.8112 >0.8112 >0.8112
This table was modified and taken from González et al. paper [6], the MIC values were changed from µg·mL to mM.
Compound
CompoundX
6
7a
7b
7c
7d
7e
7f
7g
8a
8b
8c
8d
8e
8f
8g
7a–g
X
This table was modified and taken from González et al. paper [6], the MIC values were changed from µg·mL−1 to mM.
Molecules 2017, 22, 427
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The local Fukui functions for nucleophilic f + (r), electrophilic f − (r), and radical f 0 (r) attacks
were calculated using Equations (1)–(3) [32].
f + (r ) = ρ N +1 (r ) − ρ N (r )
Nucleophilic attack
(1)
f − (r ) = ρ N (r ) − ρ N −1 (r )
Electrophilic attack
(2)
f 0 (r) =
1
(r) − ρ N −1 (r)]
[ρ
2 N +1
Radical attack
(3)
where ρ N +1 (r), ρ N (r) and ρ N −1 (r) are the electronic densities for the systems with N + 1, N and N − 1
electrons, respectively, calculated with the geometry of the neutral species.
The condensed Fukui functions were calculated using the charge of each atom qk instead of the
electron density ρ (r) (Equations (4)–(6)) [32–35]. The Hirshfeld population analysis scheme was used
+
for the systems with N, N − 1 and N + 1 number of electrons. The condensed softness s+
k = S fk ,
−
−
+
+
−
o
o
o
o
sk = S f k and sk = S f k and condensed electrophilicity indexes ωk = Sωk , ωk = ω f k , ωk = ω f k−
were obtained. The local Fukui function isosurfaces were plotted with GaussView 5.0 [36].
Condensed Fukui functions:
f k+ = qk ( N + 1) − qk ( N )
Nucleophilic attack
(4)
f k− = qk ( N ) − qk ( N − 1)
Electrophilic attack
(5)
f k0 =
1
(q ( N + 1) − qk ( N − 1))
2 k
Radical attack
(6)
where qk is the electronic population value of kth atom in the molecule.
3. Structure-Activity Relationship (SAR) Statistical Procedure
A simple and multiple regression analysis were made for the antifungal activities and the global
and condensed reactivity indexes for each series of compounds. The Pearson and Determination
Coefficients were obtained using SAS software [37] considering p < 0.05 as a significant value; the
analysis was made for each time of testing: 24 and 48 h for yeast; and 48 and 72 h for filamentous fungus.
4. Results and Discussion
4.1. Global Reactivity Parameters
Table 2 shows the values of the calculated global chemical reactivity parameters for the
15 indol-4-ones compounds. The chemical reactivity values vary with the molecular structure and
the substituent. According to the structural homology, the analyzed compounds were divided into
two series: series I that includes compounds 6 and 7a–g (N-1 substitution with phenyl moieties)
and series II that includes compounds 8a to 8g (C-2 substitution with phenyl moieties). Table 2
shows that for series I compound 6 has the highest hardness value (4.18 eV) and 7g has the lowest
hardness value (3.80 eV); the difference is 0.38 eV. In contrast, for series II the highest hardness value
(3.84 eV) corresponds to compound 8c and the lowest value (3.73 eV) to 8f and the difference is 0.11 eV.
According to the maximum hardness principle, compounds 7g and 8f (8g and 8d also) are more
reactive than 6 and 8c, respectively. The electronegativity equalization principle assures in the course
of a chemical reaction energetic stabilization through equalization of middle HOMO-LUMO levels
among ligand and receptor active molecular structures [38]. Table 2 reflects that compounds 7g in
series I and 8g in series II present the highest electronegativity values (3.90 eV and 3.87 eV, respectively).
The electrophilicity index ω value for the same compounds (7g 2.00 eV and 8g 2.01 eV), reflects the
ability of 7g and 8g to behave as the stronger electrophiles on each series. The relative change between
the maximum and minimum values of ω in the Series I of Table 2 (ωmax − ωmin /ωmax ) = 0.21 is larger
Molecules 2017, 22, 427
5 of 16
than the corresponding change of 0.17 for series II. This indicates that the capacity of series I to accept
Molecules 2017,
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5 of 16
electrons
(electrophilic
character) is more sensitive to the specific substituent than series II.
15compounds
compoundsindol-4-ones
indol-4-ones6,6,7a–g
7a–gand
and8a–g.
8a–g.
Table2.2.Global
Globalreactivity
reactivitydescriptors
descriptorsfor
forthe
the15
Table
Compound
6
8a–g
7a–g
Compound
a
b
c
d
e
f
g
η (eV)
χ (eV)
X
H
2-F
4-F
2,4-diF
2-Cl
4-Cl
2,4-diCl
ω (eV)
6
4.18
3.63
1.58
4.18 η (eV) χ3.63
Compound
(eV)
ω
(eV)1.58
7a
3.92
3.65
1.70
1.70
3.92
3.65
7b 3.89 3.89
3.74
1.80 1.80
3.74
3.77
7c 3.91 3.91
3.77
1.82 1.82
3.91
3.81
7d
3.91
3.81
1.86 1.86
3.89
3.71
1.76
7e 3.85 3.89
3.71
1.76 1.92
3.84
7f 3.80 3.85
3.84
1.92 2.00
3.90
3.57
7g 3.82 3.80
3.90
2.00 1.67
3.80
3.67
1.77
8a
3.82
3.57
1.67
3.84
3.64
1.72
8b 3.74 3.80
3.67
1.77 1.90
3.77
3.73
8c 3.78 3.84
3.64
1.72 1.84
3.72
8d 3.73 3.74
3.77
1.90 1.85
3.74
3.87
2.01
8e
3.78
3.73
1.84
8f
3.73
3.72
1.85
Simple linear regression of the 8g
minimum3.74
inhibitory
concentration
(MIC) vs. global reactivity
3.87
2.01
parameters for both series was obtained (Tables 3 and 4). The Pearson coefficient was positive and the
relationships
were directly
proportional:
when the
antifungal
activity decreased,
Simple linear
regression
of the minimum
inhibitory
concentration
(MIC) the
vs. global
global reactivity
reactivity
values
increased.
Then,
when
global (Tables
reactivity
of those
15Pearson
indol-4-ones
decreases,
the higher
parameters
for both
series
wasthe
obtained
3 and
4). The
coefficient
was positive
and
antifungal
activity
is
obtained.
The
best
statistically
significant
relationships
(the
Pearson
coefficient
the relationships were directly proportional: when the antifungal activity decreased, the global
preactivity
< 0.05) between
both variables
obtained
for reactivity
yeast in series
I: global
hardness for
C. glabrata
values increased.
Then,were
when
the global
of those
15 indol-4-ones
decreases,
the
48
h
(r
=
0.98),
C.
krusei
24
h
(r
=
0.95),
C.
tropicalis
24
h
(r
=
0.95),
C.
guilliermondii
24
(r
=
0.96)
η
η
η
η
higher antifungal activity is obtained. The best statistically significant relationships (the Pearson
and
48 h (rηp =< 0.94),
and fungi:
A.variables
fumigatuswere
72 h obtained
(rη = 0.79)
a strong
linear
coefficient
0.05) between
both
for(Table
yeast 3.
in This
seriesmeans
I: global
hardness
for
2
relationship
between
hardness
and biological
r values
0.96),C.with
only 4% of
C. glabrata 48
h (rη = 0.98),
C. krusei
24 h (rη = activity
0.95), C.(96%,
tropicalis
24 h (runtil
η = 0.95),
guilliermondii
24
variance
of
activity
left
to
explain
after
taking
into
account
the
hardness
in
a
linear
way.
For
series
II,
(rη = 0.96) and 48 h (rη = 0.94), and fungi: A. fumigatus 72 h (rη = 0.79) (Table 3. This means a strong
global
and global
electrophilicity
index
had a (96%,
higherr2Pearson
coefficient
C. only
albicans
linearelectronegativity
relationship between
hardness
and biological
activity
values until
0.96),for
with
4%
48
and C. glabrata
24 hleft
(rχ,ω
= 0.98) and
tropicalis
h (rχ =the
0.82hardness
and rω =in0.80)
(Table
4). For
Thisseries
shows
ofhvariance
of activity
to explain
afterC.taking
into48
account
a linear
way.
II,
the
same
tendency
as
series
I,
with
electronegativity
and
electrophilicity.
global electronegativity and global electrophilicity index had a higher Pearson coefficient for C.
The 48
relationship
was strong
for
all cases,
except48
forhC.
the(Table
relationship
albicans
h and C. glabrata
24 h (r
χ,ω almost
= 0.98) and
C. tropicalis
(rχparapsilosis
= 0.82 and where
rω = 0.80)
4). This
did
not
have
statistical
significance.
shows the same tendency as series I, with electronegativity and electrophilicity.
Pearson
coefficientwas
in simple
regression
for series
I had
theparapsilosis
following where
hierarchy
higher
The relationship
stronglinear
for almost
all cases,
except
for C.
the from
relationship
to
lower
values:
η > ω >significance.
χ while χ = ω > η for series II. This could be related to results obtained by
did
not have
statistical
Putz et
al.
[24],
where
they
monolinear
of the
activity
of uracil
derivatives
Pearson coefficient in report
simplevalues
linear of
regression
forcorrelation
series I had
following
hierarchy
from
(anti-HIV
vs. chemical
the tendency
was
η > ωto>results
χ, which
is not
higher to action)
lower values:
η > ω >reactivity
χ while χindices,
= ω > ηand
for series
II. This shown
could be
related
obtained
the
expect
the established
hierarchy
for chemical
binding
scenario
given
by tendency
Putz et al.one
[24],may
where
theyobeying
report values
of monolinear
correlation
of activity
of uracil
derivatives
by
Putz
[39],
according
which
a
chemical
reaction/interaction
is
triggered
by
the
electronegativity
(anti-HIV action) vs. chemical reactivity indices, and the tendency shown was η > ω > χ, which is not
difference,
followed
by chemical
hardness
electrophilicity:
χ>
> ω, due to
chemical–biological
the tendency
one may
expect obeying
theand
established
hierarchy
forη chemical
binding
scenario given
interactions.
The
higher
Pearson
coefficient
presented
by
Putz
is
0.67
for
hardness,
lower
than the
by Putz [39], according which a chemical reaction/interaction is triggered by the electronegativity
calculated
value
of
the
same
parameter,
0.98.
Although
a
different
pharmacological
activity
is
evaluated,
difference, followed by chemical hardness and electrophilicity: χ > η > ω, due to chemical–biological
itinteractions.
is possible toThe
seehigher
the relation
thatcoefficient
can exist with
these electronic
of systems.
Pearson
presented
by Putz isproperties
0.67 for hardness,
lower than the
6
7a
7b
7c
7d
7e
7f
7g
8a
8b
8c
8d
8e
8f
8g
calculated value of the same parameter, 0.98. Although a different pharmacological activity is
evaluated, it is possible to see the relation that can exist with these electronic properties of systems.
Stachowicz et al. evaluated thioamides derivatives and their activity against C. albicans and
correlated their activity vs. hardness, softness, and electrophilicity, with r values around 0.72 to 0.93
[40]. These results coincide with those obtained by us with r values around 0.73 to 0.98; the chemical
Molecules 2017, 22, 427
6 of 16
evaluated thioamides derivatives and their activity against C. albicans and correlated
6 of 16
their activity vs. hardness, softness, and electrophilicity, with r values around 0.72 to 0.93 [40]. These
results for
coincide
with those
obtained
us with r values
0.73 to 0.98;
the chemical structure
structure
thioamides
are similar
to by
indol-4-ones,
=onlyaround
in the presence
of N-heterocyclic
system for
thioamides
areand
similar
indol-4-ones,
in the presence
of N-heterocyclic
of five
members,
of five
members,
thisto
similarity
could=only
be responsible
for similar
correlationssystem
between
biological
and
this
similarity
could
be
responsible
for
similar
correlations
between
biological
activities
and
activities and chemical reactivity parameters.
chemical
Differentreactivity
biologicalparameters.
activities have been correlated with chemical reactivity parameters: hardness,
activities have been
correlated with
reactivity
parameters:
hardness,
softness,Different
chemical biological
potential, electronegativity,
electrophilicity,
andchemical
other electronic
parameters
looking
for
chemical
potential,
electronegativity,
other Examples
electronic parameters
looking
anysoftness,
relationship
between
electronic
parameterselectrophilicity,
and biologicaland
activity.
of studies with
for anyparameters
relationshipare:
between
electronic parameters
activity.
studies with
different
for testosterone
derivativesand
rω biological
= 0.42–0.94
[10,11];Examples
carbonicofanhydrase
differentrχ,µ,S,εLUMO
parameters
are:
foranti
testosterone
derivatives
= 0.42–0.94
[10,11];
carbonic
inhibitory
= 0.92
[12];
HIV-1 integrase
rLogP,χ r=ω0.93
[22]; anti-HIV
activity
withanhydrase
uracil
inhibitoryrχr=χ,µ,S,εLUMO
= 0.92rω[12];
antirω,χ
HIV-1
integrase
0.93 [22];
anti-HIV activity
with uracil
derivatives
0.24, rη = 0.65,
= 0.65,
= 0.69,
and rω,ηrLogP,χ
= 0.68,= [24];
etc. Although
our analysis
of
derivatives
rχ = does
0.24, rnot
0.65, rωwith
= 0.65,
rω,χdescribed
= 0.69, and
rω,η =
0.68,
[24]; etc.
Although
our
analysis of
antifungal
activity
those
above,
the
obtained
values
of r are
better.
η = match
antifungal activity does not match with those described above, the obtained values of r are better.
Stachowicz
Molecules 2017,
22, 427 et al.
Table 3. Pearson coefficient for each simple lineal regression for series I: Compounds 6 and 7a–g.
Table 3. Pearson coefficient for each simple lineal regression for series I: Compounds 6 and 7a–g.
7a–g
6
(eV)
ω (eV)
χχ(eV)
ω (eV)
r
r r
pp
p
r r
pp
p
24 24
0.87
0.0048
0.43 0.2868
0.2868 0.600.600.11240.1124
0.87
0.0048
0.43
C.C.albicans
albicans
48
0.82
0.0128
0.77
0.0246
0.83
0.0099
48
0.82 0.0128 0.77 0.0246 0.83 0.0099
0.90
0.0022
0.55
0.1602
0.70
0.0550
24
C. glabrata
0.90 0.00002
0.0022 0.55
48 24
0.98
0.74 0.1602
0.0358 0.700.860.05500.0055
C. glabrata
48
0.98
0.00002
0.74
0.0358
24
0.95
0.0003
0.69
0.0572 0.860.820.00550.0126
C. krusei
48 24
0.76
0.0283
0.75
0.0302
0.95 0.0003 0.69 0.0572 0.820.800.01260.0166
C. krusei
24 48
0.95
0.69 0.0302
0.0572 0.800.820.01660.0126
0.76 0.0003
0.0283 0.75
C. tropicalis
48
0.74
0.0363
0.75
0.0331
0.79
0.0199
0.95 0.0002
0.0003 0.69
24 24
0.96
0.61 0.0572
0.1109 0.820.760.01260.0285
C.
tropicalis
C. guilliermondii
0.74 0.0004
0.0363 0.75
48 48
0.94
0.57 0.0331
0.1393 0.790.730.01990.0396
24 24
0.46
0.2571
0.41
0.3145
0.96 0.0002 0.61 0.1109 0.760.460.02850.2544
C. guilliermondii
parapsilosis
C.
48 48
0.15
0.39 0.1393
0.3419 0.730.330.03960.4221
0.94 0.7242
0.0004 0.57
48
0.75
0.0500
0.25
0.5875
0.47
0.2899
A. niger
24
0.46 0.2571 0.41 0.3145 0.46 0.2544
72
0.78
0.0650
0.49
0.3236
0.68
0.1398
C. parapsilosis
0.15 0.1062
0.7242 0.39
48 48
0.61
0.01 0.3419
0.9797 0.330.220.42210.6061
A. fumigatus
0.75 0.0191
0.0500 0.25
72 48
0.79
0.29 0.5875
0.4893 0.470.490.28990.2188
A. niger
72
0.0650 index.
0.49 In0.3236
0.1398
h = hours, η = hardness, χ = electronegativity,
and 0.78
ω = electrophilicity
gray color0.68
is indicated
the values
that are statically significant p < 0.05.
48
0.61 0.1062 0.01 0.9797 0.22 0.6061
A. fumigatus
72
0.79 0.0191 0.29 0.4893 0.49 0.2188
lineal regression
for global reactivity
indexes indicated
bothcolor
hardness
and softness
h = Multiple
hours, η = hardness,
χ = electronegativity,
and ω = electrophilicity
index.that
In gray
is indicated
are
significant
variables
for
series
I
(see
Table
5).
The
relationship
was
strong
for
C.
guilliermondii
24 h
the values that are statically significant p < 0.05.
(r = 0.99) and 48 h (r = 0.99). Hardness and electrophilicity as well as hardness and chemical potential
Multiple lineal regression for global reactivity indexes indicated that both hardness and softness
had strong relationship for fungi, and are indicated specifically for A. fumigatus 48 h (rη,s = 0.91)
are significant variables for series I (see Table 5). The relationship was strong for C. guilliermondii
and 72 h (rη,µ = 0.91). For series II, there is no statistically significance (p > 0.05) linking two or
24 h (r = 0.99) and 48 h (r = 0.99). Hardness and electrophilicity as well as hardness and chemical
more descriptors.
potential had strong relationship for fungi, and are indicated specifically for A. fumigatus 48 h
(rη,s = 0.91) and 72 h (rη,µ = 0.91). For series II, there is no statistically significance (p > 0.05) linking two
or more descriptors.
Microorganism
of of
Testing
(h) (h)
Microorganism Time
Time
Testing
η (eV)
η (eV)
Molecules 2017, 22, 427
7 of 16
Table 4. Pearson coefficient for simple lineal regression for series II: Compounds 8a–g.
Molecules
22, 427
Molecules
2017,2017,
22, 427
7 of 16
7 of 16
Table 4. Pearson coefficient for simple lineal regression for series II: Compounds 8a–g.
Table 4. Pearson coefficient for simple lineal regression for series II: Compounds 8a–g.
8a–g
η (eV)
χ (eV)
ω (eV)
r
r
r
p
p
p
8a–g
24
0.54 0.2155 0.71 0.0731
0.70
0.0821
C. albicans
η (eV)
χ (eV)
ω (eV) 0.0002
48
0.78
0.0406
0.98
0.00006
0.98
η (eV)
χ (eV)
ω (eV)
Microorganism
Testing (h)
Microorganism Time
Timeofof24
Testing (h) 0.78
r r 0.0406
pp
r r 0.00006
p p
r0.98r p0.0002
0.98
p
C. glabrata
0.2155 0.66
0.71
0.0731 0.70
0.0821
24
0.54 0.3173
48
0.44
0.1060
0.63
0.1285
C. albicans
24
0.54 0.0406
0.2155 0.98
0.71 0.00006
0.0731 0.980.700.0002
0.0821
48
0.78
C. albicans
2448
0.54
0.2155
0.71
0.0731
0.70
0.0821
0.78
0.0406
0.98
0.00006
0.98
0.0002
24
0.78
0.0406 0.98
0.00006 0.98
0.0002
C.
krusei
C. glabrata
48
0.54
0.2155
0.71
0.0731
0.70
0.0821
4824
0.44
0.78 0.3173
0.0406 0.66
0.98 0.1060
0.000060.630.980.1285
0.0002
C. glabrata
24
0.54
0.2155
0.71
0.0731
0.70
0.0821
2448
0.54
0.2155
0.71
0.0731
0.70
0.0821
0.44
0.3173
0.66
0.1060
0.63
0.1285
C. C.
tropicalis
krusei
48
0.54 0.1673
0.2155 0.71
0.0731 0.70
0.0821
48
0.58
24
0.54 0.2155 0.82
0.71 0.0250
0.0731 0.80
0.70 0.0315
0.0821
C. krusei
0.2155
0.71
0.0731
0.70
0.0821
2448
0.54
24
0.54
0.2155
0.71
0.0731
0.70
0.0821
0.54
0.2155
0.71
0.0731
0.70
0.0821
C. tropicalis
C. guilliermondii
48
0.58 0.1488
0.1673 0.78
0.82
0.0250 0.80
0.0315
48
0.61
0.0400
0.76
0.0472
24
0.54 0.2155
0.2155 0.71
0.71 0.0731
0.0731 0.700.700.0821
0.0821
24
0.54
C. tropicalis
C. guilliermondii
2448
0.14
0.7712
0.49
0.2594
0.44
0.3164
0.58
0.1673
0.82
0.0250
0.80
0.0315
48
0.61
0.1488 0.78
0.0400 0.76
0.0472
C. parapsilosis
48
0.13
0.7774
0.27
0.5546
0.2547
0.5814
2424
0.14
0.7712
0.49
0.2594
0.44
0.3164
0.54 0.2155 0.71 0.0731
0.70
0.0821
C. guilliermondii
parapsilosis
C.
4848
0.13
0.7774
0.5546
0.2547
h = hours,
η = hardness, χ = electronegativity,
and
ω = electrophilicity
In gray
color
is indicated
0.61
0.1488 0.27
0.78index.
0.0400
0.760.5814
0.0472
the
values
are statically
significant
p < 0.05.
h=
hours,
η = that
hardness,
χ = electronegativity,
ω = electrophilicity
index.0.49
In gray 0.2594
color is indicated
24 and
0.14 0.7712
0.44the values
0.3164
C. parapsilosis
that are statically
significant p < 0.05.
48
0.13 0.7774 0.27 0.5546 0.2547 0.5814
Microorganism
Time of Testing (h)
Table 5. Multiple regression analysis for series I: Compounds 6 and 7a–g.
h = hours, Table
η = hardness,
χ = electronegativity,
and
= electrophilicity
index.
In7a–g.
gray color is indicated
5. Multiple
regression analysis
forωseries
I: Compounds
6 and
the values that are statically significant p < 0.05.
Table 5. Multiple regression analysis for series I: Compounds 6 and 7a–g.
7a–g
6
r2r2
r
0.97 0.94
0.94
0.83 0.70
0.70
0.94
0.97r 0.94r2
0.96
0.98
0.97 0.96
0.94
0.95
0.91
0.83 0.91
0.70
0.64
0.80
0.64
0.97 0.94
0.91
0.95
0.98 0.91
0.96
0.62
0.79
0.62
0.95 0.91
0.99
0.99
0.99
0.80 0.99
0.64
0.99
0.99
0.95 0.91
0.51
0.72
0.51
0.79 0.24
0.62
0.49
0.99 0.24
0.99
0.57
0.75
0.57
0.99 0.61
0.99
0.78
0.72 0.61
0.51
0.84
0.91
0.84
0.49 0.83
0.24
0.91
0.75 0.83
0.57
SignificantIndexes
Indexes
Significant
pp
24
0.00070
η, η,
SS
24
0.97
0.00070
7a–g
6
C. albicans
C. albicans
48
0.83
0.01000
48
0.01000
ωω
24
0.00100
0.00100
η, η,
S S Indexes
Significant
Microorganism
Time
of24Testing0.97
(h)
p
C. glabrata
C. glabrata
48
0.98
<0.0001
4824
<0.0001
ηη,ηS
0.00070
C. albicans
24
0.95
0.00030
η
2448
0.00030
ηω
0.01000
C. krusei
C. krusei
48
0.80
0.01660
ω
4824
0.01660
ωη, S
0.00100
C. glabrata
24
0.95
0.00030
24
0.00030
η ηη
C. tropicalis
48
<0.0001
C. tropicalis
48
0.79
0.02000
4824
0.02000
ωω
0.00030
η
C. krusei
24
0.99
<0.0001
2448
<0.0001
η, η,
SωS
C. guilliermondii
0.01660
C. guilliermondii
48
0.99
<0.0001
η, S
4824
<0.0001
η, Sη
0.00030
24
0.72
0.60230
variable
C. tropicalis
2448
0.60230
NoNo
variable
C. parapsilosis
0.02000
ω
C. parapsilosis
48
0.49
0.89800
No variable
4824
0.89800
No variable
<0.0001
η, S
0.75
0.05070
C. guilliermondii 48
4848
0.05070
ηη,ηS
A. niger
<0.0001
A. niger
72
0.78
0.06480
η
7224
0.06480
0.60230
No ηvariable
48
0.91
0.01080
η, ω
C. parapsilosis
4848
0.01080
ω
A. fumigatus
0.89800
Noη,variable
72
0.91
0.01140
η, µ
A. fumigatus
7248
0.01140
η,
µη
0.05070
A. niger
72
0.78 0.61 0.06480
η
4.2. Local and Fragment Reactivity Parameters
48
0.91 0.84 0.01080
η, ω
fumigatus
The localA.
Fukui
function is related72with the frontier
soft–soft interactions.
Figure 2
0.91 controlled
0.83 0.01140
η, µ
shows the isosurface plot of the Fukui function for an electrophilic attack f − (r), and the positive values
Microorganism
Time of
Testing
(h)
Microorganism
Time
of Testing
(h)r
Molecules 2017, 22, 427
8 of 16
4.2. Local and Fragment Reactivity Parameters
The local Fukui function is related with the frontier controlled soft–soft interactions. Figure 2
8 of 16
( ), and the positive
shows the isosurface plot of the Fukui function for an electrophilic attack
values are shown in purple. For series I, the carbon atoms neighboring the nitrogen atom of the
pyrrole
ring in
arepurple.
susceptible
to beI,attacked
by aatoms
soft electrophile
by the
oxygen
of the
are shown
For series
the carbon
neighboringfollowed
the nitrogen
atom
of theatom
pyrrole
ring
carbonyl
group and
vinylic
atoms of the
pirrolicbyring.
For compounds
incarbonyl
series II,group
the
are susceptible
to bethe
attacked
bycarbon
a soft electrophile
followed
the oxygen
atom of the
Fukui
function
sameofreactive
sitesring.
thanFor
series
I. In addition,
theII,carbon
atom
in the paraand the
vinylicshows
carbonthe
atoms
the pirrolic
compounds
in series
the Fukui
function
shows
position
of the
phenyl
ring
is susceptible
electrophilic
attack.
the same
reactive
sites
than
series I. In for
addition,
the carbon
atom in the para-position of the phenyl
Molecules 2017, 22, 427
ring is susceptible for electrophilic attack.
6
7a
7b
7c
7d
7e
7f
7g
8a
8b
8e
8c
8f
8d
8g
Figure 2. Fukui function isosurface plots for an electrophilic attack f − (r) of series I and II of
compounds 6, 7a–g, and 8a–g. In purple (positive values) are the favorable sites for an electrophilic
( ) of series I and II of
Figure 2. Fukui function isosurface plots for an electrophilic attack
attack; cutting value 0.01 a.u.
compounds 6, 7a–g, and 8a–g. In purple (positive values) are the favorable sites for an electrophilic attack;
cutting value 0.01 a.u.
Figure 3 shows the Fukui function for nucleophilic attack f + (r), and the regions in purple color
are Figure
positive
valuesthe
andFukui
showfunction
the mostfor
favorable
sites for
the attack
a soft
nucleophile.
For series
3 shows
nucleophilic
attack
( ), of
and
the regions
in purple
color I,
the
carbonyl
and
phenyl
carbon
atoms
are
prone
to
nucleophilic
attack.
For
series
II,
these
regions
are positive values and show the most favorable sites for the attack of a soft nucleophile. For series are
I,
the
carbonyl
group
andcarbon
carbonatoms
atomsare
from
vinyl
phenyl ring.
the
carbonyl
and
phenyl
prone
to and
nucleophilic
attack. For series II, these regions are
The local
Fukui
is localized
the phenyl
carbonyl,
pyrrole and phenyl moieties. In order
the carbonyl
group
andfunction
carbon atoms
from within
vinyl and
ring.
to understand which molecular fragments are responsible for antifungal activity, the softness and
electrophilicity were calculated for different fragments of compounds 6, 7a–g and 8a–g. Table 6 shows
the ID of the analyzed fragment, microorganisms, experimental time of testing, fragment chemical
reactivity parameter, statistical correlation coefficient (r) for MIC and softness and electrophilicity
fragments, and the atoms (marked in orange) considered in the fragment for series I and II. The basic
fragment ID a (g and i) is related with the oxygen atom, fragment ID b (f and h) includes the carbon
atom to gets the carbonyl group, fragment ID c includes carbon and nitrogen atoms from pyrrole ring
and ipso- and ortho-carbon atoms of the phenyl ring, fragment ID d includes meta and para-carbon
atoms of the phenyl ring, and so on. For Aspergillus niger in series I, high correlation values were
obtained for sk − [fragment a = g (oxygen atom, r = 0.90, 48 h) and fragment b = f (carbonyl group,
Molecules 2017, 22, 427
9 of 16
r = 0.93, 48 h)] and sk + [fragment c (r = 0.98, 72 h) and fragment d (r = 0.95, 48 h)]. As we can observe
for Aspergillus niger, the addition of the pyrrole and phenyl fragments to the carbonyl group increases
the correlation coefficient for series I (the time of testing more representative for this species was 72 h).
Molecules
2017, 22, 427linear regressions for s + (or s 0 ) includes the carbonyl group r = 0.83 (or r = 0.82)
9 ofand
16
For A. fumigatus,
k
k
the oxygen atom r = 0.81 (or r = 0.80). The more significant time of testing was 48 h.
6
7a
7b
7c
7d
7e
7f
7g
8a
8b
8e
8c
8f
8d
8g
Figure 3. Fukui function isosurface plots for a nucleophilic attack f + (r) of series I (6, 7a–g) and II
(8a–g) of compounds. In purple color (positive values) are the favorable sites for a nucleophilic attack;
Figure 3. Fukui function isosurface plots for a nucleophilic attack
( ) of series I (6, 7a–g) and II
cutting value 0.01 a.u.
(8a–g) of compounds. In purple color (positive values) are the favorable sites for a nucleophilic attack;
cutting value 0.01 a.u.
For series II, C. albicans has the higher correlation values for ω k − ; the addition of carbon atom to
−
oxygen
to obtain
the carbonyl
group
keeps
the
correlation
for ωand
fragments
m,Inr order
= 0.92
The atom
local Fukui
function
is localized
within
the
carbonyl,
pyrrole
phenyl
moieties.
k (see
and
n, r = 0.92).
Fragments
thatfragments
include the
atomfor
ofantifungal
the pyrroleactivity,
ring dothe
notsoftness
increaseand
the
to
understand
which
molecular
arenitrogen
responsible
correlation value
when
increasing
the number
of carbon
atoms of the6,phenyl
ring8a–g.
(j, k Table
and l, 6r shows
= 0.75).
electrophilicity
were
calculated
for different
fragments
of compounds
7a–g and
TheID
addition
the pyrrole
ring, ipso
carbon atom, and
the meta-C atom
the phenyl
ring, chemical
improves
the
of the of
analyzed
fragment,
microorganisms,
experimental
time from
of testing,
fragment
the correlation
(q, r = 0.86).
For other
species,coefficient
linear regressions
withand
higher
r wereand
found
when oxygen
reactivity
parameter,
statistical
correlation
(r) for MIC
softness
electrophilicity
0 : C. krusei 48 h (r = 0.78), C. tropicalis 24 h (r = 0.78), C. guilliermondii 48 h (r = 0.76),
was
included
in
ω
fragments, and thekatoms (marked in orange) considered in the fragment for series I and II. The basic
and C. parapsilosis
24 i)
h (r
0.78). with the oxygen atom, fragment ID b (f and h) includes the carbon
fragment
ID a (g and
is =
related
the Parr
functions
[41,42]
calculated
electrophilic
P− (r)from
and pyrrole
nucleophilic
atom Additionally,
to gets the carbonyl
group,
fragment
ID were
c includes
carbonfor
and
nitrogen atoms
ring
+
P
(r)
attacks.
They
had
similar
tendency
than
Fukui
functions
(See
Tables
S1
and
S2).
and ipso- and ortho-carbon atoms of the phenyl ring, fragment ID d includes meta and para-carbon
atoms of the phenyl ring, and so on. For Aspergillus niger in series I, high correlation values were
obtained for sk− [fragment a = g (oxygen atom, r = 0.90, 48 h) and fragment b = f (carbonyl group, r = 0.93,
48 h)] and sk+ [fragment c (r = 0.98, 72 h) and fragment d (r = 0.95, 48 h)]. As we can observe for
Aspergillus niger, the addition of the pyrrole and phenyl fragments to the carbonyl group increases
the correlation coefficient for series I (the time of testing more representative for this species was 72 h). For
A. fumigatus, linear regressions for sk+ (or sk0) includes the carbonyl group r = 0.83 (or r = 0.82) and the
oxygen atom r = 0.81 (or r = 0.80). The more significant time of testing was 48 h.
Molecules 2017, 22, 427
10 of 16
Molecules 2017, 22, 427
10 of 16
Atoms Considered
in the
reactivity
criterions
by fragment
for series
I (fragment
a–i) and ID:
series
Table
6. Chemical
Table 6. Chemical
reactivity
criterions
by fragment
for series
I (fragment
ID: a–i)
and series ID:
II (fragment
j–z).II
Fragment
(fragment ID: j–z).
(Marked in Orange)
Fragment
Time of Time
of Fragment
Atoms Considered in the Fragment
Chemical
r
ID
Microorganism
Testing
Chemical
r
ID
Microorganism
Testing
(Marked in Orange)
Parameter
(h)
Parameter
(h)
0.81
+
Aspergillus Aspergillus
fumigatus fumigatus
48
48sk
s0.81
k+
a, g, i
b, f, h
a
a
ωk +
ω0.77
k+
0.77
48sk +
s0.83
k+
0.83
Aspergillus Aspergillus
fumigatus fumigatus
48
b
b
+ 0.79
ω
k
+
c
72
Aspergillus niger
72 k
d
Aspergillus
niger
72
72
d
e
e
Aspergillus niger
Aspergillus Aspergillus
niger
niger72
Aspergillus
niger
f
48
72
Aspergillus fumigatus
f
Aspergillus fumigatus
Aspergillus niger48
g
i
j
48
Aspergillus
fumigatus fumigatus
48
i
Aspergillus
Candida albicans
j
Candida
Aspergillus fumigatus glabrata48
Candida albicans
k
Candida
albicans
48
Candida glabrata
48
sk −
sk
−
0
48sk
48
ωk 0
24s 0
k
48
ω +
24 k
48
+
48
24
ωk +
Candida glabrata
24
Candida parapsilosis
24
m
48
Candida albicans
Candida glabrata
Candida glabrata24
n
Candida parapsilosis
24
Candida parapsilosis
48
Candida albicans
24
Candida glabrata
Candida glabrata
Candida parapsilosis
24
Candida albicans
48
Candida parapsilosis
Candida glabrata
24
p
Candida tropicalis
Candida parapsilosis
q
q
k
−
Candida glabrata48
Candida albicans
Candida tropicalis
p
−
48sk
ωk
24
o
o
−
Candida albicans
Candida glabrata48
Candida albicans
n
48sk
Candida glabrata
Candida albicans24
Candida albicans
m
+
72
+
48sk
72sk −
48
l
l
sk
+
ωk +
Aspergillus fumigatus
Candida glabrata
Candida albicans24
k
ω
72s
h
Aspergillus
fumigatus
h
sk +
g
Aspergillus
niger
48
Aspergillus fumigatus
72
0.79
ωk
Aspergillus niger
Aspergillus
niger
c
24
Candida glabrata48
Candida albicans
r
Candida albicans
Candida glabrata
24
0.89
sk+ 0.95
0.95
ωk+
0.91
0.93
s0.93
k− 0.85
k−0.75
s0.85
0.75
sk− 0.90
0.83
sk0 0.82
0.74
ω0.72
k0
0.82
sk0 0.80
k+ 0.75
ω0.72
−
48
sk −
24
k+
ω0.75
0.75
0.750.75
0.92
ω0.75
k−
ω0.92
k−
0.75
O
n, z
m
p
o
q
r
k−
s0.83
0.76
sk
−
48
ω
k
24
ω
k
−
−
ωk−
0.76
0.76
ω0.86
k−
0.76
0.86
0.86
0.80
ωk−
0.86
X
N
H
0.77
0.83
0.77
48
l
0.75
0.77
ωk −
j
k
0.750.80
+
ωk0.75
sk
s −
24k
e
s0.90
k− 0.83
sk−0.74
48 −
ω
24 k
ωk
48
ωk −
24
d
c
0.91 0.88
sk +
s0.88
k−
k− 0.78
s0.75
0.92 0.92
ωk−
0.92ω0.92
k−
0.77
0.78
sk−
0.83
0.92
sk −
0.92
0.83
−
48
Candida albicans
0.98
sk +
0.98
ωk+ 0.89
s
t
Molecules 2017, 22, 427
11 of 16
Molecules 2017, 22, 427
s
ID
r
s
t
u
v
w
Candida glabrata
Candida albicans
u
Table 6. Cont. 0.80
sk −
0.76
Fragment
Chemical
Parameter
sk −
Candida albicans
Candida
glabrata
Candida
albicans
Candida
glabrata
Candida
albicans
48 24
24 48
sk −
48 24
24
−
Candida
albicans
Candida
glabrata
Candida glabrata
ωk−
sk
0.76
0.79
0.800.79
0.800.86
v
w
Candida
albicans
Candida
albicans
Candida
glabrata
Candida
glabrata
48 48
24 24
−
ω k − ωk
0.860.86
0.860.86
x
Candida
albicans
Candida
albicans
Candida
glabrata
Candida glabrata
48 48
24 24
sk − ω k −
0.790.83
0.790.83
Candida
albicans
Candida
albicans
Candida glabrata
48 48
24
ω k − sk −
0.860.76
0.86
Candida albicans
Candida
albicans
Candida
glabrata
48
24 24
ωk −
0.83
0.830.78
Candida albicans
Candida glabrata
48
24
sk −
y
Candida glabrata
Candida krusei
y
z
Candida tropicalis
Candida albicans
Candida krusei
Candida guilliermondii
Candida tropicalis
Candidad parapsilosis
Candida guilliermondii
Candidad parapsilosis
24
24
48
24
48
24
24
24
48
24
48 48
24
48
ωk 0
ωk 0
ωk 0
ωk 0
ωk 0
ωk 0
sk 0
ω
ωk0
ωk0
ωk0
ωk0
ωk0
sk 0
v
u
O
X
0.79
0.79
0.79
0.79
0.76
k0
Atoms Considered in the Fragment
(Marked in Orange)
0.760.86
0.76
48
48
24 24
sk −
sk −
r
Candida albicans
Candida albicans
Candida
glabrata
Candida glabrata
x
z
24
48
Time of
24
Testing
(h) 48
Candida glabrata
Microorganism
t
11 of 16
0.78
0.76
0.760.78
N
H
x
w
O
X
N
H
y
0.78
0.78
0.780.76
0.780.78
0.78
0.760.74
0.78
0.74
For series II, C. albicans has the higher correlation values for ωk−; the addition of carbon atom to
oxygen atom to obtain the carbonyl group keeps the correlation for ωk− (see fragments m, r = 0.92 and n,
4.3. MEPr =and
Dipole
Moment
0.92).
Fragments
that include the nitrogen atom of the pyrrole ring do not increase the correlation
value
when
increasing
the number
of carbon atoms
of the (MEP)
phenyl ring
k and l, r = 0.75).
The addition
Figure 4 shows the molecular
electrostatic
potential
for (j,
compounds
6, 7a–g
and 8a–g.
of
the
pyrrole
ring,
ipso
carbon
atom,
and
the
meta-C
atom
from
the
phenyl
ring,
improves
The MEP is a useful descriptor for understanding which sites in the molecules have affinitythe
to a
correlation (q, r = 0.86). For other species, linear regressions with higher r were found when oxygen
proton (charge controlled0hard-hard interactions [43]) and the relative polarity of the molecule [44–52].
was included in ωk : C. krusei 48 h (r = 0.78), C. tropicalis 24 h (r = 0.78), C. guilliermondii 48 h (r = 0.76),
Regions in red color indicate higher negative charge, higher electron density, and higher affinity to a
and C. parapsilosis 24 h (r = 0.78).
proton. Regions
in blue color
indicate
more
positive
a low
density
a low affinity
Additionally,
the Parr
functions
[41,42]
werecharge,
calculated
for electron
electrophilic
P−(r) and
and nucleophilic
to a proton.
For series
I and
the red
region
is located
near the(See
oxygen
from
P+(r) attacks.
They
had II,
similar
tendency
than
Fukui functions
Tablesatom
S1 and
S2). carbonyl group,
and the blue region is located near the nitrogen atom for both series, and the phenyl group for series
4.2. MEP
and Dipole Moment
I. In general,
compounds
in series I show a higher dipolar moment than compounds of series II as
we can observe
in 4Table
dipoleelectrostatic
moment was
calculated
all of the 15
indol-4-ones
the
Figure
shows7.theThe
molecular
potential
(MEP) for
for compounds
6, 7a–g
and 8a–g. at
The
B3LYP/6-311+G
(d,
p)
level
of
theory.
The
dipole
moment
follows
the
trend:
7b
>
7e
>
7a
>
8b
>
MEP is a useful descriptor for understanding which sites in the molecules have affinity to a proton6 >
controlled
hard-hard
theI,relative
polarity
of the molecule
[44–52].
7d = 8a (charge
> 7g > 8f
> 8c > 7c
> 7f > 8einteractions
> 8g > 8d.[43])
For and
series
compound
7b shows
the highest
value
in red
color
higher8b
negative
charge,
higher
electron
andcompounds
higher affinity
to a
(7.26 D),Regions
and, for
series
II,indicate
compound
has the
highest
value
(6.69density,
D). Both
present
Regionsin
in the
bluearomatic
color indicate
charge, that
a lowthere
electron
and a low
affinity
a 2-fluorproton.
substitution
ring.more
Thispositive
can suggest
is adensity
correlation
between
the
to a proton. For series I and II, the red region is located near the oxygen atom from carbonyl group,
relative polarity of the compounds 6, 7a–g and 8a–g and the kind of interactions that these compounds
and the blue region is located near the nitrogen atom for both series, and the phenyl group for series I.
can have with the active site of the receptor to antifungal activity.
In general, compounds in series I show a higher dipolar moment than compounds of series II as we
can observe in Table 7. The dipole moment was calculated for all of the 15 indol-4-ones at the
B3LYP/6-311+G (d, p) level of theory. The dipole moment follows the trend: 7b > 7e > 7a > 8b > 6 > 7d
= 8a > 7g > 8f > 8c > 7c > 7f > 8e > 8g > 8d. For series I, compound 7b shows the highest value (7.26 D),
and, for series II, compound 8b has the highest value (6.69 D). Both compounds present a 2-fluor
substitution in the aromatic ring. This can suggest that there is a correlation between the relative
Molecules 2017, 22, 427
12 of 16
Molecules 2017,
22,compounds
427
12 can
of 16
polarity
of the
6, 7a–g and 8a–g and the kind of interactions that these compounds
have with the active site of the receptor to antifungal activity.
8.046 × 10-2
7.668 × 10
-2
7.587 × 10
6
-7.668 × 10
-8.046 × 10-2
7.395 × 10
7d
-2
-7.395 × 10
-2
8.086 × 10
6.938 × 10
7.618 × 10
-2
7e
-2
-2
8a
-2
-2
8.448 × 10
-8.448 × 10
8d
7c
7.383 × 10
-7.440 × 10
-2
7f
7.387 × 10
-7.387 × 10
8b
-2
8.450 × 10
-2
7g
-2
-2
-2
7.139 × 10
-2
-2
-7.383 × 10
-2
-2
8c
-8.450 × 10
-2
-2
8e
-7.139 × 10
-6.938 × 10
7.440 × 10
7b
-7.587 × 10
-2
-7.618 × 10
-8.086 × 10
-2
7a
8.589 × 10
-2
-2
-2
-8.589 × 10
7.426 × 10
8f
-2
-2
8g
-7.426 × 10
-2
Figure 4. Molecular electrostatic potential maps from series I (6, 7a–g) and II (8a–g). This chart
Figure 4. Molecular electrostatic potential maps from series I (6, 7a–g) and II (8a–g). This chart shows
shows regions with negative values (red), and positive values (blue). The color code is different range
regions with negative values (red), and positive values (blue). The color code is different range
depending of the structure; units are given in a.u. for each scale.
depending of the structure; units are given in a.u. for each scale.
Molecules
2017,2017,
22, 427
Molecules
22, 427
13 of13
16of 16
Table 7. Dipole Moment of indol-4-one; series I compounds 6 and 7a–g and series II compounds 8a–g.
Table 7. Dipole Moment of indol-4-one; series I compounds 6 and 7a–g and series II compounds 8a–g.
6
8a–g
7a–g
Compound
Compound
6 6
7a 7a
7b 7b
7c 7c
7d 7d
7e 7e
7f 7f
7g
7g
8a
8a
8b
8b 8c
8c 8d
8d 8e
8e 8f
8f 8g
8g
µ (D)
µ (D)
5.985.98
6.706.70
7.267.26
4.864.86
5.495.49
7.257.25
4.734.73
5.40
5.40
5.49
5.49
6.69
6.695.30
5.304.00
4.004.47
4.475.31
5.314.41
4.41
5. Conclusions
5. Conclusions
Hardness, electronegativity, and electrophilicity of indol-4-ones were the chemical reactivity
Hardness, that
electronegativity,
and electrophilicity
of indol-4-ones
were the was
chemical
reactivity
parameters
had a higher correlation
with antifungal
activity. Hardness
the index
that had
parameters
that
had
a
higher
correlation
with
antifungal
activity.
Hardness
was
the
index
higher correlation for series I, and chemical potential, electronegativity, and electrophilicitythat
hadhad
higher
higher
correlation
for
series
I,
and
chemical
potential,
electronegativity,
and
electrophilicity
had
correlation with antifungal activity for series II.
higher correlation
with antifungal
activityattack
for series
Fukui function
for electrophilic
hadII.the higher correlation with molecular fragments
Fukui
function
for
electrophilic
attack
had
the higher
with
molecular
fragments
around both pyrrole and carbonyl groups, suggesting
that correlation
nature of the
reactivity
operative
between
around
both
pyrrole
and
carbonyl
groups,
suggesting
that
nature
of
the
reactivity
operative
between
the electrophilic sites of the indol-4-ones and the biologically active site in the studied fungi.
the electrophilic
sites ofcorrelation
the indol-4-ones
and the biologically
active
sitewith
in the
The strongest
with biological
activity was
found
C.studied
albicans,fungi.
C. glabrata, and
The
strongest
correlation
with
biological
activity
was
found
with
C.
albicans,
C.
glabrata,
and
A. fumigatus.
A. fumigatus.
The molecular electrostatic potential and the dipole moment calculated for compounds 6, 7a–g
The8a–g
molecular
and the
dipolethe
moment
calculated
forthe
compounds
6, 7a–g
and
suggestelectrostatic
that there ispotential
a correlation
between
relative
polarity of
compounds
and the
andkind
8a–gofsuggest
that
there
is
a
correlation
between
the
relative
polarity
of
the
compounds
and
the
interactions that these compounds can have with the active site of the receptor, as has
been
kind
of
interactions
that
these
compounds
can
have
with
the
active
site
of
the
receptor,
as
has
been
suggested by González et al.
suggested by González et al.
Supplementary Materials: Supplementary materials are available online.
Supplementary
Materials:
materials
are389176
available
Acknowledgments:
WeSupplementary
thank CONACYT
(Grants
andonline.
291061) for student financial support for M.A.
Zermeño-Macías
and
we
thank
Brent
E.
Handy
PhD
for
editing
English
and style.support for M.A.
Acknowledgments: We thank CONACYT (Grants 389176 and 291061)
for language
student financial
Zermeño-Macías
and we thank
Brent E.
Handy
PhD designed
for editing
English
andhas
style.
Author Contributions:
M.M.G.-C.
and
F.M. have
the
work. language
M.-d.A.Z.-M.
performed all calculations
and has written the first draft of the manuscript. R.G.-C. performed some molecule optimization. A.R.
Author
Contributions:
M.M.G.-C. and
andreviewed
F.M. have
designed
the work.calculations.
M.-d.A.Z.-M.
has performed
all
helped
in preparing manuscript
some
of the theoretical
All authors
have reviewed
calculations
and has written the first draft of the manuscript. R.G.-C. performed some molecule optimization.
this manuscript.
A.R.Conflicts
helped in
preparingThe
manuscript
and reviewed
of the theoretical calculations. All authors have
of Interest:
authors declare
no conflictsome
of interest.
reviewed this manuscript.
References
Conflicts
of Interest: The authors declare no conflict of interest.
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