Solubility of thiophene-, furan- and pyrrole-2-carboxaldehyde phenylhydrazone derivatives in 2.82 mol?L-1 aqueous DMSO at 298.15 K, inhibition of lymphoproliferation and tubulin polymerization: A study based on the scaled particle theory

Article abstract of DOI:10.1007/s10953-010-9568-z

In this work, the solubilities of nine phenylhydrazone derivatives in water and in 2.82 mol ? L^-1 aqueous DMSO at 298.15 K, expressed on the molar fraction scale, are reported. The estimated value of the standard Gibbs energy for transferring t

Full text of DOI:10.1007/s10953-010-9568-z

J Solution Chem (2010) 39: 1099–1112
DOI 10.1007/s10953-010-9568-z
Solubility of Thiophene-, Furan-
and Pyrrole-2-Carboxaldehyde Phenylhydrazone
Derivatives in 2.82 mol·L−1 Aqueous DMSO at 298.15 K,
Inhibition of Lymphoproliferation and Tubulin
Polymerization: A Study Based on the Scaled Particle
Theory
Ysaías J. Alvarado · Melchor Álvarez-Mon · Joanna Baricelli ·
José Caldera-Luzardo · Néstor Cubillán · Gladys Ferrer-Amado · Manzur Hassanhi ·
Yovani Marrero-Ponce · Victoria Mancilla · Miguel A. Rocafull ·
María Esther San Antonio-Sánchez · José Ojeda-Andara · Luz E. Thomas
Received: 24 September 2009 / Accepted: 10 March 2010 / Published online: 20 August 2010
© Springer Science+Business Media, LLC 2010
Abstract In this work, the solubilities of nine phenylhydrazone derivatives in water and in
2.82 mol·L−1 aqueous DMSO at 298.15 K, expressed on the molar fraction scale, are re-
ported. The estimated value of the standard Gibbs energy for transferring the solute from
water to 2.82 mol·L−1 DMSO, ꢀGW0 →mix, for each system, indicates that it is a spontaneous
Y.J. Alvarado ( ) · G. Ferrer-Amado
ꢀ
Departamento de Investigación en Tecnología de los Materiales y el Ambiente (DITeMA), Instituto
Venezolano de Investigaciones Científicas (IVIC), Avenida 74 con calle 14A, Maracaibo, República
Bolivariana de Venezuela
e-mail: yalvaradofec@yahoo.com
M. Álvarez-Mon · M.E. San Antonio-Sánchez
Laboratorio de Inmunología y Oncología, Departamento de Medicina, Facultad de Medicina,
Universidad de Alcalá, Alcalá de Henares, Madrid, España
J. Baricelli · M.A. Rocafull · L.E. Thomas
Laboratorio de Fisiología Molecular, Centro de Biofísica y Bioquímica, Instituto Venezolano
de Investigaciones Científicas (IVIC), Carretera Panamericana Km 11, Apartado 21827, Caracas
1020-A, República Bolivariana de Venezuela
Y.J. Alvarado · J. Caldera-Luzardo · N. Cubillán · V. Mancilla · J. Ojeda-Andara
Laboratorio de Electrónica Molecular(LEM), Departamento de Química, Facultad Experimental
de Ciencias, La Universidad del Zulia, Ap. 526, Grano de Oro, Módulo No. 2, Maracaibo, Estado Zulia,
República Bolivariana de Venezuela
M. Hassanhi
Laboratorio de Farmacología, Facultad de Medicina, La Universidad del Zulia, Maracaibo, Estado
Zulia, República Bolivariana de Venezuela
Y. Marrero-Ponce
Laboratorio de Diseño de Fármacos, Departamento de Farmacia, Centro de Química Bio-activa,
Universidad Central de las Villas, Santa Clara, Cuba

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J Solution Chem (2010) 39: 1099–1112
process. Some of the phenylhydrazone derivatives inhibited the induction of T lymphocyte
proliferation by phytohaemagglutinin (PHA) but only DPCT and NPCF efficiently inhibited
Guinea pig brain tubulin polymerization. Scaled Particle Theory (SPT) was used to inter-
pretate solubility and biological activity results. Based on the results we suggested that the
difference in the work of cavity creation ꢀꢀGc, associated with the transfer of the phenyl-
hydrazone derivatives from water to 2.82 mol·L−1 aqueous DMSO, is the dominant factor
in the magnitude of ꢀG0W→mix. The later quantity was considered to be an indirect measure-
ment of the hydrophobic character of these derivatives, and it can be used to interpret the
biological results.
Keywords Solubility · SPT · Tubulin polimerization · Lymphoproliferation ·
Phenylhydrazone derivatives
1 Introduction
The hydrazones have proved to be important molecules due to their potential antitumor, an-
tileukemic, antipsychotic, antiseptic, antifungal and antibacterial activities [1–4]. Morgan
and co-workers have proposed that the presence of a nitro group in the ortho-position and
a hydrazone bridge appear to be important conditions for interactions with surface tumor
markers via electrostatic/non-covalent binding with the arginine, serine/threonine and, cys-
teine moieties [4]. Even though the exact mechanism of anticancer activity for these mole-
cular systems is still unknown, the biological action of such compounds could be related to
their exceptional electronic properties and hydrophobicity [4, 5]. In fact, the hydrophobic
effect is the major driving force involved in the binding of drugs to their receptor target [6].
Data about the chemical processes in solution, of hydrazone compounds, are quite scarce,
probably due to their hydrophobic character and their low solubility in common organic
solvents [5, 7]. Nevertheless, these data are very important for understanding the role that
the specific and nonspecific solvent–solute interactions play in the binding between these
compounds and their target sites [8]. In order to overcome this difficulty, DMSO is often
used as co-solvent to improve the solubility of organic compounds which are not soluble in
common aprotic solvents and water, since most of the compounds screened for biological
activities are more soluble in dimethylsulfoxide (DMSO) than in water (W) at room temper-
ature [1–4]. In addition, this solvent is frequently used for the in vivo administration and in
vitro experimentation of several water-insoluble compounds [9].
There is a growing interest in our group in the study of thermodynamics of solvation and
its relationship with biological activity, especially the anticancer activity. Previously, we
have described the relationship between the DNA-phenylhydrazone association constant,
the antiproliferative activity on the breast tumor line MDA231 and the Gibbs energy of
cavity creation in a medium within the Scaled-Particle Theory framework [10].
Now, in this paper we report the experimental equilibrium solubility of the thiophene-
2-, furan-2- and pyrrole-2-carboxaldehyde phenylhydrazone, 4-phenylhydrazone and 2,4-
dinitrophenylhydrazone derivatives (henceforth referred to as PCT, PCF, PCP, NPCT, NPCF
and NPCP, DPCT, DPCF and DPCP, respectively, see Fig. 1) at 298.15 K in water and in
2.82 mol·L−1 aqueous DMSO. From these data, the Gibbs energies of solution ꢀG0i and
Gibbs energies of transfer from water to the mixed solvents ꢀG0W→mix were estimated for
each compound. Additionally, the anti-inflammatory activity of a selected group of these
compounds was evaluated by measuring the inhibitory activity on T-lymphocyte prolifer-
ation activated by phytohemagglutinin (PHA) [11], and the inhibition of Guinea pig brain

J Solution Chem (2010) 39: 1099–1112
1101
Fig. 1 Structure and nomenclature of phenylhydrazone derivatives of furan, pyrrole and thiophene
tubulin polymerization [12, 13]. Tubulin is an accepted target for treatments against can-
cer [14]. The results obtained in this work were analyzed and interpreted in terms of the
scaled particle theory (SPT) (i.e., in terms of the work to create the cavity in the solution
and the molar solute-solvent interaction energy). It is important to mention that this theory
has been used previously to study liquid solutions and proteins [15–17] and to evaluate the
interaction of phenylhydrazone with DNA [10].
2 Experimental Section
2.1 General Considerations
The phenylhydrazone derivatives (see Fig. 1) used in this work were synthecized follow-
ing a method developed by our group and reported elsewhere [7, 10]. The method is based
on the solvent free or aqueous condensation assisted by microwave irradiation of phenyl-
hydrazine, 4-nitrophenylhydrazine, or 2,4-dinitrophenyl-hydrazine with the corresponding
furan, pyrrole and thiophene carboxaldehyde. Water was sterilized and deionized in all the
cases. Dimethylsulfoxide (DMSO) was purchased from Aldrich and rigorously dried by ap-
propriate drying agents, fractionally distilled and collected and stored over molecular sieves
[7, 18–22]. DMSO was chosen as co-solvent in order to improve the solubility of phenyl-
hydrazone derivatives in water. Solubility studies were carried out by using aqueous DMSO
(20% V/V, 2.82 mol·L−1).
2.2 Solubility and Thermodynamics of Solution
The solubility determination was carried out following the procedure reported by our group
[10], based on the spectrometrical method of Zielenkiewicz and co-workers [23], using an
UV-Vis-NIR spectrophotometer (Shimadzu UV-3101PC) with a diode array detector ther-
moelectrically thermostated at 298.15 K in a cell holder (Shimadzu TCC-260). The exper-
iments were repeated at least five times for each solubility value. The reproducibilities, as
relative standard deviations, were better than 2%. The standard Gibbs energies ꢀG0i were
calculated from the molar fraction χ2 of each solute in a saturated solution using the follow-
ing equation
ꢀG0i = −RT lnχ2,i
(1)
where R is the gas constant, T is the absolute temperature, and i represents the medium:
water (W) or 2.82 mol·L−1 aqueous DMSO (mix).

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J Solution Chem (2010) 39: 1099–1112
From these solubility measurements of phenylhydrazone derivatives at 298.15 K in
2.82 mol·L−1 aqueous DMSO mixture, the Gibbs energy of transfer ꢀGW0 →mix from wa-
ter as reference solvent to the mixed solvents was estimated as [24]
ꢀ
ꢁ
χ2,W
ꢀGW0 →mix = ꢀG0mix − ꢀGW0 = RT ln
(2)
χ2,mix
The Ben-Naim standard Gibbs energy change, ꢀG∗W→mix, upon transfer of a solute mole-
cule from a fixed position in water to a fixed position in 2.82 mol·L−1 aqueous DMSO at
constant pressure, temperature and composition, was calculated by the relation [16, 17,
25–29]
ꢀ
ꢁ
Vmix
VW
ꢀG∗W→mix = ꢀG0W→mix + RT ln
(3)
Here, VW and Vmix are the molar volume at 298.15 K of water (VW = 18.07 cm3·mol−1) and
mean molar volume of 2.82 mol·L−1 aqueous DMSO (Vmix = 20.74 cm3·mol−1), respec-
tively. In this work Vmix was estimated as Vmix = χWVW + χDMSOVDMSO supposing that they
formed an ideal solution. In consequence, the term RT ln(Vmix/VW) = 0.341 kJ·mol−1
2.2.1 Scaled-Particle Theory Calculation of ꢀGW∗ →mix
.
The standard Gibbs energy change ꢀGW∗ →mix in this model is divided in two subprocesses:
(a) creation of a cavity to accommodate the solute molecule in the medium and (b) turning
on the solute–solvent interactions. Their magnitudes can be estimated by [26, 29]
ꢀG∗W→mix = [ꢀGc(mix) − ꢀGc(W)] + [Gint(mix) − Gint(W)] = ꢀꢀGc + ꢀGiθnt (4)
where ꢀGc is the work of cavity creation, and Gint is the Gibbs energy of solute–solvent
interaction. The Gibbs energy required to create a cavity in each medium was calculated by
Eq. 5 following the scaled-particle theory (SPT)
ꢂ
ꢃ
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
3
2 + K3
(5)
σ2
σ1
σ2
σ1
σ2
σ1
ꢀGc = RT K0 + K1
+ K2
where σ2 and σ1 are the hard-sphere diameters of solute and solvent, K0 = −ln(1 − ξ),
K1 = ꢁ = 3ξ/(1 − ξ), K2 = ꢁ(ꢁ + 2)/2, K3 = ξpV1/RT , with p as the hydrostatic pres-
sure over the liquid, V1 the molar volume of the medium, and ξ as the volume packing
density of pure solvent, that can be mathematically expressed as: ξi = πNAσi3/6Vi , and it
is defined as the ratio of the physical volume of a mole of solvent molecules to the mo-
lar volume of the solvent with NA as Avogadro’s number. For water and DMSO, we used
σW = 2.80 × 10−8 cm, VW = 18.07 cm3·mol−1, ξW = 0.383, σDMSO = 4.91 × 10−8 cm,
VDMSO = 71.37 cm3·mol−1 and ξDMSO = 0.523 as suggested by Graziano [16, 29, 30]. It is
well-known that the estimation of Gc from SPT strongly depends on the values of solute and
solvent hard-sphere diameters. These quantities are very important and affect the magnitude
of others parameters as, for example, ξ. Graziano selected σ = 2.80 × 10−8 cm (ξ = 0.383)
since this value is closer to the location of the first peak in the oxygen-oxygen radial distrib-
ution function of water determined experimentally by means of x-ray and neutron-scattering
measurements (i.e., the effective size of two H-bonded water molecules is 2.80 × 10−8 cm),
and also because the corresponding reported values of Gc are reliable in comparison to those
obtained by means of computer simulations in several water models [30].

J Solution Chem (2010) 39: 1099–1112
1103
Although the 2.82 mol·L−1 aqueous DMSO calculations were made by assuming an
ideal solution, the mean hard-sphere diameter of the mixed solvent systems (σmix = 2.91 ×
10−8 cm) was estimated as σmix = χWσW + χDMSOσDMSO and ξmix = 0.373 calculated with
ξmix = πNAσm3ix/6Vmix
.
The solute–solvent interaction energy Gθint can be considered as the sum of two standard
energy contributions [16, 17, 31, 32], Gθsp and Gnθsp, due to solute–solvent specific (donor–
acceptor interactions) and nonspecific (van der Waals forces) interactions, respectively,
Gθint = Gθsp + Gθnsp
(6)
and for ꢀGθint
ꢀGθint = ꢀGθsp + ꢀGnθsp = (Gsθp(mix) − Gθsp(W)) + (Gθnsp(mix) − Gθnsp(W))
(7)
It is important to recognize that the energy contribution from the chemical interactions
Gθsp is difficult to estimate. In contrast, the second term is considered as the sum of en-
ergy contributions from dipole–dipole (Gdd), induction (Gind), dispersion (Gdisp), dipole–
quadrupole (GμQ), and quadrupole-quadrupole (GQQ) solvent–solute interactions [31–34].
In this work the energy contribution in each medium was estimated using Eq. 8, and neglect-
ing the quadrupolar and dipole–quadrupole forces yields
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
16(ε1 − 1)ξ
(2ε1 + 1)σ23
NA 48(ε1 − 1)ξkBT
3NA
I1I2
I1 + I2 d6
α1α2
Gθnsp = −NA
μ22 −
α2 −
(8)
(2ε1 + 1)σ23
2
2
where the first, second and third terms correspond to the contributions from intermolecular
interactions of dipole–dipole, induction and dispersion (London) types, respectively, and
the parameters kB, ε, I, μ and α are the Boltzmann constant, dielectric constant, vertical
ionization energy, dipole moment and electronic polarizability, respectively (the subscript
1 and 2 represent the solvent and solute), and d is the distance between two hard-spheres
that is defined as d = (σ1 + σ2)/2. The mixture parameters α and I for the 2.82 mol·L−1
aqueous DMSO were empirically estimated as α1 = χWαW +χDMSOαDMSO and I1 = χWIW +
χDMSOIDMSO. We have treated the 2.82 mol·L−1 (1:18 DMSO:W mole ratio) aqueous DMSO
as an ideal mixture with a continuum dielectric since the results of neutron diffraction have
shown that the tetrahedral hydrogen bonding network of water remains largely intact at the
1:20 mole ratio [35]. Consequently, the solution can be characterized by its mean parameters
(volume, dielectric constant, etc.).
Alternatively, as proposed by Graziano [16], the values of ꢀGθsp can be empirically esti-
mated from
ꢀGθint = ꢀG∗W→mix − ꢀꢀGc
(9)
The difference between ꢀGθint and ꢀGnθsp can give information about the chemical in-
teractions (weak hydrogen bonds or weak electron donor–acceptor complexes) that occur
between the solute and DMSO molecules in the hydration shell. In the systems where the
specific solute–solvent component of the van der Waals ꢀGθsp is very small or negligible,
Eq. 4 can be rewritten as
ꢀG∗W→mix = ꢀꢀGc + ꢀGnθsp
(10)

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21
Table 1 Quantum mechanical calculation results of the vertical ionization energy (I/kJ×10 ), polarizabil-
23
ity (α/esu×10 ) and dipole moment (|μ|/Debye) of the phenylhydrazones under study
Compound
I
α
|μ|
PCF
1.089
1.185
1.232
1.048
1.141
1.184
1.090
1.185
1.233
2.785
3.547
3.673
2.842
3.431
3.732
3.012
3.547
3.893
3.775
8.764
8.993
0.749
7.732
8.472
2.280
8.777
8.727
NPCF
DPCF
PCP
NPCP
DPCP
PCT
NPCT
DPCT
2.2.2 Theoretical Calculation of Vertical Ionization Energy, Dipole Moment, Electronic
Polarizability and Molecular Volume
With the purpose of estimating Gθnsp in Eq. 8, several quantities for phenylhydrazones were
calculated with quantum mechanical methods (I, μ, α and V ). The geometrical structures
were optimized considering Cs symmetry, using Density Functional Theory with the B3LYP
functional and 6-311++G(3d,3p) basis set. The vertical ionization energy (I) was calculated
through the strategy proposed by Librando and Alparone based on the energy difference
between a neutral molecule and its cation [36]. The dipole moment (μ) and electronic po-
larizability (α) were calculated by analytical methods. The hard-sphere diameter of each
solute σ2 was calculated using Suppan’s equation [37], i.e. σ2 = 2(3V2/4πNA)1/3, where V2
is the corresponding molar volume in the gas phase calculated by Monte Carlo integration
of an envelope space of electron density with a contour value of 0.001 atomic units [38]. All
calculations were carried out in the Gaussian 2003 quantum chemistry package [39]. The
results obtained for these molecular systems are shown in Table 1.
2.3 Preparation of Primary Human T-lymphocytes, Lymphoproliferation and Measurement
of Inhibitory Effects of Phenylhydrazone Derivatives on T-lymphocyte Proliferation
The experimental protocol was reviewed and approved by the Human Experimentation
Committee. Written informed consent was obtained from each and every subject. Prepa-
ration of primary human T lymphocytes: Heparinized human peripheral blood (40 mL)
was obtained from normal healthy volunteers. Human peripheral blood mononuclear
cells were isolated by the Ficoll-Hypaque gradient centrifugation method as described
previously [40, 41]. The cells resuspended in RPMI-1640, counted and their viability
checked by trypan blue exclusion [40–42]. Cells were cultured (duplicate) in RPMI-1640
medium supplemented with 10% heat-inactivated fetal calf serum and antibiotics. 50 µL
(1000 cells·μL−1) aliquots of cell suspensions were placed in a 96-well microtitre, followed
by incubation with PHA (10 µg·mL−1) (Sigma-Aldrich) and phenylhydrazone derivatives
(10−5 mol·L−1) for 5 days. Incubations were at 310 K in a humidified CO2 atmosphere [42].
The concentration of DMSO in these studies for each solution was less than 1% V/V. Cy-
closporine A was used as negative and positive. Subsequently, 20 µL of tritiated thymidine
(1 mCi·mL−1) was added to each well. After 24 h of incubation, the cells were harvested on
fiberglass filters by an automatic harvester system. Radioactivity in the filters was measured

J Solution Chem (2010) 39: 1099–1112
1105
by scintillation counting (Wallac Perkin Elmer) [43, 44]. Cell proliferation is determined by
estimating the incorporation of [3H]thymidine into DNA, a process which is closely related
to underlying changes in the cell number. The inhibitory activity IA(%) of compounds on
T-lymphocyte proliferation was determined by us as [11]
CPM(control) − CPM(drug)
IA =
· 100
(11)
CPM(control)
2.4 Preparation of Pure Tubulin
All operations were at 275 K unless otherwise indicated. Guinea pig brain tubulin was
prepared by three cycles of polymerization–depolymerization followed by chromatogra-
phy on DEAE-sepharose FF [12]. The eluted tubulin, depleted of microtubule-associated
proteins, was concentrated by ultrafiltration, adjusted to 0.05 mol·L−1 2-(N-morpholino)
ethanesulfonic acid (MES)–NaOH, pH = 6.8, 0.25 mmol·L−1 MgCl2, 0.5 mmol·L−1 EGTA,
3.4 mol·L−1 glycerol, and 0.2 mmol·L−1 GTP (30% glycerol buffer), and stored at 301 K at
a concentration of 2 mg·mL−1
.
2.5 Microtubule Assembly Assay
Tubulin, at 273 to 275 K in 30% glycerol buffer, was supplemented with 6 mmol·L−1
MgCl2 and 1 mmol·L−1 GTP and used within a concentration range of 1 to 1.5 mg·mL−1
.
The final buffer composition was 0.05 mol·L−1 MES–NaOH, pH = 6.8, 6.25 mmol·L−1
MgCl2, 0.5 mmol·L−1 EGTA, 3.4 mol·L−1 glycerol, and 1.2 mmol·L−1 GTP, and was
called the assembly buffer. Polymerization was initiated by a temperature shift from 283
to 310 K [12] in a thermostated 1-cm light path cell and was monitored turbidimetri-
cally at 350 nm with a spectrophotometer Synergy HT (Biotek Instruments), equipped
with a thermostatically-controlled cell holder. The concentration of drug stock solutions
in DMSO solution was 2×10−3 mol·L−1. These compounds were added to the tubulin
solution before polymerization. The content of DMSO in all cases was less than 2% by
volume. In this study colchicine was used as a control of assembly inhibition. The IC50
value for colchicine in this assay is near to 1.4 µmol·L−1, which agrees with the reported
value [45].
3 Results and Discussion
3.1 Solubility and Thermodynamics of Solution
The solubility, on the mole fraction scale, determined by UV-Vis spectrometry for each
compound in water χ2(W) and 2.82 mol·L−1 DMSO χ2(mix) at 293.15 K, is presented
in Table 2. As it can be seen, independently of the heteroatom in the heterocyclic ring, the
solubility diminishes with incremental increases of the number of nitro groups on the phenyl
ring moiety. Also, the solubilities of compounds in 2.82 mol·L−1 DMSO are markedly larger
than in water. The values of the Gibbs energy for the dissolution process in water ꢀGW0
and in 2.82 mol·L−1 aqueous DMSO mixture ꢀGm0 ix are large and positive for each studied
compound (see Table 2), and their magnitude increases with the increment of the substitution
of H by a nitro group on the phenyl ring—i.e., the highest values of ꢀG0mix were obtained
for the hydrazone derivatives containing the 2,4-dinitrophenyl ring. In the same table in the

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J Solution Chem (2010) 39: 1099–1112
−1
Table 2 Solubilities of phenylhydrazones (molar fraction) and thermodynamic quantities (kJ·mol ) associ-
−1
ated with the dissolution process in water (W), in 2.82 mol·L DMSO(mix), and the transfer of solute from
W to the mixture, inhibitory activity IA(%) of phenylhydrazone derivatives on T-lymphocyte proliferation
−1
stimulated with PHA, and inhibitory effects (IC /µmol·L ) on tubulin polymerization
50
7
5
0
W
0
mix
0
∗
a
Compound χ (W)×10 χ (mix)×10 ꢀG ꢀG
−ꢀG
−ꢀG
IA(%) IC
50
2
2
W→mix
W→mix
PCF
5.73
1.72
0.14
5.86
1.73
0.16
5.19
1.68
0.07
2.28
1.05
0.17
5.95
2.09
0.36
7.40
3.08
0.24
35.63 26.50
9.13
9.47 (9.34)
10.52 (9.42)
12.24 (9.99)
11.80 (9.97)
12.22 (10.14)
13.71 (10.60)
12.64 (10.05) 37.50 inactive
13.25 (10.11) 18.75 inactive
14.70 (10.65) 62.50 0.52 0.03
NPCF
DPCF
PCP
NPCP
DPCP
PCT
38.61 28.43 10.18
44.88 32.97 11.90
35.57 24.12 11.45
38.60 26.71 11.88
44.43 31.06 13.37
35.87 23.58 12.30
38.66 25.75 12.91
46.41 32.05 14.36
25.00 0.58 0.03
37.50
NPCT
DPCT
a
Values in parenthesis were calculated with Eq. 10
sixth and seventh columns are listed the corresponding values of ꢀG0W→mix and ꢀGW∗ →mix
calculated by means of Eqs. 2 and 3.
From these results it is clear that the transfer from water to 2.82 mol·L−1 aqueous DMSO
at 298.15 K is a spontaneous process in all considered systems, as expected, due clearly to
the high solubility of the compounds in 2.82 mol·L−1 DMSO with respect to water. Inter-
estingly, the absolute values of ꢀG∗W→mix have a increasing trend with σ2 (see Table 3).
This means that the transfer of a molecule from a fixed position in liquid water to a fixed
position in 2.82 mol·L−1 aqueous DMSO is mainly governed by the molecular size of the
solute. As shown in Table 2 and 3, the absolute value of ꢀG∗W→mix decreases in the fol-
lowing order: phenylhydrazone derivatives (PCF < PCP < PCT); p-nitrophenylhydrazone
derivatives (NPCF < NPCP < NPCT) and 2,4-dinitrophenylhydrazone derivatives (DPCF
< DPCP < DPCT). Consequently, we suggest that the value of ꢀG∗W→mix may be consid-
ered as a direct measurement of the interactions between the solute and DMSO molecules
in the hydration shell, resulting in an indirect measurement of the hydrophobic character for
each phenylhydrazone derivative.
Table 3 collects the values obtained for the work of cavity creation ꢀGc, the nonspecific
components of the van der Waals forces Gθnsp, the values of ꢀꢀGc, the solute–solvent van
der Waals interaction energy ꢀGiθnt, and the values of ꢀGnθsp associated with the transfer
of the nine phenylhydrazone derivatives from water to 2.82 mol·L−1 DMSO at 298.15 K.
From this table it can be seen that the work for cavity creation ꢀGc in water is greater
than in 2.82 mol·L−1 DMSO. The observed increment in ꢀꢀGc is a consequence of the
small hard-sphere diameter of water in comparison to the mean hard-sphere diameter of a
binary solvent system, and is also due to the higher volume packing density in water in
relation to the mixture (ξW > ξmix). It is known that ꢀGc has an inverse trend with σ of
the solvent and a direct increasing trend with ξ [26, 28]. These results indicate that the
excluded volume effect is significant and could be the cause of the low solubility of these
derivatives in water. As a consequence ꢀꢀGc is negative, which favors the transfer from
water to 2.82 mol·L−1 DMSO. In fact, when ꢀꢀGc was correlated with the hard-sphere
diameter of the solute σ2 in this non homologous family of compounds, a linear trend was
found with a coefficient of correlation of -0.9999 0.0084 and p < 0.0001 (graph omitted
for simplicity).

J Solution Chem (2010) 39: 1099–1112
1107
8
Table 3 Hard-sphere diameter of phenylhydrazones (σ × 10 cm) and thermodynamic quantities
2
−1
−1
DMSO(mix), and
(kJ·mol ) associated with the dissolution process in water (W) and in 2.82 mol·L
the transfer of solute from W to mix
θ
int
θ
θ
θ
nsp
θ
sp
σ
2
ꢀG (W) ꢀG (mix) −ꢀꢀG ꢀG
−G (W) −G (mix) ꢀG
−ꢀG
c
c
c
nsp
nsp
PCF
7.66 80.60
71.03
75.79
79.64
74.40
79.32
83.04
75.27
80.17
83.60
9.57
10.24
10.78
10.04
10.74
11.26
10.17
10.86
11.34
0.10
7.31
7.08
0.23
0.13
1.10
2.25
1.82
2.09
3.11
2.59
3.14
4.05
NPCF 7.94 86.03
DPCF 8.16 90.42
−0.28 29.64
−1.46 28.71
28.82
27.92
1.55
0.82
0.79
0.07
0.60
0.66
0.12
0.75
0.69
PCP
7.86 84.44
−1.75
1.62
NPCP 8.14 90.06
DPCP 8.35 94.30
−1.49 21.65
−2.45 23.93
21.05
23.27
3.27
PCT
7.91 85.44
−2.47
3.39
NPCT 8.19 91.03
DPCT 8.38 94.94
−2.40 27.04
−3.35 25.10
26.29
24.40
With the data of ꢀG∗W→mix and ꢀꢀGc, the Gibbs energy of solute–solvent interaction
ꢀGθint was calculated with Eq. 9 and their values are negative in all cases with the excep-
tion of PCF (see Table 3). The numerical contribution of this quantity, in comparison with
ꢀꢀGc, becomes important when the electronegativity of the heteroatom decreases (furan <
pyrrole < thiophene) and with the number of nitro groups on the phenyl moiety. In fact, the
highest, as absolute values, were obtained for dinitrophenylhydrazone derivatives in each
family.
On the other hand, the values of Gθnsp calculated with Eq. 8 for each solute in each
medium are negative and slightly lower (as absolute value) in 2.82 mol·L−1 DMSO than
in W, and become more negative with the presence of nitro groups in the derivatives of
thiophene, furan and pyrrole. However, the values obtained for p-nitro and dinitrophenylhy-
drazone derivatives are close (see Table 3). This is likely to be a consequence of the small
difference between the polarizability values for p-nitro and dinitrophenylhydrazone deriva-
tives, as well as the dipole moments, estimated at the DFT-B3LYP/6-311++G(3d,3p) level
(see Table 1). As expected, the values of ꢀGθnsp are small and positive.
The value for the specific contribution ꢀGθsp (due to hydrogen bonding and/or electron
donor–acceptor interactions), empirically estimated using Eq. 7, are negative in each case.
However, their magnitude in absolute value is higher than the value obtained for ꢀGθnsp. It is
very important to mention that our studies show that the hydrogen bonding constants Kassoc
between a protic solvent such as methanol with PCT, PCF, NPCT and NPCF derivatives in
benzene at 298 K, determined by means of densitometric and refractometric methods, are
low in magnitude (Kassoc < 1) [46], which is evidence of the poor proton acceptor character
of these phenylhydrazones. In this way, Singh and co-workers showed, by experimental and
theoretical methods, that complex formation by hydrogen bonding between thiophene and
methanol or DMSO (stoichiometry 1:1) is small [47]. In consequence, the high magnitude
of ꢀGθsp may be due to other types of specific interactions such as electron donor–acceptor
complexes between DMSO and phenylhydrazones, which is favored by the incremental in-
crease of electrophilicity with the number of nitro groups on the phenyl ring [3, 4].
Also, the difference between ꢀG∗W→mix(experimental) and ꢀG∗W→mix(SPT, Eq. 10) in-
dicates that the magnitude of ꢀGθsp is significant and has an important contribution to the
value of ꢀG∗W→mix in all cases. These experimental and theoretical results support the inter-
pretation that the energy contribution from solute–solvent van der Waals interactions ꢀGint

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J Solution Chem (2010) 39: 1099–1112
to the Ben-Naim standard energy change ꢀG∗W→mix are significant, but the magnitude of
this property is dominated by the ꢀꢀGc term (about 80%).
Additionally, we think that the reorganization of water H-bonds can be considered as a
compensating process that does not affect the Gibbs energy change of transfer. At this point,
it is noteworthy to mention that we suggest that the magnitude of ꢀG∗W→mix or ꢀꢀGc can
be used as an interpretative tool for biological activity of these materials since both thermo-
dynamic properties give information about the hydrophobic character of these solutes. The
mentioned properties might determine the possible preferential interaction of these mole-
cules with the strongly dipolar and polarizable groups in the interior of the hydrophobic
cavities of the respective target sites. In fact, Klapper in 1971 [48], based on estimates of
the atomic densities of six proteins, suggested that the interior of a protein is solid-like,
notwithstanding its heterogeneity. Later, Richards in 1974, reached the same conclusion
from atomic coordinates provided by crystal structure studies and Voronoi polyhedra [49].
In addition, Graziano has recently found that the experimental translated cavity size distrib-
ution inside globular proteins can be reproduced by means of SPT calculations [29].
The binding of drug to proteins in aqueous solutions involves the hydrophobic transfer
and anchoring of the hydrated drug by formation of covalent and/or non-covalent mole-
cular interactions. In fact, water is an essential part of the protein structure [50] and the
hydrophobic hydration of the drug. So then, the water-mediated interaction between drug
and a hydrophobic binding pocket of the proteins, as well as the hydrophobicity of drugs,
provides the driving force underlying favorable complex formation [8, 51]. In consequence,
these parameters can play an important role in apoptosis and in the biophysical chemistry of
the design of new antineoplastic drugs. Interestingly, the ligand binding to biomolecules can
be empirically partitioned into two contributions arising from the Gibbs energy of van der
Waals interactions and cavitation Gibbs energy for the transfer of the hydrated drug into the
hydrophobic pocket in the protein or a biomolecule (e.g. T lymphocytes and tubulin) [52].
In this sense, tubulin exists as a heterodimer consisting of α and β subunits which poly-
merize to form microtubules; this process is critical for the proper functioning of micro-
tubules within the cell. Therefore, tubulin is an accepted target in treatments against can-
cer, since there are drugs that bind and stabilize these microtubules and inhibit the tubulin
polymerization and trigger apoptosis (e.g. colchicine) [13]. It is very important to note that
the participation of water and hydrophobic character of drugs in small-molecule binding to
tubulin have not been well-characterized. Therefore, the process of creation of a cavity in-
side a solvent is relevant for the understanding of hydrophobic hydration and to determine
the hydrophobic character of the solute.
The results obtained here about the activity to inhibit proliferation of human T lym-
phocytes, stimulated by phytohaemagglutinin (PHA) of selected hydrazone derivatives as
a function of molecular size, are shown in Table 2. Almost all of the evaluated derivatives
showed low biological activity. In spite of the complexity of these systems, these results
clearly reveal a significant increment in the antiproliferative activity with both the incre-
ment of |ꢀꢀGc| and the increment of the number of nitro groups on the phenyl ring moiety
of the analyzed thiophene and furan derivatives. The antiproliferative activity follows the
following order in each family of compounds: DPCT > NPCT and DPCF > NPCF. DPCT
was the most-active and corresponds to the highest |ꢀꢀGc| value (11.34 kJ·mol−1). Inter-
estingly, the value of the inhibitory activity obtained for PCT was similar to the value for
DPCF but higher than the value determined for NPCT, and the magnitude of ꢀꢀGc for PCT
is very close to the value obtained for NPCF, giving a possible anomalous behavior.
Furthermore, none of the thiophene derivatives tested, with the magnitude of ꢀꢀGc
in this range, displayed inhibition of tubulin polymerization with the exception again of

J Solution Chem (2010) 39: 1099–1112
1109
the DPCT derivative, which has an IC50 value higher than that of the control (colchicine
drug). However, the compound NPCF has a value of IC50 very close to that determined for
DPCT. The mechanism of these compounds for inhibition of tubulin assembly apparently
is complex and remains as a research line for future studies. Despite results that are not
conclusive with these molecular systems, it seems like there are at least three relevant factors
for the antiproliferative activity of human T-lymphocytes and inhibitory activity of tubulin
polimerization. First, the mechanism of cavity formation in DMSO-containing medium;
second, the transfer of the solute molecule from this cavity to the cavity in the target site,
and third the high hydrophobic character of the solute.
Finally, the use of SPT (spherical model) for non-spherical molecules may seem inad-
equate, but we do think that random rotations of the solute in a medium give an approx-
imately spherical cavity even when the molecules are not spherical. This is possibly the
reason why excellent results are obtained in these rigid asymmetric molecular systems with
this spherical model. It is clear that an implementation of more elaborate models using a
spherocylindrical molecular shape as the proposed by Cotter and Martire [53], Benzi and
co-workers [54], and Graziano [55] should give more detailed information about the effects
of these non-specific and specific forces, and cavitation upon solvation of these materials
and their role in biological activity. Studies to consider a spherocylindrical cavity for these
phenylhydrazone derivatives are actually in progress in our group.
4 Conclusions
The experimental and theoretical results obtained show that the solubility of the phenylhy-
drazone derivatives in water diminishes with an increment in the number of nitro groups on
the phenyl ring moiety in each family of compounds, and that the solubility of compounds
in 2.82 mol·L−1 DMSO is larger than in water—in general. The corresponding value of the
Gibbs energy for the dissolution process in water ꢀG0W and in a mixture ꢀG0mix is large
and positive for each studied compound, and the highest absolute values were obtained
for the hydrazone derivatives containing the 2,4-dinitrophenyl ring, but the values obtained
in 2.82 mol·L−1 DMSO are lower than in water. The corresponding values of ꢀG0W→mix
and ꢀG∗W→mix indicate that the transfer from water to 2.82 mol·L−1 aqueous DMSO at
298.15 K is a spontaneous process in all of the systems considered. The value of ꢀGW∗ →mix
might be considered a direct measurement of the interactions between the solute and DMSO
molecules in the hydration shell, and in consequence, is an indirect measurement of the hy-
drophobic character of each phenylhydrazone derivative. In spite of the crudeness of the SPT
theory, the analysis∗performed appears to agree with the main observations of this work, es-
tablishing that ꢀGW→mix is practically dominated by the magnitude of the difference in the
work of cavity creation ꢀꢀGc. In general, the hydrazones studied in this work show low
biological activity for inhibiting the proliferation of human T-lymphocytes stimulated by
phytohaemagglutinin (PHA). Furthermore, a significant increment of antiproliferative activ-
ity with the increment of both the magnitude (in absolute value) of ꢀꢀGc and ꢀGW∗ →mix
,
and the increment of the number of nitro groups on the phenyl ring moiety in the thio-
phene and furan derivatives was observed. In relation to the tubulin polimerization, NPCF
and DPCT showed an important inhibitory activity when compared with colchicine. The
rest of the thiophene derivatives were inactive. Apparently, the biological activities of these
compounds are directly related to their hydrophobicity.

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J Solution Chem (2010) 39: 1099–1112
Acknowledgements The authors thank to the Fondo Nacional de Ciencia, Tecnología e Innovación
(FONACIT, Proyecto de apoyo a Grupos No. G-2005000403), Instituto Zuliano de Investigaciones Tecnológ-
icas (INZIT), CONDES-LUZ, Avícola La Rosita S. A. and Petroregional del Lago S. A. (PERLA) for partial
financial support of this work. The authors thank Dr. Juan Chirinos Colina for his help in the discussion of
this manuscript, and the referees for important observations and very helpful comments on the present work.
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