MOLECULAR DYNAMICS SIMULATIONS OF POLYGLYCEROL
DENDRIMERS AS CARRIERS FOR HALOPERIDOL: THEORETICAL
AND EXPERIMENTAL RESULTS
Silva, A. O.1, de Queiroz, A. A. A.2
1, 2
Center for Research and Innovation in Advanced Materials biofunctional – Federal University of Itajubá –
Unifei, Itajubá (MG), Brazil
[email protected]
The aim of this study was to prepare polyglycerol (PGLD) dendrimers conjugated with haloperidol (Hal) to give
PGLD-Hal conjugates, a novel controlled delivery system through the intravenous (i.v.) route to reduce the
frequency of administration, dose and adverse effects during the short-term management of manifestation of
psychotic disorders. Experimental analysis of the PGLD-Hal showed that, on average, six haloperidol molecules
were covalently bound to PGLD. In order to better understand the surface loading and distribution of the
haloperidol molecules, molecular reactivity was determined by evaluation of electronic properties using frontier
molecular orbital theory (FMOT) and molecular dynamics simulations. It was shown that the surface loading
and distribution of the haloperidol molecules was determined by both electronic effects and by the different
dynamic conformations adopted by the modified dendrimer during the incremental addition of haloperidol. The
analysis of the dynamic behavior of the PGLD-Hal generation 1.0 showed that its flexibility and its polarity
changed with the incremental addition of haloperidol.
Key words: Polyglycerol dendrimer, Haloperidol, antipsychotic therapy, schizophrenia,
bipolar disorder.
1.
INTRODUCTION
Dendrimers are a class of polymeric compounds that can be distinguished from
conventional linear polymers by their highly branched and symmetrical architecture [1, 2].
Due to their structural characteristics (nanosize dimensions, controlled size and shape,
multifunctionality, globular topology and presence of internal cavities) makes them
interesting candidates for applications such as drug delivery, and controlled release [3, 4].
The broad spectrum of applications being developed for dendrimers in areas such as
microencapsulation, drug delivery, light harvesting, molecular recognition, and bio catalysis
is a result of these remarkable features [5].
Dendrimers is now frequently used as drug carriers in medicine to improve the
therapeutic value of various water soluble/insoluble medicinal drugs and bioactive molecules
by improving bioavailability, solubility and retention time reducing the patient expenses, and
risks of toxicity [6, 7, 8].
Encapsulation of medicinal drugs in dendrimers (nanomedicine) increases drug
efficacy, specificity, tolerability and therapeutic index of corresponding drugs improving the
protection of premature degradation and interaction with the biological environment,
enhancement of absorption into a selected tissue, bioavailability, retention time and
improvement of intracellular penetration [9, 10].
Haloperidol (Hal) is an extensively used, highly potent antipsychotic drug. Haloperidol
is a first-generation antipsychotic drug used for the treatment of schizophrenia and more
acutely in the treatment of acute psychotic states [11]. Haloperidol possesses a strong activity
against delusions and hallucinations, most likely due to an effective dopaminergic receptor
blockage in the mesocortex and the limbic system of the brain.
Since the uninterrupted supply of antipsychotic medication therapy [12] is vital for
patient health long-term drug delivery system would be an ideal candidate to improve drug
adherence and to ensure a continuous supply of optimum dosage levels of the drug. The aim
of our research is to understand under the perspective of the quantum chemistry the various
factors that affect the crucial performance metrics of haloperidol-loaded water soluble
dendrimers including- size, drug incorporation, loading and release.
Structure-based modeling and quantum chemistry studies [13] can be used to
accurately understand the interactions between functionalized dendrimers and molecules of
pharmaceutical and medicine interest. In this work, frontier molecular orbital theory coupled
with molecular dynamics simulations were used to understand the structural features of the
experimentally determined loading and distribution of covalently bound haloperidol and its
impact on the biological properties of the PGLD dendrimer (Figure 1).
F
F
OH
O
O
OH
OH
OH
O
O
HO
OH
OH
O
O
Cl
OH
HO
N
OH
N
O
HO
O
O
Cl
HO
OH
(A)
(B)
(C)
Figure 1 – Illustration of chemical structures of PGLD (A), Haloperidol (B) and the
conjugate PGLD-Hal (C).
2.
MATERIALS AND METHODS
2.1
PGLD-Hal synthesis
PGLD with generation 0(G0), 2(G2), 3(G4) and 4(G4) were synthesized by a modified
step-by step allylation and dihydroxylation divergent synthesis reactions [14]. The PGLD
with a number average molecular weight of 1.7 kDa and an average of 26 hydroxyls per
molecule were synthesized in a step-growth was used for the haloperidol immobilization. The
successful synthesis of PGLD G-3 (88% yield) was confirmed by 1H-NMR, 300 MHz, D2O;
shift (, ppm): 4.8 (OH), 4.04 (OCH2-CH-CH2), 3.95-3.40 (CH2-O-CH2); 13C-NMR (75 MHz,
D2O); Shift (, ppm): 62.9 (CH2OH, terminal unity), 82.0-81.5, 80.6-79.8, 74.7-73.9, 73.872.2, 71.8-70.7, 64.7, 63.1 (CH2-O-CH2, polyether backbone).
A Bruker Biflex (Bremen, Ge) matrix-assisted laser desorption/ionization-time of
flight-mass spectrometry (Maldi-Tof-MS) was used for the determination of isomolecularity
of PGLD molecules. The energy source was nitrogen laser operating at wavelength of 337 nm
and pulse width of 3 ns. The matrix used was in doleacrylic acid, which was prepared by
forming a saturated solution in acetone. Then, a target plate was spotted with 5 L of dilute
sample. The sample was allowed to completely dry before use. Standards were used to
calibrate the instrument. The real mass of the PGLD G-3 determined from Maldi mass spectra
was found to be 1,721.8 (Na+) (Figure 2). This value was consistent with the theoretical
molecular weight of PGLD G-3 (1,689) reported by the literature [14].
Figure 2 – MALDI-TOF mass spectra of polyglycerol G3.0 dendrimer.
Following recrystallisation from ethanol, Hal was suspended in acetone (~20 mL) and
then heated under reflux with the acylchloride derivative of PGLD for approximately 24
hours. Et3N was employed as a base to scavenge HCl that was liberated from the reaction.
The reaction was monitored by TLC until completion. The solvent was removed under
vacuum leaving crude PGLD-Hal prodrug. The product was then purified by column
chromatography using a silica gel stationary phase. The mobile phase was diethyl ether:
methanol (95:5). The eluent was subsequently removed under vacuum, followed by overnight
drying of the product at 37°C and clear amber-coloured oil was obtained.
The percent conjugation of Hal was determined by the 1H NMR spectrum on the basis
of the peak intensity ratio of the methylene protons of PGLD (OCH2CH2,  = 3.5 ppm) and
the two protons on the aromatic ring closest to the fluorine atom (= 8.1 ppm). Using this
ratio, on average 56.8 +8 % of the PGLD end groups were conjugated to haloperidol
molecules
2.2
In vitro properties
2.2.1. Determination of entrapment efficiency and drug loading in the PGLD
The Hal loading percent was determined by measuring the concentration of free drug
in aqueous medium. The aqueous medium was separated through dialysis (Sigma 3K30,
Germany). The amount of Hal in the aqueous phase was estimated by HPLC. The Hal loading
percentage was calculated from Equation (1):
 Analyzed weight of drug in PGLD

Loading (%)  
x100 
Analyzed weight of PGLD


(1)
2.2.2. In- vitro release of haloperidol from PGLD
To determine the release rate of Hal from PGLD, 4 mL of aqueous solution of PGLDHal was added to the dialysis bags with a molecular weight cutoff of 12,400 Da and the sealed
bags were placed in the glass test-tube with 30 mL of the phosphate buffer solution (PBS) 0.1
M (pH7.4) at 37 ºC containing 3% polysorbate 80 to provide sinking conditions with agitation
of 150 rpm. One-milliliter aliquots were taken out of the dissolution cells at pre-determined
time intervals, replaced by fresh PBS buffer and analyzed for released haloperidol by HPLC.
The cumulative % release profiles were obtained by taking the ratio of the amount of
haloperidol released to the total drug content in the same volume of sample.
2.2.3. Hydrophobicity of PGLD
To describe the hydrophobicity of PGLD, the binding constant of Rose Bengal to
PGLD of different generation was used. Adsorption isotherms were measured in 0.1 M PBS
(pH 7.4). A mass of 250 g/mL of PGLD were incubated with concentrations of 1–45 g/mL
of dye solution for 4 h at 375°C. After dialysis for 1 hour the supernatants were determined
photometrically at 542.1 nm. Control samples were used in each experiment to omit the effect
of binding of Rose Bengal to the dialysis bag, tubes and pipette tips. The binding constant Kb
of Rose Bengal was calculated using Scatchard transformation according to Equation 2,
where r is the amount of adsorbed dye, a is the Rose Bengal equilibrium concentration or free
dye, and N is the maximum amount of dye bound.
r
 Kb N  Kbr
a
(2)
The surface hydrophobicity or binding constant of Rose Bengal (Kb) was obtained
from the slopes of the straight lines from a plot of Rose Bengal ratio of the amount adsorbed
and the free amount (r/a) versus adsorbed Rose Bengal concentration (r). Repeated analysis
(n=3) produced consistent slopes.
2.2.4. Study of the red blood cells hemolysis
The human fresh blood containing anticoagulant was centrifuged at 1000 g for 5 min.
After discarding the plasma, erythrocytes were washed 3 times with PBS to remove the serum
proteins. The stock of erythrocyte dispersion was usable within 24 hours at 6 ºC. 100 μL of
the erythrocyte dispersions were added to 1000 μL of PGLD-Hal, shaken and incubated at
37°C for 1 hour. To remove intact erythrocytes from debris the mixture was centrifuged for 3
min at 750 g and100 μL of the supernatant were added to 2000 μL of a mixture of absolute
ethanol and concentrated HCl (40/1 (v/v) and centrifuged again. The absorption of the
supernatant was measured by UV/Vis spectrophotometer at 398 nm [22]. No lysis (0%) and
100% lysis were taken as the control samples in PBS and deionized and bidistilled water
respectively [23].
2.3.
In silico properties
2.3.1. Determination of electronic properties by semi-empirical methods
The electronic properties of the PGLD-Hal were evaluated utilizing a PM3 semiempirical method, with the Polak-Ribiere algorithm (a technique of conjugated gradient
which uses one-dimensional searches) being used for the optimizations using Hyperchem 8.0
program package [15].
2.3.2. Molecular dynamics simulation of PGLD-Hal
The PGLD-Hal structures were generated with hyperchem and saved in pdb format by
Open Babel. The pdb file was used to make the molecular dynamics simulation in Gromacs
program for the three generations of PGLD and to determine the log P by Marvin program.
VMD program [11, 14] were used to visualize the results of the performed using the
molecular dynamics Gromacs. The dendrimer system was prepared for molecular dynamics
simulations using Desmond with explicit solvent [16]. The PGLD-Hal system was built using
the SPC solvation model and the size of the box was determined automatically by creating a
10 Å, buffer zone around the dendrimer. The molecular dynamics simulation [17, 18],
structure, minimization and relaxation steps were performed for 4.8 ns at 300K and 1.03 bar.
Snapshot structures were recorded every 4.8 ps.
3.
RESULTS E DISCUSSION
In spite of the reports on the preparation of dendrimers as drug carriers there is no
study about PGLD-Hal on their theoretical results and biological safety for use as drug
delivery systems. Meanwhile none of the prepared PGLD-Hal can circulate for a long time in
the blood. For this purpose in the present study the experimental and theoretical of PGLD-Hal
were prepared and evaluated for their biological safety.
Frontier Molecular Orbital Theory (FMOT) postulates that the interaction between the
HOMO and the LUMO of molecules undergoing a reaction can provide a good approximation
of reactivity [19]. A reaction will occur with increasing and often maximal overlap of the
HOMO and LUMO orbitals. These electronic properties were calculated using PM3 method
implemented in Hyperchem. For this study, the LUMO of the Haloperidol molecule and the
HOMO of the dendrimer was determined. The difference in the energy between the dendrimer
HOMO and Haloperidol LUMO was then determined and analyzed.
The HOMO of the PGLD was located on one of the terminal hydroxyl groups. This
would allow an interaction with the LUMO in the Hal, which was found to be located on the
Fluor group (Figure 3).
a)
b)
c)
Figure 3 – The HOMO orbital from a PGLD dendrimer portion of a hydroxyl end group
(right) and the LUMO orbital of a Haloperidol molecule (left) a) Electrostatic potential map,
b) HOMO, c) LUMO.
a)
b)
c)
Figure 4 - Top - Increasing branches of PGLD dendrimer modified with one haloperidol
submitted to semi-empirical calculations with Hyperchem to determine the HOMO energy
value and its location (arrow). Bottom – HOMO-LUMO gap as defined by the HOMO energy
value determined for each dendrimer structure and the LUMO of a haloperidol molecule (4.61 eV); a) Electrostatic potential map, b) HOMO, c) LUMO.
These electronic property calculations were applied to increasing sizes of PGLD
generation with and without Hal (Figure 4). This approach enabled confirmation that the
position of the HOMO was in the terminal hydroxyl groups where the interaction with the
LUMO of Hal was expected to take place. An important new observation was that when the
first Hal molecule was covalently attached to the PGLD, the HOMO was always located on
the opposite branch to the one with the zero length ether bonds between the dendrimer and the
haloperidol.
The gap between the HOMO of the PGLD and the LUMO of the haloperidol
decreased as the size of the dendrimer molecule increased (Figure 4, Table 1). According to
the FMOT, the smaller the gap between the HOMO and LUMO the more likely is the reaction
to take place. By analogy, it was expected that this gap would be even smaller if the whole
PGLD was considered.
a)
b)
c)
Figure 5 - Dependence of the HOMO-LUMO of the PGLD generation number. PGLD G2
(left) and PGLD G3 (right); a) Electrostatic potential map, b) HOMO, c) LUMO.
A detailed analysis of the dendrimer segments showed that the energies of both the
HOMO and LUMO, with three haloperidol molecules attached was almost double the LUMO
energy value of the haloperidol molecule. This would make the addition of a fourth drug to
the dendrimer section under study very unlikely. Therefore, the theoretical maximum loading
of a generation 3.0 PGLD with Haloperidol was found to be 12. However, electronic effects
on their own are insufficient to completely understand the loading and distribution of the
haloperidol molecules on the surface of PGLD. Observation of the position of the HOMO,
and defining both the location and availability of the terminal group, was necessary to better
understand the loading and distribution of the haloperidol molecules.
Table 1 – Average values of the HOMO energy determined for the PGLD studied, and
differences between the HOMO of the dendrimer of generation 3.0 and the LUMO of the
haloperidol (-9.67 eV).
Poliglicerol G1
Poliglicerol G2
Poliglicerol G3
Haloperidol
H1_PGLD G1
Energia HOMO (eV)
-10,45124
-10,4185
-10,33021
-9,199816
-9,026786
Energia LUMO (eV)
2,163702
2,097654
2,054429
-0,6687754
-0,4633388
HOMO-LUMO
(GAP) (eV)
-12,614942
-12,516154
-12,384639
-8,5310406
-8,5634472
The addition of the first haloperidol is favorable because the HOMOs of the hydroxyl
groups are available. After one haloperidol has covalently bound to one of the end groups, the
HOMO is again located on a peripheral hydroxyl group making the addition of a second
haloperidol favorable. When two drug molecules are bound to the dendrimer, it becomes
much less likely that the addition of third haloperidol will take place because there is only a
50:50 chance that the HOMO will be available for interaction with a hydroxyl end group.
The addition of a fourth haloperidol molecule is very unlikely to occur within the same
PGLD. Thus, the conjugation of additional haloperidol molecules requires overcoming
increasingly higher energy barriers with available positions for conjugation being available
for only half of the time. Additional conjugation reactions of haloperidol on the whole
dendrimer are very unlikely because the energy gap and the overlap between the LUMO of
glucosamine and the HOMO of the newly formed conjugate are large, and the carboxylic acid
end group is not available. These molecular modeling based observations are consistent with
the experimental data that averages of 6 haloperidol molecules were conjugated to the surface
of a generation 3.0 PGLD dendrimer.
3.1
Molecular dynamics simulation analysis of PGLD dendrimers
To better understand the dynamic behavior of these dendrimers, molecular dynamics
simulations were carried out for 4.8 ns. Molecular properties including the gyration radius and
RMSD were estimated and plotted as a function of time using the VegaZZ trajectory analysis
tool (Fig. 6). The molecular properties determined for the generations of dendrimers PGLDs
G1, G2 and G3, a trajectory of 4.8 nm were determined in water at temperatures of 298, 310
and 315 K.
1,4
1,4
310 K
298 K
1,3
RMSD (nm)
RMSD (nm)
1,3
1,2
1,1
1,2
1,1
PGLD G1
PGLD G2
PGLD G3
PGLD G1
PGLD G2
PGLD G3
1,0
0
200
400
600
800
1000
1,0
0
200
400
Tempo (ps)
600
800
1000
Tempo (ps)
1,4
315 K
RMSD (nm)
1,3
1,2
1,1
PGLD G1
PGLD G2
PGLD G3
1,0
0
200
400
600
800
1000
Tempo (ps)
Figure 6 – Molecular properties determined for a generation PGLD G1, G2 and G3
dendrimer along a trajectory of a 4.8 ns. Root mean square (RMSD) in Angstroms.
The RMSD analysis, as a measure of flexibility and dendrimer folding [20-22], was
conducted for all of the PGLD structures. A plateau was seen after the first 200 ps (Fig. 6).
This means that the molecule explored the conformational space with similar differences
when compared to the initial structure set as reference for the RMSD calculations. However,
further changes in the explored conformational space were observed as indicated by the
increase of the RMSD values towards the end of the simulation. Although the RMSD reached
a plateau after 200 ps, RMSD values of approximately 13 Å indicated a flexible structure.
This plateau was consistent with the profile that was obtained for the gyration radius where,
after only at about 900 ps, limited fluctuations occurred. These fluctuations indicated that the
overall shape of the structure was not undergoing major changes during the simulation period.
Figure 7 shows the haloperidol release profiles from PGLD dendrimers having a drug
content of 2%. The drug release profile from PGLD dendrimer scan be divided into four
zones: (i) initial burst period, during which the surface drug is dumped into the release
medium; (ii) induction period, during which the drug is released at a gradually decreasing fast
rate and (iii) slow release period, during which the drug is released at a steady slow rate; (iv).
The increase in dendrimer generation influences the absolute release profiles such that
both, the cumulative amount of drug released at any time (including initial burst) and the
induction period increases. The increase in generation increases the amount of drug close to
the surface as well as the drug in the core of dendrimer. The former is responsible for an
increased initial burst while the latter causes an increase during the induction period.
For the cumulative haloperidol release profiles, the increase in the drug released is
offset by the increase in the total amount of drug contained in the particles. The final effect on
release profile is determined by the larger of the above-mentioned ratios. The drug released
during initial burst is predominantly the drug located close to the surface. For our system, the
slight decrease in initial burst on increasing the drug content probably happens due to uneven
drug distribution inside the particles.
As the PGLD increases, the initial burst decreases and the induction period increases.
The burst is reduced because on increasing the size, the total surface area of a constant weight
of particles decreases. Increasing the size of particles increases the length of diffusion
pathways for the drug molecules. For the same amount of drug inside the PGLD, increasing
the length of diffusion pathways exercises two opposing effects on the induction period. The
induction period increases because the drug molecules have to traverse a longer distance
within the PGLG to reach the surface.
(I)
(II)
Figure 7 – Absolute and normalized haloperidol release profiles from PGLD having a drug
content of 2%: G0 (A), G2 (B) and G4 (C) (I) and mechanisms of the haloperidol release from
PGLD.
The adsorption isotherms of Rose Bengal for PGLD G 0-3 are presented in Figure 8.
The plateau value of the adsorption isotherm indicates that the relative hydrophobicity scale
strongly depends on the dendrimer generation.
Figure 8 – Adsorption of Rose Bengal onto PGLD at 37 ºC: G4 (A), G3 (B) and G2 (C).
The partition coefficients of PGLD and PGLD-Hal in octanol/water by phasic system
were obtained using phosphate buffered saline solution pH 7.4 at 37 ºC. The partition
coefficients of biomolecule in the aqueous two-phase systems (ATPS) can be defined as the
following equation [21].
Top
K bio 
Wbio
Bottom
Wbio
(3)
where w is weight fraction of biomolecule and superscripts “top" and "bottom" stand for the
top and bottom phases.
The variations of the partition coefficients (log P) of PGLD vs dendrimer generation
from molecular dynamics simulation were reported in Figure 9. Among the partition
coefficients for PGLD, the dendrimer with high generation number had the greatest value and
PGLD with low generations had the lowest log P. The results showed that there are good
agreements between the theoretical and experimental data.
Figure 9 – Plot of experimental (■) and theoretical (○) partition coefficient of PGLDaqueous two phase system vs. the simulated data from the optimum structure data.
A preliminary hemolysis study evaluated the change in membrane destabilizing
activity of PGLD as a function of generation number. Figure 10 shows that the hemolytic
activity of PGLD increased with higher dendrimer generation. Based on these results, the
different PGLD-Hal compositions may be synthesized with similar molecular weights in the
range of 30–35 kDa, which correlates with the size/molecular weight requirements for
potential in vivo applications where renal excretion is needed. Hemolysis results show that the
increase in the hydrophobic character of PGLD results in an increase in the membranedestabilizing activity. Results show that the observed hemolytic activities and PGLD
generation profiles could be designed across a range that matches the properties needed for
drug carriers to enhance the cytoplasmic delivery of therapeutic drugs.
Figure 10 – Hemolytic activity of PGLD as function of dendrímero generation.
CONCLUSIONS
The experimental and theoretical studies describe the relative roles, contribution and
importance of both the peripheral hydroxyl end groups and of the surface loading and
distribution of haloperidol molecules on generation 3.0 PGLD dendrimer to their observed
biological activity. The structural heterogeneity of the molecule appears to be consequence of
both electronic effects and of the different conformations that the molecule could adopt. The
dynamic flexibility of the PGLD (G3) modified with haloperidol molecules was an important
property of this biologically active molecule. Additional factors identified as being important
were the conformational space explored by the PGLD-Hal conjugates its overall surface
polarity. The availability of peripheral haloperidol molecules for interaction with the
biological target was not impaired by intra molecular hydrogen bonds.
ACKNOWLEDGMENTS
The authors are grateful for funding from the Capes, Finep and CNPq by the financial
support.
REFERÊNCIAS
[1] Tomalia, D.A., Dvornic, P.R. (1994) What promise for dendrimers? Nature 372: 617–618, 1994.
[2] Tomalia, D.A., Naylor, A.M. & Goddard III, W.A.Starburst dendrimers: Molecular-level control of size,
shape, surface chemistry, topology, and flexibility from atoms to macroscopic matter. Angew. Chem., Int. Edn.
29: 138–175, 1990.
[3] Vögtle F, Richardt G, Werner N. Dendrimer Chemistry. Wiley-VCH Verlag
GmbH & Co KGaA, 2009.
[4] Fischer, M. & Vögtle, F. Dendrimers: From design to applications – A progress report. Angew.Chem., Int.
Edn. 38: 884–905, 1999.
[5] Fréchet, J.M.J. Functional polymers and dendrimers: Reactivity, molecular architecture,
and interfacial energy. Science 263: 1710–1715, 1994.
[6] Malik, N., Wiwattanapatapee, R., Klopsch, R., Lorenz, K., Frey, H., Weener, J.-W., Meijer, E.W., Paulus, W.
& Duncan, R. Dendrimers: Relationship between structure and biocompatibility in vitro, and preliminary studies
on the biodistribution of 125I-labelled polyamidoamine dendrimers in vivo. J. Controlled Release 65: 133–148,
2000.
[7] Jansen, J.F.G.A., de Brabander van den Berg, E.M.M. & Meijer, E.W. Encapsulation of
guest molecules into a dendritic box. Science 266:1226–1229, 1994.
[8] Jansen, J.F.G.A. & Meijer, E.W. The dendritic box: Shape-selective liberation of encapsulated guests. J. Am.
Chem. Soc. 117: 4417–4418, 1995.
[9] Twyman, L.J., Beezer, A.E., Esfand, R., Hardy, M.J., Mitchell, J.C. The synthesis of water soluble
dendrimers, and their application as possible drug delivery systems. Tetrahedron Lett. 40: 1743–1746, 1999.
[10] Liu, M., Kono, K. & Fréchet, J.M.J. Water-soluble dendritic unimolecular micelles: Their potential as drug
delivery agents. J. Controlled Release 65: 121–131, 2000.
[11] Zhuo, R.X., Du, B. & Lu, Z.R. In vitro release of 5-fluorouracil with cyclic core dendritic polymer. J.
Controlled Release 57: 249–257, 1999.
[12] Tandon R, Fleischhacker WW: Comparative efficacy of antipsychotics in the treatment of schizophrenia: a
critical assessment. Schizophr Res 79: 145–155, 2005.
[13] LEACH, A. R. Molecular Modelling: Principles and Applications, second edition, 2001, Pearson Education
Limited.
[14] Haag R, Sunder A, Hebel A, Roller S. Dendritic aliphatic polyethers as high-loading soluble supports for
carbonyl compounds and parallel membrane separation techniques. J Comb Chem. 4: 112–9, 2002.
[15] THIEL, W. Semiempirical Methods. Neumann Institute for Computing, Alemanha, 2000.
[16] Humphrey W, Dalke A, Schulten K J Mol Graph 14: 33-38, 1996.
[17] Schrödinger Inc [cited; Available from: www.schrodinger.com
[18] Levy RM, Gallicchio E Annu Rev Phys Chem 49: 531-567, 2003.
[19] Fukui K Science 218:747-754, 1982.
[20] Maiorov VN, Crippen GM J Mol Biol 235:625-634, 1994.
[21] G.R. Pazuki, V. Taghikhani ,M. Vossoughi, Modeling of Aqueous Biomolecules using A New FreeVolume Group Contribution Model, Ind. Eng. Chem. Res. 48: 4109-4118, 2009.