Currently, he is a CSIR senior resemited his PhD thesis entitled “Pdendrimeric nanoparticles and thcules”. He published 14 research arHis research interests encompassbiomolecular simulations and comspecial focus on dendrimers.
Department of Medicinal Chemistry, Depar
Institute of Pharmaceutical Education and R
160 062, India. E-mail: pvbharatam@nipe
172-2292018; +91-9417503172
Cite this: DOI: 10.1039/c3nr05400d
Received 11th October 2013Accepted 15th November 2013
atic approaches to understandcomplexation of dendrimeric nanoparticles withdrugs
Vaibhav Jain and Prasad V. Bharatam*
Nanoparticle based drug delivery systems are gaining popularity due to their wide spectrum advantages
over traditional drug delivery systems; among them, dendrimeric nano-vectors are the most widely
explored carriers for pharmaceutical and biomedical applications. The precise mechanism of
encapsulation of drug molecules inside the dendritic matrix, delivery of drugs into specific cells,
interactions of nano-formulation with biological targets and proteins, etc. present a substantial challenge
to the scientific understanding of the subject. Computational methods complement experimental
techniques in the design and optimization of drug delivery systems, thus minimizing the investment in
drug design and development. Significant progress in computer simulations could facilitate an
understanding of the precise mechanism of encapsulation of bioactive molecules and their delivery. This
review summarizes the pharmacoinformatic studies spanning from quantum chemical calculations to
coarse-grained simulations, aimed at providing better insight into dendrimer–drug interactions and the
physicochemical parameters influencing the binding and release mechanism of drugs.
aibhav Jain was born in 1984Sagar, India). He obtained his.S. (Pharm.) in Pharma-oinformatics from the Nationalnstitute of Pharmaceuticalducation and ResearchNIPER), S.A.S. Nagar, India in009. His masters research topicas homology modeling ofhemokine receptor CCR3, aigand-based pharmacophore,nd 3D-QSAR model develop-ent of CCR3 antagonists.arch fellow at NIPER and sub-harmacoinformatic studies oneir complexes with drug mole-ticles in peer reviewed journals.computer-aided drug design,putational drug delivery with
tment of Pharmacoinformatics, National
esearch, Sector 67, S.A.S. Nagar, Punjab
r.ac.in; Fax: +91-172-2214692; Tel: +91-
Chemistry 2014
1. Introduction
The eld of pharmaceutical nanotechnology is ourishingrapidly as it has a strong potential to solve the key issues relatedto drug delivery in a very efficient manner.1,2 The problemsassociated with drug delivery include efficacy, solubility,
Prof. Bharatam, FRSC (PhD,University of Hyderabad) hailsfrom an Indian rural environ-ment and a highly traditionalfamily background. His researchexpertise is in the design (CADD)and synthesis of computation-ally designed compounds. Heintroduced the concepts like‘additivity of molecular elds’and ‘nitreones’. His work alsodeals with the computationalanalysis of drug metabolism,
drug toxicity and drug delivery. He has published 150 originalresearch articles. Various recognitions received by Prof. Bharataminclude the Alexander von Humboldt (AvH) fellowship (2002), theChemical Research Society of India (CRSI) medal (2008), IBMFaculty award (2007), the Ranbaxy Research Award (2008) and theOPPI Scientist award (2009).
toxicity, bioavailability, stability, potency, abrupt release,frequency of dose and poor dissolution/disintegration prole.Approximately, 40% of newly developed active pharmaceuticalingredients (API) are rejected by the pharmaceutical industry,since they are hydrophobic and thus suffer from the limitationof solubility and bioavailability.3 Moreover, several drugs(anticancer, non-steroidal anti-inammatory drug (NSAID), etc.)that fall into the category of Biopharmaceutics ClassicationSystem (BCS)4 class II (characterized by high membranepermeability and low water solubility) also pose substantialchallenges during formulation development and in vivo efficacy.In order to minimize the attrition rate of new API and toimprove the therapeutic index of existing hydrophobic drugs,the paradigm has now shied from conventional to novel andtargeted drug delivery approaches with the help of nanocarriers.These carriers have the power to overcome the existing limita-tions of drug delivery without modulating the essential phar-macophoric features of the drug responsible for bioactivity.Frequently employed nanocarrier systems include dendrimers,5
liposomes,6 carbon nanotubes,7 polymeric micelles,8 solid lipidnanoparticles,9 oil nanoemulsions,10 nanosuspensions,11 inor-ganic nanoparticles,12 etc. Among the different classes ofnanoparticles, dendrimers are the most widely explored vectorsfor the purpose of drug delivery.13
Dendrimers are a class of synthetic, hyperbranched poly-meric macromolecules with globular tree like structures.14 Theyare compositionally and structurally controlled nanoscalebuilding blocks consisting of three main architectural compo-nents (Fig. 1), a central core from which multiple arms emanatein an outward direction to form interior layers, and the reactiveperipheral surface groups.15 A particular dendrimer is charac-terized by its generation number which is the number ofbranching points present in it; they are designated as G0, G1,G2, G3, etc. There are many varieties of dendrimers available,each having a different chemical environment, topology andphysicochemical properties and thus showing different behav-iour in solution. A diverse set of dendrimers with differentchemical architectures have been explored for the purpose ofdrug delivery, including poly(amidoamine) (PAMAM), poly(-propylene imine) (PPI), poly(L-lysine), triazine, melamine,carbohydrate-based citric acid, etc. Although PAMAM and otherdendrimers are reported to be promising candidates for oraldrug delivery, their potential cytotoxicity has hampered
Fig. 1 General architectural components of a dendrimer.
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development of these dendrimers for in vivo applications. It wasfound that cationic surface amino groups present in thesedendrimers are responsible for their cytotoxic and hemolyticeffect,16 but they can be easily functionalized by acetylation,PEGylation, hydroxylation, glycosylation, amino acid conjuga-tion, etc. to make them non-toxic.17
The rapidly accelerating research and development activitiesin dendrimer mediated drug delivery are because of the excep-tional attributes of dendrimers, which include monodispersity,precise and designable architecture, ease of surface engi-neering, high loading capacity, tunable solubility, efficientmembrane transport, low toxicity and immunogenicity, solu-bilization, controlled and sustained release properties, andbioattachment capability. In the eld of drug delivery, den-drimers have been shown to augment drug solubility andbioavailability,18,19 minimize the toxicity,20,21 and modify therelease prole.22,23 In addition, dendrimers also act as a plat-form for drug targeting.24,25 Besides drug delivery, dendrimershave also found exciting applications in other elds like gene/DNA delivery,26–29 siRNA delivery,30–32 catalysis,33 cancer diag-nostics,34 biosensors,35 supramolecular chemistry,36 elec-tronics,36 etc. The functions of the dendrimers are determinedby their structure; thus by modifying the chemical properties ofthe core, shells and surface layer, they can be easily tailored tomeet the requirements of specic applications. Experimentally,the chemical composition, the morphology, the shape, and thehomogeneity of dendrimers are characterized by variety ofanalytical techniques,37,38 which includes small angle X-rayscattering (SAXS), small angle neutron scattering (SANS), NMR,transmission electron microscopy (TEM), uorescence reso-nance energy transfer (FRET), differential scanning calorimetry(DSC), scanning electron microscopy (SEM), and atomic forcemicroscopy (AFM), etc. Molecular modeling approaches havealso turned out to be very promising in predicting the structuraland dynamical aspects of dendrimers.39–41
Dendrimers can interact with drug molecules either in acovalent or non-covalent fashion (Fig. 2). Conjugation involvesthe attachment of the drug molecule to the surface functionalgroups via a precisely selected linker. Non-covalent attachmentinvolves physical encapsulation of the drug molecules either inthe internal cavities via hydrophobic and or hydrogen bondinginteractions, or on the surface via electrostatic phenomena.Reports show that attachment of drugs to dendrimers by
Fig. 2 Covalent and non-covalent complexation of drug moleculeswith a dendrimer.
covalent or non-covalent manner has signicant impact on thepharmacokinetic (dissolution rate, the aqueous solubility, thestability, biodistribution and intracellular release prole, andother physicochemical properties), and pharmacodynamic(systemic toxicity, cellular uptake, bioavailability, and thera-peutic efficacy) properties of the drugs.42 Due to the presence ofa hydrophobic interior and a hydrophilic surface layer, den-drimers show micelle like behaviour in solution, which isresponsible for their ‘container’ property and solubilizationeffect.43 This feature of dendrimer enhances the solubility ofhydrophobic drugs by encapsulating them within the dendriticstructure.44 Several mechanisms are responsible for the encap-sulation of drug molecules; these include van der Waals,hydrophobic, electrostatic and hydrogen bondinginteractions.45
Today, investigating the dendrimer–drug complexes is oneof the most active research areas in the pharmaceutical andbiomedical elds, and also it has generated a lot of interest dueto the need to understand the fundamental mechanisms of theencapsulation and release of cargo from the dendrimer carrier.Extensive experimental studies have been carried out tounderstand dendrimer–drug complexation in solution. Speci-cally, these studies aimed at providing a qualitative/quantitativepicture of drug binding at specic conditions along with theapparent stoichiometry of the dendrimer–drug complex andstructural properties of the complex, but could not delineate themolecular description of the binding mechanism involved andthe reason for such behaviour.46–49 Moreover, these experi-mental approaches are time consuming, expensive and requiresophisticated instruments like NMR,50 FRET,46 DLS,51 ITC,52
SANS,53 etc. which need to be run by skilled operators. There-fore, prior to these experiments it is highly desirable to usecomputational methods for the prediction of the encapsulationefficiency of dendrimers, the solubility and release of drugs, theoptimum conditions for delivery and the stability of dendrimer–drug complexation in order to help reduce the level of invest-ment and effort required for drug development. Molecularmodeling approaches can supplement fundamental experi-mental studies, for instance to facilitate rational design ofdendrimer carriers, and provide an explanation for thephenomena that occur at the atomistic, molecular and bulklevel scales.40,41 There is an increasing interest in understandingdendrimer–drug interactions at a molecular level and thequantitative estimation of the intermolecular interaction ener-gies, since these factors govern the binding affinity between thecarrier and host, and also help in tuning of the delivery system.With the advancement in computational algorithms to makethem more efficient, as well due to the availability of hugecomputational resources, it is now possible to correctly predictthe binding affinity of drugs, and elucidate the mechanism ofdendrimer–drug interactions along with their structural prop-erties using computer simulation techniques. Depending onthe problem that needs to be solved or in-depth understandingof the system required, computer simulations can be run toachieve various length and time scales on the basis of thepotential function, i.e. the force eld (all-atom simulations) andcoarse-grained (mesoscale modeling) degrees of models.
Molecular dynamics (MD) simulations are being routinelyimplemented to address the issues that are difficult to exploreby laboratory drug delivery experiments, and with othercomputational approaches they have also found to be veryuseful in the design and optimization of dendrimer-based drugdelivery systems.
Several review articles have appeared on the experimentalstudies of dendrimers as nanocarriers for drugdelivery.3,18–20,45,54–62 The focus of these reports generally is on thesolubility and bioavailability enhancement of drugs via den-drimers,3,18,54,55 applications of various NMR techniques toanalyse dendrimer–drug complexes,56 dendrimer-mediateddrug delivery based on various routes of administration,57,58
dendrimers as carriers for delivery of chemotherapeutic agentsand cancer targeting,20,59 physical encapsulation and chemicalconjugation of drugs with dendrimers,19,45,60,61 the potential ofPEGylated dendrimers in drug delivery,62 etc. To the best of ourknowledge, only four review articles included the topic oftheoretical or computational studies on dendrimers and theirinteraction with guest molecules. The review article by Li andHou63 summarizes the recent progress resulting from compu-tational simulation strategies adopted for four categories ofdrug delivery systems: dendrimers; polymer micelles; lipo-somes; and carbon nanotubes. In the case of dendrimers, asmall number of dendrimer–drug complexation studies arediscussed together with structural properties determination ofmodied/unmodied dendrimers using MD simulations bythese authors. Huynh et al.64 briey discussed the theoreticalapproaches (analytical models and computer simulations)reported in literature for the prediction of physicochemicalparameters (lipophilicity and solubility), thermodynamic andstructural properties, as well as drug loading and retention ofnanoparticles. Four different categories of nanoparticles wereconsidered in this review also; nanoemulsions, linear and star-shaped block co-polymer micelles, and dendrimers. The reviewby Kim and Lamm40 mainly focused on all-atom MD simula-tions, coarse-grained simulations and statistical eld theorymodeling carried out on a PAMAM dendrimer in solution aswell as its complex with guest molecules (drug, DNA, siRNA,etc.) to understand their physical properties and the inuence ofthe physicochemical parameters on guest binding and releasemechanisms. It was emphasized by the authors that multiscalemodeling is needed to obtain in-depth information about thedendrimer–guest complex. Recently, Tian and Ma41 published acomprehensive review where they covered computationalstudies on dendrimers at both the monomer (bead-springmodel) and atomic/coarse-grained levels, and dendrimer–guestcomplexes. A few all-atom MD simulation studies on den-drimer–drug complexes were reviewed in addition to a reviewon theoretical and simulation studies carried out on den-drimer–DNA/siRNA complexes. In the last section, they high-lighted the interactions of dendrimers with membranes studiedby atomistic, coarse-grained MD, mesoscale simulations andeld theory.
In comparison to the above-mentioned reviews, the scope ofthe current review is focused only on in silico studies of den-drimer–drug complexes. Almost all the small molecules
considered in this review are hydrophobic, belonging to BCSclass II. When computational chemistry, computational biologyand information technology efforts are focused on the drugmolecules (pharmakon), the studies are referred to as pharma-coinformatics.65 In silico technologies like QSAR, moleculardocking, pharmacophore mapping, virtual screening, metab-olome informatics, toxico-informatics as well as molecularmodeling studies on macromolecule–drug complexes usingquantum chemical analysis, molecular dynamics studies andcoarse-grained simulations are being considered under thebroad term pharmacoinformatics. A few of these approacheshave already been applied to study dendrimer–drug complexes.Many more are desirable, this review aims to provide impetus toall the future studies in this direction in order to get in-depthinsights into dendrimer–drug complexation. A few non-drugsmall guest molecules (limited to drug-like organic molecules)are also covered in the review which leads to a thoroughunderstanding of dendrimer–guest interactions. This review iscategorized into ve sections on the basis of the pharma-coinformatic approaches adopted to study dendrimer–drugcomplexes to date. The science and technology behind themethods are given rst followed by specic examples from theliterature.
2. Quantum chemical studies ondendrimer–drug complexes
Quantum chemistry (QC) is a specialized branch of chemistrywhich is based on the postulates of quantum mechanics andtheir applications to understand the chemical phenomena ofdrugs. The calculations are based primarily on the Schroding-er's equation which is used to obtain the energy of a drug fromits wave function. Three quantum chemical methods arecommonly used to calculate atomic/molecular properties andstructures close to experiment: semi-empirical; ab initiomolecular orbital (MO);66 and ab initio density functional theory(DFT).67 Semi-empirical methods68 (AM1, PM3, PM6, CNDO,MINDO, INDO, MNDO, etc.) are based on the Hartree–Fock (HF)formalism, but also make use of many approximations andobtain some parameters from empirical data to nd the solu-tion of Schrodinger's equation. Ab initiomethods do not includeany empirical or semi-empirical parameters in their equationsand are derived directly from theoretical principles, with noinclusion of experimental data. The HF method utilizes threeapproximations to allow the solution of the Schrodinger equa-tion involving many electrons: the Born–Oppenheimer approx-imation; the HF self-consistent eld approximation; and theLinear Combination of Atomic Orbital-Molecular Orbital(LCAO-MO) approximation. Møller–Plesset perturbation theory(MP)69 is a post-HF ab initiomethod, which improves on the HFmethod by adding electron correlation effects usually to thesecond (MP2), third (MP3) or fourth (MP4) order. DFT calcula-tions are based on the Hohenberg–Kohn theorem which statesthat the ground state energy/properties of many electron systemare functionals of the electron density, thus it calculates theelectronic properties of the molecules, based on the calculation
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of electron density rather than of molecular orbitals. In terms ofaccuracy, the different quantum chemical methods follow thetrend: ab initio MO > DFT > semi-empirical, but it in terms ofcomputational cost the trend is completely opposite. Therefore,semi-empirical approaches can be employed on large molecularsystems and ab initio DFT/ab initio MO are generally limited tosmall size systems. All these methods employ the denition ofwave function in the form of numerical solution using basis sets(e.g. 6-31+G(d)).
In the eld of dendrimer based drug delivery, quantumchemical calculations provide details of the electronic structureof the drug molecules and dendrons, and therefore help toidentify important electronic and energetic features requiredfor the binding of drug with the dendrimer. In particular, studyof the plausible tautomeric and protonated/deprotonatedspecies of the drug molecules, conformational preferences,inter and intramolecular interaction energies or hydrogen bondstrengths, absolute and relative energies, dipole moments,partial atomic charges, molecular orbital energies anddiagrams, second order interactions, molecular electrostaticsurface potentials (MESP) and potential energy surface analysisof dendron–drug complexes assists in designing and opti-mizing the arms of the dendrimer in order to obtain maximumstabilization of the drug molecules. In this section, a summaryof the reported quantum chemical studies carried out on den-drimers/dendrons and drugs to tune the delivery system ispresented. The 2D structures of the drugs or small guestcompounds is presented in Fig. 3, which were intended to bedelivered using designed dendrons.
Salicylanilides (brotianide, clioxanide, niclosamide, chlo-santel and oxyclozanide) are a family of drugs widely used inveterinary medicine as ascaricides and antihelminthics, buttheir effectiveness is compromised by their low water solubility.Since dendrimers are known to increase the solubility ofhydrophobic drugs, Soto-Castro et al.70 rationally designeddifferent fractal patterns (FPs) using computational tools likequantum chemical (DFT) and MESP to encapsulate the salicy-lanilides primarily via hydrogen bonding. It was found thatincreasing the exibility in the aliphatic chains of the FPs fav-oured more hydrogen bonds formation and the efficient FPswere identied to be carbamate-amine alcohol (FP1), di-amide(FP2), amide-hydroxy-amine (FP3) and amide-sulphonic-acid(FP4). The encapsulation efficiency of FPs as revealed throughinteraction energies calculated at the B3LYP/LAV3P* level wasin the order FP1 > FP2 > FP3 > FP4. In addition, hybrid func-tionals BHandHLYP showed improved performance overB3LYP, since they describes the close contacts in a bettermanner and reproduced the interactions in a more realisticmanner, close to that observed experimentally for the PAMAM–
The glitazone family of drugs like pioglitazone, rosiglitazoneare PPARg agonistic sensitizers acting as antidiabetic agents.Our research group has utilized the MESP tool to design den-drons effectively for the encapsulation of glitazones.71 Thebinding strength between one arm of the designed dendrimerand thiazolidinedione (common moiety in glitazones) was
Fig. 3 Chemical structures of drugs or small guest compounds studied using quantum chemical methods to evaluate dendron–drug interactionenergies.
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calculated to be about 15–20 kcal mol�1 using ab initio DFTmethod at B3LYP/6-31G* level. In addition, the stabilizationenergies for triazine-2,4-diamine dendron with pioglitazone,rosiglitazone and anticancer drug 5-urouracil were 19.45,21.79 and 22.36 kcal mol�1, respectively. This stabilizationenergy originates from the three hydrogen bonds formed
Fig. 4 Lowest energy conformation of a single branch dendron containinsimulations. The intramolecular hydrogen bonding (as green lines) and thrange from �8.5 (intense red) to 8.5 (intense blue) e�2, and LUMO distribe�2. The carbon atoms are in gray, oxygen in red, nitrogen in blue and hyblack arrows. Reprintedwith permission from J. Giarolla, D. G. Rando, K. F2010, 939, 133–138. Copyright 2010 Elsevier.
between the drug and dendrimer. This strength was attributedto the complementary molecular electrostatic potential of thedrugs, which help in the formation of the self-assemblingcomplex.
Hydroxymethylnitrofurazone (NFOH), quercetin and3-hydroxyavone have shown to exhibit good antichagasic and
g (1) 3-hydroxyflavone, (2) quercetin, and (3) NFOH obtained from MDe CPK models are also presented. MEPs are represented using a colorution using a color range from �4.5 (intense red) to 4.5 (intense blue)drogen atoms are in white. The breaking points are indicated as white/. M. Pasqualoto, M. H. Zaim and E. I. Ferreira, J. Mol. Struct: THEOCHEM,
Scheme 1 Workflow to generate and analyze the interaction energyaverages for dendrimer–drug conformations. Adapted with permissionfrom F. Avila-Salas, C. Sandoval, J. Caballero, S. Guinez-Molinos, L. S.Santos, R. E. Cachau and F. D. Gonzalez-Nilo, J. Phys. Chem. B, 2012, 116,2031–2039. Copyright 2012 American Chemical Society. The averagesfor the same “n ¼ 8” fragments, extracted from the “m ¼ 10” differentconformations of dendrimer PAMAM-G4 and four NSAIDs, were denotedas D1¼ diflunisal, D2¼ ibuprofen, D3¼ ketoprofen, and D4¼ naproxen.
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antileishmanial activity in vitro, but demonstrated lower in vivoactivity due to pharmacokinetic problems. Thus, molecularmodeling studies were applied by Giarolla et al.72 to design adendrimer based prodrug (myo-inositol as a core, L-malic acidas a spacer group) in which the active agents are covalentlylinked through an ester bond. It was speculated that this den-drimer based prodrug releases the active agents by esterhydrolysis through enzymatic (esterase) action. The enzymecould act on one of the two carbonyl groups present in thestructure, thus to identify the possible sites of cleavage differentmolecular modeling techniques were applied. A CPK model ofthe lowest energy conformation of the dendrimer designed withone (Fig. 4), two and three dendrons showed that the carbonylgroup next to the active agent is easily accessible. A map of theelectrostatic potential (MEP), the lowest unoccupied molecularorbital energy (ELUMO) and LUMO distribution analysis usingthe ab initio HF/3-21G* method indicates that the carbonylgroup next to the active agent presented a lower electrondensity, thus can be considered as potential point for enzymaticnucleophilic attack and ester breakage (Fig. 4). Later on thesame research group also performed molecular modelingstudies on dendrimers with four, ve and six dendrons; here thecarbonyl group adjacent to myo-inositol is the most promisingester breaking point.73
Avila-Salas et al.74 have proposed an efficient method toevaluate the quantitative structure–affinity relationship in adendrimer–drug system. To test the accuracy of their compu-tational protocol to calculate the interaction energies, they haveconsidered a cationic G4 PAMAM dendrimer and four hydro-phobic drugs naproxen, ketoprofen, ibuprofen and diunisal(all NSAIDs), all carrying a negative charge at physiological pHdue to the presence of a carboxyl group. Initially, the MetropolisMonte Carlo algorithm was implemented to obtain large sets ofPAMAM–drug conformational pairs which ensure a good
Fig. 5 Correlation of the experimental constants of the competitive dissociation rate ln(ki/kj) (naproxen¼ 0, ketoprofen¼ 1.1, ibuprofen¼ 2.1, anddiflunisal ¼ 2.5), derived from Cooks' kinetic method, between the PAMAM dendrimer and four NSAIDs, versus the average of the total interactionenergies calculated using the methodology shown in Scheme 1. Reprinted with permission from F. Avila-Salas, C. Sandoval, J. Caballero, S. Guinez-Molinos, L. S. Santos, R. E. Cachau and F. D. Gonzalez-Nilo, J. Phys. Chem. B, 2012, 116, 2031–2039. Copyright 2012 American Chemical Society.
Fig. 6 A selected set of chemical structures of small guestcompounds studied using molecular docking for understandingdendrimer–drug interactions.
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conformational sampling for calculating intermolecular inter-action energies. Aerwards, an efficient and fast GRIDcomputing system based on a distribution algorithm was usedto calculate the energy of each pair. The energy calculationcomprises three steps: (1) optimization of the PAMAMdendrimer fragment and specic drug separately using a PM6semi-emperical approach; (2) formation of the dendrimerfragment–drug complex with the conformations previouslyoptimized; (3) calculation of the heat of formation (DHf) for thefragment, drug, and complex using the 1SCF and PM6-DH+methods, and nally the intermolecular interaction energy (DE)was estimated by subtracting DHf of the fragment and the drugfrom the complex (Scheme 1). Excellent agreement was foundbetween the dissociation constants calculated for dendrimer–drug complexes experimentally using Cooks' kinetic method(based on ESI-MS/MS) and interaction energies estimated by acomputational approach with r2 > 0.9 (Fig. 5). The bindingaffinity of the drug molecules to the G4 PAMAM dendrimerfollows the trend: naproxen > ketoprofen > ibuprofen > diu-nisal. The difference in interaction energies between naproxenand diunisal was found to be approximately �15.4 kcal mol�1.
The molecular docking approach involves the prediction of theligand conformation and preferred orientation in the bindingsite of a macromolecule. Ligand exibility is usually treated bythree different methods to ensure maximum exploration of theconformational space, these are: systematic methods (incre-mental construction, conformational search); random orstochastic methods (Monte Carlo, genetic algorithms, tabusearch); and simulation methods (molecular dynamics, energyminimization).75 The binding interaction energy between theligand and macromolecule is evaluated by scoring functions.There are basically four types of scoring functions which differ inthe energetic terms included in the equation, these are: force-eld-based (D-Score, G-Score, GOLD, AutoDock, DOCK);empirical-based (LUDI, F-Score, ChemScore, SCORE); knowl-edge-based (PMF, DrugScore, SMoG); and consensus
Fig. 7 Bindingmode of substrate hydroxypyrene trisulfonate butyrate est3D model of a RG3 dendrimer with a docked substrate. (b) 3D model ofsurface representation, color-coded by generation number (red¼ G0, blgreen, nitrogens in blue, oxygens in red, and sulfurs in yellow. (c) Catalyticbase (blue arrow). Reprinted with permission from S. Javor and J.-L. ReymChemical Society.
(X-CSCORE) scoring functions.75 Nonetheless, molecular dock-ing suffers from drawbacks such as an imperfection of scoringfunctions in the correct prediction of the binding free affinity,negligence of inherent exibility, induced t or other confor-mational changes that occur on binding, and also it does notinclude the solvation and entropy effects as well as participationof watermolecules in the intra/intermolecular interactions.76 Butstill this molecular modeling approach is robust and useful tosome extent as it has the ability to reproduce the crystallographicpose and interactions of the ligand inside the cavity of amacromolecule.77
In the eld of computational analysis of dendrimer–drugcomplexation, molecular docking is employed to encapsulatedrug inside the dendritic cavity.78–81 This approach provides thebest suitable conformation of the drug molecule inside thecavity along with the details of atomistic interactions of the drugwith the dendrimer and its binding affinity. Aer encapsulationof the drug in the dendrimer cavities, the complex is furthertaken up for MD simulations for obtaining more rigorousresults in terms of the stability of the complex and interactionsin dynamic conditions (discussed in the subsequent section).
Javor and Reymond82 delineated the three dimensional (3D)structures of a series of peptide dendrimers using MD simula-tions and their hydrodynamic radii were found to be compa-rable to those of data obtained from diffusion-NMRexperiments. Aer model validation, the substrate, hydrox-ypyrene trisulfonate butyrate ester (Fig. 6), was docked into thecatalytic site of the dendrimers (lower energy conformationsobtained from MD) using Autodock 3.05. Dendrimer–substratecomplexes were stabilized by one or two salt bridges formed
er in the catalytic site of the dendrimers and its catalysis mechanism. (a)a HG3 dendrimer with a docked substrate. The dendrimer is shown inue¼ G1, green¼ G2, black¼ G3). Substrate carbons are represented inrole of the core histidine residue as nucleophile (red arrow) or generalond, J. Org. Chem., 2009, 74, 3665–3674. Copyright 2009 American
between the sulfonate of the substrate and the protonatedarginine or histidine residues of the dendrimer, as well as byseveral van der Waals contacts. Docking analysis showed aremarkable difference between substrate interaction with the“R” and the “H” series peptide dendrimers. “R” series den-drimers showed a positive dendritic effect on catalysis, wherethe substrate formed van der Waals contacts with the outerdendritic layers and the core residues were not involved(Fig. 7a). In contrary, in “H” series dendrimers the substratemostly showed van der Waals contacts with the core residuesand the outer dendritic branches were not involved (Fig. 7b). Itwas suggested that catalytic mechanism initially involvedsubstrate recognition followed by conformational equilibrationwhere nucleophilic attack of the core histidine residue on theester carbonyl of substrate is feasible (Fig. 7c).
Curcumin (Fig. 6), a natural active compound exhibits anti-oxidant, anti-inammatory, antimicrobial, antiviral and che-mopreventive properties. To overcome the shortcomingsassociated with the delivery of curcumin, recently Cao et al.83
encapsulated this compound in a 25% modied G4 PAMAMdendrimer functionalized with N-(2-hydroxydodecyl) groups.Experimental study (uorescence spectroscopy) indicates thatthere are ve binding sites of curcumin in the dendrimer, whichwere further identied using a molecular docking approach.These results suggested that ve molecules of curcumin can besuccessfully docked into the dendrimer and their bindingenergies were estimated to be �7.28, �5.07, �4.65, �4.06, and�4.04 kJ mol�1. The stabilization of the complex resulted fromthe hydrophobic, hydrogen bonding and van der Waals inter-actions between the dendrimer and curcumin molecules.
Manymore examples are available in whichmolecular dockingwas performed to encapsulate drug inside the dendrimer andestimate dendrimer–drug interactions.Most of these are extendedto MD simulations analysis, as discussed in the next section.
4. Molecular dynamics (MD)simulation studies on dendrimer–drugcomplexes
The concept of MD simulations was introduced by Alder andWainwright in the the 1950s to study interaction of hardspheres (atoms that interact through perfect collisions). MDsimulations are a computer simulation technique whichdescribes how the positions, velocities and orientations ofmolecules change over time (oen known as trajectory), andthus observations are made based on the evolution of a system.MD simulations consist of the numerical, step-by-step solutionof the classical equations of motion proposed by Newton,commonly used algorithms for this purpose are Verlet, Leap-frog, velocity Verlet and Beeman's.84
Newton's equation of motion: Fi ¼ �ViVThe force can be written as the gradient of the potential
energy: Fi ¼ miai
We combine the two equations to obtain: � dVdri
¼ mid2ridt2
A trajectory is obtained by solving this differential equation.
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The Verlet algorithm for estimating the new position is:r(t + Dt) ¼ 2r(t) � r(t � Dt) + a(t)Dt2 + O(Dt4)
In MD simulations, the macroscopic properties of a systemare explored through microscopic simulations and theconnection between these two states is made via statisticalmechanics. The potential energy of the system is calculated viamolecular mechanics, i.e. force eld based methods wherebonded (bond stretching, bending and rotation) and non-bonded (electrostatic and van der Waals) potentials are used inthe calculation. (QuantumMDmethods85 can also be employedto analyze dendrimer–drug complexes, where bond breakingand bond formation phenomenon needs to be evaluated;however no study has been taken up till now, it's worthpursuing.)
Fully atomistic simulations are one of the most promisingapproaches to study dendrimer–drug interactions, obtainingstructural information of complexes, and understanding theinuence of different physicochemical parameters on theencapsulation efficiency of a host molecule. Computer simula-tions are very efficient since they capture useful informationwithin a nanosecond time frame, which is sometimes difficultto obtain from costly and time consuming experiments such asdiffusion, dynamics, etc. Among the several classes of den-drimers, PAMAM and its modied version are the most widelyused dendrimers to study host–guest complexation/conjugationby implementing MD simulation techniques. In the future,
however, it will be necessary to explore other well-known (PPI,PETIM, poly(L-lysine), etc.) or novel dendrimers with the aid ofMD simulations in order to rationally design the deliverysystem, and tune-up the parameters necessary for the optimumtherapeutic effect. During the last decade, MD simulationsimplementing different atomistic force elds have beensuccessfully employed by researchers at various solvent condi-tions to understand the molecular-level interactions betweendendrimer and drug. The list of all the simulation studiesreported in the literature along with their particulars isprovided in Table 1 in chronological order. In the section below,a few details of the all the computational studies on the den-drimer–drug complexes are given. The 2D structures of thedrugs or small guest compounds studied using MD simulationsto decipher the mechanism of their complexation with den-drimers or structural analysis of their conjugates with den-drimers is depicted in Fig. 8.
Bengal Rose dye is a potential anticancer agent (melanomaand breast cancer). Meijer and co-workers103,104 performedextensive experimental studies on the encapsulation of BengalRose in G5 PPI dendrimer capped with tert-butyloxycarbonyl-L-Phe (tBOC-L-Phe) and selective liberation of guest molecules inCH2Cl2 solvent. It was demonstrated that up to four moleculesof Bengal Rose can be entrapped in the dendritic box. Further,Goddard and co-workers86 carried out fully atomistic simula-tions on the G5 PPI-(tBOC-L-Phe)-Bengal Rose complex, and thisis one of the pioneering works in the eld of dendrimer–drugcomplexation study using computer simulations. Aer simula-tion, four guest molecules were found to be entrapped in theinterior voids of the dendrimer as identied through the center-of-mass separation distance between the dendrimer and drug. Aclose agreement of the theoretical results with the experimentalndings demonstrated that computer simulations can be usedto understand such systems, and also assist in designingeffective delivery systems prior to experiments. Later on, byusing MD simulations they showed that the PEGylated G5 PPIdendrimers have the capability to encapsulate 32 molecules ofBengal Rose, while amine-terminated dendrimer is unable toperform the same function.63
Dansyl terminated PPI dendrimers possess photophysicalproperties as revealed by Vogtle et al.105 These dendrimers havethe ability to encapsulate Eosin Y (uorescent molecule) guest,which upon binding causes uorescence quenching andsensitization processes.106 Teobaldi and Zerbetto90 performedMD simulations in CH2Cl2 solvent to understand the details ofthe interactions in this host–guest system. The calculationswere performed rst with an excess of Eosin molecules (12 innumbers) complexed with dendrimer in comparison to the 6Eosin molecules reported in experiments. This was done withthe intention of obtaining instantaneous structural informa-tion; results showed that the presence of guest molecules in thesystem makes the dendrimer compact and more spherical. Outof the 12 guest molecules, at least 6 remain persistently in vander Waals contact with the host and within the radius of gyra-tion of dendrimer, while others 6 showed multiple entrances–exits from the macromolecule within a short time frame of lessthan a nanosecond and were nally expelled irreversibly from
the system. Center-of-mass separation distance analysis showedthat Eosin molecules clustered into two groups inside thedendrimer, 3 molecules located near the core and 3 residing inits periphery. Interestingly, it was also observed that Eosinmolecules move inside the dendrimer in a similar fashion tosolvent molecules and occasionally form aggregates. This studyshows the exibility of the dendrimer and the mobility of theguest molecules inside the host system. Later on, scientistssuccessfully explained the reason behind the bi-exponentialdecay of the excited states displayed by Eosin Y once it binds todansyl-terminated G4 PPI dendrimer with the help of MDsimulations and quantum chemical calculations.92 It was sug-gested that two different mechanisms are responsible for Eosinquenching: (i) interactions between the carbonyl or the carboxylof guest with the amine groups of dendrimer; and (ii) an elec-tron transfer from the nitrogen lone pair of dendrimer to thehalf-lled orbital of Eosin.
Four active drugs: acetyl salicylic acid (NSAID); dopamine(drug for Parkinson disease); testosterone (agent for hormonalreplacement therapy); and cortisone (anti-inammatory agent);were considered by Pricl et al.87 for MD simulations to analyzethe dendrimer size vs. drug encapsulation property. Initially,molecular surface areas and volumes were calculated usingmolecular modeling approaches for the rst two generations oflactodendrimers obtained from MD simulations to understandtheir structural features, and possible inclusion complexes withthe above-mentioned drugs. Calculated stabilization enthalpiesshowed that the G1 lactodendrimer can easily host small drugmolecules (acetylsalicylic acid and dopamine), whereas largerguest molecules such as testosterone and cortisone are easilyentrapped in the G2 lactodendrimer to form stable complexes.The predominant mechanism for the complex stabilization wasdetermined to be van der Waals contacts followed by electro-static interactions due to the favourable dipole–dipoleinteractions.
Folic acid (FA) and its conjugate with drug delivery systemslike dendrimers bind selectively to the folate receptor and areinternalized into the cells through a receptor-mediated endo-cytosis mechanism. This phenomenon can be exploited for thedelivery of drugs into the cells. For example, anticancer drugslike methotrexate (MTX) can be delivered selectively into thecancerous cells via an FA conjugate–MTX complex, since folatereceptors are over-expressed in several cancerous cells. There-fore, FA conjugates are used for the purpose of selective cellulartargeting. When imaging agents, such as uorescence iso-thiocyanate (FITC) are conjugated with the above drug deliverysystem, it is possible to identify the concentration of drugdelivered into the targeted cells. In case of dendrimers, it isimportant to identify which surface groups of dendrimer areideal for cellular targeting. For this purpose Baker and co-workers88 performed atomistic MD simulations on amine,acetyl, hydroxyl and carboxyl terminated G5 PAMAM den-drimers conjugated with FA and FITC. The equilibrated struc-tures of FA and FITC-conjugated dendrimers with a primaryamine surface group and with a carboxyl group depicted inter-molecular branch aggregation which might cause potentialsolubility problems. Meanwhile, most of the FA molecules on
the hydroxyl surface were found to be buried inside the den-drimer, indicating less accessibility to the folate receptors forinteraction. On the other hand, FA conjugated on the acetylsurface extends away from the surface of dendrimers, thusincreasing the likelihood of interaction with the folic acidreceptors on cells. These results indicate that acetyl capping forFA and FITC-conjugated G5 PAMAM dendrimers is optimal fortargeting. Furthermore, experimental targeting data in KBcancer cells (a human epithelial carcinoma cell line) using owcytometry and 3D confocal microscopy supported themodeling predictions.89 On the basis of the clues obtainedfrom the above study, authors have further implemented MDsimulations to explore the effect of the method of conjugation(amide and ester) of drug molecule to 80% acetylated G5PAMAM on the accessibility of ligand FA and drug MTX in thepresence of the imaging moiety FITC.95 The nal congurationof the amide bond conjugated system (G5-Ac(80)-FITC-FA-MTX) aer simulation showed that MTX and FA appear tocompete with each other, thus reducing the accessibility of FAto the folate receptor cells. Whereas, in case of ester bondconjugated systems the FA moieties seem to stretch in anoutward direction and the shape of this system was found to bemore spherical than the former. Moreover, experimental studyshowed that the ester bond conjugated system binds better toKB cancer cells in comparison to amide bond conjugatedsystem, therefore corroborating the in silico prediction. Thisresearch group has also investigated the effect of dendrimersurface charge on the bioactivity of the anticancer drug 2-methoxyestradiol (2-ME) encapsulated with various function-alized G5 PAMAM dendrimers.97 Cytotoxicity assays againsttumor cell line (KB cells) showed that amine, hydroxyl andacetyl-terminated G5 PAMAM dendrimers complexed with 2-ME have potential to inhibit cancer cell growth, but on theother hand 2-ME complexed with carboxyl-terminated den-drimer does not show signicant bioactivity. In order to probethe reason behind the difference in the bioactivity of den-drimer–drug complexes observed in experiments, all-atom MDsimulations were performed using the CVFF force eld. Thesimulation results exemplied that the molecular structure ofamine, hydroxyl and acetyl-terminated G5 PAMAM dendrimers(Fig. 9a–c) are quite ‘open’ at lysosomal pH 5, which mightfacilitate the release of 2-ME from the dendritic matrix. On thecontrary, the structure of the carboxyl-terminated G5 PAMAMdendrimer (Fig. 9d) at low pH was found to be compact, due tostrong interactions between the surface carboxyl groups andthe internal tertiary amines. This conformation of dendrimerwith negative charge on the surface presumably holds the drug2-ME tightly in the inner cavities and does not allow its releasein the lysosome, which ultimately results in the loss ofbioactivity.
Veterinary medicines belonging to the class of avermectins(e.g., ivermectin), milbemycins (e.g., moxidectin) and salicyla-nilides (e.g., chlosantel) are known for their parasiticide activity.In order to enhance the bioavailability of these drugs Evangel-ista-Lara and Guadarrama91 have investigated the potential oftwo designed families of dendrimer, denamide (oxy-amide) anddenurea (oxy-urea) of the G2 and G3 generations with different
Fig. 8 Chemical structures of drugs or small guest compounds studied using MD simulations to evaluate the structural features of theirconjugates with dendrimers or to understand dendrimer–drug interactions.
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fractal pattern lengths to encapsulate parasiticide drugs.Geometric description of the dendrimer models and drugmolecules was carried out using Connolly's algorithm. MDsimulation results showed that in comparison to the denurea
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family, the denamide family is more suitable for the encapsu-lation of the drug molecules. Since in addition to an adequatesize of cavities for hosting, denamide based dendrimers possessthe best fractal pattern with a balance between exibility and
Fig. 9 Equilibrated configurations of dendrimer–drug complexesafter 100 ps MD simulations. (a) G5 PAMAM (amine terminated) and 2-ME, (b) G5 PAMAM (acetyl terminated) and 2-ME, (c) G5 PAMAM(hydroxyl terminated) and 2-ME (d) G5 PAMAM (carboxyl terminated)and 2-ME. Dendrimers are shown as sticks, while drug molecules areshown in space-filling representation. Reprinted from ref. 97.
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functionalization. Interaction energies calculated at the B3LYP/3-21G* level of theory for fractal patterns of dendrimer andguest molecule showed the following trend of stability dena-mide > PAMAM > denurea.
The chemical nature of the core, repeating branches andconnecting units of the dendrimer determines the size, shapedirectionality, volume of interior void spaces, etc., and thusgreatly inuences its structural and physicochemical proper-ties. To explore this direction, Posocco et al.93 implemented MD
Table 2 Binding free energy for benzamidinium compounds (Benza1 andCH2) and dendrimer b (connecting unit –CH2–O–) estimated using MFermeglia and S. Pricl, Macromolecules, 2007, 40, 2257–2266. Copyrigh
simulations to study the effect of connecting units (–CH2–CH2
and –CH2–O–) in G1–G3 generations of two series of naph-thyridine-based dendritic structures on the complexation of twobenzamidinium based guest molecules. Initially, structuralproperties like the radius of gyration, aspect ratio and relativeshape anisotropy, volume of internal cavities, solvent accessiblesurface area (SASA) and volume, surface fractal dimensions, etc.were calculated. The molecular characterization of dendrimersrevealed that the core naphthyridine moiety is available forcomplexation with guest molecules in all cases. It was alsoobserved that the geometry of the core strongly inuences thegenerational growth of the dendrimer which results in similar,owerlike, shape-consistent macromolecular hosts. Subse-quently, the Molecular Mechanics Poisson Boltzmann SurfaceArea (MM-PBSA) method was used to calculate the binding freeenergies between two guest molecules and dendrimers; theresults were found to be in accordance with experiment (Table2). The binding free energy for the guest molecules complexedwith G1–G3 dendrimers with two different connecting units wasin the range of �3.7 kcal mol�1 to �4.2 kcal mol�1 (Table 2),indicating that size and internal chemistry of the dendrimersdoes not have any impact on the binding affinity. MD analysisfurther demonstrated that guest molecules formed severalpersistent hydrogen bonds with the nitrogen atoms of thedendrimer core. The dendrimer–guest complexation was foundto be driven mainly by favourable van der Waals interactionsirrespective of dendrimer generation and the nature of thedendrimer branches.
It is important to understand the structure and behaviour ofdynamic multivalent dendrimers in solution and how the guestoccupied the binding sites and showed multiple interactions.Meijer and co-workers108 proposed the structure of an admantyl-urea dendrimer complexed with carboxylic acid–guest in solu-tion with the help of X-ray crystallography of admantyl/phenylpincers and guest molecules, as well as by MD simulations of G3and G5 adamantyl and phenyl–urea PPI dendrimers encapsu-lated with 8 and 32 guest molecules, respectively. The secondaryinteractions observed in both methods were found to be
Benza2) with G1–G3 generation dendrimer a (connecting unit –CH2–M-PBSA. Adapted with permission from P. Posocco, M. Ferrone, M.t 2007 American Chemical Society
consistent and in the suggested molecular picture of theaggregate, the guest sandwiched between the urea groups of thepincer-like moiety and form multiple interactions. The drivingforce involved in the formation of a stable host–guest complexwas hydrogen bonding, which arises due to interactionsbetween urea and/or carboxylic acid groups of the guest withurea groups of the dendrimer, and electrostatic interactions oracid–base interactions between the carboxylic acid of the guestand the protonated tertiary amines of the dendritic host. Inaddition, intramolecular hydrogen bonding between the ureagroups of the dendrimer was also observed.
Adenosine receptors, belonging to the class of G protein-coupled receptors (GPCR) are promising drug targets for avariety of disease conditions. CGS21680, a specic A2A adeno-sine receptor (AR) agonist shows an anti-aggregatory effect onplatelets. It was observed that multivalent dendrimer conju-gates (G3 PAMAM-CGS21680) have a better pharmacologicalactivity as compared to the lead CGS21680.109 A2A AR is ahomodimer which can interact with twomolecules of the ligandconjugated with dendrimer; however there is no experimentalsupport for this speculation. Therefore, in order to explorewhether bivalent binding of PAMAM-CGS21680 to an A2A ARdimer is theoretically feasible, Ivanov and Jacobson94 carriedout MD simulations to delineate the molecular structure of theGPCR–ligand–dendrimer (GLiDe) conjugate. The resultsshowed that two terminal CGS21680 units of the dendrimer canoccupy both the subunits of the A2A adenosine receptor simul-taneously (Fig. 10), and moreover the binding mode ofCGS21680 conjugated to dendrimer was found to be similar tothat of the docked ligand molecule into the receptorbinding site.
Fig. 10 The final model of G3 PAMAM–CGS21680 with the fluo-rophore (Alexa Fluor 488), bound to the A2A adenosine receptorhomodimer. The carbon atoms of PAMAM and CGS21680 units arecolored in green, carbon atoms of the fluorophore are colored in cyan.Reprinted with permission from A. A. Ivanov and K. A. Jacobson, Bio-org. Med. Chem. Lett., 2008, 18, 4312–4315. Copyright 2008 Elsevier.
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Selective A3 AR agonists are known for their anti-inamma-tory, anticancer, anti-ischemic, and myeloprotective activitiesand a few of them are currently in clinical trials. To furtherexplore this area Jacobson and co-workers99 synthesized a seriesof 50-methyluronamide adenosine derivatives along with threeconjugates with PEGylated G4 PAMAM dendrimer. The GLiDeconjugates were found to be highly potent and selective towardsA3 AR, thus to investigate their atomistic level details, one of theconjugate (N6-triazolylmethyl adenosine derivative) was sub-jected to MD simulations. The molecular model of the thisGLiDe conjugate revealed that the dendrimer molecule is sur-rounded by hydrophilic PEG chains, while the conjugatedligands are exposed to the solvent and easily accessible forbinding with the receptor. In particular, the nucleoside moietyof the ligand was stabilized in the binding site of A3 AR byseveral van der Waals and hydrogen bonding interactions(Thr94, Asn250, Ser271, and His272) with the key amino acidresidues. P2Y14 is another GPCR which has implications inimmune function and this receptor is activated by uridine-50-diphosphoglucose (UDPG) and other UDP-sugars. It was envis-aged by Jacobson and co-workers110 that covalent binding of theP2Y14 receptor agonist uridine-50-diphosphoglucuronic acid(UDPGA) to PAMAM dendrimers could enhance the therapeuticactivity. In this respect, the authors synthesized the conjugatesof UDPGA with G2.5, G3, G5.5 and G6 PAMAM dendrimers. Inaddition, prosthetic groups, such as biotin, AlexaFluor488, andthe metal chelating group DTPA were attached to the den-drimer–UDPGA conjugates to target the P2Y14 receptor. Inter-estingly, the G3 PAMAM–UDPGA conjugate was found to be 100times more potent than the native agonist UDPGA, while forother multivalent dendrimer conjugates the potency was eitherretained or was signicantly enhanced. Furthermore, molecularmodeling was performed to reveal the structure of the GLiDeconjugate and interaction of ligand with the receptor. The 3Dstructure of the G3 PAMAM–UDPGA conjugate illustrates thatthe arms of the dendrimer-bearing ligands extended far beyondthe dimensions of the receptor and might be available formultivalent interaction with receptor aggregates. These studiesthus demonstrate the general applicability of the GLiDe strategyto modulate the pharmacological activity of other GPCRligands.
Ibuprofen is a weakly acidic NSAID (bearing carboxylicgroup), which is used for the treatment of conditions likerheumatoid arthritis, osteoarthritis and ankylosing spondylitis.Experiments have shown an increase in the the PAMAM den-drimer mediated solubilization of ibuprofen,111 but have notprovided the precise mechanism of encapsulation. Therefore,Tanis and Karatasos96 utilized static and dynamic approaches tostudy the specic and associative behavior of the complexation/encapsulation of the ibuprofen with the G3 PAMAM dendrimerat three different pH conditions. MD simulation analysisshowed that at low pH conditions the dendrimer–drug complexis unstable and the ibuprofen molecules formed clusters(Fig. 11a) and diffused away from the dendrimer (the center ofmass separation distance between the dendrimer and drugconstantly increases throughout the simulation, Fig. 12). Thisobservation is in agreement with the pertinent experiment112
Fig. 11 Average distance between the drug and the dendrimer centerof mass (CM) as a function of time within the examined window atdifferent pH conditions. The average has been performed over allibuprofen molecules. The description of the labels is as follows:G3_Ionized– basic pHwith ionized drug, G3_Basic– basic pHwithoutionized species, G3_Neutral – neutral pH and G3_Acid – low pH.Reprinted with permission from I. Tanis and K. Karatasos, J. Phys.Chem. B, 2009, 113, 10984–10993. Copyright 2009 AmericanChemical Society.
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where no signicant enhancement in the solubility wasobserved for the drug in the presence of dendrimer. Thisbehaviour is due to the absence of intermolecular hydrogenbonding between the drug molecules and the ‘open’ confor-mational state of dendrimer. At physiological pH condition, the
Fig. 12 Snapshots of the simulated systems: (a) acid pH (G3_Acid); (b)neutral pH (G3_Neutral); (c) basic pH with ionized drug (G3_Ionized);and (d) basic pH (G3_Basic) without ionized species system. Ibuprofenmolecules are shown in a light yellow color. Purple and green beadsrepresent the Na+ and Cl� counterions, respectively. Adapted withpermission from I. Tanis and K. Karatasos, J. Phys. Chem. B, 2009, 113,10984–10993. Copyright 2009 American Chemical Society.
dendrimer–drug complex is stable; the drug molecules pene-trate well in the dendritic architecture and formed hydrogenbonds with the PAMAM amide hydrogens and carbonyl oxygens(Fig. 12b). Meanwhile, in basic pH conditions, ionizedibuprofen molecules were found preferentially at the den-drimer's surface (Fig. 12c), similar to observations on a virtualsystem composed of nonprotonated PAMAM dendrimer andunionized ibuprofen molecules (Fig. 12d). Here, the primarymechanism of complexation was proposed to be electrostaticinteractions. In addition, the self- and collective drug dynamicsof the system were found to be faster at low pH, a sluggishcollective motion at neutral pH and a very slow motion at highpH conditions. This analysis suggested the existence of weakand strong physical binding between the dendrimer and drug atlow and high pH conditions, respectively. The proposedmechanism of encapsulation in the PAMAM dendrimer atdifferent pH conditions could be extended to other carboxylbearing drug molecules, which in turn provides valuableinsights to tune and optimize the delivery system.
Besides applications of dendrimers in drug delivery, theyhave also demonstrated their potential in removing environ-mental pollutants such as by exclusion of perchlorates, pesti-cides, volatile organic compounds and polychlorinatedbiphenyls in drinking water.113 A spectrouorometry studyusing the FRET technique has been carried out by Lard et al.46 tostudy the adsorption-induced energy transfer between phen-anthrene (a polycyclic aromatic hydrocarbon and a majorenvironmental pollutant) and a G5 PAMAM dendrimer. Withthe help of this experiment, the authors obtained the molarratio of the dendrimer and guest, and the pH conditionsnecessary for optimal binding. To probe the microscopic detailsof binding between phenanthrene molecules (25 in number)and G5 PAMAM dendrimer at different pH conditions, fullyatomistic MD simulations were performed using the Dreidingforce eld. Simulation results showed that more phenanthrenemolecules penetrate into the interior of the dendrimer atneutral pH in comparison to low pH conditions; at high pHconditions most of the guest molecules located preferentiallynear the surface (Fig. 13). Moreover at low pH, stacking of thephenanthrene molecules hindered their strong binding withthe cationic PAMAM dendrimers, while at high pH the aggre-gation of the dendrimers provided fewer interior sites for theguest molecules to bind, which resulted in the lower FRETefficiency observed at low and high pH than neutral pHconditions. It was also found that the strongest binding inter-actions occur between phenanthrene and the primary amines ofthe dendrimer at pH 8 (near to neutral).
Elkin and Hildgen114 designed novel biocompatible den-drimers and investigated their efficiencies to encapsulate itra-conazole (a triazole antifungal agent) with the help of simplegeometry optimization and MD simulations. The role of coreand spacer was explored and effective encapsulation was said tobe achieved when the change in potential energy of dendrimer–drug complex was at maximum. The dendritic structures with1,2,3,4-butanetetracarboxylic acid core and decanediol spacersshowed good, energetics and thus proposed to be potentialcandidate for itraconazole encapsulation, while MD results
Fig. 13 Representative images of G5 PAMAM dendrimer with 25 phenanthrene molecules after 1 ns of atomistic MD simulations at different pHconditions. The dark red arrows indicate the stacked phenanthrene molecules. Reprinted from ref. 46 with permission from the PCCP OwnerSocieties.
Fig. 14 PMF variation as a function of the dendrimer–drug center ofmass distance for all the cases studied in this work. Reprinted withpermission from V. Maingi, M. V. S. Kumar and P. K. Maiti, J. Phys.Chem. B, 2012, 116, 4370–4376. Copyright 2012 American ChemicalSociety.
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demonstrated that the tetracarboxy benzene core was optimalfor the purpose of hosting the guest molecule.
Zhang and co-workers98 synthesized a saccharide terminatedG3 PAMAM dendrimer in order to enhance the solubilizationproperties and biocompatibility of the dendrimer; the func-tionalized dendrimer was further conjugated with MTX in orderto improve its chemotherapeutic index. In order to see whetherthe attachment of saccharide to the dendrimer causes signi-cant structural changes at neutral pH, MD simulation studieswere performed on a simple G3 PAMAM, saccharide terminatedG3 PAMAM and its conjugate with MTX. The results demon-strated that saccharide-terminated and MTX-conjugated den-drimers displayed a smaller radius of gyration (13.1 A and 14.0A, respectively) than amine terminated dendrimers (18.8 A).Moreover, conjugation of drug molecules to the dendrimer didnot signicantly change the size and structure of thedendrimer.
Li et al.101 explored the dual activity of the anticancer drugMTX, which shows cytotoxicity due to the inhibition of dihy-drofolate reductase enzyme and acts as targeting ligand bybinding to folate receptors, a tumor biomarker. MD simulationsof partially acetylated G5 PAMAM–MTX nanoconjugates wereperformed under implicit solvent conditions to identify theeffect of the linker functional group and length of the spacer onthe structure and bioactivity. Structural models obtained aersimulations showed that a longer spacer with an ester linkageprovides exibility and a variable distance from the dendrimersurface; due to which MTX is exposed to the solvent to a greaterextent in comparison with the drug conjugated with a partiallyacetylated G5 PAMAM dendrimer via a direct amide linkage. Asa result, in the experimental study, conjugates with longerspacers and labile ester linkages showed more cytotoxicity thanconjugation with stable amide linkage.
Simanek et al.100 adopted a prodrug approach and developeda system composed of 12 molecules of the anticancer drugpaclitaxel conjugated with a triazine dendrimer via linkerscontaining both an ester and disulde. PEGylation of thesedendrimer–drug conjugates was carried out to increase theirsolubility, biocompatibility and increase their plasma half life.To obtain insights into the role of degree of PEGylation on thesystem, MD simulations were performed on hexaPEGylated,nonaPEGylated and dodecaPEGylated models. The simulation
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results showed that the water penetration and accessibility ofthe linkers vary with the degree of PEGylation. Solvation energyvalues (DGsol) for the hexaPEGylated, nonaPEGylated anddodecaPEGylated models were found to be about �1848.5,�1946.8 and �1620.1 kcal mol�1, respectively. A radial distri-bution function (RDF) plot revealed that an increase in PEGy-lation leads to a signicant crowding near the surface of thetriazine/PEG interface where the sites of the biolabile linkersthat facilitate drug release are located. Thus, it is preferrable touse low molecular weight and less bulky PEG chains.
Abderrezak and co-workers78 studied the interaction andbinding affinity of hydrophilic (cisplatin – anticancer) andhydrophobic drug molecules (resveratrol, genistein and curcu-min) with G4 PAMAM dendrimer using FTIR, UV-visible spec-troscopic methods and a molecular modeling approach.Analysis of the structures obtained aer MD simulationsrevealed that curcumin, genistein and resveratrol are primarilylocated in the internal cavities and undergo complexation withthe dendrimer through both hydrophobic and hydrophiliccontacts. The binding energy for the dendrimer–drug complexwas observed to be in the order: genistein > curcumin >
resveratrol; this trend is observed because of more hydrophobicnature of genistein in comparison to other drugs.
Maingi et al.79 studied the release prole of two soluble(salicylic acid (Sal) and L-alanine (Ala)) and 2 insoluble (phenyl-butazone (Pbz)- NSAID and primidone (Prim)- anticonvulsant)ligands from the G5 PAMAM dendrimer at neutral pH condi-tions by utilizing Potential of Mean Force (PMF) calculations.The results showed that the free energy barrier for the insolubleligands is greater as compared to the soluble ligands and therelease prole follows the trend: Ala > Sal > Prim > Pbz (Fig. 14).Interestingly, it was also observed that the free energy barriersfor ligands Sal (�14 kcal mol�1) and Pbz (�43 kcal mol�1) fromprotonated dendrimers (neutral pH) are much higher ascompared to non-protonated dendrimers (high pH, Sal – 3 kcalmol�1 and Pbz – 17 kcal mol�1). This difference arises due to thefavorable electrostatic interactions between the negativelycharged ligands and the positively charged primary amines ofthe PAMAM dendrimer at neutral pH conditions. Also, it wasobserved that the large energy barriers primarily resulted fromthe van der Waals interactions between the dendrimer andguest molecules and hydrogen bonding does not play anysignicant role. The authors suggested that due to the high PMFbarrier at physiological pH, the drug binds tightly to the den-drimer cavity, as a result of which drug might release at acontrolled rate in the bloodstream. The study concluded thatthe release pattern and encapsulation of ligands in the den-drimer depends on several factors such as solubility, size andcharge on the drug molecules, and protonated state of thedendrimer.
More recently, MD simulations have been performed by ourresearch group on dendrimer–drug complexes to understandthe inuence of pH-induced conformational changes in thedendrimer, ionization states, dendrimer type and pKa of theguest molecules on the stability of complexation, solubility and
Fig. 15 (a) PMF plot (with error bars) for Famo and Indo drug moleculesPlots showing the hydrogen bond formation ability of the drugmolecule Fcored G5 dendrimer (primary and tertiary amino groups) at low, neutralwindow (each 1 ns simulation run, and hydrogen bonds were calculated oand distance cutoff were set to 120� and 3.0 A, respectively. Reprinted f
release prole.80 Full atomistic MD simulations have been per-formed at three different pH conditions on two drugs, famoti-dine (H2 receptor antagonist) and indomethacin (NSAID)encapsulated in G5 PPI dendrimer EDA core. Theoretical anal-ysis showed that dendrimer–drug complexes are relativelyunstable at low pH as compared to neutral and high pHconditions, since the center-of-mass separation distancebetween the dendrimer and drug increases continuously in thecase of low pH, while it was almost constant at the other two pHconditions. PMF calculations by the umbrella sampling methodshowed that the release of drugs from the G5 PPI dendrimer atlow pH is spontaneous, a median release occurs at neutral pHand slow release is observed in high pH conditions (Fig. 15a).Additionally, PMF analysis provides clues regarding the solu-bility prole of the dendrimer–drug complexes and suggested atrend of high pH > neutral pH > low pH. MM-PBSA calculationsat each umbrella sampling window revealed various energycontributions to the overall binding free energy of the den-drimer–drug complexes; van der Waals interactions were foundto be the primary mechanism of drug encapsulation at neutraland high pH conditions. Furthermore, in order to understandthe effect of dendrimer chemistry and topology on the solubilityand release prole of drugs, PMF calculations were also per-formed on the drug Pbz complexed with G3 PAMAM (EDA core)and G4 PPI (DAB core) dendrimers. The results indicate that atphysiological pH, Pbz experiences sustained release from theG3 PAMAM dendrimer (PMF – 8.6 kcal mol�1) in contrary to afast release from the G4 PPI dendrimer (PMF – 1.1 kcal mol�1),and the solubility trend of complexes appears to be G3 PAMAM-Pbz > G4 PPI-Pbz (Fig. 16a). The theoretical results were foundto be in agreement with the pertinent experimental observa-tions.115,116 Intermolecular hydrogen bonding analysis betweendendrimer and drug molecules in all cases showed that theseinteractions played a crucial role in the stabilization of the
bound with G5 PPI dendrimer (EDA core) at all three pH conditions. (b)amo (N0-sulfamoylpropanamidine and guanidinemoiety) with the EDAand high pH conditions. The x-axis represents the umbrella samplingn each snapshot after 1 ps). For calculating hydrogen bonds, the anglerom ref. 80.
Fig. 16 (a) PMF plot (with error bars) for a Pbz drug molecule bound with G3 PAMAM (EDA core) and G4 PPI (DAB core) at neutral pH conditions.(b) Plots showing the hydrogen bond formation ability of the drug molecule Pbz (carbonyl groups) with the EDA-cored G3 PAMAM (amide andprimary amino groups) and DAB-cored G4 PPI (primary and tertiary amino groups) dendrimers at neutral pH conditions. The x-axis represents theumbrella samplingwindow (each 1 ns simulation run, and hydrogen bondswere calculated on each snapshot after 1 ps). For calculating hydrogenbonds, the angle and distance cutoff were set to 120� and 3.0 A, respectively. Reprinted from ref. 80.
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complex and contributes signicantly to raise the free energybarrier (Fig. 15b and 16b), and follows a trend similar to that ofthe binding free energy.
Fig. 17 Free energy profile obtained from ABF calculation for the movemacross G3 PAMAM. The sampling distribution characteristics of each MDmovement of nicotinate across G3 PAMAM obtained from 57.5 ns (solid linenergy profiles for the movement of 3-pyridiniumcarboxylate across Gsimulations are represented in red. Reprinted with permission from J. CabModel., 2013, 39, 71–78. Copyright 2012, Elsevier.
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Nicotinic acid (vitamin B3) is used in the treatment ofschizophrenia and other mental disorders. Experimental studyhas shown to increase the solubility of the drug via the PAMAM
ent of the nicotinate (high pH) and 3-pyridiniumcarboxylate (low pH)simulation are included in the inset. The free energy profiles for thee) and 69 ns (dotted line) simulations are represented in black. The free3 PAMAM obtained from 57.5 ns (solid line) and 69 ns (dotted line)allero, H. Poblete, C. Navarro and J. H. Alzate-Morales, J. Mol. Graphics
dendrimer and it was found to be pH-dependent: neutral pH >low pH.117 In order to decipher the reason behind the differ-ences in solubility, Caballero et al.102 investigated the interac-tion of nicotinic acid with G3 PAMAM dendrimer at low (pH 3)and neutral pH (pH 6) conditions using the Adaptive BiasingForce (ABF) method and MD simulations. The free energyprole of the drug molecule across the dendrimer as charac-terized by ABF revealed that, at high pH, there are several localminima with free energies between �1.5 and �3.0 kcal mol�1
(Fig. 17). However, at low pH conditions there are few minimawith free energies of only about �0.5 kcal mol�1; this is due tothe fact that at low pH, dendrimer cavities are more polar anddendrimer–drug interactions behave more like dendrimer–solvent interactions. This clearly reects that nicotinic acidinteracts more strongly with the dendrimer at high pH and theinclusion complex is more stable at this pH condition than atlow pH. MD simulations performed on complex structures(corresponding to free energy minima at high pH) showed thatthe drug molecules prefer to localize near the surface of thedendrimer instead of encapsulating in the interior cavities. Itwas also observed that host–guest complexation is stabilized bythe hydrogen bonds formed between the carboxylate moiety ofthe nicotinate with surface amines and amide NH groups of thedendrimer, as well as by van der Waals interactions between thearomatic ring of the nicotinate and methylene groups ofthe dendrimer. Superposition of the different conformations ofthe electrostatic potential 3D map of G3 PAMAM–nicotinatedivulged that the drug molecule ‘jumped’ from one positivecenter to another during the course of MD simulations, and thiswas due to the electric eld induced by the dendrimer (Fig. 18).
A computationally efficient protocol to study atomistic-leveldetails of dendrimer–drug complexes has been proposed byVergara-Jaque et al.81 The adopted methodology was validatedby investigating the binding affinity of anti-inammatory drugdexamethasone 21-phosphate (Dp21) with amine and acetyl-terminated G5 PAMAM dendrimers at low and neutral pHconditions using the Molecular Mechanics Generalized BornSurface Area (MM-GBSA) approach, and comparing the resultswith that of available experimental ndings. In this study,cavities in the dendrimers were forcefully generated at threedifferent positions, around the core, on the middle region andon the outer surface; and in addition boundary potentials werealso applied during the simulation to restrict the sampling of
Fig. 18 Electrostatic potential 3D map of G3 PAMAM during 5 ns simuReprinted with permission from J. Caballero, H. Poblete, C. Navarro and J2012, Elsevier.
drug to three different regions 0 to 10 A (core), 15 to 20 A(middle) and 25 to 30 A (surface). Binding free energy calcula-tions indicated that the binding affinity of the drug is morefavourable when it binds to the middle region of the dendrimerin comparison to the core and surface regions (see all the casesin Table 3). In agreement with experimental results, the highestand lowest affinity of drug was shown by acetyl-terminateddendrimer at low pH and neutral pH conditions, respectively. Itwas suggested that a balance of multiple mechanisms such aselectrostatic, van der Waals, hydrogen bonds and charge–charge interactions are the driving forces behind the stabiliza-tion of the complex.
From the above reviewed studies it is clear that computa-tional studies performed on dendrimer–drug complexes usuallyconsider 1 : 1 stoichiometry, which is far away from the reality,since in experiments more number of drug molecules encap-sulates inside a dendrimer. Therefore, in this direction we haverecently developed a computationally efficient protocol tocharacterize the more realistic molecular model of dendrimer–drug complex in order to understand the effect of high drugloading on the structural properties and also to unveil theatomistic level details (unpublished).118 The possible inclusioncomplex of the model drug nateglinide (Ntg) (antidiabetic) withamine- and acetyl-terminated G4 PAMAM (G4 PAMAM(NH2)and G4 PAMAM(Ac)) dendrimers were studied at neutral andlow pH conditions. The most stable structure of Ntg obtained inthe solvent phase (using ab initio (DFT) calculations)119 wasutilized to undergo complexation with the dendrimers (corre-sponding to neutral and low pH) using a molecular dockingapproach. MD simulation analysis on dendrimer–drugcomplexes revealed that the drug encapsulation efficiency of G4PAMAM(NH2) and G4 PAMAM(Ac) at neutral pH was 5 and 6respectively, while at low pH it was 12 and 13 respectively.Interestingly, it was observed from the equilibrated structure ofdendrimer–drug complexes at low pH that encapsulated drugmolecules in the G4 PAMAM(NH2) dendrimer formed clusters,while in case of non-toxic G4 PAMAM(Ac) dendrimers they wereuniformly distributed in the dendrimer. Thus, the later den-drimer is suggested to be a suitable nanovehicle for the deliveryof Ntg.
The initial 3D conguration of dendrimers with GAFF atomtypes and RESP partial atomic charges were generated with theaid of the Dendrimer Builder Toolkit (DBT)120 developed by our
lation with nicotinate molecule at (a) site I, (b) site II, and (c) site III.. H. Alzate-Morales, J. Mol. Graphics Model., 2013, 39, 71–78. Copyright
Table 3 Results of the MM-GBSA calculations (all energies in kcal mol�1) for amine- and acetyl(Ac)-terminated G5 PAMAM dendrimers inter-acting with the Dp21 drug molecule. Adapted with permission from A. P. Vergara-Jaque, J. R. Comer, L. F. Monsalve, F. D. Gonzalez-Nilo and C.Sandoval, J. Phys. Chem. B, 2013, 117, 6801–6813. Copyright 2013, American Chemical Society
Fig. 19 Atomistic and coarse-grained representation of a PAMAMdendrimer (for clarity, only the core is shown; for coarse graining, red,green and blue circles of the atoms map into N0, Nda and Qd,respectively). In the atomistic structures, the color representation is asfollows: Gray – carbon; Blue – nitrogen; Red – oxygen; and White –hydrogen. Adapted from ref. 123.
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research group. This toolkit, in conjugation with the AMBERprogramme, can be used to obtain dendrimer structures of thedesired generation with various dendrimeric architectures. Thevalidation of dendrimer structures generated by this tool wascarried out by studying their structural properties (radius ofgyration, shape tensor and monomer density distribution) atneutral and high pH conditions and comparing the results withthat of the available theoretical and experimental values. Forthis purpose, two well known classes of dendrimers: EDA-coredPAMAM (G3–G6) and DAB-cored PPI (G5) dendrimers followedby a novel nitrogen cored PETIM (G3) dendrimer were studied.
5. Coarse-grained simulation andstatistical field theories on dendrimer–drug complexes
From the above discussion it is apparent that quantum methodsand full atomisticMD simulations provide unparalleled electronicand microscopic properties of the dendrimer–drug complexes.Nonetheless, these two approaches suffer from the limitation ofcarrying out calculations only on small or medium sized systemsand also they are computationally expensive. In addition, they donot provide bulk level details and also do not consider aconcentrated solution of the dendrimer–drug complex, wherecomplex–complex interactions in solution could have implica-tions for structural and delivery aspects. The simulation of densemacromolecular systems is virtually impossible if one takes intoaccount all degrees of freedom and interactions of a chemicallyrealistic chain. Therefore, it is imperative to reduce the complexityin order to ll the time-scale and length-scale gap between thecomputational and experimental methods of the studyied system.This reduction of the complexity of the model and elimination ofne interaction details is known as coarse-graining of the model,and here the potential needs to be calculated only between newinteracting units, oen called grains/beads. Coarse-grainedmodeling approaches can be broadly classied into two cate-gories: (i) indirect parameterization methods in which thermo-dynamic or structural properties are used for the calibration to
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optimize the potential parameters of the preselected analyticalform (e.g. the MARTINI force eld121); and (ii) direct parameteri-zation methods in which coarse-grained potentials are derivedfrom an explicit all atom MD simulation using force matchingalgorithm122 (e.g. multiscale coarse-graining).
Kim and Lamm123 introduced a computationally efficient,novel coarse-grained modeling scheme (Fig. 19) that integratessolvent-free multiscale coarse-graining algorithm (i.e., forcematching) for a exible macromolecule with an existing coarse-grained solventmodel. The accuracy of thismethod was evaluatedby studying the binding interaction of G5 PAMAM with phenan-threne molecules. It was observed that solvent-free coarse-grainedsimulations overestimated the interactions between PAMAM andphenanthrene molecules, and this is due to the signicantcongurational entropy loss from the absence of explicit solvent.To overcome this problem, coarse-grained solvent molecules wereadded to the system and this new approach predicted correctly theexperimentally measured binding capacity. In addition, thedistribution of phenanthrene molecules around the dendrimerwas in complete agreement with the atomistic MD simulation
results. Authors have also evaluated the effect of the molar ratioon the binding capacity in the model system; the number ofdendrimers was increased from 27 to 216, while retaining thenumber of phenanthrene molecules at 216. The results werefound to be consistent with the FRET experiments46 and theincreased peak intensity in case of 216 dendrimers was observedin the two-dimensional probability distribution graph. Thisapproach has vast potential in the eld of drug delivery and couldreveal whether interactions among macromolecules in solutionsare imperative driving forces for system stabilization.
Self-consistent eld theory (SCFT)124 is a statistical eldtheory, where the fundamental degrees of freedom of a macro-molecular system can be effectively captured by several contin-uous eld variables in a coarse-grained level. The SCFT is greatlybased on the mean eld approximation, which reduces anymulti-body problem into an effective one-body problem byassuming that the partition function (free energy) integral of themodel is dominated by a single eld conguration. In compar-ison to MD simulations, SCFT is a much better theoreticalapproach to study the thermodynamic limits (entropy andenthalpic contributions) and phase boundary for multicompo-nent and multiphase systems (like inhomogeneous polymersystems). Moreover, the intrinsic properties of the polymer likepolydispersity and its diffusion dynamics can also be investigatedusing SCFTwhich is difficult to determine usingMD simulations.
To gain an insight into the mechanism behind the solubili-zation of weakly acidic drugs via dendrimeric nanoparticles,Lewis and Ganesan125,126 developed self-consistent eld theorymodel for charged dendrimers and studied the individual as wellas synergistic effects of excluded volume interactions, electro-static attractions, and enthalpic interactions (hydrophobic andhydrogen bonding) on the solubilisation of weakly acidic drugmolecules. The relative importance of different parameters likegeneration number, solution pOH and Bjerrum length, drugsize, concentration and hydrophobicity, and strength of drug–polymer interactions were explored in terms of encapsulationefficiency of dendrimer. In the rst study125 it was observed thatincorporation of the electrostatic/enthalpic interactions in themodel improves solubilization of the drugs and it increases withan increase in drug charge density and dendrimer generationnumber. In the second study126 the authors found that thegraed dendrimers have a higher potential to encapsulate thedrug molecules in comparison to their non-graed counterpart,and this is due to the enhanced ability of the graed dendrimerto make strong electrostatic and/or enthalpic interactions.
Lewis and Ganesan125 employed a semi-grand-canonicalframework to describe the equilibrium characteristics of thedendrimer, salt, drug, solvent and ion mixture and solved itwithin a mean eld approximation.124 In this framework, thefree energy was identied as:
F ¼ F conf + F int + F comp + F mix + F chem + F elec
(i) The term F conf accounts for the conformational entropyof polyelectrolyte dendrimer. bF conf ¼ ln QP +
Ðdrwp(r)4p(r)
where b ¼ 1/kBT, QP is the partition function for a single
noninteracting graed dendrimer molecule subjected to theexternal eld wp(r), and 4p(r) denotes the concentration of thedendrimer chain monomers.
(ii) The term F int accounts for the pairwise steric interac-tions betweenmonomers of the dendrimer, drug molecules andsolvent molecules.
bF int ¼Ðdr{cPS4P(r)4S(r) + cPD4P(r)4D(r) + cDS4D(r)4S(r)}
where cij is the Flory–Huggins interaction parameter betweenthe ith and jth species.
(iii) The term F comp accounts for the uctuations in overallaverage density from the bulk density.
bF comp ¼ z
2
ðdr½4PðrÞ þ 4SðrÞ þ 4DðrÞ � 1�2
where z is a dimensionless parameter that quanties themagnitude of the harmonic energy penalty for local densityuctuations away from the average bulk density.
(iv) The entropies of mixing of free ions are accounted in theterm F mix.
bF mix ¼ðdr
(Xi
4iðrÞ�ln 4iðrÞ � 1þ bmo
i
�þ 4SðrÞ�ln 4SðrÞ � 1
þ bmoS
�þ ð1� aDðrÞÞ4DðrÞ�lnð1� aDðrÞÞ4DðrÞ � 1
þ bmoDH
�þ aDðrÞ4DðrÞ�ln aDðrÞ4DðrÞ � 1þ bmo
D��)
where i¼ OH�, H+, Cl�, and Na+, aD(r) is the local probability ofa drug molecule being in the charged state, and moj is thestandard chemical potential of the jth species.
(v) The term F chem accounts for the free energy contributionfrom the dendrimer acid–base equilibrium.
bF chem ¼ Ðdr[aP4P(r)[a(r)(ln a(r)) + bmoPH+)
+ (1 � a(r))(ln(1 � a(r)) + bmoP]]
The notations a(r) and 1 � a(r), represents the local fractionof disassociated dendrimer polymer monomers and unchargedmonomers respectively.
(vi) The electrostatic interactions between the charged enti-ties are accounted within F elec.
bF chem ¼ðdr
�r04eðrÞfðrÞ �
1
8PlBjVfj2
�
where f(r) is the electrostatic potential (normalized by e/kBT)conjugate to the charge density eld, r04e(r).
6. Other computational chemistrymethodsNano QSAR
Today, modeling the quantitative structure–activity relationship(QSAR) based paradigm for assessing the biological effects/toxicological hazards of nanoparticles is an emergingareas,127–129 which has received substantial attention in recent
years due to the reported in vitro/in vivo cytotoxicity, oxidativestress/inammation, immunotoxicity, genotoxicity, carcino-genesis and ecotoxicity for the nanomaterials.130–132 QSAR aimsto establish a relationship between the biological/toxicityendpoints of the nanoparticles with their properties (structuraland physicochemical descriptors) using multivariate dataanalysis techniques. Oberdorster et al.133 suggested someimportant features that should be characterized by experi-mental and computational methods to assess the toxicity ofnanomaterials, these include: size distribution; agglomerationstate; shape; porosity; surface area; chemical composition;structure-dependent electronic conguration; surface chem-istry; surface charge; and crystal structure. Since dendrimers arealso known to possess signicant cytotoxicity, hemolytic andhaematological toxicities,17 it is highly desirable to establish aQSAR model for the dendrimer–guest complexes in order topredict risk assessment and safety prior to their therapeutic use.In this course, Pricl and co-workers134 attempted to establish anSAR between atomistic-MD-simulation based calculated struc-tural features for the set of novel dendrimers (differing only insurface motifs) and the corresponding experimentally observedcytotoxicity or non-cytotoxicity of these dendrimers. This studyconcluded that all the investigated non-cytotoxic dendrimers incommon were characterized by a globular and compact shapewith a higher density, low fractions of internal surface areas andinternal volumes and by a smoother surface pattern. Moreover,experimentally determined ecotoxicological135 and cytotoxico-logical136 studies of G4–G6 PAMAM dendrimers together withtheir characterized physicochemical properties to understandSAR could act as a good starting point in this direction.
Virtual screening
Due to fast and efficient docking algorithms, the moleculardocking approach is routinely being used in drug discovery for thepurpose of virtual screening of databases in order to identify thepotential ligands against targets of interest on the basis of theirbinding affinity.137 Till now no reports are available implementingvirtual screening for screening the drug–guest molecules showingstrong complexation with the dendrimers, but it is highly desir-able to use this technology in near future. High-throughputscreening (HTS) of dendrimer-binding drugs50 and commonamino acids138,139 using different NMR techniques such as satu-ration transfer difference (STD) NMR, Hadamard-encodednuclear Overhauser effect (NOE) measurements, proton NMRtitrations, nuclear Overhauser effect spectroscopy (NOESY) andpulsed gradient spin echo (PGSE) NMR have recently beenreported. These experimental reports further provide momentumto employ virtual screening in the eld of dendrimer based drugdelivery, since these studies offer a good source of datasets and anopportunity to establish in silico HTS protocols which can bevalidated by comparing the computational results with those ofthe experimental ndings. It is generally expected that virtualscreening of dendrimer-binding drugs may lead to large falsepositive results because docking does not consider the exibilityof the macromolecule. In order to improve the virtual screeningresults one could use ensemble docking140with consensus scoring
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functions,141 which will consider the different conformations ofthe dendrimer and ligands for the purpose of screening thepotential binding drugs/guests on the basis of binding affinity.
QM/MM
The Quantum Mechanical/Molecular Mechanical (QM/MM)methods are now widely used computationally efficient hybridtechniques to decipher the electron transfer mechanism andother electronic processes that occur in macromolecularsystems.142,143 In comparison to QMmethods, which only considerthe reactive atoms/small molecules and ignore the effect of thesurrounding chemical environment, QM/MM takes account of theentire system which is divided into the inner QM region (involvedin electron transfer with ligand) that is treated quantum-mechanically and the outer MM region (involved in non-bondinginteractions with ligand) that is described by a force eld. Theconcept of QM/MM, which was initially established as a two-layerapproach, is now also extended to multi-layer approaches such asuse of a continuum solvation model as a third layer to mimic theeffects of bulk solvent, and the ONIOM method144 which inte-grates two or more QM regions (dening the inner layer by DFT,the middle layer by semi-empirical and the outer layer by MMmethods). To our knowledge, no reports have mentioned theusage of QM/MM methods for studying dendrimer–drugcomplexes, but these are highly efficient methods which canprovide unprecedented detail of host–guest interactions. Thisapproach should be implemented by researchers in the future tostudy dendrimer–drug interactions, specically where electrontransfer mechanisms are involved such as peptide dendrimer–substrate complex82 and organocatalysis via dendrimers.33
7. Conclusions and futureperspectives
The pharmacoinformatic studies discussed in this review haveprovided in-depth insights into dendrimer–drug interactions atelectronic, atomistic, molecular and bulk levels; therefore helpin deciphering the mechanism involved in host–guest complexformation. Quantum chemical calculations provide electroniclevel details which facilitate novel dendron design, the effect oflinker and fractal patterns on the stability of dendrimer–drugcomplexation and interaction energies calculation. Moleculardocking primarily assists in the encapsulation of drug mole-cules in the most appropriate manner which is free from stericstrain and clashes inside the dendrimer cavity; this approachalso helps to identify the atomistic interactions between thedendrimer and drug. From the computational simulations ithas been evident that the hydrogen bonding, van der Waals/hydrophobic and electrostatic/ionic interactions play animportant role in the stabilization of dendrimer–drugcomplexes. Notably, complexation is inuenced by variousfactors such as the physicochemical properties of the drug anddendrimer, solvent conditions, counterions distribution, forceelds, length of simulation run, etc., thus these factors must beconsidered carefully in order to get realistic molecular modelsclose to experiments. In comparison to full atomistic
simulations, with coarse-grained models with reduced degreesof freedom it is possible to achieve a higher order of magnitudein the simulated length and time scale to understand the largestructural properties of the system. It is now clear that imple-menting solely one theoretical approach cannot providedetailed insights and a thorough understanding of the host–guest complexation, therefore multiscale modeling approachesshould be employed in future to get a complete static anddynamic picture of complexation. Other pharmacoinformaticapproaches based on QSAR, virtual screening and QM/MM havenot yet been implemented in the eld of dendrimer–drugcomplexes, thus need to be taken up in future for furtherexploration in computational drug delivery paradigms.
There are several open challenges for pharmacoinformaticapproaches in theeld of drugdelivery; a fewof themare listedbelow:
1. The dependence of the drug delivery on the environ-ment is currently addressed only by using broad level pHconditions – low (pH � 4), neutral (pH � 7) and high (pH �10). It is worth developing pharmacoinformatic protocols fora range of pH values with various concentrations of ions. Forexample, a difference of one pH unit does bring changes inthe protonation level of dendrimer and thus drug deliverycharacteristics; modeling these changes is an importantchallenge.
2. The dielectric constant of the medium inside variousorganelles (cytoplasm, mitochondria, nucleus, etc.) in the cell isdifferent. The current pharmacoinformatic tools are not yettuned to incorporate these minute differences in the dielectricconstant of the medium, which inuences the drug deliveryprole from the dendrimers. It is worth developing computa-tional tools/protocols to model these aspects.
3. Till now efforts have only been made to identify a quali-tative estimation of the solubility enhancement of drug via adendrimer and its release proles using pharmacoinformaticapproaches. However, it is necessary to develop an efficientcomputational protocol for the quantitative estimation of theseparameters, which are sensitive to the changes in localtemperature and other physicochemical parameters. Moreover,the predicted results should be comparable to those ofexperiments.
4. Targeted drug delivery by dendrimers is primarily basedon receptor-mediated endocytosis i.e. entry of the complexinside the cells by interaction of the specic ligand attached tothe dendrimer with the receptors present on the surface of thecells. Therefore, it is important tomodel the precise mechanismof the nano-formulation entry inside the cells as well as itsinteraction with the lipid bilayer membrane using pharma-coinformatic approaches.
5. The proton sponge effect is the main mechanism for thelysosomal escape of the dendrimer–guest complex inside thecell, which has not so far been modelled using any pharma-coinformatic tools. It is worth pursuing the exploration of thismechanism using computational methods.
6. Predicting the cytotoxicities of the dendrimer–drugformulation for therapeutic and toxicological effects using insilico models is one of the unexplored areas that needs a hugeamount of attention.
Authors are thankful to the Department of Science and Tech-nology (DST) Nanomission, and the Council of Scientic andIndustrial Research, New Delhi, India for support.
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