Encapsulation of Antitumor Drug Doxorubicin and Its Analogue by

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Encapsulation of Antitumor Drug Doxorubicin and its Analogue by Chitosan Nanoparticles Sriwanna Sanyakamdhorn, Daniel Agudelo, and Heidar-Ali Tajmir-Riahi Biomacromolecules, Just Accepted Manuscript • DOI: 10.1021/bm3018577 • Publication Date (Web): 10 Jan 2013 Downloaded from http://pubs.acs.org on January 15, 2013

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Encapsulation of Antitumor Drug Doxorubicin and its Analogue by Chitosan Nanoparticles

Sriwanna Sanyakamdhorn, Daniel Agudelo and Heidar-Ali Tajmir-Riahi* Département de Chimie-Biologie, Université du Québec à Trois-Rivières, C. P. 500, TroisRivières (Québec), G9A 5H7, Canada

Key words: doxorubicin, chitosan, binding site, FTIR, fluorescence spectroscopy, modeling

Abbreviations: Ch, chitosan; Dox, doxorubicin, FDox, N(trifluoroacetyl) doxorubicin, FTIR, Fourier transform infrared

* Corresponding author: [email protected]: Tel: (819) 376-5011 (3310), Fax: (819) 376-5084

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ABSTRACT Biodegradable chitosan of different sizes were used to encapsulate antitumor drug doxorubicin (Dox) and its N-(trifluoroacetyl) doxorubicin (FDox) analogue. The complexation of Dox and FDox with chitosan 15, 100 and 200 KD was investigated in aqueous solution, using FTIR, fluorescence spectroscopic methods and molecular modeling. The structural analysis showed that Dox and FDox bind chitosan via both hydrophilic and hydrophobic contacts with overall binding constants of KDox-ch15 =

8.4 (±0.6) x 103 M-1 , KDox-ch-100 = 2.2 (±0.3) x 105 M-1, KDox-ch-200 = 3.7 (±0.5) x 104 M-1 and KFDox-

ch-15

= 5.5 (±0.5) x 103 M-1, KFDox-ch-100 = 6.8 (±0.6) x 104 M-1 and KFDox-ch-200 = 2.9 (±0.5) x 104 M-1

with the number of drug molecules bound per chitosan (n) 1.2 to 0.5. The order of binding is ch100>200>15 KD with stronger complexes formed with Dox than FDox. The molecular modeling showed the participation of polymer charged NH2 residues with drug OH and NH2 groups in the drug-polymer adducts. The presence of hydrogen-bonding system in FDox-chitosan adducts stabilizes the drugpolymer complexation with the free binding energy of -3.89 kcal/mol for Dox and -3.76 kcal/mol for FDox complexes. The results show chitosan 100 KD is more suitable carrier for Dox and FDox delivery.

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INTRODUCTION Chitosan (Scheme 1) is a natural polymer obtained by deacetylation of chitin.1 Chitin is the second most abundant polysaccharide in nature after cellulose. It is non-toxic, biocompatible and biodegradable polysaccharide. Chitosan nanoparticles have gained more attention as drug delivery carriers because of their better stability, low toxicity, simple and mild preparation method and providing versatile routes of administration.1-4

The deacetylated chitosan backbone of

glucosamine units has a high density of charged amine groups, permitting strong electrostatic interactions with proteins and genes that carry an overall negative charge at neutral pH conditions.1,2 The fast expanding research of the useful physicochemical and biological properties of chitosan has led to the recognition of the cationic polysaccharide, as a promising natural polymer for drug delivery, especially for therapeutic proteins and genes.4-6 Therefore it is of a major interest to study the encapsulation of doxorubicin and its analogue with chitosan of different sizes, in order to evaluate the efficacy of chitosan in drug delivery. In the last 50 years, the antitumor drug doxorubicin (Scheme 1) is widely used as chemotherapeutic agents for the treatment of several types of cancers including leukemias, lymphomas, breast, uterine, ovarian and lung cancers.7 Doxorubicin intercalates into DNA duplex preventing DNA replication and transcription.8 However, the use of doxorubicin has been limited by a dose-related and irreversible cardiotoxicity, as well as drug resistance.9 Nano-particle delivery systems of doxorubicin constitute a promising approach to increase its antineoplastic

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efficacy and lower its side-effects by site-specific drug delivery via active targeting mechanism.10,11 Several nanoparticles delivery systems have been used for doxorubicin transport in vitro and in vivo.12-18 Synthetic polymer conjugates such as PEG-proteins have been recently used for distribution of doxorubicin in vivo.19,20 Complexation of doxorubicin and its derivative with human and serum albumins has been recently reported and the possibility of using serum proteins as carriers for doxorubicin and its derivatives was discussed.21,22 Fluorescence quenching is considered as a useful and reliable method for measuring binding affinities.23 Fluorescence quenching is the decrease of the quantum yield of fluorescence from a fluorophore induced by a variety of molecular interactions with quencher molecule.24 Therefore, it is possible to use quenching of the Dox and FDox molecules in an attempt to characterize the nature of drug-chitosan interaction. Furthermore, molecular docking is an important tool to predict the binding sites of Dox and FDox with chitosan nanoparticles. We report spectroscopic analysis and docking studies of the interaction of chitosan nanoparticles 15, 100 and 200 KD with doxorubicin and N-(trifluoroacetyl) doxorubicin in aqueous solution at acidic pH, using constant polymer concentration and various drug contents. The structural analysis regarding drug binding sites, the effect of chitosan sizes on the stability of drug-polymer complexes and the efficacy of chitosan nanoparticles in drug delivery are reported here.

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EXPERIMENTAL SECTION

Materials. Purified chitosans 15, 100 and 200 KD (90% deacetylation) were from Polysciences Inc. (Warrington, USA) and used as supplied. Doxorubicin hydrochloride was generously provided by Pharmacia/Farmitalia Carlos Erba, Italy and N(trifluoroacetyl) doxorubicin was synthesized according to the published methods.25,26 Other chemicals were of reagent grades and used as supplied. Preparation of Stock Solutions. An appropriate amount of chitosan was dissolved in acetate solution (pH 5.5-6.5). The Drug solutions (1 mM) Dox in water and FDox in ethanol/water (25/75%) were prepared and then diluted by serial dilution in acetate buffer. FTIR Spectroscopic Measurements. Infrared spectra were recorded on a FTIR spectrometer (Impact 420 model, Digilab), equipped with deuterated triglycine sulphate (DTGS) detector and KBr beam splitter, using AgBr windows. Solution of drug was added dropwise to the chitosan solution with constant stirring to ensure the formation of homogeneous solution and to reach the target drug concentrations of 30, 60 and 120 µM with a final chitosan concentration of 30 µM. Spectra were collected after 2h incubation of chitosan with drug solution at room temperature, using hydrated films. Interferograms were accumulated over the spectral range 4000-600 cm-1 with a nominal resolution of 2 cm-1 and 100 scans. The difference spectra [(chitosan solution + drug solution) - (chitosan solution)] were generated using free chitosan band around 902 cm-1, as standard. This band is related to chitosan ring stretching27,28 and does not show alterations upon

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drug complexation. When producing difference spectra, this band was adjusted to the baseline level, in order to normalize the difference spectra. Fluorescence Spectroscopy. Fluorimetric experiments were carried out on a Perkin-Elmer LS55 Spectrometer. Stock solution of drug (30 µΜ ) in acetate (pH 5.5-6.5) was also prepared at 24 ± 1 °C. Various solutions of chitosan (1 to 200 µM) were prepared from the above stock solutions by successive dilutions at 24 ± 1 °C. Samples containing 0.06 ml of the above drug solution and various polymer solutions were mixed to obtain final chitosan concentrations ranging from 1 to 200 µΜ with constant drug content (30 µΜ). The fluorescence spectra were recorded at λex = 480 nm and λem from 500 to 750 nm. The intensity of the band at 592 nm from doxorubicin and its analogue.29 was used to calculate the binding constant (K) according to previous reports.30-35 On the assumption that there are (n) substantive binding sites for quencher (Q) on protein (B), the quenching reaction can be shown as follows: nQ + B ⇔ Qn B

(1)

The binding constant (KA), can be calculated as:

K A = [Qn B ] /[Q ] [B ] n

(2)

where, [Q] and [B] are the quencher and protein concentration, respectively, [QnB] is the concentration of non fluorescent fluorophore-quencher complex and [B0] gives total protein concentration:

[Qn B] = [B0 ] − [B]

(3)

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n

K A = ([ B0 ] − [ B ]) / [Q ] [ B ]

(4)

The fluorescence intensity is proportional to the protein concentration as described:

[B]/[B0 ] ∝ F / F0

(5)

Results from fluorescence measurements can be used to estimate the binding constant of drugpolymer complex. From eq 4: log[(F0 − F ) / F ] = log K A + n log[Q ]

(6)

The accessible fluorophore fraction (f) can be calculated by modified Stern-Volmer equation: F0 / (F0 − F ) = 1 / fK [Q ] + 1 / f

(7)

where, F0 is the initial fluorescence intensity and F is the fluorescence intensities in the presence of quenching agent (or interacting molecule). K is the Stern-Volmer quenching constant, [Q] is the molar concentration of quencher and f is the fraction of accessible fluorophore to a polar quencher, which indicates the fractional fluorescence contribution of the total emission for an interaction with a hydrophobic quencher.23,24 The K will be calculated from F0/F= K[Q] +1. Molecular Modeling. The docking studies were carried out with ArgusLab 4.0.1 software (Mark A. Thompson, Planaria Software LLC, Seattle, Wa, http://www.arguslab.com). The chitosan structure was obtained from literature report36 and the drug three dimensional structures were generated from PM3 semi-empirical calculations using Chem3D Ultra 11.0. The whole polymer was selected as a potential binding site, since no prior knowledge of such site was available in the literature (Modeling ref.). The docking runs were performed on the

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ArgusDock docking engine using regular precision with a maximum of 150 candidate poses. The conformations were ranked using the Ascore scoring function, which estimates the free binding energy. Upon location of the potential binding sites, the docked complex conformations were optimized using a steepest decent algorithm until convergence, with a maximum of 20 iterations. Chitosan donor groups within a distance of 3.5 Å37 relative to the drug were involved in complex formation.

RESULTS AND DISCUSSION FTIR Spectra of Drug-Chitosan Complexes. The drug-chitosan interactions were characterized by infrared spectroscopy and its derivative methods. Since there was no major spectral shifting for the chitosan amide I band at 1633-1620 cm-1 (mainly C=O stretch) and amide II band at 1540-1520 cm-1 (C-N stretching coupled with N-H bending modes)27,28 upon drug interaction, the difference spectra [(chitosan + drug solution) – (chitosan solution)] were obtained, in order to monitor the intensity variations of these vibrations and the results are shown in Figures 1 and 2. Similarly, the infrared spectra of the free chitosan in the region of 3500-2800 cm-1 were compared with those of the drug-polymer adducts in order to examine the drug binding to OH and NH2 groups, as well as the presence of hydrophobic contacts in drug-chitosan complexes. At low drug concentration (30 µM), a minor increase in the intensity was observed for the chitosan amide I at 1633-1620 cm-1 and amide II at 1540-1520 cm-1, in the difference spectra of the drug-polymer complexes (Figs 1 and 2, diff., 30 µM). The positive features are located at

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1628-1026 (Dox-ch-15), 1621-1026 (Dox-ch-100), 1643-669 (Dox-ch-200), 1655-673 (FDoxch-15), 1640-668 (FDox-ch-100) and1682-1668 cm-1(FDox-200) in the spectra of drugchitosan complexes (Figs 1 and 2, diff., 30 µM). These positive features are related to the increase in the intensity of the chitosan vibrational frequencies upon drug complexation. The increase in the intensity of the polymer amide I and amide II bands is due to Dox and FDox bindings to polymer C=O, C-N and N-H groups (hydrophilic interaction). Additional evidence to support drug interaction with C-N and N-H groups comes from the shifting of the polymer OH stretching at 3500-3400 cm-1 and N-H stretching mode at 3300-3200 cm-1, upon drug complexation that will be discussed further on. Further increase in the intensity of the polymer amide I and amide II vibrations as well as other frequencies was observed, as the drug concentration increased to 120 µM, with positive features at 1627-665 (Dox-ch-15), 1626-667 (Dox-ch-100), 1646-668 (Dox-ch-200), 1643-669 (FDox-ch-15), 1648-667 (FDox-ch-100) and 1640-627 cm-1 (FDox-ch-200) in the spectra of drug-chitosan adducts (Figs 1 and 2, diff., 120 µM). In addition, the polymer amide I and amide II bands exhibited major shifting upon drug complexation (Fig. 1 and 2, complex 120 µM). The major shifting and increase in the intensity of the amide I band in the spectra of the drug-polymer complexes suggests a further interaction of drug with chitosan polar groups. Analysis of the infrared spectra of chitosan in the region of 3500-2800 cm-1 showed major shifting of polymer OH, NH and CH stretching modes (Fig. 3). The polymer OH stretching vibrations at 3460, 3427 ( free ch-15), 3423 (free ch-100) and 3449, 3390 cm-1 (free ch-200) showed major shifting and intensity changes, in the spectra of Dox and FDox- chitosan

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complexes (Fig. 3). Similarly, the NH stretching vibrations at 3230 (free ch-15), 3245 (free-ch100 and 3239 cm-1 (free ch-200) exhibite shifting upon drug complexation (Fig. 3). The spectral changes of the polymer OH and NH stretching modes are due to the participation of chitosan OH and NH2 group in drug-polymer complexes (hydrophilic contacts). However, the shifting of the polymer symmetric and antisymmetric CH stretching vibrations observed at 2979, 2862 (free ch-15), 2941, 2887 (free ch-100) and 2938, 2879 (free ch-200) in the spectra of Dox and FDox-polymer complexes is related to the hydrophobic contacts in the drugchitosan complexes (Fig. 3). The overall spectral changes observed in this region 3500-2800 cm-1 are due to the presence of both hydrophilic and hydrophobic contacts, in the drug-chitosan complexes. Fluorescence Spectra and Stability of Drug-Chitosan Complexes. Since chitosan is a weak fluorophore, the titrations of Dox and FDox were done against various polymer concentrations, using drug excitation at 480 nm and emission at 500-750 nm.29 When drug interacts with chitosan, fluorescence may change depending on the impact of such interaction on the drug conformation, or via direct quenching effect. The decrease of fluorescence intensity of Dox or FDox has been monitored at 592 nm for drug-chitosan systems (Figs 4-A-C and 5AC). The plot of F0 / (F0 – F) vs 1 / [chitosan] is shown in Figs 4A’-C’ and 5A’-C’. Assuming that the observed changes in fluorescence come from the interaction between the drug and chitosan, the quenching constant can be taken as the binding constant of the complex formation. The K value given here averages four and six-replicate run for drug-polymer systems. Each run involves several different concentrations of chitosan (Figs 4A-C and 5A-C).

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The overall binding constants were KDox-ch-15 = 8.4 (±0.6) x 103 M-1 , KDox-ch-100 = 2.2 (±0.3) x 105 M-1, KDox-ch-200 = 3.7 (±0.5) x 104 M-1 and KFDox-ch-15 = 5.5 (±0.5) x 103 M-1, KFDox-ch-100 = 6.8 (±0.6) x 104 M-1 and KFDox-ch-200 = 2.9 (±0.5) x 104 M-1 (Figs 4A’-C’and 54A’-C’ and Table 1). The order of binding constants calculated for the drug-chitosan adducts, showed ch100>200>15 KD with more stable complexes formed with Dox than FDox (Table 1).

It is

important to note that ch-15 is smaller than ch-100 and ch-200, while drug-interaction is mainly via positively charged chitosan NH2 groups, as polymer size gets larger more increases in overall polymer charges will result in stronger drug-polymer complexation. However, in the case of ch-200 aggregation of polymer occurs at pH near 6, which leads to lesser affinity of the aggregated polymer for drug interaction (self-aggregation is less observed for ch-15 and ch100). Therefore, ch-100 forms more stable complexes than the ch-15 and ch-200 (Table 1). On the other hand, Dox forms more stable complexes than FDox, due to more hydrophilic character of doxorubicin than that of its analogue FDox (Table 1). The f value calculated from Eq. 7 represents the mole fraction of the accessible population of fluorophore to quencher. The f values were from 0.15 to 0.50 for these drug-chitosan complexes indicating a large portion of fluorophore was exposed to quencher. In order to verify the presence of static or dynamic quenching in drug-chitosan complexes we have plotted F0/F against Q to estimate the quenching constant (KQ) and the results are show in Fig.6. The plot of F0/F versus Q is a straight line for drug-chitosan adducts indicating that the quenching is mainly static in these drug-polymer complexes (Fig. 6). The quenching constant KQ was estimated according to the Stern-Volmer equation:

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F0/F=1+ kQt0[Q]= 1+ Ksv[Q]

(8)

where F0 and F are the fluorescence intensities in the absence and presence of quencher, [Q] is the quencher concentration and Ksv is the Stern-Volmer quenching constant,38 which can be written as Ksv = kQt0; where kQ is the bimolecular quenching rate constant and t0 is the lifetime of the fluorophore in the absence of quencher about 1.1 ns for free Dox and FDox around neutral pH.29 The quenching constants (KQ) are 1.8 x 1019M-1/s for Dox-ch-15, 1.3 x 1018M-1/s for Dox-ch-100, 2.6 x 1017M-1/s for Dox-ch-200,1.5 x 1018M-1/s for FDox-ch-15, 9.3 x 1017 M1

/s for FDox-ch-100 and 2.7 x 1017M-1/s for FDox-ch-200 (Fig. 6 and Table 1). Since these

values are much greater than the maximum collisional quenching constant (2.0×1010M-1/s), the static quenching is dominant in these drug-polymer complexes.38 The number of drug molecules bound per polymer (n) is calculated from log [(F0 -F)/F] = logKS + n log [chitosan] for the static quenching.39-41 The n values from the slope of the straight line plot showed 0.5 to 1.2 drug molecules that are bound per chitosan molecule (Fig. 7 and Table 1). The results indicate some degree of cooperativity for drug-polymer interaction. Docking Study. The spectroscopic results were combined with docking experiments in which Dox and FDox molecules were docked to chitosan to determine the preferred binding sites on the polymer. The models of the docking for drug are shown in Fig. 8. The docking results showed that Dox is surrounded by several donor atoms of chitosan residue on the surface with a free binding energy of -3.89 kcal/mol (Fig. 8). However, FDox is located near chitosan C-O, NH and NH2 groups with a hydrogen bonding system between drug O-213 and chitosan N-19 atoms (2.922 Ǻ) with the free binding energy of -3.76 kcal/mol (Fig. 8). As one

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can see Dox and FDox are not surrounded by similar donor groups showing different binding modes, in these drug-chitosan complexes with more stable Dox-polymer complexes, which is consistent with our spectroscopic results (Fig 8 and Table 1).

SUMMARY The spectroscopic and docking studies presented here show that Dox and FDox do not share similar binding modes with chitosan. Major hydrophilic interactions via chitosan charged NH2 groups are observed in the drug-polymer complexes with a minor hydrophopic contact. The order of drug-polymer binding is ch-100>ch-200>ch-15. Stronger complexes formed for Dox than FDox due to a more hydrophilic nature of Dox. Chitosan-100 KD is a stronger carrier for Dox and FDox delivery in vitro. Acknowledgments. The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is highly appreciated.

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(30) Dufour, C.; Dangles, O. Biochim. Biophys. Acta 2005, 1721, 164-173. (31) Froehlich, E.; Jennings, J. C.; Sedaghat-Herati, M.R.; Tajmir-Riahi, Η. Α. J. Phys. Chem. B. 2009, 2009 113, 6986−6993. (32) He, W.; Li, Y.; Xue, C.; Hu, Z.; Chen, X.; Sheng, F. Bioorg. Med. Chem. 2005, 13, 1837-1845. (33) Sarzehi, S,; Chamani, J. Intl. J. Biol. Macromol. 2010, 47, 558-569. (34) Bi, S.; Ding, L.; Tian, Y.; Song, D.; Zhou, X.; Liu, X.; Zhang, H. J. Mol. Struct. 2004, 703, 37-45. (35) Jiang, M.; Xie, M.X.; Zheng, D.; Liu,Y.; Li, X. Y.; Chen, X. J. Mol. Struct. 2004, 692, 71-80. (36) Skovstrip, S.; Hansen, S. G.; Skrydstrup, T.; Schiott. B. Biomacromolecules, 2010, 11, 3196-3207. (37) Manikrao, A. M. ; Mahajan, N.S.; Jawarkar, D.R.; Khatale, P.N.; Kedar, K.C.; Thombare, K.S. J. Comput.Methods Mol. Design 2012, 2, 29-43. (38) Zhang, G.; Que, Q.; Pan,J.; Guo. J. J. Mol. Struct. 2008, 881, 132-138. (39) Mandeville, J.S.; Tajmir- Riahi, H.A. Biomacromolecules 2010, 11, 465-472. (40) Charbonneau, D.M.; Tajmir-Riahi, H. A. J. Phys. Chem. B 2010, 114, 1148-1155. (41) Bourassa, P.; Kanakis, D. C.; Tarantilis, P.; Polissiou, M.G.; Tajmir-Riahi, H. A. J. Phys. Chem. B 2010, 114, 3348-3354.

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Captions for Figures

Scheme 1. Chemical structures of doxorubicin, N-(trifluoroacetyl) doxorubicin and chitosan. Figure 1. FTIR spectra in the region of 1800-600 cm-1 of hydrated films (pH 6.5) for free chitosan (30 µM) and its Dox complexes for (A) chitosan-15 KD, (B) chitosan-100 KD and (C) chitosan-200 KD with difference spectra (diff.) (bottom two curves) obtained at different drug concentrations (indicated on the figure). Figure 2. FTIR spectra in the region of 1800-600 cm-1 of hydrated films (pH 6.0) for free chitosan (30 µM) and its FDox complexes for (A) chitosan-15 KD, (B) chitosan-100 KD and (C) chitosan-200 KD with difference spectra (diff.) (bottom two curves) obtained at different drug concentrations (indicated on the figure). Figure 3. FTIR spectra in the region of 3500-2800 cm-1 of hydrated films (pH 6.0) for free chitosan and their Dox and FDox complexes obtained with 30 µM polymer and 120 µ M drug concentrations.

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Figure 4. Fluorescence emission spectra of drug-chitosan systems in 10 mM acetate buffer pH 6 at 25 °C presented for (A) Dox-ch-15: (a) free Dox (30 µM), (b-l) with chitosan at 30, 40, 50, 60, 80, 100, 120, 140, 160, 180, and 200 µM; (B) Dox-chitosan-100: (a) free Dox (30 µM), (bl) chitosan at 1, 3, 5, 7, 10, 15, 20, 30, 40, 50, and 60 µM;(C) Dox-ch-200: (a) free Dox (30 ) (b-l) with chitosan at 7.5, 10, 12.5, 15, 20, 25, 30, 35, 40, 45, and 50 µM; Inset: K values calculated by F0 / (F0 – F) vs 1 / [chitosan] for A’ (Dox-chitosan-15), B’ (Dox- chitosan 100) and C’ (Dox-chitosan-200).

Figure 5. Fluorescence emission spectra of drug-chitosan systems in 10 mM acetate buffer pH 6 at 25 °C presented for (A) FDox-ch-15: (a) free FDox (30 µM), (b-l) with chitosan at 30, 40, 50, 60, 80, 100, 120, 140, 160, 180, and 200 µM; (B) FDox-chitosan-100: (a) free FDox (30 µM), (b-l) chitosan at 1, 3, 5, 7, 10, 15, 20, 30, 40, 50, and 60 µM;(C) FDox-ch-200: (a) free Dox (30 ) (b-l) with chitosan at 7.5, 10, 12.5, 15, 20, 25, 30, 35, 40, 45, and 50 µM; Inset: K values calculated by F0 / (F0 – F) vs 1 / [chitosan] for A’ (FDox-chitosan-15), B’ (FDoxchitosan 100) and C’ (FDox-chitosan-200).

Figure 6. Stern-Volmer plots of fluorescence quenching constant (Kq) for the chitosan and its drug complexes at different chitosan concentrations (A) Dox-ch-15, (B) Dox-ch-100, (C) Doxch-200, (D) FDox-ch-15, (E) FDox-ch-100 and (F) FDox-ch-200.

Figure 7. The plot of Log (F0-F)/F as a function of Log (chitosan concentrations) for the number of bound drug molecules per chitosan (n) for drug-polymer complexes.

Figure 8. Best docked conformations of drug–chitosan complexes. (A) for Dox bound to chitosan and (B) for FDox bound to chitosan with H-boding between FDox-O-213 and chitosan N-19.

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Table1. Binding parameters for drug-chitosan complexes Complex

Ksv (M-1) Dox FDox

Ka (M-1) Dox FDox

n Kq (M-1 s-1) Dox FDox Dox FDox

ch-15

2.0 x 1010 1.7 x 109

8.4 x 103

5.5 x 103

0.6

0.8

1.8 x 1019

1.5 x 1018

ch-100

1.4 x 109

1.0 x 109

2.2 x 105

6.8 x 104

0.5

0.5

1.3 x 1018

9.3 x 1017

ch-200

2.9 x 108

3.0 x 108

3.7 x 104

2.9 x 104

1.0

1.2

2.6 x 1017

2.7 x 1017

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Scheme 1

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TOC Graphic

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