Association of Methotrexate with Native and PEGylated PAMAM-G4

Subscriber access provided by UNIV OF CALIFORNIA SAN DIEGO LIBRARIES

Article

Association of Methotrexate With Native and PEGylated PAMAM-G4 Dendrimers: Effect of the PEGylation Degree on the Drug-Loading Capacity and Preferential Binding Sites Luis F. Barraza, Veronica A. Jimenez, and Joel B. Alderete J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b08882 • Publication Date (Web): 16 Dec 2016 Downloaded from http://pubs.acs.org on December 20, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Association of Methotrexate with Native and PEGylated PAMAM-G4 Dendrimers: Effect of the PEGylation Degree on the Drug-Loading Capacity and Preferential Binding Sites Luis F. Barraza,a Verónica A. Jiméneza* and Joel B. Aldereteb*

Departamento de Ciencias Químicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Sede Concepción, Talcahuano, 4260000, Chile Departamento de Química Orgánica, Facultad de Ciencias Químicas, Universidad de Concepción, Casilla 160-C, Concepción, 4070371, Chile

ACS Paragon Plus Environment

1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 44

ABSTRACT. PEGylated PAMAM dendrimers (PEG-PAMAM) have been extensively studied as versatile vehicles for drug delivery. Nevertheless, little information has been reported regarding the effect of the PEGylation degree on the drug-loading properties of these systems, aimed at maximizing their performance as drug carrier nanocarrriers. In this work, fullyatomistic molecular dynamics (MD) simulations were employed to examine the association of methotrexate (MTX) with native and diversely PEGylated PAMAM-G4 dendrimers, using 2 kDa PEG chains with substitution degrees from 25% to 100% and 100:1 drug:dendrimer ratios to mimic experimental conditions of drug excess in saturated solution. MD results regarding complex stoichiometries and preferential binding sites were compared to experimental data retrieved from aqueous solubility profiles and 2D-NOESY experiments showing an outstanding level of agreement. The maximum theoretical drug loading capacity was achieved by the system with 34% PEGylation (42:1) through the simultaneous complexation of MTX within internal PAMAM-G4 branches and external PEG chains. On the other hand, higher PEGylation degrees were found to be detrimental for drug complexation due to PEG chains crowding on the dendrimer surface. These results provide valuable information to design more efficient PAMAM-based drug nanocarriers and explain the positive effect that partial PEGylation exerts on the drug-loading capacity of PAMAM-G4 over native and fully PEGylated systems.


2

Page 3 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1. Introduction Poly-amidoamine (PAMAM) dendrimers are synthetic macromolecules with unique structural features such as hyperbranched shape, nanoscalar size, very low polydispersity, internal hydrophobic cavities and multivalent surface groups.1 Due to these properties PAMAM dendrimers have become the subject of extensive research as versatile nanocarriers for drug delivery.2-5 Previous studies have established that the surface conjugation of PAMAM dendrimers with polyethylene glycol (PEG) chains improves the drug-loading and release properties of these systems, and induces significant advances in their biological performance by reducing cytotoxicity, enhancing cell permeation and extending circulation half-life in physiological environments.6-8 Additionally, dendrimer PEGylation has proven to be beneficial for drug accumulation into cancer cells through the well-known enhance permeability and retention (EPR) effect.9 In the past years, PEGylated PAMAM dendrimers have been extensively studied as potential drug carriers for a diversity of therapeutic compounds

10-12

, but considerably little efforts have

been carried out to identify the optimum PEGylation degree that maximizes the performance of these systems as drug carrier platforms. In a previous work we examined the supramolecular complexation of methotrexate (MTX) with native and diversely PEGylated PAMAM-G4 dendrimers (28%, 34%, 67%, and 100%) from aqueous solubility profiles and 2D-NOESY experiments.13 Our results showed that a PEGylation degree of 34 % maximized the drugloading capacity and internal complexation capability of these systems unlike higher PEGylation ratios, which were found to be detrimental for the internal complexation of MTX within dendrimer branches. These experimental findings are reexamined in the present work through molecular dynamics (MD) simulations, aimed at testing the capability of this computational


3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 44

approach to reproduce experimental trends in complex stoichiometries and preferential binding sites and provide atomic-level information to explain the positive effect that partial PEGylation exerts on the drug-loading capacity of PAMAM dendrimers. In the past years, MD simulations have been widely employed to study the structure and dynamic properties of native and modified PAMAM dendrimers and their supramolecular complexes with model drug compounds.14-22 In 2014 Yang et al. reported a MD study dealing with the microstructure of PAMAM of generations G2-G5 with PEGylation degrees of 0-50 % using PEG chains of 500 and 1000 Da, showing that PEGylation increases the overall size of these systems, expands the dendrimer core, and creates a PEG layer on the dendrimer surface that might interfere on drug complexation and release phenomena.23 In a recent work, our group studied the effect of PEGylation on the complexation of 5-fluorouracil with native PAMAM-G4 and PEG-PAMAM-G4 dendrimers using 2 kDa PEG chains showing that internal drug complexation reached a maximum at a PEGylation degree of 25%.24 Based on this background the present report addresses the complexation of MTX with native and diversely PEGylated PAMAM-G4 dendrimers in aqueous solution from MD simulations aimed at providing molecular insight into drug-dendrimer complexation phenomena to account for the experimental trends in the drug-loading capacity of native and PEGylated dendrimers, and the differential distribution of MTX within internal PAMAM branches and external PEG chains obtained from aqueous solubility profiles and 2D-NOESY experiments, respectively. Stepwise MD data was obtained for systems with 0%, 25%, 50%, 75% and 100% PEGylation using PEG chains of 2 kDa in explicit aqueous media. Additionally, a system with 34% of PEGylation was included in the present study considering that this substitution percentage maximizes the MTX complexation capacity according to experimental data. Simulated systems


4

Page 5 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


were built by mimicking experimental conditions of drug excess in saturated solution using 100:1 drug:dendrimer ratios, as found in similar literature reports dealing with the complexation of ibuprofen, piroxicam and mefenamic acid with PAMAM dendrimers in aqueous solution.14, 1617

The importance of using realistic models in the computational study of drug-dendrimer

interactions has been recently addressed by Maiti et al.

25

Nevertheless, this represents a

challenging strategy due to the size of the simulated systems and the large number of possible intermolecular interactions between PEGylated PAMAM dendrimers and excess of drug molecules in explicit water solution. Thus, careful parameterization, equilibration and production simulation protocols must be followed in order to obtain reliable results that contribute to a better molecular understanding of the structure and complexation properties of PEGylated PAMAM systems, which is a relevant subject to assist the design and optimization of novel PAMAMbased drug carrier systems.

2.

Experimental Section

2.1. Simulation details The initial equilibrated structure of PAMAM-G4 and PEGylated PAMAM-G4 (PEGPAMAM-G4) systems with ethylene diamine core and NH2 terminal groups were retrieved from our previous work.24 PEGylated systems were built considering PEGylation degrees of 25%, 34%, 50%, 75% and 100% with PEG chains of 2 kDa size, which were distributed symmetrically around the dendrimer structure to account for the micellar-like structure of PEGylated PAMAM dendrimers.7 The number of PEG chains included on each PEGylated system was 16, 22, 32, 48, and 64 for PEGylation degrees of 25%, 34%, 50%, 75% and 100%, respectively. To mimic physiological pH conditions (pH~7.4), all surface primary amine groups were protonated, given


5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 44

that the reported pKa values for the PAMAM external primary amines are in the range of 9.4– 9.7, while tertiary amines remain neutral (pKa 3–6).26 The initial structure of MTX was obtained from ab initio calculations at B3LYP/6-31+G(d,p) level using the Gaussian 09 software.27 To simulate the structure of MTX at physiological conditions, the carboxyl groups of this compound were considered in their anionic deprotonated form (α-COOH, pKa1 2.89-3.36; γ-COOH, pKa2 4.56-4.70).28-29 The initial structures of drug-dendrimer complexes were built considering a drug excess of 100:1 to mimic a saturated drug aqueous solution condition.13 In these models, MTX molecules were randomly located around of one equilibrated dendrimer molecule within a spherical shell between 11-15 Å from dendrimer surface. In order to preserve charge neutrality, an appropriate number of Na+ counterions were added considering 5 Å as the minimum distance from dendrimer and drug molecules. The drug-dendrimer complex models were solvated with explicit TIP3P water molecules,30 in a cubic water box with dimensions to provide an appropriate solvation layer around the dendrimer structure and drug molecules. Details of all simulated systems are provided in Table 1. MD simulations were carried out with the NAMD software.31 The force field parameters for PAMAM-G4 dendrimers were obtained from the CHARMM C27 force field,32 while PEG chains were modeled using the CHARMM C35r parameters package.33 The topology files and force field parameters for MTX were retrieved from the SwissParam web interface at http://www.swissparam.ch/, which provides parameters derived from the Merck Molecular Force Field (MMFF9) for small organic compounds.34 Solvated systems were subjected to a three-stage potential energy minimization process: (i) water molecules and counterions were subjected to a minimization of 1000 steps allowing their structural reorganization while dendrimer, PEG and MTX molecules were kept fixed in their initial conformation; (ii) PAMAM-G4, PEG-PAMAM-G4 and drugs were minimized in 1000


6

Page 7 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


steps keeping water molecules and counterions fixed; (iii) the entire system was minimized in 1000 steps. Next, a series of short MD runs of 200 ps (in 1 fs time step) in the canonical ensemble (NVT) at different temperatures were carried out aimed at simulating a progressive heating from 0 K to 800 K in steps of 100 K, followed by a cooling process from 800 K to 300 K in 100 K steps. The aim of this heating-cooling process is to allow the systems to explore different conformations and distributions of water molecules, counterions and drug molecules around the dendrimer structure. Then, 500 ps of equilibration dynamics were performed at 300 K using the NVT ensemble. Finally, 50 ns of unrestrained production dynamics were carried out using the isobaric-isothermal ensemble (NPT, p = 1 atm and T= 300 K), with a time step of 2 fs. The time length of the produced MD trajectories was considered appropriate to describe the complexation of MTX with PAMAM-G4 and PEGylated systems. The Langevin thermostat with a damping coefficient of 5 ps−1 was employed for the temperature control and constant pressure was fixed at 1 atm using the Nose−Hoover Langevin Piston method.35 The standard particle mesh Ewald method36 was used with periodic boundary conditions to calculate the long-range electrostatic interactions of the system, whereas the van der Waals interactions were modeled by a 12-6 Lennard-Jones potential. For all non-bonded calculations, a cutoff of 12 Å was used, whereas all bonds involving hydrogen were kept rigid using the SHAKE algorithm. 2.2. Trajectory analysis 250 structures retrieved from the last 25 ns of equilibrated NPT simulations were employed to conduct the trajectory analysis for the systems under study using the VMD software.37 Equilibration of the systems was checked by RMSD and mean-square radius of gyration (Rg) calculations. Rg values for PAMAM-G4 and PEG-PAMAM-G4 systems were obtained using the following equation


7


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

〈 〉 =

〈 ∑ | − | 〉

Page 8 of 44

(1)

where R is the center of mass of the system, ri is the position vector of the i-th atom of mass mi and M is the total mass of the system. Additionally, the number of complexed drug molecules within PAMAM-G4 and PEGPAMAM-G4 systems was calculated along the simulation run and employed as a more accurate criterion to assess the systems equilibration. Drug molecules were considered to be complexed if they were located at distances shorter than the radius of gyration of PAMAM-G4 and PEGPAMAM-G4 systems measured from the center of mass of the dendrimer core. 2.3. NMR experiments 2D-NOESY measurements were employed to examine the preferential binding sites for the supramolecular interaction between MTX and native and PEGylated PAMAM-G4 dendrimers. 2D-NOESY experiments were carried out using PEGylated systems with substitution degrees of 0%, 34% and 100%, which were synthesized as reported in our former work.6 An excess (1 mg) of MTX was added to 500 µL of dendrimer solutions [100.0 mmol L−1 in D2O] at pD 7.0. Solutions were shaken to reach the solubility equilibrium and analyzed on a Bruker Ascend TM 400 MHz spectrometer. 2D-NOESY spectra were acquired at 400.13 MHz using a 300 ms mixing time and 8.7 µs 1H 90° pulse width. Pre-saturation was applied during relaxation delay and mixing time (55 Hz). The experiments were carried out with a 1 s relaxation delay and 160 ms acquisition time. 160 transients were averaged for each 256 × 2,048 complex t1 increment. The data were processed with Lorentz–Gauss window function and zero filling in both dimensions.


8

Page 9 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3. Results and Discussion MD simulations were carried out to examine the association of MTX with native PAMAM-G4 and PEGylated counterparts with 25%, 50%, 75% and 100% substitution ratios. Additionally, a PEGylation percentage of 34% was studied, considering that this PEGylation ratio maximizes the drug-loading capacity of MTX in PEGylated PAMAM-G4 systems according to former experimental reports.6 MD simulations were performed on systems that mimicked experimental conditions of drug excess using 100:1 drug:dendrimer ratios in aqueous solution with explicit solvent. The initial structures of drug:dendrimer systems were built by randomly locating 100 MTX molecules around of one native or PEGylated PAMAM-G4 moiety within a spherical shell. After 50 ns of MD simulations the equilibrated structures of drug:dendrimer systems revealed the partial complexation of MTX molecules within PAMAM-G4 and PEG chains as exemplified in Figure 1. Analysis of equilibrated trajectories for MTX complexes with native and PEGylated PAMAM-G4 dendrimers was employed to test the predictive capability of MD simulations in reproducing the experimental trends of complex stroichiometry and preferential binding sites to provide a molecular interpretation about the favorable effect that partial PEGylation puts forth on the drug-loading capacity of PAMAM-G4 dendrimers over native and fully PEGylated systems. 3.1. Systems equilibration and complex stoichiometries Conformation and size equilibration of the systems under study during 50 ns of MD trajectories was assessed by means of RMSD and radius of gyration (Rg) calculations, which


9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 44

revealed that all systems reached equilibrium after 25 ns of production trajectory (Figure 2). The predicted Rg value for native PAMAM-G4 in complex with MTX (20 Å) is consistent with former experimental and theoretical reports dealing with the Rg of PAMAM-G4 thus accounting for the reproducibility of this property in our current simulation approach.38-41 Calculated Rg values for PEGylated counterparts indicate that these systems undergo a steady size expansion as the substitution degree becomes higher. Nevertheless, higher PEGylation ratios induce less pronounced size increases than lower substitution degrees, which can be a consequence of PEGshell adopting a more compact and dense structure as the PEGylation degree increases. The variation of Rg with the molar mass M for PEGylated systems follows a scaling relationship of the type Rg = Mα, where α=0.30, which reproduced the universal power law followed by non PEGylated systems as previously described in the literature (Figure S1 in Supporting information section).24 It is worth to note that no changes in the measured overall size and shape of native and PEGylated dendrimers were observed during MTX association, which can be a consequence of MTX accommodation within the supramolecular host through local structural changes as described earlier in the literature.42 MD trajectories were employed to calculate the number of complexed MTX molecules within native PAMAM-G4 and PEGylated systems to verify the equilibration of the associative behavior of the supramolecular complexes under study. MTX molecules were considered as part of a supramolecular complex if they remained at distances shorter or equal than Rg of the carrier system (PAMAM-G4 or PEG-PAMAM-G4) measured from the center of mass of the dendrimer core along the simulation run. Our results revealed that complex stoichiometries reached a maximum at 25 ns of simulation and remained in equilibrium during the second half of MD trajectories, which is reflected by the stabilization on the average number of complexed drug


10

Page 11 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


molecules (N) in the carrier systems, as displayed in Figure 3. Nevertheless, analysis of MD trajectories indicated that dynamic complexation equilibria were attained as revealed by the simultaneous entrance and release of drug molecules from the outermost branches of the dendritic host systems. Estimated average stoichiometries calculated from the last 25 ns of MD simulations are reported in Table 2. MD simulations predicted a drug:dendrimer complex stoichiometry of 20:1 for the MTX complex with native PAMAM-G4, which is in very good agreement with previous experimental reports by Jiang et al. (22:1)43 and Barraza et al. (19:1).13 In the case of the PEGylated dendrimers, average stoichiometries of 30:1, 42:1, 32:1, 30:1, and 19:1 were predicted for the systems with 25%, 34%, 50%, 75% and 100% of PEGylation, respectively. These results are consistent with the experimental trends obtained from aqueous solubility profiles, in which complex stoichiometries of 30:1, 47:1, 36:1, and 25:1 have been reported for systems with 28%, 34%, 67%, and 100% of PEGylation, respectively (Figure 4).13 According to these results, MD simulations succeeded in reproducing the experimental complex stoichiometry trends showing that partial PEGylation enhanced the drug-loading capacity of PAMAM-G4 over native and fully PEGylated systems. 3.2. Preferential binding sites A relevant aspect of drug-dendrimer interactions is the differential distribution of drug molecules within internal PAMAM branches and external PEG chains. In general, high internal complexation ratios are desirable to achieve low release rates for efficient drug delivery systems. Representative equilibrated structures of the MTX complexes with native and PEGylated PAMAM-G4 dendrimers are displayed in Figure 5, showing that associated MTX molecules are distributed from PAMAM-G4 internal cavities to the outermost PEG chains. MD trajectory


11


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 44

analysis was employed to discriminate between internally and externally complexed drug molecules using a geometric criteria based on the relative location of drug molecules respect to the center of mass of PAMAM-G4. Internally complexed drug molecules were considered to be located at distances shorter or equal than Rg of native PAMAM-G4 (20.0 Å), whereas externally complexed MTX molecules were considered to be located between 20.0 Å and Rg of the PEGylated system. According to our MD results, partial PEGylation at 25% and 34% increased the overall drug-loading capacity of PAMAM-G4, while retaining the amount of internally complexed drug molecules compared to the native dendrimer. On the other hand, higher PEGylation degrees shifted the drug complexation towards the more external PEG chains (Table 2). Theoretical predictions were compared with experimental information retrieved from 2DNOESY experiments recorded for MTX complexes with native and PEGylated PAMAM-G4 dendrimers with 0%, 34% and 100% PEGylation as shown in Figure 6. The presence of cross peaks in the NOESY spectra between 2.2-3.2 ppm is indicative of the supramolecular interaction (≤ 5Å) between PAMAM branches and MTX molecules. The relative intensity of the cross peaks within the set of spectra indicates that increasing PEGylation decreases the proportion of internally complexed MTX molecules. On the other hand, cross peaks between 3.4-4.2 ppm correspond to the supramolecular interaction between PEG chains and drug molecules. In this case, the highest intensity of cross peaks was found for the fully PEGylated system suggesting that the association of MTX molecules with the carrier occurs preferably within outermost PEG chains. Radial distribution functions (RDF) obtained from MD simulations were attached to the 2D-NOESY plots to further illustrate the preferential distribution of drug molecules within PAMAM-G4 and PEG branches predicted from MD simulations. A peak in a RDF plot indicates


12

Page 13 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the distance from the center of mass of PAMAM-G4 at which drug atoms remain in a fixed position along the simulation run. In consistency with 2D-NOESY spectra, MD simulations predict that partial PEGylation results in the simultaneous complexation of MTX within dendrimer branches and external PEG chains, whereas full PEGylation leads to a preferential distribution of drug molecules within surface PEG chains in detriment to internal dendrimer complexation. The reduced internal complexation capacity of the fully PEGylated system can be a consequence of the high surface density of PEG chains, which restricts the diffusion of drug molecules towards PAMAM innermost cavities. PEG chains crowding has been previously discussed in the literature as a detrimental factor for drug complexation in highly PEGylated systems and is expected to play a relevant role in determining the drug-loading capacity of PEGylated PAMAM dendrimers.7, 13, 24, 44 A relevant phenomena observed in the supramolecular interaction between MTX and the PEGylated systems under study is the existence of PEG chains back-folding, as revealed by the self-penetration of external PEG chains into PAMAM-G4 dendrimer cavities during the MD simulation run.44 Radial distribution profiles g(r) indicate that PEG chains are able to penetrate dendrimer branches and participate in the cooperative complexation of drug molecules within PAMAM-G4 (Figure 7). Back-folding is also expected to be beneficial for the controlled release of the drug from the supramolecular complex, which is a favorable aspect for drug delivery purposes. The comparison between g(r) profiles for PEGylated PAMAM-G4 systems in MTX complexes and in the absence of the ligand (Figure 7) revealed that PEG back-folding is enhanced after MTX complexation, which is a valuable result to understand the role of PEGylation on determining the complexation properties of PEGylated PAMAM-G4 systems.


13


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 44

According to our results, substantial PEG back-folding is triggered by complexation of the drug in PEGylated systems with 25%, 34% and 50% substitution degrees, whereas higher PEGylation ratios lead to reduced PEG back-folding and a negligible effect of drug complexation on PEG chains distribution (Figure S2 in Supporting Information). Regarding to non-complexed MTX molecules, MD simulations revealed the formation of bimolecular MTX aggregates through the formation of pi-pi stacking interactions with distances between the ring centroids lesser than 4.2 Å. The self-association of MTX molecules is consistent with previous investigations on the behavior of carboxylic acids, purines, and pyrimidines in aqueous solution at neutral pH (Supplementary Information Section).29 3.3. Drug-dendrimer interactions MD trajectories were employed to retrieve quantitative information about the driving forces involved in the association of MTX with native and PEGylated PAMAM-G4 systems. Understanding the details of these interactions is relevant for designing and optimizing novel PAMAM-based system with customized affinity with drug molecules. In this work, drugdendrimer interactions were addressed from two perspectives, namely the calculation of interaction energies and the identification of the specific chemical moieties involved in the supramolecular association of the guest with native and PEGylated dendrimers. Average energy terms corresponding to van der Waals and electrostatic interactions normalized by the average number of drug molecules interacting with PAMAM-G4 branches and PEG chains are reported in Table 3. Our results reveal that electrostatic forces govern the intermolecular interaction between MTX and native PAMAM-G4. These forces are progressively lost as the number of charged surface primary amines diminishes due to PEGylation. In the case of PEG chains, similar contributions of electrostatic and van der Waals


14

Page 15 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


interactions are involved in the association with MTX. The overall calculated binding energies suggest that MTX molecules have more affinity towards PAMAM branches over external PEG chains. Therefore, the preferential PEG-complexation of drug molecules in the fully PEGylated system can be attributed to the steric hindrance produced the high density of PEG chains in the dendrimer periphery, which restricts the diffusion of MTX towards the innermost PAMAM cavities. Additionally, we have examined the formation of intermolecular hydrogen bonds in the supramolecular systems under study, considering heavy donor−acceptor distances shorter than 3.2 Å and donor−hydrogen−acceptor bond angles larger than 120°. Our results reveal that PAMAM branches can act as hydrogen donors in specific interactions involving the γcarboxylate oxygen atoms of MTX and (A) the primary amide groups of third-generation branches, (B) the primary amide groups of fourth-generation branches, and (C) the terminal ammonium surface groups, with average distances of 2.7-2.8 Å, as displayed in Figure 8. Additionally, the amino groups attached to the pyrimidine ring of MTX can act as hydrogen donors in hydrogen bonding interactions with (D) PAMAM carbonyl oxygens of the fourthgeneration branches, and (E) PEG ether oxygen atoms, with average distances of 2.8-3.0 Å (Figure 8). Further details about hydrogen-bonding occupancies in MTX complexes with native and PEGylated PAMAM systems are provided in Table S1 (Supporting Information section).

4. Conclusions Fully-atomistic MD simulations were carried out to elucidate the molecular details of the supramolecular association of MTX with native and PEGylated PAMAM-G4 dendrimers. Predicted stoichiometries are consistent with experimental data and account for the positive


15


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 44

effect that partial PEGylation (< 50%) exerts on the drug-loading capacity of PAMAM dendrimer over full PEGylation. MD simulations suggested that partial PEGylation allows the simultaneous complexation of the drug in both internal dendrimer branches and external PEG chains. Additionally, equilibrated MD trajectories revealed that internal complexation in systems with PEGylation degrees < 50% was assisted by back-folded PEG chains that penetrated dendrimer cavities and participated in cooperative interactions with MTX and PAMAM-G4 moieties. In the case of full PEGylation, MD simulations revealed a preferential distribution of drug molecules within outermost PEG chains over internal PAMAM-G4 cavities. This is a result of the restricted diffusion of drug molecules towards more internal dendrimer branches due to PEG chains crowding on the dendrimer surface. These results are valuable to enlarge understanding about the molecular details of the supramolecular complexation of drug molecules with PEGylated PAMAM dendrimers and provide a structural support to guide the future design and optimization of PAMAM-based drug delivery systems.


16

Page 17 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1. Initial and final structures of MTX complexes with 34% PEG-PAMAM-G4 systems.


17


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 44

Figure 2. Time evolution of RMSD (Å), radius of gyration Rg (Å) for native and PEGylated PAMAM-G4 dendrimers in complex with MTX obtained from 50 ns fully atomistic molecular dynamics simulations


18

Page 19 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3. Number of complexed MTX molecules (N) as a function of time for MTX complexes with native and PEGylated PAMAM-G4 dendrimers


19


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 44

Figure 4. Comparison of experimental and theoretical predictions regarding the average number of complexed drug molecules (N) obtained for MTX complexes with native and PEGylated PAMAM-G4 dendrimers


20

Page 21 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5. Representative structures of MTX complexes with native and PEGylated PAMAM-G4 systems. The internal association, external complexation and aggregation in solution of MTX molecules is detailed for the 34% PEGylated system


21


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 44

Figure 6. 2D-NOESY spectra and radial distribution functions for MTX molecules in complex with PAMAM-G4, 34% PEG-PAMAM-G4, and 100% PEG-PAMAM-G4. Rg, Rg' and Rg'' represent the radius of gyration of PAMAM-G4, 34% PEG-PAMAM-G4 and 100% PEGPAMAM-G4 respectively.


22

Page 23 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7. Back-folding of PEG chains in the 34% PEGylated PAMAM-G4 system. PAMAMG4 (silver), external PEG chains (orange), back-folded PEG chains (cyan).


23


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 44

Figure 8. Schematic representation for hydrogen-bonding interactions between carriers and drug molecules along the last 25 ns of MD simulations. Details are provided in the text.


24

Page 25 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1. Details of the simulated systems.

Number of atoms (without waters)

Number of water molecules

Water box volume (×10-6 Å3)

Dendrimer charge

Number of Na+

MTX:PAMAM-G4

5700

158057

4.97

64

136

MTX: 25% PEG-PAMAM-G4

12728

181603

5.33

48

152

MTX:34%PEG-PAMAM-G4

14648

179512

5.38

42

158

MTX:50%PEG-PAMAM-G4

17848

178299

5.42

32

168

MTX:75%PEG-PAMAM-G4

22968

176190

5.44

16

184

MTX:100% PEG-PAMAM-G4

28088

171483

5.46

0

200

System


25


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 44

Table 2. Estimated complex stoichiometries for drug-dendrimer complexes formed by MTX with native and PEGylated PAMAM-G4 dendrimers, from the analysis of MD trajectories during the last 25 ns of simulation.

Externally complexed MTX

System

Average stoichiometry

Internally complexed MTX

MTX:PAMAM-G4

20 : 1

12 ± 1

8±3


30 : 1

13 ± 1

17 ± 2

30:113*


42 : 1

12 ± 1

30 ± 2

47:1


32 : 1

9±1

23 ± 2

-


26 : 1

4±1

22 ± 3

-


19 : 1

1.0 ± 0.3

18 ± 3

26:124 ; 25:113

Experimental 21:143 ; 19:113

* Experimental stoichiometry corresponds to a system with 28% of PEGylation


26

Page 27 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3. Average normalized interaction energies for MTX complexes with native and PEGylated PAMAM-G4 systems, obtained from the last 25 ns of MD simulations. The van der Waals (EvdW) and electrostatic (Eelec) interaction energies are reported in kcal mol-1.

System

MTX-PAMAM interaction (kcal mol-1)

MTX-PEG interaction (kcal mol-1)

EvdW

Eelec

EvdW

Eelec

MTX:PAMAM-G4

-15 ± 2

-42 ± 4

-

-

MTX:25%PEG-PAMAM-G4

-17 ± 1

-32 ± 4

-9 ± 1

-10 ± 2

MTX:34%PEG-PAMAM-G4

-18 ± 2

-26 ± 3

-8 ± 1

9±2

MTX:50%PEG-PAMAM-G4

-17 ± 1

-21 ± 3

-12 ± 1

-10 ± 1

MTX:75%PEG-PAMAM-G4

-17 ± 1

-13 ± 3

-13 ± 1

-13 ± 2

MTX:100%PEG-PAMAM-G4

-17 ± 2

-7 ± 2

-13 ± 1

-15 ± 3


27


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 44

ASSOCIATED CONTENT Supporting Information. Details of the simulated systems and hydrogen bonds formed in drug:dendrimer complexes. This material is available free of charge via the Internet at http://pubs.acs.org.” AUTHOR INFORMATION Corresponding Author *Verónica A. Jiménez. Departamento de Ciencias Químicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Sede Concepcion. Autopista Concepción-Talcahuano 7100, Talcahuano, Chile. E-mail: [email protected] *Joel B. Alderete. Departamento de Química Orgánica, Facultad de Ciencias Químicas, Universidad de Concepción. Casilla 160-C, Concepción, Chile. E-mail: [email protected]. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources FONDECYT Grant numbers 1130531 and 1120250. ACKNOWLEDGMENT Authors thank FONDECYT Grant numbers 1130531 and 1120250. ABBREVIATIONS PAMAM Poly(amidoamine); PEG polyethylene glycol; MD molecular dynamics.


28

Page 29 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


REFERENCES 1.

Tomalia, D. A.; Baker, H.; Dewald, J.; Hall, M.; Kallos, G.; Martin, S.; Roeck, J.; Ryder, J.; Smith, P., A New Class of Polymers: Starburst-Dendritic Macromolecules. Polym. J. 1985, 17, 117-132.

2.

Svenson, S., Dendrimers as Versatile Platform in Drug Delivery Applications. European J. Pharm. Biopharm. 2009, 71, 445-462.

3.

Medina, S. H.; El-Sayed, M. E. H., Dendrimers as Carriers for Delivery of Chemotherapeutic Agents. Chem. Rev. 2009, 109, 3141-3157.

4.

Jain, V.; Bharatam, P. V., Pharmacoinformatic Approaches to Understand Complexation of Dendrimeric Nanoparticles with Drugs. Nanoscale 2014, 6, 2476-2501.

5.

Boas, U.; Heegaard, P. M. H., Dendrimers in Drug Research. Chem. Soc. Rev. 2004, 33, 43-63.

6.

Kojima, C.; Kono, K.; Maruyama, K.; Takagishi, T., Synthesis of Polyamidoamine Dendrimers Having Poly(ethylene glycol) Grafts and their Ability to Encapsulate Anticancer Drugs. Bioconjugate Chem. 2000, 11, 910-917.

7.

Kim, Y.; Klutz, A. M.; Jacobson, K. A., Systematic Investigation of Polyamidoamine Dendrimers Surface-Modified with Poly(ethylene glycol) for Drug Delivery Applications: Synthesis, Characterization, and Evaluation of Cytotoxicity. Bioconjugate Chem. 2008, 19 , 1660-1672.

8.

Bhadra, D.; Bhadra, S.; Jain, S.; Jain, N. K., A PEGylated Dendritic Nanoparticulate Carrier of Fluorouracil. Int. J. Pharm. 2003, 257, 111-124.


29


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

9.

Page 30 of 44

Shen, M.; Huang, Y. Z.; Han, L. M.; Qin, J.; Fang, X. L.; Wang, J. X.; Yang, V. C., Multifunctional

Drug

Delivery System

for Targeting Tumor

and

its

Acidic

Microenvironment. J. Control. Release 2012, 161, 884-892. 10.

Thakur, S.; Kesharwani, P.; Tekade, R. K.; Jain, N. K., Impact of Pegylation on Biopharmaceutical Properties of Dendrimers. Polymer 2015, 59, 67-92.

11.

Ma, Q.; Han, Y. C.; Chen, C.; Cao, Y. N.; Wang, S. L.; Shen, W. W.; Zhang, H. Y.; Li, Y. Z.; van Dongen, M. A.; He, B. et. al., Oral Absorption Enhancement of Probucol by PEGylated G5 PAMAM Dendrimer Modified Nanoliposomes. Mol. Pharmaceut. 2015, 12, 665-674.

12.

Liao, H. H.; Liu, H.; Li, Y. L.; Zhang, M. G.; Tomas, H.; Shen, M. W.; Shi, X. Y., Antitumor Efficacy of Doxorubicin Encapsulated Within PEGylated Poly(amidoamine) Dendrimers. J. Appl. Polym. Sci. 2014, 131, 40358.

13.

Barraza, L. F.; Jiménez, V. A.; Alderete, J. B., Methotrexate Complexation with Native and PEGylated PAMAM-G4: Effect of the PEGylation Degree on the Drug Loading Capacity and Release Kinetics. Macromol. Chem. Phys. 2016, 217, 605-613.

14.

Tanis, I.; Karatasos, K., Association of a Weakly Acidic Anti-Inflammatory Drug (Ibuprofen) with a Poly(Amidoamine) Dendrimer as Studied by Molecular Dynamics Simulations. J. Phys. Chem. B 2009, 113, 10984-10993.

15.

Maiti, P. K.; Bagchi, B., Diffusion of Flexible, Charged, Nanoscopic Molecules in Solution: Size and pH Dependence for PAMAM Dendrimer. J. Chem. Phys. 2009, 131, 214901.

16.

Barra, P. A.; Barraza, L.; Jiménez, V. A.; Gavín, J. A.; Alderete, J. B., Complexation of Mefenamic Acid by Low-Generation PAMAM Dendrimers: Insight from NMR


30

Page 31 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Spectroscopy Studies and Molecular Dynamics Simulations. Macromol. Chem. Phys. 2014, 215, 372-383. 17.

Barra, P.; Barraza, L.; Jiménez, V.; Gavin, J.; Alderete, J., Drug-Dendrimer Supramolecular Complexation Studied From Molecular Dynamics Simulations and NMR Spectroscopy. Struct. Chem. 2014, 25, 1443-1455.

18.

Porcar, L.; Liu, Y.; Verduzco, R.; Hong, K. L.; Butler, P. D.; Magid, L. J.; Smith, G. S.; Chen, W. R., Structural Investigation of PAMAM Dendrimers in Aqueous Solutions Using Small-Angle Neutron Scattering: Effect of Generation. J. Phys. Chem. B 2008, 112, 1477214778.

19.

Paulo, P. M. R.; Lopes, J. N. C.; Costa, S. M. B., Molecular Dynamics Simulations of Charged Dendrimers: Low-to-Intermediate Half-Generation PAMAMs. J. Phys. Chem. B 2007, 111, 10651-10664.

20.

Chong, L.; Aydin, F.; Dutt, M., Implicit Solvent Coarse-Grained Model of Polyamidoamine Dendrimers: Role of Generation and pH. J. Comput. Chem. 2016, 37, 920-926.

21.

De Luca, S.; Seal, P.; Ouyang, D. F.; Parekh, H. S.; Kannam, S. K.; Smith, S. C., Dynamical Interactions of 5-Fluorouracil Drug with Dendritic Peptide Vectors: The Impact of Dendrimer Generation, Charge, Counterions, and Structured Water. J. Phys. Chem. B 2016, 120, 5732-5743.

22.

Freire, J. J.; Rubio, A. M.; McBride, C., Coarse-Grained and Atomistic Simulations for the G=4 PAMAM-EDA Dendrimer. Macromol. Theory Simul. 2015, 24, 432-441.


31


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

23.

Page 32 of 44

Yang, L.; da Rocha, S. R. P., PEGylated, NH2-Terminated PAMAM Dendrimers: A Microscopic View From Atomistic Computer Simulations. Mol. Pharmaceut. 2014, 11, 1459-1470.

24.

Barraza, L. F.; Jiménez, V. A.; Alderete, J. B., Effect of PEGylation on the Structure and Drug Loading Capacity of PAMAM-G4 Dendrimers: A Molecular Modeling Approach on the Complexation of 5-Fluorouracil with Native and PEGylated PAMAM-G4. Macromol. Chem. Phys. 2015, 216, 1689-1701.

25.

Jain, V.; Maiti, P. K.; Bharatam, P. V., Atomic Level Insights Into Realistic Molecular Models of Dendrimer-Drug Complexes Through MD Simulations. J. Chem. Phys. 2016, 145, 15.

26.

Cakara, D.; Kleimann, J.; Borkovec, M., Microscopic Protonation Equilibria of Poly(amidoamine) Dendrimers From Macroscopic Titrations. Macromolecules 2003, 36, 4201-4207.

27.

Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, Gaussian, Inc.: Wallingford, CT, USA, 2009.

28.

Meloun, M.; Ferencikova, Z.; Vrana, A., The Thermodynamic Dissociation Constants of Methotrexate by the Nonlinear Regression and Factor Analysis of Multiwavelength Spectrophotometric pH-Titration Data. Cent. Eur. J. Chem. 2010, 8, 494-507.

29.

Poe, M., Acidic Dissociation Constants of Folic Acid, Dihydrofolic Acid, and Methotrexate. J. Biol. Chem. 1977, 252, 3724-8.


32

Page 33 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


30.

Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L., Comparison of Simple Potential Functions for Simulating Liquid Water. J. Chem. Phys. 1983, 79, 926-935.

31.

Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kale, L.; Schulten, K., Scalable Molecular Dynamics with NAMD. J. Comput. Chem. 2005, 26, 1781-1802.

32.

MacKerell, A. D.; Bashford, D.; Bellott, M.; Dunbrack, R. L.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S. et. al., All-Atom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins. J. Phys. Chem. B 1998, 102, 3586-3616.

33.

Lee, H.; Venable, R. M.; MacKerell, A. D., Jr.; Pastor, R. W., Molecular Dynamics Studies of Polyethylene Oxide and Polyethylene Glycol: Hydrodynamic Radius and Shape Anisotropy. Biophys. J. 2008, 95, 1590-1599.

34.

Zoete, V.; Cuendet, M. A.; Grosdidier, A.; Michielin, O., SwissParam: A Fast Force Field Generation Tool for Small Organic Molecules. J. Comput. Chem. 2011, 32, 2359-2368.

35.

Feller, S. E.; Zhang, Y. H.; Pastor, R. W.; Brooks, B. R., Constant-Pressure MolecularDynamics Simulation - The Langevin Piston Method. J. Chem. Phys. 1995, 103, 46134621.

36.

Darden, T.; York, D.; Pedersen, L., Particle Mesh Ewald - an n.log(n) Method for Ewald Sums in Large Systems. J. Chem. Phys. 1993, 98, 10089-10092.

37.

Humphrey, W.; Dalke, A.; Schulten, K., VMD: Visual Molecular Dynamics. J. Mol. Graph. Model. 1996, 14, 33-38.

38.

Maiti, P. K.; Çaǧın, T.; Lin, S.-T.; Goddard, W. A., Effect of Solvent and pH on the Structure of PAMAM Dendrimers. Macromolecules 2005, 38, 979-991.


33


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

39.

Page 34 of 44

Maiti, P. K.; Çaǧın, T.; Wang, G.; Goddard, W. A., Structure of PAMAM Dendrimers: Generations 1 through 11. Macromolecules 2004, 37, 6236-6254.

40.

Chen, W.-R.; Porcar, L.; Liu, Y.; Butler, P. D.; Magid, L. J., Small Angle Neutron Scattering Studies of the Counterion Effects on the Molecular Conformation and Structure of Charged G4 PAMAM Dendrimers in Aqueous Solutions. Macromolecules 2007, 40, 5887-5898.

41.

Porcar, L.; Hong, K.; Butler, P. D.; Herwig, K. W.; Smith, G. S.; Liu, Y.; Chen, W.-R., Intramolecular Structural Change of PAMAM Dendrimers in Aqueous Solutions Revealed by Small-Angle Neutron Scattering. J. Phys. Chem. B 2010, 114, 1751-1756.

42.

DeFever, R. S.; Sarupria, S., Association of Small Aromatic Molecules with PAMAM Dendrimers. Phys. Chem. Chem. Phys. 2015, 17, 29548-29557.

43.

Jiang, Y.-Y.; Tang, G.-T.; Zhang, L.-H.; Kong, S.-Y.; Zhu, S.-J.; Pei, Y.-Y., PEGylated PAMAM Dendrimers as a Potential Drug Delivery Carrier: in Vitro and in Vivo Comparative Evaluation of Covalently Conjugated Drug and Noncovalent Drug Inclusion Complex. J. Drug Target. 2010, 18, 389-403.

44.

Lee, H.; Larson, R. G., Effects of PEGylation on the Size and Internal Structure of Dendrimers: Self-Penetration of Long PEG Chains into the Dendrimer Core. Macromolecules 2011, 44, 2291-2298.


34

Page 35 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Insert Table of Contents Graphic and Synopsis Here


35


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1. Initial and final structures of MTX complexes with 34% PEG-PAMAM-G4 systems 170x80mm (300 x 300 DPI)


Page 36 of 44

Page 37 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2. Time evolution of RMSD (Å), radius of gyration Rg (Å) for native and PEGylated PAMAM-G4 dendrimers in complex with MTX obtained from 50 ns fully atomistic molecular dynamics simulations 85x125mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3. Number of complexed MTX molecules (N) as a function of time for MTX complexes with native and PEGylated PAMAM-G4 dendrimers 109x80mm (300 x 300 DPI)


Page 38 of 44

Page 39 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. Comparison of experimental and theoretical predictions regarding the average number of complexed drug molecules (N) obtained for MTX complexes with native and PEGylated PAMAM-G4 dendrimers 83x83mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 5. Representative structures of MTX complexes with native and PEGylated PAMAM-G4 systems. The internal association, external complexation and aggregation in solution of MTX molecules is detailed for the 34% PEGylated system 170x109mm (300 x 300 DPI)


Page 40 of 44

Page 41 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6: 2D-NOESY spectra and radial distribution functions for MTX molecules in complex with PAMAM-G4, 34% PEG-PAMAM-G4, and 100% PEG-PAMAM-G4. Rg, Rg' and Rg'' represent the radius of gyration of PAMAM-G4, 34% PEG-PAMAM-G4 and 100% PEG-PAMAM-G4 respectively 170x210mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 7. Back-folding of PEG chains in the 34% PEGylated PAMAM-G4 system. PAMAM-G4 (silver), external PEG chains (orange), back-folded PEG chains (cyan) 160x80mm (300 x 300 DPI)


Page 42 of 44

Page 43 of 44

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 8. Schematic representation for hydrogen-bonding interactions between carriers and drug molecules along the last 25 ns of MD simulations. Details are provided in the text 160x65mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table of contents graphics 50x39mm (300 x 300 DPI)


Page 44 of 44

Association of Methotrexate with Native and PEGylated PAMAM-G4

Recommend Documents