Binding and conformation of dendrimer-based drug delivery systems: a molecular dynamics study

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1 Adv. Manuf. (2015) 3: DOI /s Binding and conformation of dendrimer-based drug delivery systems: a molecular dynamics study Fa-Da Zhang 1,2,3 Yi Liu 1,2 Jing-Cheng Xu 2 Sheng-Juan Li 2 Xiu-Nan Wang 2,3 Yue Sun 2 Xin-Luo Zhao 1 Received: 15 May 2015 / Accepted: 16 August 2015 / Published online: 22 September 2015 Shanghai University and Springer-Verlag Berlin Heidelberg 2015 Abstract All atomistic molecular dynamics simulations were performed on poly (amidoamine) (PAMAM) dendrimers that compound non-covalently with anticancer drug molecules including DOX, MTX, CE6, and SN38. The binding energies as well as their associated interaction energies and deformation energies were combined to evaluate the relative binding strength among drug, PAMAM, and PEG chains. We find that the deformation of dendrimers due to drug loading plays a crucial role in the drug binding. It is energetically favorable for the drug molecules to bind with PAMAM while the drugs bind with PEG metastable chains via kinetic confinement. Surface PEGylation helps dendrimers to accommodate more drug molecules with greater strength without inducing too much expansion. This work indicates that tuning the functionalized terminal groups of dendrimers is critical to design efficient dendrimer-based drug delivery systems. Electronic supplementary material The online version of this article (doi: /s ) contains supplementary material, which is available to authorized users. & Yi Liu YiLiu@shu.edu.cn & Jing-Cheng Xu jchxu@usst.edu.cn Department of Physics and Materials Genome Institute, Shanghai University, Shanghai , P. R. China School of Materials Science and Engineering, University of Shanghai for Science and Technology, Shanghai , P. R. China School of Energy & Power Engineering, University of Shanghai for Science and Technology, Shanghai , P. R. China Keywords Dendrimer PAMAM PEGylation Anticancer drug Drug delivery systems Molecular dynamics 1 Introduction Dendrimers are dendritic polymers consisting of core, branch, and terminal groups where each branch layer is called generation (G) [1 3]. The architecture of dendrimers with hollow interior spaces allows their applications as potential nanoplatforms for drug delivery [4, 5]. Dendrimers help to improve solubility and pharmaceutical kinetics. Furthermore, dendrimer nanoplatform can be decorated with targeted functional groups and/or imaging agents for targeted therapy and molecular diagnosis [6 9]. Poly (amidoamine) (PAMAM) dendrimers are the first commercialized dendrimer family synthesized by Esfand and Tomalia [10]. PAMAM consists of a series of highly dendritic macromolecules with typical molecular weights kg/mol (G0-G10). PAMAM consists of three basic parts with various functions. Firstly, the internal core leads to the differences in symmetry and has the electrostatic interactions with the dendritic repeated layers [11]. Secondly, the middle repetitive units can provide hollow spaces to encapsulate drug molecules. The middle parts are distinguished by the same concentric circles determined by the repetitive units as generation [12] (see Fig. 1), e.g., G0, G1, G2,,Gn are defined from the central core to the peripheral surface. The diameters of PAMAM dendrimers have approximately linear correlation with the generation of the dendrimers [13, 14]. Thirdly, the external surface terminated with amine groups can compound with various guest molecules, such as drugs, genetic materials, fluorescent molecules, and HBVc (FA, etc.) [15 18]. The primary

2 222 F.-D. Zhang et al. the PEGylation. We load four types of anticancer drugs, including CE6, DOX, MTX, and SN38, respectively, gradually to saturated doses. In this work we address the issues of the binding strength and locations of the drug molecules as well as the sizes of complexes via the analyses of the binding energy (E b ) of drug molecules incorporated into dendrimers, the distribution of drug molecules, and the radius of gyration (R g ). 2 Computation methods 2.1 Computation models and simulation procedures Fig. 1 Schematic molecular structure of PAMAM G2 dendrimer amino groups on the surfaces of PAMAM can be modified by different functional groups to be used as a multifunctional vector molecule in drug delivery systems [19 22]. However, the charged surface groups may destroy the structures of cell membranes and induce the hemolysis of human red blood cells. Wang et al. [23] modified the surface of dendrimers with poly (ethylene glycol) (PEG) to reduce the cytotoxicity of dendrimers significantly. The PEGylation of the denrimer can also improve the aqueous solubility and circulation time in blood system of human body [24 26]. Many anticancer drugs (such as CE6, DOX, MTX, and SN38) are limited in clinical use due to their poor solubility and biocompatibility [27, 28]. It is shown that the dendrimer-based drug-delivery systems can improve drug s solubility and biocompatibility, realizing the targeted delivery and the controlled release of drugs [13, 29]. The influence of ph environment of human body can release the drugs carried in dendrimers in a controlled manner [30, 31]. In dendrimer-based drug delivery systems, drug molecules can either bind covalently with dendrimers to form dendrimer-drug conjugates or incorporate non-covalently into dendrimers to form complexes [32]. In drug@dendrimer complex, drug molecules can be released more readily than conjugated system. On the other hand, it is not desirable if dendrimers release drugs too soon before reaching targeted cells [33]. Therefore, it is critical to understand the binding mechanisms of drug@dendrimer complex including binding strength and binding sites as well as the effects of surface functionalization. This work focuses on how binding strength and conformation vary with the number of loaded drug molecules. In order to understand the mechanism of the interaction between the drug molecules and dendrimers at an atomic level, we carried out all-atom classical molecular dynamics (MD) simulations to study the dendrimers with and without To study the influences of PEGylation of dendrimers as well as the types and numbers of drug molecules, we built full atomic models of non-covalently bound drug-dendrimer complexes, denoted as D (or D and D (or D respectively, for the dendrimers of generations G0 G3 with and without surface PEGylation. In the case of PEGylation, each terminal group binds covalently with a single PEG chain with atomic weight * D N represents drug molecules among one of the four types: CE6, DOX, MTX, and SN38, where N (0,1,2,4, ) is the number of drug molecules that compound with PAMAM. The drug@dendrimer complexes were first relaxed by geometry optimization (GO), followed by MD at the NVT ensemble at 298 K in vacuum. To examine the solvent effects, some systems, e.g., D and D were simulated in water solutions using MD at the NPT and NVT ensembles after geometry optimization. Four types of anticancer drug molecules were studied in this work: Chlorin e6 (CE6, C 34 H 36 N 4 O 6,M= 596), Doxorubicin (DOX, C 27 H 29 NO 11, M = 543), Methotrexate (MTX, C 20 H 22 N 8 O 5,M= 454) and 7-ethyl-10-hydroxycampothecin (SN38, C 22 H 20 N 2 O 5, M = 392). The dendrimers G0(C 22 H 48 N 10 O 4,M= 516), G1(C 62 H 128 N 26 O 12, M = 1 428), G2(C 142 H 288 N 58 O 28, M = 3 252) and G3(C 302 H 608 N 122 O 60,M= 6 900) were built using dendrimer module in materials studio (MS) software package. The charges of the dendrimers and drugs were assigned by Gasteiger method. And they were electrically neutral as a whole. The PEG (C 90 H 182 O 45, M = 1 982) chain was covalently bonded with the primary amine groups on the surface of dendrimer to build G0-PEG, G1-PEG, G2-PEG and G3-PEG. Then we added drug molecules to the hollow spaces of PAMAM to form the D complex. To study the influence of solvation, we built the periodic cubic cell structure with a number of drug molecules carried in various generations of dendrimer where the distances between the adjacent complexes are 1 nm. H 2 O molecules were added by amorphous cell module of MS. The density of

3 Binding and conformation of dendrimer-based drug delivery systems: a molecular dynamics study 223 H 2 O was 1.0 g/cm 3. The CE6 DOX PEG, CE6 and DOX complex systems have 7 870, 8 704, and H 2 O molecules, respectively. In this work we used the classical MD simulation software (forcite module implemented in MS [34]) to execute the GO and MD calculations. We used the Dreiding force field in both GO and MD computations [35]. The convergence tolerance of the energy and force in GO is J/mol and 41.8 J/(mol nm), respectively. The NPT MD was executed at 298 K and Pa, followed by NVT MD runs at 298 K for 1 ns. The other details of the MD simulation conditions are set as follows. (1) Dynamics parameters: in the NPT and NVT ensemble we use the thermostat (nose) to keep the target temperature equal to 298 K. The time step is 1.0 fs and the total simulation time is 1 ns. (2) Energy parameters: we use Dreiding force field to calculate the electrostatic, van der Waals and Hydrogen bond force. For these three long-range force terms, the cut-off of the distances are 1.55 nm, 1.55 nm and 0.45 nm, spline widths are 0.1 nm, 0.1 nm and 0.05 nm, respectively. The buffer widths are 0.05 nm and truncation methods are cubic spline. After equilibrium is reached, the last 0.5 ns in the MD trajectories was used for statistical analyses. 2.2 Definitions of binding energy and its associated components To evaluate binding strength quantitatively, we calculated binding energy and its associated components including interaction energy and deformation energy. The relationships among these energies can be written E b PD ¼ E i PD þ E d P þ E di D ; ð1þ where E b-pd is the instantaneous binding energy of drug molecules and PAMAM of the last snapshot of NVT MD; E i-pd is the instantaneous interaction energy of PAMAM and drug molecules; E d-p is the instantaneous deformation energy of PAMAM; E di-d is the instantaneous deformationand-interaction energy of drug molecules. These energy components are defined in Eqs. (2) (6) Binding energy of D complex E b ¼ ðe P D NE D E P Þ=N; ð2þ where E b is the average binding energy of D complex; E P-D is the total energy of D complex averaged over equilibrium MD trajectories; E D and E P are the total energies of an isolated drug molecule and PAMAM averaged over equilibrium MD trajectories, respectively; N is the number of drug molecules Instantaneous binding energy of D complex E b PD ¼ ðe 1 PD NE D E P Þ=N; ð3þ where E 1-PD is the single-point energy of D complex based on a single snapshot structure Instantaneous interaction energy between PAMAM and drug molecules in D complex E i PD ¼ ðe 1 PD E 1 D E 1 P Þ=N; ð4þ where E 1-D is the single-point energy of all drug molecules as a whole; E 1-P is the single-point energy of PAMAM Deformation energy of PAMAM in D complex E d P ¼ ðe 1 P E P Þ=N: ð5þ Deformation-and-interaction energy of drug molecules in D complex E di D ¼ ðe 1 D NE D Þ=N: ð6þ The binding energy (E b-pd ) defined in Eq. (3) is obtained based on the energy difference between thermodynamic equilibrium structures and often involves the deformation energies, while the instantaneous interaction energy (E i-pd ) defined in Eq. (4) is calculated as the difference of singlepoint energies of the frozen snapshot structures so that pure interaction of drug-pamam can be evaluated alone. Therefore, both the binding energy and interaction energy are used in this work to understand the drug-dendrimer bindings from different points of views. The deformation energy (E d-p ) defined in Eq. (5) measures the energy change of PAMAM structures caused by deformation with respective to the corresponding equilibrium MD structures. The deformation-and-interaction energy of drug molecules (E di-d ) defined in Eq. (6) evaluates the energy changes caused by both the deformation of drugs and the interactions among drug molecules. 2.3 Radius of gyration R g represents the size of D complex, defined as follows * + D E R 2 g ¼ 1 X N m i jr i Rj 2 ; ð7þ M i¼1 where M is the mass of the whole complex, m i the mass of an atom i, r i the position of an atom i, and R the center of mass of the complex [36].\[ refers to average value in a NVT ensemble (T = 298 K).

4 224 F.-D. Zhang et al. Fig. 2 Binding energy E b of a single drug molecule loaded into G3 at 36 different binding sites in a CE6 b DOX c MTX and d SN Diffusion coefficient of D complex in water 1 D E D ¼ lim jr i ðþ r t i ð0þj 2 ; ð8þ t!1 6t where D is the total diffusion coefficient of the drug-dendrimer complex; r i (t) and r i (0) stand for the position at time t and 0, respectively. The coordinates of the last 500 ps in MD trajectories were used when the systems reached equilibrium in NVT simulations. 3 Results and discussions 3.1 Binding energy Binding energy (E b ), defined in Eq. (2), measures the binding strength of dendrimer-drug complex including the interaction energies of drug-dendrimer and drug-drug (if any) as well as the deformation energies of drug and dendrimers. Smaller E b with larger absolute value means stronger binding. When a single drug molecule is loaded into PAMAM or PAMAM-PEG, the E b scatters at various binding positions (see Figs. 2 and 3). The average E b of the studied drug molecules decreases as DOX (( ± 3.09) J/mol) & CE6 (( ± 3.17) J/mol) [ MTX (( ± 2.16) J/mol) & SN38 (( ± 3.16) J/mol) in the D complexes. The negative E b indicates that it is energetically favorable to incorporate these drug molecules into PAMAM. The standard deviations of E b are * 20% around their averaged value indicating the large site dependence of binding energy. Considering both interaction energy and deformation energy (confirmed later in Fig. 5 when N is small), we find that the interaction energy between PAMAM and drug is larger than the deformation energy of PAMAM leading to overall attractive PAMAMdrug interactions. This indicates that PAMAM-drug interactions are stronger than the intramolecular interactions among PAMAM branches. InthecaseofD (see Fig. 3), the average E b of the studied drug molecules decreases as CE6 ((6.28 ± 23.91) J/mol) [ DOX ((8.60 ± 21.30) J/mol) [ (MTX (11.06 ± 17.76) J/mol) [SN38 ((11.83 ± 23.30) J/mol). The positive average E b indicates that it is energetically unfavorable to incorporate drug molecules into PAMAM-PEG. Further analyses on deformation energies show that E b becomes positive mainly due to large deformation energy of PAMAM-PEG upon drug insertion. The drug

5 Binding and conformation of dendrimer-based drug delivery systems: a molecular dynamics study 225 Fig. 3 Binding energy E b of a single drug molecule loaded into G3-PEG at 42 different binding sites in a CE6 b DOX c MTX and d SN38 Fig. 4 Binding energy E b as functions of the number of drug molecules in a D@G3 and b D@G3-PEG where D is CE6, DOX, MTX, and SN38 molecules can bind with either PAMAM or PEG in D1@G3- PEG. The earlier results show that E b of drug-pamam is negative. Therefore, we conclude that positive E b of drug- PEG dominates and drug-peg interactions are weaker than the intramolecular interactions among PEG chains. When multiple drug molecules are encapsulated into PAMAM, we calculated E b as functions of the number of drug molecules (N) showninfig.4. TheE b fluctuates when N is small as they scatter depending on various possible binding sites. However, E b tends to approach towards constant values

6 226 F.-D. Zhang et al. Fig. 5 Instantaneous E b-pd, E i-pd,e d-p, and E di-d vs. N of the D complexes where D is a CE6, b DOX, c MTX, and d SN38 between ( ) J/mol as N increases beyond certain values, e.g., * 20 in D or * 30 in D PEG. Both systems have similar trends E b (CE6) & E b (DOX) [ E b (MTX) [ E b (SN38) when N is large. On the basis of analyses above, the drug-pamam binding is stronger than the intramolecular interactions of PAMAM, but the drug-peg binding is weaker than the intramolecular interactions among PEG chains. Although drugs bind with PAMAM energetically more favorable, when the number of drug molecules increase, drug should bind with PEG chains that provide more hollow spaces. Even though the drug-peg binding energy is thermodynamically unfavorable, the complexes remain stable in the MD simulations, suggesting that the complexes are kinetically metastable once they form. 3.2 Instantaneous binding energy, interaction energy, and deformation energy of D complex In order to better understand the relationship among the four types of energies (see Eq. (1)), E b-pd,e i-pd,e d-p, and E di-d, we calculated and plotted theses energies for the D in Fig. 5 and D complexes in Fig. 6. The studied systems correspond independently to different numbers and types of drug molecules, so the trends obtained from these results are statistically meaningful. As the number of drug molecules N increases, the instantaneous binding energies approach to constant values quickly after initial fluctuations at small N (\ 12). We find that the trends of deformation energies of dendrimers coincide well with those of instantaneous binding energies, indicating that the conformations of dendrimers within the complexes are critical to determine the binding strength of drug-dendrimer. As the number of loaded drug molecules N increases, the deformation energies of drug molecules decrease and the interaction energies become weaker until both level off. The trends discussed above are qualitatively similar in both D and D PEG complexes. Quantitatively, the interaction energies of drug-(g3-peg) are stronger than those of drug-g3, but the deformation energies of G3-PEG are larger than those of G3.

7 Binding and conformation of dendrimer-based drug delivery systems: a molecular dynamics study 227 Fig. 6 Instantaneous E b-pd, E i-pd, E d-p, and E di-d vs. N of the D complexes where D is a CE6, b DOX, c MTX, and d SN38 Table 1 Radii of gyration of drug molecules (D 1 ), dendrimers (G3 or G3-PEG), and drug-dendrimer complexes (D or D Drug D 1 /nm D 1 (D D 1 (D G3 G3(D G3(D D None CE ± ± ± (1.3%) (45.6%) (48.4%) DOX ± ± ± (1.0%) (41.0%) (41.9%) MTX ± ± ± (-1.6%) (43.3%) (35.5%) SN ± ± ± (-0.1%) (37.0%) (34.3%) Drug D 1 (D D 1 (D G3)/nm G3-PEG G3-PEG(D G3-PEG(D D None CE ± ± ± (-1.5%) (12.6%) (4.7%) DOX ± ± ± (-1.3%) (9.6%) (2.7%) MTX ± ± ± (-1.1%) (8.2%) (1.9%) SN ± ± ± (-1.0%) (7.5%) (1.6%) Note: In the case of multiple calculations, the averaged R g values were taken, followed by the standard deviations. Values in the parentheses are percentage of relative changes with respective to isolated drug and dendrimers 3.3 R g To examine the size changes, the radii of gyration of the drug molecules, dendrimers, and D complexes are calculated and averaged over the equilibrium MD trajectories at 298 K (see Table 1). The R g of isolated drug molecules (D) studied in this work is R g (CE6) = nm, R g (DOX) = nm, R g (MTX) = nm, and R g (SN38) = nm, respectively. The R g values of these drug molecules change little when they are incorporated

8 228 F.-D. Zhang et al. Fig. 7 R g vs. N of the a D and b D complexes where D is CE6, DOX, MTX, and SN38 Fig. 8 a Probability and b density distributions of the distances between the COM of the dendrimers and drug molecules in the D complexes Fig. 9 a Probability and b density distributions of the distances between the COM of the dendrimers and drug molecules in the D complexes into PAMAM regardless of the number of molecules and PEGylation except that the largest floppy MTX molecules expand slightly 3% 8%. The whole D complexes expand 34% 48% relative to the pristine G3. The R g of D is slightly larger or smaller than that of G3 embedded within the complex [G3(D indicating that some drug molecules reside on the periphery of PAMAM. These results show that pristine PAMAM expands significantly when drug molecules are inserted while the drug molecules themselves are relatively rigid without large deformation.

9 Binding and conformation of dendrimer-based drug delivery systems: a molecular dynamics study 229 Fig. 10 Atomic structures of a DOX snapshot where G3 is in blue and DOX 36 is in red. b and c are the structures of the DOX 36 and G3 separated from the DOX respectively. For sake of clarity H atoms are not shown Fig. 11 Atomic structures of a DOX snapshot where G3-PEG is in blue and DOX 42 is in red. b and c are the structures of the DOX 42 and G3-PEG separated from the DOX respectively. For sake of clarity H atoms are not shown Table 2 Diffusion coefficients of the D and D complexes in water Complex D/(10-4 nm 2 ps -1 ) Complex D/(10-4 nm 2 ps -1 ) CE6 4.9 CE6 5.4 DOX 4.8 DOX 4.9 MTX 5.4 MTX 7.8 SN SN When PAMAM is PEGylated, the R g of D increases only 2% 5% after 36 drug molecules are inserted. These results imply that PEG chains have more empty interior spaces to accommodate drugs than pristine PAMAM. The R g values of D are always smaller than those of G3-PEG within D complexes, indicating that the drug molecules are encapsulated deeply inside G3-PEG. When a single molecule is inserted, most G3 and G3- PEG shrink slightly (\ 2%). When many molecules are inserted (e.g., N = 36), the R g of G3 increases 37% 46%, while that of G3-PEG increases only 8% 13%. These results indicate that small number of drug molecules shrink PAMAM as glue while many drug molecules expand PAMAM. R g values as functions of the number of drug molecules are plotted in Fig. 7 for D and D The R g of D is linearly proportional to the number of the drug molecules. The R g of D fluctuates and has weaker dependence on the number of drugs. When the drugs are encapsulated into the G3, the R g increases 34.3% 48.4% specifically from nm (N = 0) to nm (N = 36). The R g of G3-PEG complexes increase 1.6% 5.0% specifically from nm (N = 0) to nm (N = 36). The R g of G2(G2-PEG) is nm (1.996 nm). The other results of G2(G2-PEG) system are similar to G3(G3-PEG) system. 3.4 Distributions of the distances between drugs and dendrimers It is crucial to understand the binding sites of drug molecules embedded in dendrimers. The probability and density distributions of the distances between the centers of masses (COM) of the dendrimers and drug molecules are

10 230 F.-D. Zhang et al. calculated based on the averaged equilibrium MD trajectories of D and D complexes (see Figs. 8 and 9). The results show that most drug molecules stay 1.5 nm away from the COM of G3. These distances are close to the R g of complex 1.6 nm, indicating that the positions of drug molecules determine the R g of the complexes and many of drug molecules expose on the surface of D On the other hand, most drug molecules are located 2.0 nm away from the COM of G3-PEG. These distances are smaller than the R g of complexes 2.7 nm, implying that drug molecules are encompassed by the PEG chains and deeply embedded. Indeed, visual inspection of MD snapshots shown in Figs. 10 and 11 supports the results of R g. The information about the binding sites suggests that PEGlyation not only can reduce the cytotoxicity and improve the aqueous solubility of the dendrimers but also can directly interact with drug molecules. Therefore, designing functional groups of PEG chains is critical to develop efficient drug-delivery system. 3.5 Diffusion coefficient of D complex in water To examine the diffusion behaviors of dendrimer-based drug-delivery system (DDS), we calculated the diffusion coefficients D of D in water (see Table 2). The calculations are converged as shown in Figs. S1 and S2 in Supporting Information. The diffusion coefficients of D and D complexes are , which are smaller than the diffusion coefficient of water Therefore, the dendrimer-based DDS diffuse slowly in solvents, which elongates the retention time of DDS in human body. 4 Conclusions This work carried out molecular dynamics study on the dendrimer-based drug delivery systems focusing on the binding strength and conformation of DDS as functions of the numbers and types of drug molecules. The studied DDSs are PAMAM dendrimers loaded with the anticancer drug molecules DOX, MTX, SN38, and CE6, respectively. The PEGylated PAMAM was also studied to examine the effects of functionalization. On the basis of analyses of binding energies and their associated components including interaction energies and deformation energies, we find that the drugs bind with PAMAM more strongly than the intramolecular bindings of PAMAM, while the drugs bind with PEG chains more weakly than the intramolecular bindings among PEG chains. The deformed conformations of dendrimers embedded in the complexes are crucial to determine the binding strength of the drug-dendrimer complex. These results indicate that weakening the intramolecular interactions among functionalization groups of PAMAM can facilitate the incorporation of drug molecules. Loading multiple drug molecules enlarges PAMAM dendrimers significantly but has much weaker effects on the PEGylated PAMAM. The drug molecules themselves remain similar sizes even after loaded into dendrimers. The PAMAM-PEG can accommodate more drug molecules and encompass drugs more deeply and strongly than pristine PAMAM. Our studies show that the drug molecules directly bind with PEG chains suggesting that designing the functionalization groups of PAMAM is critical to improve its drug bindings. The information extracted from this work provides helpful theoretical evidence to develop more effective dendrimer-based drug delivery systems. Acknowledgments The authors are grateful for financial supports from Shanghai Pujiang Talent program (Grant No. 12PJ ), Shanghai High-tech Area of Innovative Science and Technology (Grant No ), STCSM; Key Program of Innovative Scientific Research (Grant No. 14ZZ130) and Key Laboratory of Advanced Metal-based Electrical Power Materials, the Education Commission of Shanghai Municipality; State Key Laboratory of Heavy Oil Processing, China University of Petroleum (Grant No. SKLOP ); National Natural Science Foundation of China (Grant Nos , , and ). 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