Hybrid Dendrimers of PPI(core)âPAMAM(shell): A Molecular

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Hybrid Dendrimers of PPI(core)-PAMAM(shell): A Molecular Dynamics Simulation Study Sajjad Kavyani, Sepideh Amjad-Iranagh, Mitra Dadvar, and Hamid Modarress J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b05142 • Publication Date (Web): 24 Aug 2016 Downloaded from http://pubs.acs.org on August 25, 2016

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The Journal of Physical Chemistry

Hybrid Dendrimers of PPI(core)-PAMAM(shell): A Molecular Dynamics Simulation Study Sajjad Kavyani, Sepideh Amjad-Iranagh, Mitra Dadvar, Hamid Modarress,* Department of Chemical Engineering, Amirkabir University of Technology

* Corresponding Author Email: [email protected] Tel:

+982164543176 Fax: +982166405847

Abstract The structural properties of hybrid dendrimers PPI(core)-PAMAM(shell) for application in drug delivery is studied by coarse-grained molecular dynamics simulation and their capacity to encapsulate drug guest molecules such as pyrene is investigated by changing the core (PPI) in the PPI-PAMAM hybrids. For this purpose, a coarse-grained model for PPI dendrimer is developed and is used to predict the structural properties as a function of PPI core size, such as the size of hybrids dendrimers, the depth of water penetration, the extent of back folding of their chain terminals, the size and distribution of created cavities and asphericity. The results show that the location of pyrene in the interior structure of the hybrids is independent of PPI core size and the branching chains create a barrier against the penetrating molecules in the shell of PPI. Then by adding the PAMAM to the surface of PPI this barrier is removed, and this will enhance the encapsulation capacity of the hybrid.

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Keyword: Polyamidoamine, Polypropyl ether imine, Hybrid Dendrimer, Pyrene, Niacin, CoreShell Structure, Molecular Dynamics Simulation


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Introduction Remarkable properties of dendrimer molecules are their uniform structure, low viscosity, controlled mass, monodispersity1,2 surface functionality and solubility.3 These properties make them a versatile tool for various applications such as drug delivery4–7 and biosensors8,9. Dendrimers can easily encapsulate drugs and other guest molecules into their branched structure10–12 or attach them to their surface.13–15 Depending on the type of monomer in a dendrimer structure, they manifest different abilities. For example, the dendrimers, Poly(amidoamine) (PAMAM) and Poly(propylene imine) (PPI), because of their unique molecular structure, have been used in various applications. The molecular structure of these dendrimers are presented in the Figure 1a. Prosa et. al.16 utilized small-angle x-ray scattering to investigate the inner structure of PPI dendrimers. Scherrenberg et. at.17 measured the PPI size by small-angle neutron scattering (SANS) and viscosimetry and indicated that the dendrimer size increases linearly with the generation number. In another study, Shao et. al.18 compared the encapsulation capacity of the third generation (G3) of PAMAM and fourth generation (G4) of PPI and determined that the PPI dendrimer with more hydrophobic inner structure can encapsulate more phenylbutazone than the G3 and G4 PAMAM dendrimers. One of the unique characteristic of the dendrimers is their ability to encapsulate other molecules. Kannaiyan et. al.19 presented a synthesized dendrimer with the core of G2 PPI (with 16 terminals) and the shell of PAMAM and they found that in aqueous solution and at higher pHs, this dendrimer has higher encapsulation capacity for pyrene molecules. They also found that the location of the encapsulated pyrene molecules were near the PPI core. Watkins et al.


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enhanced the encapsulation capacity of PAMAM dendrimer for the nile red compound by increasing the number of carbons in its core. Molecular dynamics (MD) is recognized as an efficient technique for studying physicochemistral properties of systems at molecular level. Maiti et. al.21 studied PAMAM dendrimer structure from generation 1 to 11 by MD simulation. All-atom MD simulation of PPI dendrimer indicated that, the dendrimer is almost a perfect sphere specially at higher pHs.22 In another work, Maiti et. al.23 performed an atomistic simulation to investigate the complexation of PAMAM dendrimer with DNA and found that the complex formed is quite stable. Jain et. al.24 performed an all-atom MD simulation for investigating a G4 PPI dendrimer (with 64 terminals) complexed with famotidine and indomethacin. Their simulations demonstrated that, the complexes formed were unstable at low pHs. Alongside the all-atom (AA) MD simulations, the coarse-grained (CG) MD simulation was developed by collecting the atoms into beads and this innovation facilitated the computational procedure at a significantly reduced CPU time with producing accurate results. Lee et. al.25 by coarse grained (CG) method, conjugated a PAMAM with PEG. They indicated that longer PEG chains with higher number of grafting yield PEGPEG crowding which moves the dendrimer terminals outward facing the solvent water molecules. Kavyani et. al.26 investigated the effect of core type on the PAMAM dendrimer at low and neutral pHs by CG-MD simulation and they found that, with the enhancement of the core length of PAMAM, the encapsulation capacity of the dendrimer increased. They also indicated that at low pHs, the hydrophobic core of the dendrimer creates empty spaces around the core which make large enough space to accommodate the water molecules as the guest molecules. Lee et. al.27 performed a MD simulation and showed that, with increasing the number of histidine and arginine conjugated on the PAMAM surface, at low pHs, the dendrimer complex tends to


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form a dens-shell rather than a dens-core structure, which is formed at pH = 7. Smeijers et. al.28, simulated the G4 and G5 of the PPI dendrimer and evaluated the radius of gyration and some other physical properties by using a CG model of PPI dendrimer by using a previously developed force field.29 CG-MD simulation is a convenient approach to understand molecular behavior of systems at molecular level, especially for highly branched molecules like dendrimers which, just one generation increase, makes a multiple in the number of atoms. Also, among various kind of dendrimers, poly(amidoamines) (PAMAM) and poly(propylene imine) (PPI) are the most widely used. But, only the structural behavior of PAMAM has been investigated by CG-MD. In addition, to the best of our knowledge, no work has been performed on studying the PPI(core)PAMAM(shell) hybrid dendrimer by MD simulation. However, the hybrid dendrimer was synthesized experimentally by Majoros et. al.30, by attaching the PAMAM layers to the surface of PPI dendrimer. Therefore, in the first step we developed a new coarse grained model for the commonly used PPI dendrimer based on the MARTINI force field31 and then we modeled the detailed structural behavior of the hybrid, PPI(core)-PAMAM(shell) dendrimer, with various PPI core size. In continuation, we changed the size of PPI core in the hybrid structure in several generations (G1, G2, G3) and compared the results with those of pristine G4 PPI dendrimer. In the second step, we studied the encapsulation capacity of this hybrid for hosting pyrene molecule. It is notable that the pyrene can be used as a monitoring agent to track RNA, proteins and small molecules in biological environment32,33, also, because of its low water solubility, it can be utilize as a model for hydrophobic drugs34. At each step, the results were validated with experimental data. Methods 5 ACS Paragon Plus Environment


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All simulations have been performed by GROMACS 5.0.4 simulation package.35,36 For calculating the interaction between particles in the simulation box, the MARTINI coarse-grained (CG) force field (FF) was utilized,31,37,38 where in the FF, almost four heavy atoms are represented as a single bead. For simulation of PAMAM dendrimer, the developed model of Lee et. al.25 which its application has produced accurate results was utilized.26,27 All the dendrimers were in neutral state. The size of simulation boxes were 10×10×10 nm3 and they were filled with 10,000 MARTINI water bead model. In this model, four water molecules are coarse grained into a single bead of P4. The periodic boundary conditions were used in the x, y, and z dimensions. Considering the zero charge for every bead in the systems, to decrease the calculation time, the single range cut-off method36 was used for calculating electrostatic interactions. For both electrostatic and van der Waals interactions, a cutoff radius of 1.2 nm was applied31,37 where the van der Waals interaction potential was smoothly shifted to zero between 0.9 to 1.2 nm. The neighbor searching update frequency was set to 10 steps. The time step of all simulations was set to 20 fs. By utilizing the Berendsen coupling method39, the temperature and pressure of the simulation boxes were fixed at 300 K and 1 bar respectively. Initial velocities were randomly generated from Maxwell-Boltzmann distribution at the desired temperature40. Visual molecular dynamics (VMD)41 was used to visualize the molecules and all the analysis were performed by GROMACS software.35,36 For modeling of the pyrene (Figure 1a), the SC4 bead type were used for benzene rings as it has been utilized successfully for graphene.42 PPI modelling In the case of PAMAM dendrimer, the previously developed PAMAM model by Lee et. al.25 was utilized. For the coarse grained modeling of the PPI dendrimer, the same bead type of the 6 ACS Paragon Plus Environment

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primary amines at the surface, as was used previously in PAMAM modeling by Lee et. al.

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was set to P3. Every interior tertiary amine and the primary amines at the surface were placed in a single bead. For the tertiary amine, the N0 bead type was used (as in the Lee’s PAMAM model25). But because of an extra carbon atom in the PPI beads, it was expected that the C5 bead type could provide a better performance in the simulation of this dendrimer. But the simulation results as presented in Table 1 indicate that, in spite of the existing reports16,17, neither C5 nor N0 beads could simulate the radius of gyration ( Rg ) of the PPI dendrimers even with a large bond lengths such as 0.65 nm. Then, the Nda bead type with ε = 4.0 kJ/mol and σ = 0.47 nm for Lennard-Jones (LJ) potential was used, but again the Rg value was small. The reason for this can be explained by the fact that, the tertiary amines in the PPI have strong interaction with water molecules and therefore the beads of C5, N0 and Nda cannot simulate the amines-water interactions. Finally, for the tertiary amines of the PPI dendrimer, the bead type P1 (ε = 4.5 and σ = 0.47) 31,37 with the bond length of 0.473 nm and the bond force constant of 4000 kJ mol-1 nm-2 which is in good agreement with Smeijers et. al.29 CG model of PPI dendrimers, and the tertiary amines angle of 120º with the force constant of 20 kJ mol-1 were used. The results indicated that by using the P1 bead type for the tertiary amines of the PPI dendrimer, the Rg could reasonably be simulated. The beads used in the simulation are shown in Figure 1a. Result and Discussion In this section, the obtained results will be presented in two parts: 1) the results related to the pristine PPI dendrimer, 2) the results related to the hybrid PPI-PAMAM dendrimers and their capacity for encapsulation of pyrene molecules.



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For naming the systems of pristine dendrimers, the first abbreviation represents the dendrimer type followed by its generation number. For example PPI:5 represents the dendrimer type PPI at generation 5. In the case of hybrid dendrimers, the first abbreviation represents the dendrimer type in the core, followed by its generation number. The second abbreviation represents the shell type dendrimer followed by its generation number. For example, PPI:3-PAMAM:1 means the hybrid dendrimer with PPI as the core at generation 3 and PAMAM as the shell at generation one. It is noteworthy that all the hybrid dendrimers are of generation 4 with 64 terminals. For the encapsulation process, a P (for pyrene) is added at the end of abbreviations. Pristine dendrimers The simulations were performed for 1500 ns and the results were obtained at the last 400 ns of the simulation. To indicate that the dendrimers have reached the equilibrium state, the Rg values versus time for randomly selected dendrimers are plotted in Figure 2 which shows that Rg remains stable at the last 400 ns and the systems have reached their equilibrium states. The snapshot of pristine PPI:5 dendrimer is presented in Figure 3a Table 1 represents the time-average value of Rg for the pristine dendrimers. For the sake of comparison, the fourth generation of PAMAM (PAMAM:4) which is neutral at high pH was simulated and was compared with PPI:4. The Rg values (in Table 1) for PPI and for PAMAM indicate that the PAMAM is slightly bigger in size than the PPI according to previously recorded results.43 Table 1 shows that the size of PPI dendrimer enhances with the generation increase, which is due to the larger number of branching layers at higher generations. The incremental percent of


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the Rg , for PPI dendrimers ( ∆Rg )% is reported in Table 2 which indicates that, the percentage increase of Rg for generation growth is in order of ( G3 → G5 ) > ( G3 → G4 ) > ( G4 → G5 ) . It should be noted that at lower generations, the branching chains of the dendrimers form an open structure, therefore the attracted solvent (water) molecules can penetrate easily in between the chains. But at higher generations, the distance between the chains reduces and the dendrimer forms a dense structure, which means that, the branching chains attract each other and do not allow the water molecules to penetrate easily in between the chains. Therefore, the chains will back fold and diffuse into the dendrimer inner spaces toward the core, and as a result the enhancement of the Rg for ( G3 → G4 ) is larger than ( G4 → G5 ) . The process of diffusing the outer layers into the inner space is a well-known “back-folding” characteristic of the dendrimers.23,33 The radial distribution functions (RDFs) of the last outer layer and the RDFs of all the dendrimer layers, both calculated in reference to the center of mass (COM) of the dendrimer core, are shown in Figure 4. This figure indicates that not only the height of the RDF highest peak is reduced with the generation increase, but it has become broader. These results can be explained by considering the back folding of the chains and their inherent thermal motions, which as a result, they cannot remain in a certain position in the course of simulation. However, the lower generations have sharper RDF peaks which show that, during the simulation, their chains are mostly positioned at fixed locations. Interestingly, as Figure 4 shows, the location of the highest RDF peak for the chain terminals of a higher dendrimer generation is exactly at the same location as that of lower generations. By considering the distance of the chain terminals from the dendrimer core, they should have back folded and diffused a long distance into the dendrimer inner space and as their RDF indicates that they are located in the vicinity of the core. This behavior can be considered as the main reason for RDF peaks broadening. Due to 9 ACS Paragon Plus Environment


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open structure of the dendrimers at the lower generations, a very small number of diffusing and back folding of the chain terminals occur (noting that there are 32 terminals for G3 and 64 for G4 dendrimers), therefore it might be advisable not to compare the back folding behavior of the outer layers for various dendrimer generations only by considering the RDF results. Thus, to obtain more information about the behavior of the chain terminals, the RDF integral (as defined by the area under the RDF curve) of the chain terminals was calculated from COM of the core (at origin) to the point A (point A is shown in Figure 4). Then this integral value was divided by the integral value of the RDF for all dendrimer layers, as obtained by calculating the area under the RDF curve from the same origin to the point A. The results of these calculations deduced from Figure 4 (a, b, c) and Figure 6 (for PAMAM RDFs), are reported in Table 3. This table demonstrates that the integral ratio, as defined above, increases with the generation and therefore, at higher generations, the terminal layer must have been back folded into the inner space of the dendrimers. These results are in good agreement with those reported in Table 2. In addition, the water radial densities (RDs) were calculated for PPI dendrimers and are presented in the Figure 5. According to this figure, the G3 generation of PPI, due to its open structure, has an advantage over its higher generations G4 and G5, in regard to water penetration. This figure also indicates that, the water penetration in G4 is smaller than G5. The RD results for water are in agreement with our previous comments that, the lower dendrimer generations with their open structure, can conveniently accommodate more guest molecules in their inner structure. For the sake of comparison in Figure 6, the RDF of the chain terminals of the pristine PPI G4 and PAMAM G4 dendrimers versus their distance from the COM of the core are shown. This figure indicates that the layers of PPI are located at a certain position with very little tendency of movement and back folding toward the core, whereas this is not the case for PAMAM. The


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values for the integral ratio, that is defined as the integrated values of RDF of the chain terminal over the integral value for all the dendrimer layers were evaluated and reported in Table 3. The results in this table indicate that more back-folding of the chain terminals into the dendrimer inner structure has occurred. The RDF of the terminal layers of the PPI and PAMAM are also potted in Figure 6b. This figure shows that PPI terminals tend to diffuse toward the dendrimer inner structure and as a result they are more back-folded than the PAMAM terminals. The RD of water beads are plotted versus their distance from COM of the core in Figure 6c which shows that PPI acts as a barrier and prevent water penetration into the dendrimer inner structure. This is quite evident for PPI from the sharp declining slope of RD from unity as compared, with this slope, for the PAMAM. It is seen that for the three dendrimers (in Figure 6c) a jump occurs in the RD value of water at a distance of ~ 0.5 nm, form the COM of the dendrimer core. This jump indicates how strongly the branching chain are penetrating into the dendrimer core and as a result the water beads are pushed and compressed toward the core, which caused an increase in the water density in the vicinity of the core. To study the asphericity of the dendrimers, the moment of inertia (MOI) for PPI dendrimers were calculated and are represented in Table 4.which indicates that upon generation increase, the aspect ratio (which is defined as Ix / Iz and Iy / Iz) 2,27 of the PPI approaches unity, therefore higher generations have more symmetrical structure and then their shape is more spherical. These results are in good agreement with the published data for PPI22. The results in this table also indicate that the PPI dendrimer has more spherical shape than the PAMAM. Hybrid Dendrimers



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The PPI-PAMAM hybrid dendrimers were simulated for 1000 ns and the analysis of the results were made in the last 400 ns. Due to overlapping of Rg results, in Figure 2, only the Rg values for one hybrid dendrimer as an example, is plotted versus time to indicate that the systems have reached their equilibrium state. The last snapshots of two randomly selected hybrids are represented in Figure 3b. The Rg values of the hybrid molecules were calculated and are reported in the Table 5. This table shows that by attaching the PAMAM to the surface of the PPI, the size of the hybrid increases significantly. One of the main reasons for this behavior of the hybrids is due to the fact that the smaller branches of the PPI in the hybrid are replaced by the larger branches of the PAMAM. The RDs of water beads around the COM of the hybrid core (PPI) were calculated and are represented in Figure 7b. This figure shows a small enhancement in water beads penetration into the interior structure of the hybrid dendrimers. But, an interesting point in comparison of Figure 7b and Figure 5 is the slope of the declining curve for water RD which is sharper for larger PPI core size, and this means that the branching chains in the shell layers act like a barrier against the water molecules penetration, (Figure 8). However, by replacing the shell layers of the PPI:4 with the PAMAM, this so called barrier is removed and water penetration is facilitated. The RDFs of the hybrids are presented in Figure 7a. This figure shows that by increasing the core size of the hybrid dendrimers, the RDF values for dendrimer layers increase, especially in the radius range of 1.5 nm to 2 nm, where due to back folding of the chains, the previously mentioned barrier has been created. But, by presence of PAMAM in the shell of PPI-PAMAM hybrid dendrimers, the interactions between the branching chains keep the chains apart from each other and as a result the local number density of chains reduces and water molecules can penetrate easily into the dendrimers interior structure. 12 ACS Paragon Plus Environment

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To study the encapsulation capacity of the pristine PPI:4 and PPI-PAMAM hybrids, pyrene molecules were added to their aqueous solution. For each system, a total number of 45 pyrene molecules were added to the simulation boxes. It is worth considering in order to see the effect of pyrene concentration on the hybrid dendrimers, for PPI:2-PAMAM:2, simulations were performed with 5, 10 and 20 number of pyrene molecules. The systems with 45 pyrene molecules were utilized for all the analysis. The final four snapshots for the number of pyrene molecules (5, 10 ,20 and 45) are represented in Figure 9. The Rg values of the dendrimers were calculated and are represented in Table 5. This table shows that, like dendrimer-water systems, the larger size belong to the PPI:1-PAMAM:3 dendrimer and the size decreases with increasing the PPI core size (from PPI:1-PAMAM:3 dendrimer to pristine PPI:4). Comparing the dendrimers size, before (Table 1) and after (Table 5) encapsulation, it can be seen that the size of all the dendrimers enhances after the encapsulation. The percentage of the size enhancements of dendrimers related to their size in absence of pyrene (their size in dendrimer-water system) are plotted in Figure 10. This figure shows that the dendrimers with larger PPI core have more size enhancement where the maximum enhancement belongs to pristine PPI:4. These enhancements are due to presence of filled cavities in the dendrimer structure. In a dendrimer, the cavities are formed a result of chain branching structure of core and shell. Cavities may also be created by structural deformation. In a dendrimer, the main process for changing the number and the volume of cavities is the back folding of the upper generation layers (chain terminals) into the lower generation layers. Figure 10 shows that for the dendrimers with larger PPI core size, there are more filled cavities, and the pristine PPI:4, is at maximum in this respect. By increasing the PPI core size, the slope of the plot in Figure 10 reduces significantly from PPI:3:PAMAM:1 to PPI:4. These results show, the effect of PAMAM shells in the hybrid PPI-PAMAM aqueous



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solution which caused the branching chains to stretch more and to distance from each other and as a result of this process, more cavities being created to make room for accommodating the penetrated water molecules. Also, it seems that, the penetrating guest molecules have pushed back the chains from the filled cavities to make room for their accommodation. The RD of G0, G1, G2, G3 and G4 layers for PPI:2-PAMAM:2 hybrid dendrimer have been calculated from the COM of the core and are represented in Figure 11. From this figure, it can be seen that nearly all of the dendrimer layers change their position during the encapsulation process. But, the G0 layer has the lowest and the G4 (terminals) has the highest displacement. Figure 11 also shows that all the dendrimer layers contribute to the back folding of branches, but, it seems that the farther layers of G4, have the main role, because they contain more number of beads in their structure, and also, they back fold along the radius of the dendrimer. Therefore the highest RD peak for the G4 layer in the dendrimer-water system in Figure 11, appears nearly at the same position as the G0 layer (Figure 11a, b). Comparing the RDs plots (Figure 11a, b and Figure 11c, d) for the PPI:2-PAMAM:2 hybrid before and after the encapsulation process shows that all the inner layers, by moving outward, change their positions to make rooms for the incoming pyrene molecules. This figure also indicates that, before the encapsulation (for a dendrimer-water system), the dendrimer layers, by back folding filled the inner cavities, and it seems that the G4 layer has the main role in this process. But, then, in the encapsulation process, the penetrating guest molecules, push the back folded layers outward, and create more cavities for their accommodation. Therefore it can be concluded that both the PAMAM layers and the penetrating molecules have a determining effect in creating the cavities. The RD variation of pyrene molecules versus their distance from COM of the dendrimer core are plotted in Figure 12. This figure shows a very small difference for the


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studied systems. By considering two previously mentioned parameters (effect of interior cavities and attraction forces) for the encapsulation enhancement, it can be seen from Figure 12 that, despite the highest attraction of PPI:4 with pyrene, due to polarity of PPI:4 branching chains, its RD indicates a small difference in comparison with other dendrimers. Therefore, it can be stated that the polarity of the interior groups has smaller effect than the cavities, on pyrene molecules encapsulation. One interesting point in the Figure 12 is that: for all of the dendrimers, the first two peaks are exactly in the same position, and with the same height, even for pristine PPI:4. This means that the guest molecules always find their exact locations in their host interior structure, regardless of the PPI core size. To find these locations, the RD of all layers for the PPI:2-PAMAM:2 hybrid were calculated and plotted in Figure 13a alongside with the pyrene molecules RD (multiplied by 10 for a clear presentation). This figure indicates that the pyrene molecules are located mostly around G0 and in the G1 layer cavities, where the G1 layer, due to its larger volume, has the main contribution in this process. By comparing Figure 13a and Figure 11, it is evident that the RD peaks for G0 and G1 layers are exactly at the same position as those of G4, G3 and G2 layers which indicates that the branching chains in these layers have been back folded mostly into the inner layers of G0 and G1. The 2-dimensional representation of the pyrene molecules number density in the interior structure of PPI:2-PAMAM:2 hybrid in Figure 13b, confirms that the location of the pyrene guest molecules in this hybrid are around the COM of the hybrid core. This is notable that the 2-dimensional map depends on where the 3-dimensional number density is cut to obtain a 2-dimentional map, but as a representative for the 3dimensional structure, the 2-dimensional map is worth considering. Considering the blue dotted line in Figure 13, it can be seen that there are five peaks A, B ,C D and E which clearly indicate the fixed location of the encapsulated pyrene molecules in a dendrimer. The A, B and C peaks



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indicate the location of the pyrene molecules in generation layers 0 to 1. The peaks D and E in the same figure indicate the location of pyrene molecules in generation layer 2 to 3. For more clear representations, the layers are also shown by separate peaks, in Figure 13. In Figure 13 (for PPI:2-PAMAM:2, as an example), the sharpness of A, B and C peaks indicate the location of pyrene molecules at a certain distances from COM of the dendrimer core. But, the D and E peaks are broader which indicates that the encapsulated pyrene molecules do not have certain position and can diffuse from one dendrimer’s cavity to another. After the point E (Figure 13), there is no peak and the pyrene molecules are positioned on the dendrimer’s surface and can easily separate from it. Therefore, the number of encapsulated pyrene molecules should be calculated to the point E (r = 1.3 nm in Figure 13 at the second generation layer) since after this point the pyrene molecules are not localized and cannot be considered as encapsulated. These unencapsulated pyrene molecules are shown clearly in Figure 9d. It should be noted that the corresponding point E (generation layer 2) is used for calculating the number of encapsulated pyrene molecules for each of the studied dendrimers in this work. The calculated results of the encapsulated pyrene molecules in a dendrimer are presented in Figure 14 and 15. Figure 15 shows that by increasing the number of pyrene molecules in the simulation box from 5 to 45, the number of encapsulated pyrene molecules increases linearly with the number of pyrene molecules in the simulation box, from 4.2 to 14.9, respectively. By extrapolating this linear line to infinitely diluted solution of pyrene in water (pyrene/water number ratio ~ 10-8, Reference 19), it is seen that a value of (~

3) for the encapsulated pyrene molecules in a dendrimer is obtained which is in very close agreement to the number of encapsulated pyrene molecules in the dendrimer (4) as reported experimentally by Kannaiyan et. al.19. Figure 14 shows the variation in the number of encapsulated pyrene molecules in the PPI-PAMAM hybrids and in the pristine PPI:4 dendrimer.


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These results are in good agreement with those obtained by Kannaiyan et. al.19,44 where it was shown that the G4 hybrid dendrimer can host more pyrene molecules than pristine PPI:4. It can be seen quite clearly in Figure 14 that, there is a very small difference between the points representing PPI:1-PAMAM:3 and PPI:2-PAMAM:2 for the pyrene molecules encapsulated into the G4 hybrid dendrimer. This indicates that the hybrid dendrimer PPI:2-PAMAM:2 in spite of having smaller size, compared with PPI:1-PAMAM:3, has the same affinity to encapsulate pyrene molecules, therefore PPI:2-PAMAM:2, due to its smaller size, is more suitable to be used as a drug carrier in the drug delivery application. Therefore, the size of the dendrimer can be considered as a crucial parameter in respect to the cytotoxicity as a drug carriers.45,46 The enhancement of the encapsulation capacity (loading) of a drug carrier mostly depends on two factors i) having large and accessible cavities to allow the guest molecules penetration into the interior structure, and ii) having an effective polarity to attract certain guest molecules into its inner structure. In the case of PPI-PAMAM hybrid, these two factors may have an opposite effect, that is; lower generation of PPI core in the PPI-PAMAM hybrid dendrimers is favorable, due to increasing the size of the hybrid, for more drug loading capacity, but on the other hand, higher generation of the PPI core is favorable, due to increasing the hydrophobicity of the interior structure of the hybrid, for attracting drug molecules. The moment of inertia (MOI) of the hybrids and PPI:4 dendrimers were calculated and are presented in Table 6 which indicates that changing the size of the core from G1 to G3 has a very small effect on their aspect ratios. However no reasonable trend is seen in the aspect ratio variation for the hybrid-water systems. This table also shows that for the hybrids PPI:1PAMAM:3 and PPI:2-PAMAM:2, the aspect ratio increases after the encapsulation, because, due to pyrene molecule penetration, the dendrimers grow in all directions, to reach their expansion



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limit. But for the PPI:3-PAMAM:1 hybrid and PPI:4 dendrimer the aspect ratios are lower. The reason for lower aspect ratio of PPI:3-PAMAM:1 and PPI:4 can be attributed to the thermal motion of unencapsulated pyrene molecules which are aggregated outside of the dendrimers structure, and the collision of these unencapsulated pyrene molecules with the dendrimer surface would deform the dendrimer structure from spherical shape. This structural deformation is clearly seen in Figure 16. Conclusion In this work, first a PPI dendrimer coarse grained (CG) model was developed, then, by utilizing this model, the structural behavior of PPI was evaluated. The PPI(core)-PAMAM(shell) hybrid dendrimers were introduced with various size of inner (core) and outer (shell) structure. Then the effect of changing the size of the core, from generation 1 to 3 (G1 to G3) were examined for the studied hybrids where all the hybrid dendrimers, studied in this work, can be considered as the fourth generation dendrimers. The hybrid PPI-PAMAM and pristine PPI:4 dendrimers, were used for investigating the dendrimers encapsulation capacity for pyrene molecules. The calculated radius of gyration ( Rg ) for the simulated pristine dendrimers were in good agreement with the experimental results. At the same generation, it was found that the PPI dendrimer is smaller than PAMAM dendrimer which can be explained by the fact that, the PPI has shorter chains and weaker interactions with water molecules. The sharpness of radial distribution function (RDF) peaks for pristine PPI indicated that at lower generations, PPI layers have more specific locations in the dendrimer structure. The back-folding of the dendrimers increased at high generations and this was approved by evaluating the integral ratio parameter (integrated RDF values of the terminals layers divided by the integrated RDF of the all layers of the dendrimer). The RD of the water beads in the PPI structure showed that the water penetration 18 ACS Paragon Plus Environment

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into the dendrimer decreased at higher generations. The calculation of the moment of inertia for the dendrimers showed that at higher generations, the PPI have more spherical shape. In the case of hybrid dendrimers, the results indicated that the Rg value of the G4 hybrid dendrimers decreases with the increase in the size (i.e. generation) of the PPI in the core. The main reason for these results can be explained by the fact that; to have a hybrid dendrimer of generation 4 (in total, including PPI in the core and PAMAM in the shell), with a larger size of PPI core, the longer chain branching of the PAMAM layers in the shell, should be reduced to keep the dendrimer generation fixed at G4. The RD results for water molecules penetration into the hybrid dendrimers represented no significant difference for different hybrid dendrimers, except that the slope of declining RD curve reduced for the smaller size of the PPI core. This indicates that due to presence of the PAMAM shell, the distance between branching chains has increased and as a results, the number density of the chain branches in the shell area is reduced. But, due to the increased distance between the chains, some pathways have been created for water molecules penetration into the hybrid interior structure. The RDF of the dendrimer beads calculated from COM of the core showed that, for larger PPI core size, the branches in the shell have higher density. Therefore, it can be concluded that due to higher density of the branching chains in the shell, they would act as a barrier against the water molecules penetration. By comparing the Rg s for the four dendrimers before and after encapsulation of pyrene molecules, it can be concluded that more cavities have been created in the pristine PPI:4 dendrimer than in the PPI-PAMAM hybrids. Then it can be stated that as a result of encapsulation process, the back folded layers in the PPI:4 dendrimer have been pushed outward, and thereby more cavities have been created to accommodate the pyrene molecules. But according to the obtained results, by increasing the PPI core size of the hybrid dendrimer (from PPI:1-PAMAM:3 to PPI:4), the 19 ACS Paragon Plus Environment


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number of encapsulated pyrene molecules is reduced. Therefore, an optimum structure can be found for the hybrids dendrimer to be suitable for application as a drug carrier. The RD result for the studied dendrimers in the encapsulation process shows that the pyrene molecules are always located around the G0 and the G1 layers. The aspect ratios calculations indicate that with increasing the core size of the hybrids, the asphericity of the dendrimers does not changes significantly. But after the encapsulation due to penetration of the guest molecules into the dendrimer structure and the dendrimer expansion, the dendrimer gain a spherical shape. Finally, the PAMAM shell in the hybrids has two important effects; first, increasing the size of the dendrimer and therefore increases the cavities in number and volume, and second, it opens some pathways for the penetration of the guest molecules into the dendrimer interior structure. The results show that the position of the created pathways is mostly located around the radius of 1.5-2 nm from the center of the dendrimer, where at this distance from the COM of the core, due to back folding of the branching chains toward the dendrimer center, they act as a barrier against penetration of more guest molecules.


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Figure captions Figure 1. (a) Molecular and coarse-grained structure of PPI, PAMAM and Pyrene, (b) schematic representation of a G4 hybrid dendrimer. Figure 2. The variation of radius of gyration ( Rg ) versus time for randomly selected pristine and hybrid dendrimers. Figure 3. The last snapshots for: (a) one randomly selected pristine dendrimers, (b) two randomly selected hybrid dendrimers. Figure 4. Radial distribution function (RDF) of the PPI dendrimers as a whole and the RDF of the terminal layers calculated from COM of the core. Figure 5. Water radial densities (RD) for PPI. Figure 6. (a) Radial distribution function (RDF) of the dendrimers as whole (b) RDF of the terminal layers (c) Water radial density (RD) for the G4 dendrimers of PPI and PAMAM (calculated from COM of the core) Figure 7. (a) Radial distribution function (RDF) of hybrid dendrimers and (b) water radial density (RD) of water in the hybrids dendrimers structure. Calculated from COM of the core. Figure 8. (a) Schematic representation of a dendrimer (PPI:4 and hybrid PPI-PAMAM) with low density of branching chains in the shell and the pyrene molecules penetrated into interior structure (b) Schematic representation of a dendrimer (PPI:4 and hybrid PPI-PAMAM) with high density of chain branches in the shell acted as a barrier (highlighted) against pyrene molecule penetration. Figure 9. The last snapshot of the PPI:2-PAMAM:2 hybrid dendrimer for encapsulated pyrene molecules, (a) 5 (b) 10, (c) 20 and (d) 45. Figure 10. Percentage increase of Rg for G4 PPI-PAMAM hybrids (PPI core generation from G1 to 3) and the pristine PPI:4 dendrimers as a result of encapsulation. Figure 11. Radial density of PPI:2-PAMAM:2 inner layers; (a), (b) before and (c), (d) after encapsulation. 26 ACS Paragon Plus Environment

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Figure 12. Radial density (RD) of pyrene in the structure of the G4 PPI-PAMAM hybrids (PPI core generation from G1 to 3) and the pristine PPI:4 dendrimers. Figure 13. (a) Radial density (RD) of pyrene and dendrimer layers in the structure of PPI:2PAMAM:2 hybrid dendrimers and (b) two dimensional number density of pyrene molecules in the structure of hybrid PPI:2-PAMAM:2 dendrimer. Figure 14. Number of encapsulated pyrene molecules in the G4 PPI-PAMAM hybrids (PPI core generation from G1 to 3) and the pristine PPI:4 dendrimers. Figure 15. Number of encapsulated pyrene molecules in the G4 PPI:2-PAMAM:2 hybrids as a function of number of dissolved pyrene molecules. Figure 16. Molecular representation of the pristine PPI:4 dendrimer from the last snapshots of the simulation: with and without encapsulated pyrene molecules. Graphical Abstract



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Table 1. The Rg (Å) for the simulated dendrimers experimental

MD simulation

simulation system

terminals

PPI:2 PPI:3 PPI:4 PPI:5 PAMAM:3 PAMAM:4

16 32 64 128 32 64

this work

Jain24 (All-atom)

9.1±0.07 11.6±0.07 14.0±0.07 16.7±0.07 16.1±0.10 20.6±0.10

12.7±0.13

Liu47 (All-atom)

21.07±0.10

Lee25 (CG-MD)

20.7±0.10


Scherrenberg17 (SANS) 9.3 11.6 13.9

Prosa16 (SAXS) 11.3±1% 13.3±1% 14.3±1%

Liu48 (SANS/SAXS)

15.8±1.20 21.4±0.80

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Table 2. Percentage increase in radius of gyration( ∆Rg % ) as a result of generation growth ( ∆G ) for PPI dendrimer ∆Rg % ∆G 43.73 G3 → G5 20.61 G3 → G4 19.16 G4 → G5

Table 3. Integral ratio (terminal layer RDF / dendrimer RDF) for PPI and PAMAM dendrimers PPI dendrimer Integral ratio PPI:3 0.70 PPI:4 0.73 0.78 PPI:5 0.63 PAMAM:4



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Table 4. Moment of inertia (Da × nm2) in x, y and z directions and the aspect ratios for the dendrimers simulation system PPI:3 PPI:4 PPI:5 PAMAM:4

Ix

Iy

Iz

Ix / Iz

I y / Iz

3270.68 10094.85 30181.78 42704.46

4051.20 11948.59 34413.27 52170.56

4792.46 13757.58 37843.85 61314.64

0.68 0.73 0.80 0.70

0.85 0.87 0.91 0.85

Table 5. The Rg (Å) for generation 4 (G4) hybrid dendrimers (with 64 terminals) simulation system PPI:1-PAMAM:3 PPI:2-PAMAM:2 PPI:3-PAMAM:1 PPI:1-PAMAM:3-45P PPI:2-PAMAM:2-45P PPI:3-PAMAM:1-45P PPI:4-P

guest molecules

core

Pyrene Pyrene Pyrene Pyrene

PPI PPI PPI PPI PPI PPI PPI

core generation and end groups number G1- 8 G2-16 G3-32 G1- 8 G2-16 G3-32 G4-64


shell-part

Rg

PAMAM PAMAM PAMAM PAMAM PAMAM PAMAM PPI

18.0±0.08 16.7±0.08 15.5±0.08 19.2±0.05 18.5±0.05 17.6±0.05 16.0±0.05

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Table 6. Moment of inertia (Da × nm2) in x, y and z directions of hybrid dendrimers simulation system PPI:1-PAMAM:3 PPI:2-PAMAM:2 PPI:3-PAMAM:1 PPI:1-PAMAM:3-45P PPI:2-PAMAM:2-45P PPI:3-PAMAM:1-45P PPI:4-P

Ix

Iy

Iz

Ix / Iz

I y / Iz

32380.17 25337.90 18601.70 38181.04 33358.53 24501.78 12646.06

37278.67 29763.37 22177.13 42484.30 36981.76 27650.95 15003.16

41869.47 33898.25 25125.30 45703.23 39729.90 32738.92 18699.02

0.77 0.75 0.74 0.83 0.84 0.75 0.67

0.89 0.88 0.88 0.93 0.93 0.85 0.80



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Figure 1


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Figure 2



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Figure 3


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Figure 4



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Figure 5


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Figure 6



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Figure 7


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Figure 8



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Figure 9


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Figure 10



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Figure 11


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Figure 12



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Figure 13


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Figure 14



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Figure 15


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Figure 16



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Graphical Abstract


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Hybrid Dendrimers of PPI(core)âPAMAM(shell): A Molecular

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