Molecular Dynamics Study of the Structure, Flexibility, and

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Molecular Dynamics Study of the Structure, Flexibility and Hydrophilicity of PETIM Dendrimers: a Comparison with PAMAM Dendrimers Subbarao Kanchi, Gorle Suresh, U. Deva Priyakumar, K Ganapathy Ayappa, and Prabal K. Maiti J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 17 Sep 2015 Downloaded from http://pubs.acs.org on September 21, 2015

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The Journal of Physical Chemistry

Molecular Dynamics Study of the Structure, Flexibility and Hydrophilicity of PETIM Dendrimers: a Comparison with PAMAM Dendrimers

Subbarao Kanchia,c, Gorle Sureshb, U. Deva Priyakumarb, K. G. Ayappac and Prabal K Maiti*a a Center for condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore b Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad, 500032, India c Department of Chemical Engineering, Center for Biosystems Science and Engineering, Indian Institute of Science, Bangalore 560012

Abstract A new class of dendrimers, the poly (propyl ether imine) (PETIM) dendrimer, has been shown to be a novel hyper branched polymer having potential applications as a drug delivery vehicle. Structure and dynamics of the amine terminated PETIM dendrimer and their changes with respect to the dendrimer generation are poorly understood. Since most drugs are hydrophobic in nature, the extent of hydrophobicity of the dendrimer core is related to its drug encapsulation and retention efficacy. In this study, we carry out long time scale fully atomistic molecular dynamics (MD) simulations to characterize the structure of PETIM (G2-G6) dendrimers in salt solution as a function of dendrimer generation at different protonation levels. Structural properties such as radius of gyration (Rg), radial density distribution, aspect ratio and asphericity are calculated. In order to assess the hydrophilicity of the dendrimer, we compute the number of bound water molecules in the interior of dendrimer as well as the number of dendrimer-water hydrogen bonds. We conclude that PETIM dendrimers have relatively greater hydrophobicity and flexibility when compared with their extensively investigated PAMAM counterparts. Hence PETIM dendrimers are expected to have stronger interactions with lipid membranes as well as improved drug encapsulation and retention properties when compared with PAMAM dendrimers. We compute the root mean square fluctuation of dendrimers as well their entropy to quantify the flexibility of the dendrimer. Finally we note that structural

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and solvation properties computed using force field parameters derived based on the CHARMM general purpose force field were in good quantitative agreement with those obtained using the generalized Amber force field (GAFF). Corresponding Author * Prabal K Maiti, Center for condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore. Phone: (091)80-2293-2865. E-mail: [email protected].

Keywords: Molecular dynamics, CHARMM/GAFF force field, Radius of gyration, Aspect ratios, Asphericity, RMSF.


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Introduction Dendrimers are three-dimensional polymeric nanostructures having a central core molecule connected by successive dendritic branching layers1-2. The structure controlled parameters of dendrimers such as size, shape, surface chemistry, flexibility and architecture facilitate a wide range of applications in bio-medicine3-12, sensing13, catalysis14 and light harvesting15. Poly (amido amine) (PAMAM) dendrimer properties and its applications have been well studied using experiments16-18 and simulations19-28 after they were introduced in 1985 by Tomalia et al29-30. Over the last decade, poly (propyl ether imine) (PETIM) dendrimers with oxygen or nitrogen cores have emerged as a new subclass of dendrimers. PETIM dendrimers have attracted a significant amount of research interest because of their lower cytotoxicity31 and potential applications in gene therapy32, drug delivery33 and siRNA delivery34-36. Compared to more well-known PAMAM dendrimer, toxicity levels of PETIM dendrimers are very mild31. Lower cytotoxicity makes them promising candidates for drug and gene delivery vehicles37. Earlier we have reported the structural properties of carboxylic acid terminated neutral PETIM dendrimer from generation 1 through 6 using fully atomistic MD simulation in combination with SAXS experiments38. Carboxyl terminated PETIM dendrimers were found to more flexible and larger in size compared to PAMAM dendrimers of similar generation. Hence one can replace a PAMAM dendrimer with a lower generation PETIM dendrimer thereby leveraging the lowered cytotoxicity associated with lower generation dendrimers. Additionally PETIM dendrimers exhibit interesting inherent photoluminescence at 390 nm39 which is absent in the case of PAMAM. All these properties point to the possibility of using PETIM dendrimers in applications where PAMAM dendrimers have shown potential. The nitrogen core (N-core) PETIM dendrimer possesses tertiary amines in the core, as well as in the branch point. N-core PETIM dendrimers having a three-directional core, offers larger number of branching sites and primary amines in a lower generation, when compared with the oxygen core (O-core) PETIM dendrimer with bi-directional core. For example, a G3 O-core PETIM dendrimer contains 16 primary amines at the periphery and



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10 tertiary amines at the interior, whereas the G3 N-core PETIM dendrimer possess 24 primary amines at the periphery and 22 tertiary amines at the interior. These differences are expected to distinctly influence the degree of solvation and hydrophilicity in PETIM dendrimers. The dendrimer structure, hydrophilicity, flexibility and PH of the solvent are important properties that influence dendrimer solubility, drug loading capacity 40-42 and binding affinity with nucleic acids43-47 or cell membranes48-50. These applications require a comprehensive understanding of the structure, dynamics and solvation of PETIM dendrimers which has thus far not been systematically investigated. In this manuscript we carry out molecular dynamics simulations on PETIM dendrimers using a CHARMM51 compatible force field (FF) and study various structural properties of both the N-core and O-core PTEIM dendrimer as a function of generation at different protonation levels. We also compare and contrast the structural properties of PETIM dendrimers with those of PAMAM dendrimers of similar generation to highlight differences which will serve as guide while selecting dendrimers for a specific biological application. The rest of the paper is organized as follows: in the methods section we give details of FF generation, dendrimer building and simulation methodologies, in section III, we discuss various results obtained from the all atom simulation for both the N-core and O-core PETIM dendrimer of various generations. In section IV, we compare the results obtained using CHARMM FF with those obtained using GAFF52. In section V, we compare various properties for both the PETIM and PAMAM dendrimer and finally we conclude.

Methods Initial structures of both O-core and N-core PETIM dendrimers were built using the dendrimer building toolkit (DBT)53. CHARMM topology and parameters files for the PETIM dendrimers were developed using CHARMM general force field (CGenFF)54 and ether parameters55. Initially, three residues corresponding to the core (CORE), the repeating unit (AMT) and terminal unit (TERM) of the two dendrimers were conceived based on the structure of the dendrimers (Figure 1). The core regions of these two dendrimers (O-core and N-core) are


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different from each other whereas the repeating unit and terminals are identical. For Ncore dendrimer, (NH3) is defined as the core residue while (NH2CH2CH2CH2OCH2CH2NH2) is defined as the core residue for O-core dendrimer. The AMT residue is defined as (CH3CH2CH2OCH2CH2CH2NH2) and CH2NH2 is defined as TERM residue. AMT residue is the repeating unit, which decides the generation stage of dendrimers. For protonated dendrimers, the terminal residue TERM is defined as CH2NH3+. Atom types were assigned to each of the atoms forming these residues based on the CHARMM general force field (CGenFF). CGenFF provides a convenient method to derive force field parameters for simple organic molecules based on analogy in reference to a set of common fragments that are rigorously parameterized. The procedure of the parameterization is similar to that of the currently existing CHARMM atomistic force fields for proteins56, nucleic acids57, lipids and carbohydrates58, and hence may be seamlessly be used together. Atom types and the corresponding charges were derived from CGenFF. The list of bonds, angles, and dihedrals were generated based on topology, and the corresponding parameters were obtained. Non-bonded parameters were obtained in a similar fashion. The charges to accommodate the two different terminals were derived based on the amine and protonated amine model systems. The topology (figures: S7, S8 and S9) and parameters (tables: S1 to S7) corresponding to these residues that were used to model the dendrimer structures are provided in the supporting information. The dendrimer structures of various generations were solvated with TIP3P59 water using VMD60 with 15 Å buffer in all directions. In addition, for 100% protonated dendrimer appropriate numbers of Cl− counter ions were add to make a charge neutral system. For example, for G3 nitrogen core PETIM dendrimer, 16 Cl− ions were added. The details of various systems simulated are given in table 1. Simulations were carried out using NAMD code version 2.961. The solvated dendrimer systems were then subjected to 500 steps of steepest−descent minimization followed by 500 steps of conjugate−gradient minimization. During the minimization, the dendrimer was restrained to its starting configuration using a harmonic potential with a force constant of 1000 kcal mol−1 Å−2. This allowed appropriate reorganization of solvent molecules and ions by removing bad contacts. Subsequently, the



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entire system was subjected to 1000 steps of steepest−descent minimization followed by 1500 steps of conjugate−gradient minimization by releasing the restraints on the dendrimer. The energy minimized systems were then subjected to 1 ns of NVT equilibration using 2 fs time step for integration. During the NVT equilibration, systems were gradually heated from 0 to 300 K by using harmonic constraints with a force constant of 10 mol−1 Å−2. The temperature was controlled using Langevin thermostat62 with a damping coefficient of 1ps. Subsequently, 50ns long MD simulations of production run were performed in the NPT ensemble at 1 atm with periodic boundary conditions in all three directions. Nosé−Hoover Langevin barostat pressure control63 was used to apply isotropic pressure of 1 atm with a piston period of 0.2 ps and damping time constant of 0.05 ps. The long rang electrostatic interactions were calculated with particle mesh Ewald (PME)64 method with a real space cutoff of 12 Å. During the simulation, the bond lengths involving hydrogen atoms were constrained using the SHAKE algorithm65. Earlier we have demonstrated the accuracy of GAFF in describing the structural properties of various dendrimer systems in quantitative agreement with experimental data 53, 66. In this manuscript we compare those results with the results in this study obtained using the CHARMM FF (Figure S1 to S6). For the purposes of comparison, we have also simulated the dendrimer system using GAFF FF52. Systems were created by solvating dendrimers with water in xleap and MD simulations were carried out using the AMBER MD package67 with GAFF FF52 for dendrimers and TIP3P59 model for water. The bonded (bond, angle, dihedral) and non-bonded (Lennard-Jones) parameters (tables S5, S6, S7 and S4) and partial charges (tables S1 to S3) are provided in the supporting information.

Results and discussions Radius of gyration The radius of gyration (Rg) of dendrimer is a measure of the size of the dendrimer and is defined as 〈

〉

( ⁄ )〈[∑

|

| ]〉

( )

where mi is the mass and ri is the position vector of ith atom, R is the position of the center of mass and M is the total mass of the dendrimer. The radius of gyration is calculated for all


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generations of O-core PETIM dendrimers and is shown as a function of generation in figure 2(a). The corresponding values have been listed in table 2. The Rg of protonated dendrimer is larger compared to those of non-protonated dendrimers due to the increased electrostatic repulsion between the terminal amine groups which increases with dendrimer generation. This increase in Rg due to protonation is observed for the O-core and N-core dendrimers. In general we observe that the N-core dendrimers have a larger Rg when compared with the O-core of similar generation due to the greater amine density and branching. This increased branching also leads to a greater % increase in Rg with protonation for N-core dendrimers. Hence in the case of N-core, protonation leads to an increase of about 46 % for the G4 dendrimer. In comparison a modest 17 % increase is observed for the O-core dendrimers for the same generation. This pH responsive swelling behavior of the PETIM dendrimer is similar to the behavior observed for PAMAM dendrimers38, 42, 66 and has implications for drug encapsulation. In the case of PETIM dendrimers the nature of the core plays a strong role in several of the dendrimer properties. The values obtained between the two force fields (GAFF and CHARMM) were found to be similar for the generation 3 and 4 dendrimers. We observed a weak dependence of Rg at the lower generations and sharp increase in Rg is observed beyond the 4th generation. We also computed the Rg of dendrimers from the principle shape tensor using where

,

and

√

are the principle moments of inertia of dendrimer shape tensor. There is

good agreement between the two Rg values as illustrated in figure 2(b). Aspect ratios and Asphericity To assess the shape anisotropy the dendrimer as a function of dendrimer generation and protonation level, we have calculated the shape gyration tensor of the dendrimer. The principle moments of inertia of the dendrimer are calculated by diagonalizing the gyration matrix Gmn, whose elements are defined as68 [∑

(

)(

)]


( )


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where rmi and Rm are co-ordinates of atoms and the center of mass of the dendrimer respectively,

is the mass of

eigenvalues of Gmn are ,

atom and M is the total mass of the dendrimer. The three

and

(descending order). The aspect ratio of the principle

moments of inertia gives the information about the shape of the dendrimer. The aspect ratios ⁄

and ⁄

of protonated and non-protonated O-core dendrimers are plotted as a

function of dendrimer generation (figure 3(a) 3(b)). The aspect ratios are higher for smaller generation (G2, G3) dendrimers and are almost constant for the larger generation (G4, G5 and G6) dendrimers. Our data clearly shows that the smaller generation dendrimers show greater shape anisotropy when compared with the larger dendrimers for both protonated and non-protonated dendrimers. The asphericity gives more quantitative information about the shape of the dendrimer in addition to the information we get from the aspect ratios. The asphericity (δ) is defined as69

( where

,

and

)

( )

are defined as

In figure 3(c) we plot the asphericity as a function of dendrimer generation. The asphericity decreases rapidly with increase in dendrimer generation indicating the fact that the smaller generation dendrimers are more anisotropic in shape and larger generation dendrimers become more spherical in shape. Figure 4 supports this behavior where we show the instantaneous snapshots of various O-core non-protonated dendrimers of different generations. The higher generation dendrimers assume a more globular shape when compared with the lower generation dendrimers. The snapshots of the protonated dendrimers (Figure 5) show a larger degree of anisotropy with extended arms that protrude outward, when compared with their non-protonated counterparts. Protonation increases the affinity toward water and the protrusions benefit from increased hydration


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with the aqueous environment. Our study shows that the larger generation dendrimers are less flexible and more isotropic in nature. The distributions of aspect ratios and asphericity as indicated by the errors are higher in case of the smaller size (G2, G3) dendrimers which also indicates that lower generation dendrimers are more flexible when compared with the higher generations (G4, G5 and G6). Density distributions The dendrimer structural attributes are to a large extent dictated by the manner in which the mass is distributed within the dendrimer with respect to its center of mass. In order to understand the monomer/mass distribution within a dendrimer, we have calculated the average radial monomer density for both the oxygen core and nitrogen core PETIM dendrimer at various protonation levels. In each case we take the origin as the center of mass. Figure 4 shows the radial monomer density profiles for non-protonated dendrimers from G2 to G6. For each generation, the plot shows the contributions to a particular generation (G) from each of its component generations (g-G).

A number of features deserve attention and are similar to other classes of dendrimers reported in the literature16,

42, 66, 70-71.

We see significant back folding of the outer

generation to the core of the dendrimer38. For higher generation dendrimers such as G4G6, there is a constant density zone in the middle of the dendrimer signifying the compact nature of the higher generation dendrimer. The radial distance over which density remains constant, increases with increasing dendrimer generation. In contrast, for protonated dendrimers (Figure 5), due to the electrostatic repulsion between the protonated amines, the degree of back folding decreases. Additionally the region of constant density is restricted to a much smaller region near the dendrimer center since the branches are more spread out.

In each case, the density shows a maximum toward the center of the

dendrimer and the overall density decays more gradually toward the surface of the dendrimer. This is a consequence of the higher level of outwardly extended arms on the dendrimer as observed in the simulation snapshots of the dendrimer. The flatter density



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distribution observed for non-protonated dendrimers is similar to the distributions observed for polymer brushes in good solvents72. The radial distributions of terminals groups with respect to other terminal groups for both the protonated and non-protonated O-core PETIM dendrimers are calculated as a function of dendrimer generation (Figure 8(a) and Figure 8(b)). These distributions as a function of dendrimer generations when compared in the units of their radius of gyrations provide information about the spatial arrangement of the terminal groups73. The peak of the radial distribution function shifts towards the core of the dendrimer with the increase in generation for both the non-protonated and protonated dendrimers and the shift in the peak is greater for protonated dendrimers when compared with non-protonated dendrimers. This is a consequence of the increase in the density of the terminals groups and the decrease in the inter-atomic distance with increase in dendrimer generation. As a result, the higher generation dendrimer is more rigid when compared to the lower generation dendrimer. This effect is more pronounced in case of protonated dendrimers due to the electrostatic repulsion between the terminal groups. Surface and Bound Water As a measure of the hydrophilicity of the dendrimer we evaluate the number of bound water molecules that hydrate the interior as well as the surface of the dendrimer. The calculation of bound water by using the simple distance cut-off criterion is not an accurate measure due to the asphericity of the dendrimer structure as well as the roughness of the dendrimer surface. To resolve this issue, we have used a criteria developed in our previous work74. We briefly outline the procedure below: The solvent accessible surface area (SASA) of each of the dendrimer atoms was calculated using a large probe of radius 6 Å. Those atoms with non-zero SASA we identified as dendrimer surface atoms. We next calculated the surface bound waters (nsurf ) which are within 4 Å from the dendrimer surface atoms. The buried domain is defined as the internal regime of dendrimer, 3 Å away from the surface atoms.

We calculated the bound waters (ninner) which are in the buried domain of the dendrimer by excluding the surface bound waters. Bulk bound waters (nbulk) are water molecules that lie


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between 4 to 7 Å from the surface dendrimer atoms, excluding the surface, inner bound waters as explained in ref74. Number of buried (ninner,), surface (nsurf) and bulk (nbulk) water as a function of dendrimer generation for O-core dendrimers are shown in Figure 6(a), (b) and (c), respectively. Number of buried, surface and bulk waters increases with dendrimer generation for both the protonated and non-protonated dendrimers. We find that nbulk > nsurf > ninner for any given generation of dendrimer. Figure 6 clearly shows that the number of bound water molecules for protonated dendrimers is always significantly higher when compared with the non-protonated dendrimers. The ninner water molecules reflect the available void space within the dendrimer to accommodate water molecules. The protonated dendrimers swells up due to the strong electrostatic repulsion between the branches and can solvate a larger number of water molecules when compared with the non-protonated dendrimers. The more uniform density distribution (Figure 4) observed for the non-protonated dendrimers is a reflection of the reduced space available for water molecules to solvate the inner core of the dendrimer. In contrast, the slowly decaying density distributions of the P dendrimers (Figure 5) indicate larger available void space to accommodate water molecules. The density distributions, which are a reflection of the topology induced by protonation of the dendrimer, determines the extent of hydrophilicity for the dendrimers. It is interesting at this point to compare the changes in solvation when the O-core is replaced with the N-core (table 2). The total amount of water uptake increases for the Ncore dendrimers due to the increased branching when compared with the O-core dendrimers. Similar to the trends observed for the O-core dendrimers, protonated N-core dendrimers show a greater propensity for water uptake and the increase in the water uptake is significantly greater for the N-core dendrimers upon protonation (table 2). Hydrogen bonds We have also calculated the number of hydrogen bonds a dendrimer makes with the buried water. We use a distance cut-off of 3.5 Å and angle cut-off of 30º between donor and



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acceptor to identify a hydrogen bond. We find that the number of hydrogen bonds increases with dendrimer generation for both the protonated and the non-protonated dendrimers as shown in table 6. The increase in the number of hydrogen bonds correlates well with the increase in the number of buried water as a function of the dendrimer generation as well as protonation levels. Lower number of hydrogen bonds for PETIM dendrimer compared to PAMAM dendrimer of equivalent generation also indicates lesser number of buried water molecules for the PETIM dendrimer. The hydrogen bonding which is a measure of the hydrophilicity, indicates that PAMAM dendrimers are significantly more hydrophilic when compared with their PETIM counterparts. The number of hydrogen bonds between water and dendrimer amines are given in table 7 on a per amine basis. This number decreases with increasing generation in all the dendrimers examined. The reason could be attributed to the increase in shared hydrogen bonds between the amine bonds as the generation is increased. As consequence the largest number of hydrogen bonds per amine is observed for G2 in the O-core dendrimers. Interestingly the number of hydrogen bonds for the N-core protonated PETIM dendrimers is similar to that observed for bulk water75. Entropy Entropy of oxygen core PETIM dendrimers is calculated using two phase thermodynamic model76-77. It is observed that the entropy increases with generation of dendrimer whereas entropy per atom remains almost constant for both protonated and non-protonated dendrimers (as shown in table 4 and 5). Translational and rotational entropy per atom both decrease with dendrimer generation and their contributions are significantly smaller when compared to the vibrational entropy of water. This reduction in translation and rotational entropy is a reflection of the greater packing and enhanced rigidity of the dendrimers with increasing generation. Due to the increase in the number of hydrogen bonds for the protonated O-core dendrimers (table 6) we observed a small but consistent decrease in the total entropy (table 5) when compared with the total entropy for the nonprotonated case (table 4). Root mean square fluctuations (RMSF)


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To quantify the flexibility of the dendrimer for a given generation we have calculated the root mean square fluctuation (RMSF) defined as ∑ √ ∑

( ( )

〈 〉)

( )

where, N is the number of terminal amines, r(t) is the position at time t and is the time average position of the amine. RMSF of amines in each inner shell of dendrimer is calculated to quantify the dendrimer flexibility. The RMSF of inner shells decreases with dendrimer generation for both protonated and non-protonated PETIM dendrimers as shown in Figure 7. This indicates that the flexibility of the inner part of the dendrimer decrease with the dendrimer generation. Comparing the RMSF for a given generation for both the N-core and O-core PETIM dendrimer, we find that O-core PETIM dendrimer is more flexible compared to the N-core dendrimer. Protonation levels do not change the RMSF values significantly for the smaller generation dendrimers, however the inner generations in the larger generation dendrimers (G5, G6) show a smaller RMSF upon protonation (figure 7a and 7b). We have also made a comparison of the RMSF between PAMAM (figure 7e and 7f) and PETIM dendrimers for equivalent generations and find that PETIM dendrimers are more flexible, as reflected in the higher RMSFs, when compared to the PAMAM dendrimer. This enhanced flexibility of PETIM dendrimers has been found to influence their interaction with lipid bilayer membranes

50.

It is worth mentioning here

that very recently Pavan and co-workers78-79 have performed enhanced metadynamics simulation on several dendrimer systems and reported lower values of Rg compared to those obtained from classical MD simulations. This led them to conclude that, possibly classical MD simulations overestimate dendrimer structural flexibility. Effect of core functionality: We compared

number of bound waters and asphericity (Table 2) of O-core and N-core

PETIM dendrimers. It is observed that

of N-core dendrimers is high compared to O-core

dendrimers because of more number of branches. The number of bound waters (ninner, nsurf and nbulk) of N-core dendrimers is more and nearly 1.5 times of the number of bound waters of O-core dendrimers for both protonated and non-protonated case. Interestingly, the entropy of N-core dendrimers is also high compared to O-core dendrimers and it is



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nearly 1.5 times of the entropy of O-core dendrimers. The reason for this trend is because of the presence of an extra branch in the N-core dendrimers compared to O-core dendrimers. Asphericity of protonated dendrimers is always higher compared to nonprotonated dendrimers but the degree of increment is very high in case of N-core dendrimers (as shown in table 2). This indicates that the N-core dendrimers become more shape anisotropic compared to O-core dendrimers at low PH because of electrostatic repulsion between large number of protonated terminal groups. RMSF of inner shells of dendrimer decreases with the generation of dendrimer for both Ocore and N-core dendrimers. The RMSF of O-core dendrimers is higher compared to N-core dendrimers as shown in figure 7c and 7d, indicating that the O-core dendrimers are more flexible compared to N-core dendrimers. This is because the N-core dendrimers have more number of branching units and becomes compact compared to O-core dendrimers.

Comparison between PETIM and PAMAM dendrimers Number of terminal groups of O-core PETIM dendrimers follows

(

)

whereas number of

terminal groups of ethylenediamine (EDA)-core PAMAM dendrimer follows

(

)

, where,

G is the generation of the dendrimer. It shows that the number of terminals in Gth generation of PAMAM dendrimer are equal to number of terminals in (G+1)th generation of O-core PETIM dendrimer. We compared properties of PETIM and PAMAM and shown in Table 3.

values of dendrimers show that size of Gth generation of PAMAM dendrimer is

almost equal to size of (G+1)th generation of O-core PETIM dendrimer. The number of inner bound waters (ninner) inside PAMAM dendrimer is significantly higher when compared when a similar sized PETIM dendrimers but the number of surface bound waters (nsurf) and bulk waters (nbulk) are almost equal for both PAMAM and PETIM dendrimers. It clearly shows that the PETIM dendrimers are less hydrophilic when compared with their PAMAM counterparts. This is a very important observation from our present atomistic simulation. The number of surface bound waters and bulk bound waters of both PETIM and PAMAM are nearly equal because of equal number of terminal groups. The comparison of hydrogen bonds number between water and dendrimer (shown in table 6) also concludes that the


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PETIM dendrimers are less hydrophilic compared to PAMAM. This is important consequence for drug encapsulation, since drugs that are predominantly hydrophobic in nature would preferably partition in to the PETIM interior when compared with the PAMAM interior due to the reduced hydrophilicity of the PETIM dendrimer as illustrated in our study. This increased hydrophobicity of the PETIM interior is also expected to enhance the free energy of interaction with the predominantly hydrophobic interior of the lipid bilayers50. The RMSF of PETIM dendrimers is higher compared to PAMAM dendrimers and indicating that the PETIM dendrimers are more flexible. We find that the RMSF of inner shells of the PETIM dendrimer decreases with increasing dendrimer generation. However in the case of PAMAM, the RMSF is relatively insensitive to the dendrimer generation. Summary and Conclusions To summarize, we have derived a CHARMM compatible FF for a new class of PETIM dendrimer of varying core functionality to understand its structure and dynamic properties as a function of dendrimer generation and protonation.

We have calculated several

structural features such as Rg, aspect ratios, asphericity and radial monomer density profile to characterize the molecular structure of this new class of dendrimers. We also compare and contrast the properties of the PETIM dendrimers with their PAMAM counterparts. Our study illustrates that the core functionality and the resulting changes in dendrimer branching topology has a significant influence on several of the structural properties evaluated in this study. Due to the decreased branching and amine density, protonation leads to a smaller increase in the Rg on the O-core PETIM dendrimers, when compared with N-core dendrimers. Shape anisotropy effects due to protonation were larger at the smaller generations (< 4). Overall the topology of the protonated O-core dendrimers had a higher degree of surface protrusions due to the increased affinity to solvate the protonated branches. Hence the density distributions showed larger variation from the dendrimer core to the outer surface when compared with the relatively uniform density distributions observed for the non-protonated O-core dendrimers. Accounting for these difference in



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density distributions are important while developing mean field theories where model distributions are required as an input. Assessing the hydrophobicity of the dendrimer is an important attribute that influences drug encapsulation and retention properties. Based on the number of water molecules bound (hydration) to the dendrimer surface and the interior of the dendrimer, two main inferences can be drawn; N-core PETIM dendrimers are more hydrophilic when compared with the O-core counterparts with hydrophilicity increasing with protonation. O-core PETIM dendrimers showed the greatest degree of inner core hydrophobicity when compared with both EDA–core PAMAM dendrimers or N-core PETIM dendrimers. RMSF calculations show that the PETIM dendrimers are in general more flexible than the PAMAM dendrimers. The increased hydrophobicity of PETIM dendrimers suggests that these dendrimers which have been shown to be less toxic31, have a greater potential for drug encapsulation and retention when compared with their PAMAM counterparts. Dendrimer interaction with the plasma membrane is another important aspect for developing effective drug and gene delivery systems. Greater flexibility combined with inner core hydrophobicity indicate that the PETIM – plasma membrane interactions will be enhanced to a greater extent when compared with the PAMAM dendrimers. Recent MD simulations of PETIM dendrimers with lipid bilayer membrane illustrate a strong tendency for PETIM dendrimers to be incorporated within the bilayer interior50. Another important contribution of the present manuscript is with reference to the currently available forcefields for dendrimer simulations. The parameters used in the manuscript for PETIM dendrimers derived using the CHARMM generalized force field capture, Rg, shape anisotropy as well as hydration properties with similar accuracy as the GAFF force field. This validates the current CHARMM parameter set developed in this manuscript for MD simulations of PETIM dendrimers, thereby facilitating simulations of these dendrimers along with other CHARMM compatible protein and lipid force fields. Acknowledgements


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We thank DST, India for financial support. SK thanks UGC (University Grants Commission, India) and GS thanks CSIR for a research fellowship. Supporting Information The average absolute dispersion (AAD), average relative dispersion (ARD) and root mean square error (RMSE) of Rg for different dendrimer systems are reported in Table S1. Simulation snapshots, radius of gyration and radial density distribution profiles for both the O-core and N-core PETIM dendrimers at different protonation levels are shown in figures S1 to S6. Residue topologies and partial charges for the residues CORE, AMT and TERM are provided in figure S7 to S9 and tables S1 to S3. Force field parameters for nonbond L-J parameters and bonded parameters (bond, angle and dihedral) are provided in the tables S4 to S7. Since we have compared several structural quantities across the different dendrimer systems, in addition to the root mean square errors (RMSE) reported in the main text we have also added the average absolute deviations (AAD) and the average relative deviations (ARD) in the supporting information. This information is available free of charge via the Internet at http://pubs.acs.org.



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 Property 33 34 35 36 (Å) 37 38 39 ninner 40 41 42 n surf 43 44 45 nbulk 46 47 δ 48 49 50 51 52 53 54 55 56 57 58 59 60

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Table1: Details of different dendrimer systems simulated. Generation

G2 G3 G4 G5 G6

Amine terminated PETIM O-core O-core N-core O-core N-core O-core O-core

Number of dendrimer atoms 277 613 949 1285 1957 2629 5317

3

Terminal nitrogens

Number of waters

Total Number of atoms

Simulation box (Å ) (X x Y x Z)

8 16 24 32 48 64 128

6438 7430 11978 15668 20293 35796 54401

19591 22903 36883 48289 62836 110017 168520

71.78 x 67.67 x 39.92 71.25 x 61.87 x 51.50 73.75 x 84.29 x 58.57 92.85 x 82.97 x 61.69 74.38 x 83.24 x 99.91 111.14 x 101.72 x 96.06 131.80 x 123.81 x 102.07

Table2: Comparison of different properties between O-core and N-core dendrimers and Rg = radius of gyration, ninner = inner bound waters, nsurf = surface bound waters, nbulk = bulk bound waters, δ= asphericity. O-core

N-core

Non-protonated G3 G4 9.70±0.41 11.78±0.17

Protonated G3 G4 11.56±0.69 13.79±0.36

Non-protonated G3 G4 11.02±0.27 14.03±0.33

Protonated G3 G4 14.46±0.63 20.53±0.81

4.36±2.01

8.46±2.46

9.68±2.61

39.74±5.19

11.1±3.01

15.74±4.66

11.87±3.22

263.40±9.34

430.64±11.93

358.50±8.93

576.88±14.08

366.85±10.64

590.12±14.82

463.83±11.80

886.86±16.53

424.0±13.66

640.60±16.10

584.10±15.32

898.22±19.28

544.94±17.02

847.31±18.38

734.79±16.74

1343.06±22.60

0.09±0.02

0.036±0.002

0.18±0.058

0.06±0.008

0.067±0.008

0.08±0.01

0.34±0.08


53.37±7.88

0.295± 0.062

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1 2 3 Table3: Comparison of different properties between O-core PETIM and PAMAM dendrimers. 4 5 O-core PETIM EDA-core PAMAM 6 Property 7 Non-protonated Protonated Non-protonated Protonated 8 G4 G5 G4 G5 G3 G4 G3 G4 9 (Å) 11.78±0.17 15.33±0.30 13.79±0.36 19.40±0.35 12.58±0.18 16.0±0.24 16.0±0.24 19.23±0.23 10 11 12 ninner 8.46±2.46 27.34±4.59 39.74±5.19 99.84±11.56 22.61±2.77 68.03±6.41 58.10±7.80 150.30±13.87 13 14 n 430.64±11.93 676.26±14.82 576.88±14.08 1017.64±18.08 468.56±11.76 764.67±16.27 558.51±13.72 1048.40±19.08 surf 15 16 640.60±16.10 952.26±23.37 898.22±19.28 1530.36±24.33 700.96±17.82 1095.75±18.86 880.84±18.54 1606.0±36.02 17 nbulk 18 δ 0.036±0.002 0.07±0.007 0.06±0.008 0.085±0.008 0.078±0.006 0.116±0.008 0.151±0.029 0.0539±0.004 19 20 21 22 23 Table4: Translational, rotational and vibrational entropy of non-protonated oxygen core PETIM 24 25 dendrimers using 2PT method. 26 27 Generation Number Translational Rotational Vibrational Total 28 of 29 atoms 30 ST ST/atom SR SR/atom SV SV/atom S S/atom 31 G2 (O-core) 277 100.01±3.86 0.36 91.52±8.83 0.33 4339.24±34.16 15.67 4530.77±38.08 16.36 32 G3 (O-core) 613 108.94±2.99 0.18 94.98±5.38 0.16 9768.65±89.06 15.94 9972.56±86.81 16.27 33 G3 (N-core) 949 111.02±1.42 0.12 94.66±1.93 0.10 15076.98±86.26 15.89 15190.59±135.68 16.01 34 35 G4 (O-core) 1285 112.73±1.67 0.09 94.94±1.32 0.07 20219.88±103.97 15.74 20427.54±104.16 15.90 36 G4 (N-core) 1957 113.97±2.71 0.06 102.59±6.90 0.05 30983.47±353.78 15.83 31200.03±349.93 15.94 37 G5 (O-core) 2629 118.16±4.17 0.05 101.73±2.80 0.04 41920.04±313.94 15.95 42139.93±309.94 16.03 38 G6 (O-core) 5317 122.29±5.36 0.02 102.73±3.78 0.02 85451.31±374.25 16.07 85676.32±369.67 16.11 39 40 41 Table5: Translational, rotational and vibrational entropy of protonated Oxygen core PETIM 42 43 dendrimers using the 2PT method. 44 45 Generation Number Translational Rotational Vibrational Total 46 of 47 atoms 48 ST ST/atom SR SR/atom SV SV/atom S S/atom 49 50 G2 (O-core) 285 98.68±2.63 0.35 89.73±4.30 0.32 4150.60±30.05 14.56 4339.00±28.23 15.23 51 G3 (O-core) 629 98.82±2.00 0.16 80.05±3.39 0.13 9420.63±34.54 14.98 9599.50±33.60 15.26 52 G3 (N-core) 973 98.94±1.64 0.10 85.66±3.59 0.09 14667.24±2.90 15.14 14914.61±61.00 15.33 53 G4 (O-core) 1317 107.38±2.44 0.08 91.98±2.61 0.06 20068.29±37.28 15.24 20261.70±35.68 15.38 54 G4 (N-core) 2005 104.68±5.86 0.05 92.80±5.78 0.05 29827.20±54.88 14.88 30024.67±59.39 14.98 55 G5 (O-core) 2693 107.38±4.68 0.04 91.98±2.61 0.03 40950.16±237.61 15.21 41149.52±240.09 15.28 56 G6 (O-core) 5445 109.62±3.27 0.02 91.48±3.02 0.02 82996.71±199.17 15.24 83197.80±156.71 15.28 57 58 59 60 ACS Paragon Plus Environment


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Table6: Number of hydrogen bonds between water and dendrimer compared for the different systems investigated Generation

G2 G3 G4 G5 G6

Oxygen core PETIM Non-protonated 14.60 24.09 43.0 73.57 130.61

Nitrogen core PETIM

protonated 25.65 48.69 95.40 187.44 363.93

PAMAM

Non-protonated

protonated

Non-protonated

protonated

33.92 59.37

74.50 146.13

114.26 217.201

148.95 295.15

Table7: Number of hydrogen bonds between water and dendrimer per amine compared for the different systems investigated. Generation

G2 G3 G4 G5 G6

Oxygen core PETIM Non-protonated 1.04 0.80 0.69 0.58 0.51

Nitrogen core PETIM

protonated 1.83 1.62 1.54 1.49 1.43

PAMAM

Non-protonated

protonated

Non-protonated

protonated

1.62 1.38

3.55 3.40

1.84 1.72

2.40 2.34


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a)

b)

Figure 1: 2D representation of a) G3 oxygen core PETIM dendrimer and b) G3 nitrogen core dendrimer.



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a)

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b)

Figure 2: Rg for O-core PETIM dendrimers function of dendrimer generation. a) Comparision of Rg from CHARMM and GAFF force fields, b) Comparing Rg derived using the shape tensor. Protonation is seen to increase the Rg, with greater differences between the non-protonated and protonated dendrimers occuring at the higher generations.


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a)

b)

c)

Figure 3: Variation of aspect ratios and asphericity for the O-core dendrimers as a function of dendrimer generation. a) Ratio of principle shape tensors Iz and Iy , b) ratio of principle shape tensors Iz and Ix and c) aspheicity (δ). In general, larger shape variations are observed due to protonation at the lower generations. Differences due to protonation are reduced at the higher generations.



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a)

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b) G2

G3

G4

G5

G6

Figure 4: a) Final snapshots of the simulation b) Radial number density profiles of non protonated O-core PETIM dendrimers from generation 2 to 6 (where “g” is the interier sub generation and “G” is the actual geneartion of the dendrimer). In general the overall density distribution is relatively constant within the dendrimer interior, consistent with the some what globular nature of the dendrimers as seen in the snapshots (b).


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b)

a) G2

G3

G4

G5

G6

Figure 5: a) Final snapshots of the simulation b) Radial number density profiles of protonated Ocore dendrimers from generation 2 to 6 (where “g” is the interier sub generation and “G” is the actual geneartion of the dendrimer). In contrast to the non-protonated case (Figure 4) the overall density distributions vary across the dendrimer to a greater extent and the density is seen to have a much slower decay toward the surface of the dendrimer. These changes in density distributions are a consequence of the extended branching observed in the simulation snapshots (a).



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

a)

d)

Protonated

Page 26 of 33

Non-protonated

b)

c)

Figure 6: Number of bound water molecules as a function of dendrimer generation for the Ocore PETIM dendrimers. a) Inner bound waters (ninner), b) surface bound waters (nsurf), c) bulk waters (nbulk) and d) snapshots showing bound waters (Green-dendrimer, Red-ninner, Blue-nsurf, Grey-nbulk). Protonation has a significant effect on the water uptake by the dendrimers, increasing both the inner and surface waters at the higher generations.


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a)

c)

e)

b)

d)

f)

Figure 7: Root mean square fluctuations as a function of dendrimer generation (“Amine generation” represents inner amines coresponding to sub generation shell of the dendrimer). a) non protonated PETIM, b) protonated PETIM, c) comparison between O-core and N-core non protonated PETIM, d) comparison between O core and N core protonated PETIM, e) non protonated PAMAM and f) protonated PAMAM.



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

a)

b)

Figure 8: Radial distribution functions of terminal groups for a) non-protonated O-core PETIM and b) protonated O-core PETIM dendrimers.


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PETIM PETIM Protonated Non-protonated

G3 O-core

G3 N-core

Dendrimer bound waters

Table of Contents (TOC) – Graphic


Molecular Dynamics Study of the Structure, Flexibility, and

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