Diffusion of flexible, charged, nanoscopic molecules in solution: Size and pH dependence for PAMAM dendrimer

In order to understand self-diffusion (D) of a charged, flexible, and porous nanoscopic molecule in water, we carry out very long, fully atomistic molecular dynamics simulation of PAMAM dendrimer up to eight generations in explicit salt water under varying pH. We find that while the radius of gyration (R-g) varies as N-1/3, the self-diffusion constant (D) scales, surprisingly, as N-alpha, with alpha=0.39 at high pH and 0.5 at neutral pH, indicating a dramatic breakdown of Stokes-Einstein relation for diffusion of charged nanoscopic molecules. The variation in D as a function of radius of gyration demonstrates the importance of treating water and ions explicitly in the diffusion process of a flexible nanoscopic molecule. In agreement with recent experiments, the self-diffusion constant increases with pH, revealing the importance of dielectric friction in the diffusion process. The shape of a dendrimer is found to fluctuate on a nanosecond time scale. We argue that this flexibility (and also the porosity) of the dendrimer may play an important role in determining the mean square displacement of the dendrimer and the breakdown of the Stokes-Einstein relation between diffusion constant and the radius.

PAMAM Dendrimer-Drug Interactions: Effect of pH on the Binding and Release Pattern

Understanding the dendrimer-drug interaction is of great importance to design and optimize the dendrimer-based drug delivery system. Using atomistic molecular dynamics (MD) simulations, we have analyzed the release pattern of four ligands (two soluble drugs, namely, salicylic acid (Sal), L-alanine (Ala), and two insoluble drugs, namely, phenylbutazone (Pbz) and primidone (Prim)), which were initially encapsulated inside the ethylenediamine (EDA) cored polyamidoamine (PAMAM) dendrimer using the docking method. We have computed the potential of mean force (PMF) variation with generation 5 (G5)-PAMAM dendrimer complexed with drug molecules using umbrella sampling. From our calculated PMF values, we observe that soluble drugs (Sal and Ala) have lower energy barriers than insoluble drugs (Pbz and Prim). The order of ease of release pattern for these drugs from G5 protonated PAMAM dendrimer was found to be Ala > Sal > Prim > Pbz. In the case of insoluble drugs (Prim and Pbz), because of larger size, we observe much nonpolar contribution, and thus, their larger energy barriers can be reasoned to van der Waals contribution. From the hydrogen bonding analysis of the four PAMAM drug complexes under study, we found intermolecular hydrogen bonding to show less significant contribution to the free energy barrier. Another interesting feature appears while calculating the PMF profile of G5NP (nonprotonated)-PAMAM Pbz and G5NP (nonprotonated)-PAMAM-Sal complex. The PMF was found to be less when the drug is bound to nonprotonated dendrimer compared to the protonated dendrimer. Our results suggest that encapsulation of the drug molecule into the host PAMAM dendrimer should be carried out at higher pH values (near pH 10). When such complex enters the human body, the pH is around 7.4 and at that physiological pH, the dendrimer holds the drug tightly. Hence the release of drug can occur at a controlled rate into the bloodstream. Thus, our findings provide a microscopic picture of the encapsulation and controlled release of drugs in the case of dendrimer-based host-guest systems.

Engineering Gold Nanoparticle Interaction by PAMAM Dendrimer

Bare faceted gold nanoparticles (AuNPs) have a tendency to aggregate through a preferred attachment of the 111] surfaces. We have used fully atomistic classical molecular dynamics simulations to obtain a quantitative estimate of this surface interaction using umbrella sampling (US) at various temperatures. To tune this surface interaction, we use polyamidoamine (PAMAM) dendrimer to coat the gold surface under various conditions. We observe a spontaneous adsorption of the protonated as well as nonprotonated PAMAM dendrimer on the AuNP surface. The adsorbed dendrimer on the nanoparticle surface strongly alters the interaction between the nanoparticles. We calculate the interaction between dendrimercoated AuNPs using US and show how the interaction between two bare faceted AuNPs can be tuned as a function of dendrimer concentration and charge (pH dependent) With appropriate choice of the dendrimer concentration and charge, two strongly interacting AuNPs can be made effectively noninteracting. Our simulation results demonstrate a strategy to tune the nanoparticle interaction, which can help in engineering self-assembly of such nanoparticles.

Simulations reveal that the HIV-1 gp120-CD4 complex dissociates via complex pathways and is a potential target of the polyamidoamine (PAMAM) dendrimer

The polyamidoamine (PAMAM) dendrimer prevents HIV-1 entry into target cells in vitro. Its mechanism of action, however, remains unclear and precludes the design of potent dendrimers targeting HIV-1 entry. We employed steered molecular dynamics simulations to examine whether the HIV-1 gp120-CD4 complex is a target of PAMAM. Our simulations mimicked single molecule force spectroscopy studies of the unbinding of the gp120-CD4 complex under the influence of a controlled external force. We found that the complex dissociates via complex pathways and defies the standard classification of adhesion molecules as catch and slip bonds. When the force loading rate was large, the complex behaved as a slip bond, weakening gradually. When the loading rate was small, the complex initially strengthened, akin to a catch bond, but eventually dissociated over shorter separations than with large loading rates. PAMAM docked to gp120 and destabilized the gp120-CD4 complex. The rupture force of the complex was lowered by PAMAM. PAMAM disrupted salt bridges and hydrogen bonds across the gp120-CD4 interface and altered the hydration pattern of the hydrophobic cavity in the interface. In addition, intriguingly, PAMAM suppressed the distinction in the dissociation pathways of the complex between the small and large loading rate regimes. Taken together, our simulations reveal that PAMAM targets the gp120-CD4 complex at two levels: it weakens the complex and also alters its dissociation pathway, potentially inhibiting HIV-1 entry.

DNA Assisted Self-Assembly of PAMAM Dendrimers

We report DNA assisted self-assembly of polyamidoamine (PAMAM) dendrimers using all atom Molecular Dynamics (MD) simulations and present a molecular level picture of a DNA-linked PAMAM dendrimer nanocluster, which was first experimentally reported by Choi et al. (Nano Lett., 2004, 4, 391-397). We have used single stranded DNA (ssDNA) to direct the self-assembly process. To explore the effect of pH on this mechanism, we have used both the protonated (low pH) and nonprotonated (high pH) dendrimers. In all cases studied here, we observe that the DNA strand on one dendrimer unit drives self-assembly as it binds to the complementary DNA strand present on the other dendrimer unit, leading to the formation of a DNA-linked dendrimer dimeric complex. However, this binding process strongly depends on the charge of the dendrimer and length of the ssDNA. We observe that the complex with a nonprotonated dendrimer can maintain a DNA length dependent inter-dendrimer distance. In contrast, for complexes with a protonated dendrimer, the inter-dendrimer distance is independent of the DNA length. We attribute this observation to the electrostatic complexation of a negatively charged DNA strand with the positively charged protonated dendrimer.

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

A new class of dendrimers, the poly(propyl ether imine) (PETIM) dendrimer, has been shown to be a novel hyperbranched 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 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 (R-g), 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 dendrirner 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 as their entropy to quantify the flexibility of the dendrimer. Finally we note that structural 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).

Synthesis of PAMAM dendrimers bearing BINOL derivative

New functional dendrimers bearing 4, 8 and 16 axial chiral units on their surface were synthesized from achiral PAMAM dendrimers and axial chiral (R)-BINOL derivative.

Defect formation induced by PAMAM dendrimers on Pt-supported bilayer lipid membranes investigated by electrochemistry

The interaction of polyamidoamine (PAMAM) dendrimers (generations 1-7) with supported bilayer lipid membranes was studied by cyclic votammetry and ac impedance. It is shown that the dendrimers (generations 4-6) can induce defects in the Pt-electrode-supported bilayer lipid membrane. The ability of dendrimers to induce defects was dependent on their shapes and surface charge. The results are consistent with a change in the morphology of the dendrimers from an open, branched structure for generations 1-4 to a closed, increasingly compact surface for generations 5-7.

First Example of Organocatalysis by Polystyrene-Supported PAMAM Dendrimers: Highly Efficient and Reusable Catalyst for Knoevenagel Condensations

This paper describes the first use of polystyrene-supported poly(amidoamine) (PAMAM) dendrimers as heterogeneous basic organocatalysts for carbon–carbon bond formation. Polystyrene-supported PAMAM dendrimers of first, second and third generations have been used as reusable base catalysts in Knoevenagel condensations of carbonyl compounds with active methylene compounds. The reactions proceed in short periods of time and with 100% selectivity. This novel catalyst eliminates the use of aromatic and halogenated solvents, as well as complex purification processes. The catalysts can be recycled ten times.

Functionalization of PAMAM dendrimers with [Ru-III(edta)(H2O)](-)

The anchoring of K[Ru-III(edta)(Cl)] on poly(amidoamine) dendrimers (PAMAM of three generations G(x)/Ru (x = 0, 2 and 3)) through a peptide type bond yielded the aquo species, [Ru-III(edta)(H2O)] on dendrimer surface, and upon NO exposure, yielded their nitrosyl analogues, Gx/RuNO. Characterization of these compounds by elemental analysis, and a UV-vis, IR and C-13 NMR spectroscopies indicated the immobilization of 4,12 and 29 molecules of [Ru-III(edta)(H2O)](-) or of the nitrosyl complex [Ru(II)edta)NO] on the dendrimer surface for G(X) = 0, 2 and 3, respectively. For each complex the electrochemical spectrum presented only one redox process with redox potential values of -0.20 and -0.32 V(vs SCE) attributed to the Ru/Run and NO+/NO0 couples in G(x)/Ru and G./RuNO, respectively. The one-electron reduction of Gx/RuNO` generates Gx/RuNOo, which undergoes aquation with a k(-NO) of 2.1 +/- 0.7 x 10(-3) s(-1) (pH 1.0, mu = 0.2 mol/L, CF3COOH/NaCF3COO, 25 degrees C). The Gx/RuNO species induced a relaxing effect in aortic rings denuded of endothelium and exhibited in vitro assay trypanocidal activity. (c) 2008 Elsevier Inc. All rights reserved.

Functionalization of PAMAM dendrimers with nitronyl nitroxide radicals as models for the outer-sphere relaxation in dentritic potential MRI contrast agents

PAMAM dendrimers functionalized with nitronyl nitroxide radicals were characterized. Quantitative determination of substitution with radicals was performed using EPR and electrochemical methods. The study of the 1H NMR relaxation of the surrounding water showed how the outer-sphere contribution to the relaxivity may be limited by the presence of the dendrimer core.

The effect of pH on PAMAM dendrimer-siRNA complexation:endosomal considerations as determined by molecular dynamics simulation

Intracellular degradation of genes, most notably within the endo-lysosomal compartment is considered a significant barrier to (non-viral) gene delivery in vivo. Previous reports based on in vitro studies claim that carriers possessing a mixture of primary, secondary and tertiary amines are able to buffer the acidic environment within the endosome, allowing for timely release of their contents, leading to higher transfection rates. In this report, we adopt an atomistic molecular dynamics (MD) simulation approach, comparing the complexation of 21-bp siRNA with low-generation polyamidoamine (PAMAM) dendrimers (G0 and G1) at both neutral and acidic pHs, the latter of which mimics the degradative environment within maturing 'late-endosomes'. Our simulations reveal that the time taken for the dendrimer-gene complex (dendriplex) to reach equilibrium is appreciably longer at low pH and this is accompanied by more compact packaging of the dendriplex, as compared to simulations performed at neutral pH. We also note larger absolute values of calculated binding free energies of the dendriplex at low pH, indicating a higher dendrimer-nucleic acid affinity in comparison with neutral pH. These novel simulations provide a more detailed understanding of low molecular-weight polymer-siRNA behavior, mimicking the endosomal environment and provide input of direct relevance to the "proton sponge theory", thereby advancing the rational design of non-viral gene delivery systems.

Structure of polyamidoamide dendrimers up to limiting generations: A mesoscale description

The polyamidoamide (PAMAM) class of dendrimers was one of the first dendrimers synthesized by Tomalia and co-workers at Dow. Since its discovery the PAMAMs have stimulated many discussions on the structure and dynamics of such hyperbranched polymers. Many questions remain open because the huge conformation disorder combined with very similar local symmetries have made it difficult to characterize experimentally at the atomistic level the structure and dynamics of PAMAM dendrimers. The higher generation dendrimers have also been difficult to characterize computationally because of the large size (294852 atoms for generation 11) and the huge number of conformations. To help provide a practical means of atomistic computational studies, we have developed an atomistically informed coarse-grained description for the PAMAM dendrimer. We find that a two-bead per monomer representation retains the accuracy of atomistic simulations for predicting size and conformational complexity, while reducing the degrees of freedom by tenfold. This mesoscale description has allowed us to study the structural properties of PAMAM dendrimer up to generation 11 for time scale of up to several nanoseconds. The gross properties such as the radius of gyration compare very well with those from full atomistic simulation and with available small angle x-ray experiment and small angle neutron scattering data. The radial monomer density shows very similar behavior with those obtained from the fully atomistic simulation. Our approach to deriving the coarse-grain model is general and straightforward to apply to other classes of dendrimers.

Complexation of siRNA with Dendrimer: A Molecular Modeling Approach

This paper reports the structural behavior and thermodynamics of the complexation of siRNA with poly(amidoamine) (PAMAM) dendrimers of generation 3 (G3) and 4 (G4) through fully atomistic molecular dynamics (MD) simulations accompanied by free energy calculations and inherent structure determination. We have also done simulation with one siRNA and two dendrimers (2 x G3 or 2xG4) to get the microscopic picture of various binding modes. Our simulation results reveal the formation of stable siRNA-dendrimer complex over nanosecond time scale. With the increase in dendrimcr generation, the charge ratio increases and hence the binding energy between siRNA and dendrimer also increases in accordance with available experimental measurements. Calculated radial distribution functions of amines groups of various subgenerations in a given generation of dendrimer and phosphate in backbone of siRNA reveals that one dendrimer of generation 4 shows better binding with siRNA almost wrapping the dendrimer when compared to the binding with lower generation dendrimer like G3. In contrast, two dendrimers of generation 4 show binding without siRNA wrapping the den-rimer because of repulsion between two dendrimers. The counterion distribution around the complex and the water molecules in the hydration shell of siRNA give microscopic picture of the binding dynamics. We see a clear correlation between water. counterions motions and the complexation i.e. the water molecules and counterions which condensed around siRNA are moved away from the siRNA backbone when dendrimer start binding to the siRNA back hone. As siRNA wraps/bind to the dendrimer counterions originally condensed onto siRNA (Na-1) and dendrimer (Cl-) get released. We give a quantitative estimate of the entropy of counterions and show that there is gain in entropy due to counterions release during the complexation. Furthermore, the free energy of complexation of IG3 and IG4 at two different salt concentrations shows that increase in salt concentration leads to the weakening of the binding affinity of siRNA and dendrimer.