Complexes Comprised of Charged Dendrimers, Linear Polyelectrolytes, and Counterions: Insight through Coarse-Grained Molecular Dynamics Simulations

Molecular Dynamics Simulations of Rhodamine B Zwitterion Diffusion in Polyelectrolyte Solutions

Polyelectrolytes continue to find wide interest and application in science and engineering, including areas such as water purification, drug delivery, and multilayer thin films. We have been interested in the dynamics of small molecules in a variety of polyelectrolyte (PE) environments; in this paper, we report simulations and analysis of the small dye molecule rhodamine B (RB) in several very simple polyelectrolyte solutions. Translational diffusion of the RB zwitterion has been measured in fully atomistic, 2 μs long molecular dynamics simulations in four different polyelectrolyte solutions. Two solutions contain the common polyanion sodium poly(styrene sulfonate) (PSS), one with a 30-mer chain and the other with 10 trimers. The other two solutions contain the common polycation poly(allyldimethylammonium) chloride (PDDA), one with two 15-mers and the other with 10 trimers. RB diffusion was also simulated in several polymer-free solutions to verify its known experimental value for the translational diffusion coefficient, D_RB, of 4.7 × 10^-6 cm²/s at 300 K. RB diffusion was slowed in all four simulated PE solutions, but to varying degrees. D_RB values of 3.07 × 10^-6 and 3.22 × 10^-6 cm²/s were found in PSS 30-mer and PSS trimer solutions, respectively, whereas PDDA 15-mer and trimer solutions yielded values of 2.19 × 10^-6 and 3.34 × 10^-6 cm²/s. Significant associations between RB and the PEs were analyzed and interpreted via a two-state diffusion model (bound and free diffusion) that describes the data well. Crowder size effects and anomalous diffusion were also analyzed. Finally, RB translation along the polyelectrolytes during association was characterized.

Conformational properties of complexes of poly(propylene imine) dendrimers with linear polyelectrolytes in dilute solutions

This study investigates the conformational properties of complexes of poly(propylene imine) dendrimers with a linear polyelectrolyte (LPE) at neutral pH in an aqueous solution via molecular dynamics simulations. Various conformational properties, such as the atomic density profile, counterion density distribution, charge distribution, cavity volume, and the static structure factor are studied as a function of the charge and chain length of the LPE. The lower generation dendrimer complexes encapsulate the shorter linear PE chains, while the longer PE chains are adsorbed on the dendrimer surface that screen the surface charge and prevent the penetration of the counterions and water molecules. However, the overall charge of the higher generation dendrimers is not neutralized by the charge of the PE chains, which results in chloride counterion penetration within the dendrimers. The adsorption of the PE chains on the dendrimers is also verified from the charge distribution of the dendrimer-PE complexes. The charge on the lower generation dendrimer complexes is overcompensated by the longer PE chains resulting in an overall negative charge on the complexes, while the PE chains do not completely neutralize the charge of the higher generation dendrimers and produce positively charged complexes. The results of the structure factor indicate a conformational transition of the dendrimer-PE complexes from a dense compact structure to an open one with an increase in the PE chain length. This transition is characterized by an increase in the cavity volume in dendrimers with an increase in the PE chain length.

Hyaluronic Acid-Conjugated with Hyperbranched Chlorin e6 Using Disulfide Linkage and Its Nanophotosensitizer for Enhanced Photodynamic Therapy of Cancer Cells

The main purpose of this study is to synthesize novel types of nanophotosensitizers that are based on hyperbranched chlorin e6 (Ce6) via disulfide linkages. Moreover, hyperbranched Ce6 was conjugated with hyaluronic acid (HA) for CD44-receptor mediated delivery and redox-sensitive photodynamic therapy (PDT) against cancer cells. Hyperbranched Ce6 was considered to make novel types of macromolecular photosensitizer since most of the previous studies regarding nanophotosensizers are concerned with simple conjugation between monomeric units of photosensitizer and polymer materials. Hyperbranched Ce6 was synthesized by conjugation of Ce6 each other while using disulfide linkage. To synthesize Ce6 tetramer, carboxyl groups of Ce6 were conjugated with cystamine and three equivalents of Ce6 were then conjugated again with the end of amine groups of Ce6-cystamine. To synthesize Ce6 decamer as a hyperbranched Ce6, six equivalents of Ce6 was conjugated with the end of Ce6 tetramer via cystamine linkage. Furthermore, HA-cystamine was attached with Ce6 tetramer or Ce6 decamer to synthesize HA-Ce6 tetramer (Ce6tetraHA) or HA-Ce6 decamer (Ce6decaHA) conjugates. Ce6tetraHA and Ce6decaHA nanophotosensitizers showed small diameters of less than 200 nm. The addition of dithiothreitol (DTT) and hyaluronidase (HAse) induced a faster Ce6 release rate in vitro drug release study, which indicated that Ce6tetraHA nanophotosensitizers possess redox-sensitive and HAse-sensitive release properties. Ce6tetraHA nanophotosensitizers showed higher intracellular Ce6 accumulation, higher ROS generation, and higher PDT efficacy than that of Ce6 alone. Ce6tetraHA nanophotosensitizers responded to the CD44 receptor of cancer cell surface, i.e., the pre-treatment of HA blocked CD44 receptor of U87MG or HCT116 cells and then inhibited delivery of nanophotosensitizers in vitro cell culture study. Furthermore, in vivo tumorxenograft study showed that fluorescence intensity in the tumor tissues was stronger than those of other organs, while CD44 receptor blocking by HA pretreatment induced a decrease of fluorescence intensity in tumor tissues when compared to liver. These results indicated that Ce6tetraHA nanophotosensitizers delivered to tumors by redox-sensitive and CD44-sensitive manner.

Multivalency in a Dendritic Host-Guest System

Multivalency is an important instrument in the supramolecular chemistry toolkit for the creation of strong specific interactions. In this paper we investigate the multivalency effect in a dendritic host–guest system using molecular dynamics simulations. Specifically, we consider urea–adamantyl decorated poly(propyleneimine) dendrimers that together with compatible mono-, bi-, and tetravalent ureidoacetic acid guests can form dynamic patchy nanoparticles. First, we simulate the self-assembly of these particles into macromolecular nanostructures, showing guest-controlled reduction of dendrimer aggregation. Subsequently, we systematically study guest concentration dependent multivalent binding. At low guest concentrations multivalency of the guests clearly increases relative binding as tethered headgroups bind more often than free guests’ headgroups. We find that despite an abundance of binding sites, most of the tethered headgroups bind in close proximity, irrespective of the spacer length; nevertheless, longer spacers do increase binding. At high guest concentrations the dendrimer becomes saturated with bound headgroups, independent of guest valency. However, in direct competition the tetravalent guests prevail over the monovalent ones. This demonstrates the benefit of multivalency at high as well as low concentrations.

Architecture, Assembly, and Emerging Applications of Branched Functional Polyelectrolytes and Poly(ionic liquid)s

Branched polyelectrolytes with cylindrical brush, dendritic, hyperbranched, grafted, and star architectures bearing ionizable functional groups possess complex and unique assembly behavior in solution at surfaces and interfaces as compared to their linear counterparts. This review summarizes the recent developments in the introduction of various architectures and understanding of the assembly behavior of branched polyelectrolytes with a focus on functional polyelectrolytes and poly(ionic liquid)s with responsive properties. The branched polyelectrolytes and poly(ionic liquid)s interact electrostatically with small molecules, linear polyelectrolytes, or other branched polyelectrolytes to form assemblies of hybrid nanoparticles, multilayer thin films, responsive microcapsules, and ion-conductive membranes. The branched structures lead to unconventional assemblies and complex hierarchical structures with responsive properties as summarized in this review. Finally, we discuss prospectives for emerging applications of branched polyelectrolytes and poly(ionic liquid)s for energy harvesting and storage, controlled delivery, chemical microreactors, adaptive surfaces, and ion-exchange membranes.

Inverted critical adsorption of polyelectrolytes in confinement

What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density σc-defining the adsorption-desorption transition-are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of σc for the concave interfaces versus the Debye screening length 1/κ and the extent of confinement a for these three interfaces for small κa values. For large κa the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/κ. We also rationalize how σc(κ) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption-the effect often hard to tackle theoretically-putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.

Theoretical and computational studies of dendrimers as delivery vectors

It is a great challenge for nanomedicine to develop novel dendrimers with maximum therapeutic potential and minimum side-effects for drug and gene delivery. As delivery vectors, dendrimers must overcome lots of barriers before delivering the bio-agents to the target in the cell. Extensive experimental investigations have been carried out to elucidate the physical and chemical properties of dendrimers and explore their behaviors when interacting with biomolecules, such as gene materials, proteins, and lipid membranes. As a supplement of the experimental techniques, it has been proved that computer simulations could facilitate the progress in understanding the delivery process of bioactive molecules. The structures of dendrimers in dilute solutions have been intensively investigated by monomer-resolved simulations, coarse-grained simulations, and atom-resolved simulations. Atomistic simulations have manifested that the hydrophobic interactions, hydrogen-bond interactions, and electrostatic attraction play critical roles in the formation of dendrimer-drug complexes. Multiscale simulations and statistical field theories have uncovered some physical mechanisms involved in the dendrimer-based gene delivery systems. This review will focus on the current status and perspective of theoretical and computational contributions in this field in recent years. (275 references).

Modeling the formation of ordered nano-assemblies comprised by dendrimers and linear polyelectrolytes: the role of Coulombic interactions

Models of mixtures of peripherally charged dendrimers with oppositely charged linear polyelectrolytes in the presence of explicit solvent are studied by means of molecular dynamics simulations. Under the influence of varying strength of electrostatic interactions, these systems appear to form dynamically arrested film-like interconnected structures in the polymer-rich phase. Acting like a pseudo-thermodynamic inverse temperature, the increase of the strength of the Coulombic interactions drive the polymeric constituents of the mixture to a gradual dynamic freezing-in. The timescale of the average density fluctuations of the formed complexes initially increases in the weak electrostatic regime reaching a finite limit as the strength of electrostatic interactions grow. Although the models are overall electrically neutral, during this process the dendrimer/linear complexes develop a polar character with an excess charge mainly close to the periphery of the dendrimers. The morphological characteristics of the resulted pattern are found to depend on the size of the polymer chains on account of the distinct conformational features assumed by the complexed linear polyelectrolytes of different length. In addition, the length of the polymer chain appears to affect the dynamics of the counterions, thus affecting the ionic transport properties of the system. It appears, therefore, that the strength of electrostatic interactions together with the length of the linear polyelectrolytes are parameters to which these systems are particularly responsive, offering thus the possibility for a better control of the resulted structure and the electric properties of these soft-colloidal systems.

Average relaxation time of internal spectrum for carbosilane dendrimers: nuclear magnetic resonance studies

A new theoretical description of the interior mobility of carbosilane dendrimers has been tested. Experiments were conducted using measurements of the (1)H NMR spin-lattice relaxation time, T(1H), of two-, three- and four-generation carbosilane dendrimers with three different types of terminal groups in dilute chloroform solutions. Temperature dependences of the NMR relaxation rate, 1/T(1H), were obtained for the internal CH(2)-groups of the dendrimers in the range of 1/T(1H) maximum, allowing us to directly evaluate the average time of the internal spectrum for each dendrimer. It was found that the temperature of 1/T(1H) maximum is practically independent of the number of generations, G; therefore, the theoretical prediction was confirmed experimentally. In addition, the average time of the internal spectrum of carbosilane dendrimers was found to be near 0.2 ns at room temperature, and this value correlates well with the values previously obtained for other dendrimer structures using other experimental techniques.

Monte Carlo simulations of charged dendrimer-linear polyelectrolyte complexes and explicit counterions

We study complexes composed of one dendrimer of generation G = 4 (G4 dendrimer) with N(t) = 32 charged terminal groups and an oppositely charged linear polyelectrolyte accompanied by neutralizing counterions in an athermal solvent using Monte Carlo simulations based on the bond fluctuation model. In our study both the full Coulomb potential and the excluded volume interactions are taken into account explicitly with the reduced temperature τ and the chain length N(ch) as the main simulation parameters. Our calculations indicate that there exist three temperature ranges that determine the behavior of such complexes. At τ(complex) stable charged dendrimer-linear polyelectrolyte complexes are formed first, which are subsequently accompanied by selective counterion localization within the complex interior at τ(loc) ≤ τ(complex), and counterion condensation as temperature is further decreased below τ(cond) < τ(loc). In particular, we observe that condensation takes place exclusively on the excess charges in the complex and thus no condensation is observed at the compensation point (N(ch) = N(t)), irrespective of τ. For N(ch) ≠ N(t) the complex is overally charged. Furthermore, we discuss the size and structure of the dendrimer and the linear polyelectrolyte within the complex, as well as spatial distributions of monomers and counterions. Conformations of the chain in the bound state are analysed in terms of loops, trains, and tails.

Structure, dynamics, and energetics of siRNA-cationic vector complexation: a molecular dynamics study

The design and synthesis of safe and efficient nonviral vectors for gene delivery has attracted significant attention in recent years. Previous experiments have revealed that the charge density of a polycation (the carrier) plays a crucial role in complexation and the release of the gene from the complex in the cytosol. In this work, we adopt an atomistic molecular dynamics simulation approach to study the complexation of short strand duplex RNA with six cationic carrier systems of varying charge and surface topology. The simulations reveal detailed molecular-level pictures of the structures and dynamics of the RNA-polycation complexes. Estimates for the binding free energy indicate that electrostatic contributions are dominant followed by van der Waals interactions. The binding free energy between the 8(+)polymers and the RNA is found to be larger than that of the 4(+)polymers, in general agreement with previously published data. Because reliable binding free energies provide an effective index of the ability of the polycationic carrier to bind the nucleic acid and also carry implications for the process of gene release within the cytosol, these novel simulations have the potential to provide us with a much better understanding of key mechanistic aspects of gene-polycation complexation and thereby advance the rational design of nonviral gene delivery systems.

Molecular dynamics study of the structure and interparticle interactions of polyethylene glycol-conjugated PAMAM dendrimers

We performed molecular dynamics (MD) simulations of one or two copies of polyethylene glycol of molecular weight 550 (PEG550) and 5000 (PEG5000) daltons, conjugated to generation 3 (G3) to 5 (G5) polyamidoamine (PAMAM) dendrimers with explicit water using a coarse-grained model. We found the radii of gyration of these dendrimer-PEG molecules to be close to those measured in experiments by Hedden and Bauer (Hedden , R. C. ; Bauer , B. J. Macromolecules 2003 , 36 , 1829.). Densely grafted PEG ligands (>50% of the dendrimer surface) extend like brushes, with layer thickness in agreement with theory for starlike polymers. Two dendrimer-PEG complexes in the box drift away from each other, indicating that no aggregation is induced by either short or long PEG chains, conflicting with a recent view that the cytotoxicity of some PEGylated particles might be due to particle aggregation for long PEG lengths.

Dissipative particle dynamics simulations of complexes comprised of cylindrical polyelectrolyte brushes and oppositely charged linear polyelectrolytes

Dissipative particle dynamics (DPD) approach is used to investigate the conformational behaviors and interactions of the complex between a cylindrical polyelectrolyte brush (CPB) and linear polyelectrolytes (LPs) with opposite charges. The effective complex between CPB and LPs and its dependence on the amount and length of LPs are examined. It is found that the CPB conformation presents collapse and reswelling with the increasing amount of LPs. The collapse is caused by the replacement of monovalent CPB counterions by LPs and the condensation of LPs on the CPB which reduce the osmotic pressure inside the brush. The swelling of the collapsed CPB is induced by the excluded volume effects of additionally absorbed LPs and LP counterions. The results show that the addition of LPs can not enhance the effective complex between the CPB and LPs when the total charge of LPs exceeds that of CPB. Our simulation also demonstrates that the increase of the LP length leads to a shrinking of the CPB which consequently exhibits rod-like or spherical conformations. The most effective complex between a CPB and LPs can be reached only when the contour length of LPs is not less than that of the CPB side chain.

Multiscale modeling of dendrimers and their interactions with bilayers and polyelectrolytes

Recent advances in molecular dynamics simulation methodologies and computational power have allowed accurate predictions of dendrimer size, shape, and interactions with bilayers and polyelectrolytes with modest computational effort. Atomistic and coarse-grained (CG) models show strong interactions of cationic dendrimers with lipid bilayers. The CG simulations with explicit lipid and water capture bilayer penetration and pore formation, showing that pore formation is enhanced at high dendrimer concentration, but suppressed at low temperature and high salt concentration, in agreement with experiments. Cationic linear polymers have also been simulated, but do not perforate membranes, evidently because by deforming into a pancake, the charges on a linear polymer achieve intimate contact with a single bilayer leaflet. The relatively rigid dendrimers, on the other hand, penetrate the bilayer, because only by interacting with both leaflets can they achieve a similar degree of contact between charged groups. Also, a "dendrimer-filled vesicle" structure for the dendrimer-membrane interaction is predicted by mesoscale thermodynamic simulations, in agreement with a picture derived from experimental observations. In simulations of complexes of dendrimer and polyelectrolyte, anionic linear chains wrap around the cationic dendrimer and penetrate inside it. Overall, these new results indicate that simulations can now provide predictions in excellent agreement with experimental observations, and provide atomic-scale insights into dendrimer structure and dynamics.

Energetic and conformational aspects of dendrimer overcharging by linear polyelectrolytes

Extensive Brownian dynamics simulations of conformational changes accompanying the overcharging of a dendrimer by an oppositely charged long linear polyelectrolyte (LPE) have been carried out. The simulated results have been compared with the predictions of the Nguen and Shklovskii correlation theory [Physica A 293, 324 (2001)] for impenetrable charged spherical macroion. Dendrimer overcharging is caused by the spatial correlations between the "excess" of the LPE charges adsorbed onto its surface. The simulated LPE-length dependence of the corresponding "correlation" energy is in agreement with the theoretical predictions. Maximum of the LPE adsorption occurs at some critical LPE length N{ch};{c} , and the first order phase transition from completely coiled conformation to the conformation with released tails takes place. The phase transition is accompanied by the drastic increase in the relative fluctuations of the polyelectrolyte size. Upon increasing the linear-chain length above N{ch};{c} , the one-long-tail conformation becomes energetically preferable; the exchange time between the long-tail conformation and the short-tail conformation is very large.