Dendritic Polyelectrolytes Research Articles

Complexation between Dendritic Polyelectrolytes and Amphiphilic Surfactants: The Impact of Surfactant Concentration and Hydrophobicity

The solution structure of complexes composed of the cationic dendrimer, anionic surfactants, and their counterions is studied by molecular dynamics simulations using the bead–spring coarse-grained model. We identify that depending on the surfactant concentration and hydrophobicity the system exists in three structural regimes. In the first regime surfactant molecules are noncooperatively absorbed by the dendrimer. Here, the pervaded volume of the dendrimer and the bulk solution contain loosely distributed unimeric surfactants and counterions. In the second regime hydrophobic attractions between surfactant tails give rise to cooperative binding. The absorbed surfactants self-assembly into multichain micellar-like aggregates, whereas the bulk solution consists of separate unimers. In the third regime the surfactants form multichain aggregates both within the interior of the dendrimer and in the bulk. Our data indicate that self-assembly of the absorbed surfactants affects the dendrimer conformations as compared to its neutral counterpart. In the case of noncooperative binding the dendritic polyelectrolyte swells due to the osmotic pressure exerted by the absorbed unimers and counterions. In the regimes characterized by cooperative binding and pronounced self-aggregation of the encapsulated surfactants swelling of the dendrimer is suppressed. This is attributed to a reduction of the osmotic pressure inside the macromolecule due to the ion exchange phenomenon appearing as a result of strong Coulomb attractions between charged monomers of the dendrimer and the encapsulated micellar aggregates. We also find that aggregate formation affects the overall charge accumulated in the dendrimer. In particular, for the dendrimer loaded with massive aggregates, we report the charge inversion effect which transforms the cationic dendrimer into an anionic dendrimer–surfactant complex. Our results provide molecular insights into self-assembly of supramolecular complexes and controlled absorption of guest surfactant molecules in dendrimer-based host–guest systems.

Spatial segregation of mixed-sized counterions in dendritic polyelectrolytes

Langevin dynamics simulations are utilized to study the structure of a dendritic polyelectrolyte embedded in two component mixtures comprised of conventional (small) and bulky counterions. We vary two parameters that trigger conformational properties of the dendrimer: the reduced Bjerrum length, lambda _B^*, which controls the strength of electrostatic interactions and the number fraction of the bulky counterions, f_b, which impacts on their steric repulsion. We find that the interplay between the electrostatic and the counterion excluded volume interactions affects the swelling behavior of the molecule. As compared to its neutral counterpart, for weak electrostatic couplings the charged dendrimer exists in swollen conformations whose size remains unaffected by f_b. For intermediate couplings, the absorption of counterions into the pervaded volume of the dendrimer starts to influence its conformation. Here, the swelling factor exhibits a maximum which can be shifted by increasing f_b. For strong electrostatic couplings the dendrimer deswells correspondingly to f_b. In this regime a spatial separation of the counterions into core–shell microstructures is observed. The core of the dendrimer cage is preferentially occupied by the conventional ions, whereas its periphery contains the bulky counterions.

Dendritic polyelectrolytes with monovalent and divalent counterions: the charge regulation effect and counterion release.

The charge regulation and the release of counterions are extremely important and substantial in determining the charge state of polyelectrolytes and the interaction between polyelectrolytes and proteins. Going beyond monovalent to multivalent cations, it is well-known that the effects of ions are qualitatively different. Therefore, the well-accepted descriptions of the charge regulation and the counterion release based on monovalent ions do not immediately apply to systems with multivalent ions. Here, we study the key structural and electrostatic features of charged dendrimers at hand of the pharmaceutically important dendritic polyglycerol sulfate (dPGS) macromolecule equilibrated with monovalent and divalent salts by molecular dynamics (MD) simulations. Following a simple but accurate scheme to determine its effective radius, the counterion condensed layer of the dPGS is determined with high accuracy and we observe the sequential replacement of condensed monovalent cations (MCs) to divalent cations (DCs) rendering a smaller dPGS effective charge versus the DC concentration. We resolve and track the release of counterions on the dPGS along its binding pathway with the plasma protein Human Serum Albumin (HSA). We find that the release of MCs remains favorable for the complexation leading to a considerable amount of release entropy as the driving force for complexation. The release of DCs only occurs above a certain DC concentration with a comparably smaller number of released ions than MCs. Its contribution to the binding free energy is small indicating a subtle cancellation between the entropy gain in releasing DCs and the enthalpy penalty from dissociating DCs from the dendrimer.

Charged Dendrimers with Finite-Size Counterions.

We report on the structure of dendritic polyelectrolytes accompanied by counterions in a good, salt-free, implicit solvent using Langevin dynamics simulations and a Flory-type approach. Our focus is on the modification of charged dendrimer conformations via the strength of electrostatic interactions and the counterion excluded volume. We study the effects caused by charges by varying the reduced Bjerrum length, λB*, between the extremes of weak and strong electrostatic interactions. The counterion excluded volume was controlled by the size of ions. We investigate counterions ranging from conventional ones, with the size comparable to the monomer size, to bulky ions. Our results indicate that, as compared to neutral dendrimers, dendritic polyelectrolytes exist in swollen conformations, and the degree of swelling changes non-monotonically with increasing λB*. For weak electrostatic couplings, counterion density within dendrimers is minor and their radius of gyration subtly exceeds the size of neutral dendrimers. For intermediate electrostatic couplings, Coulomb attraction between opposite charges promotes absorption of ions into dendrimers' pervaded volume and counterion condensation on charged monomers. As a result, counterion density inside dendrimers abruptly increases and the ionic size starts to play a crucial role. In this regime, we observe that swelling of dendrimers reaches its maximum and is more pronounced for bulky counterions. For strong electrostatic couplings, complete condensation of conventional counterions proceeds, whereas for bulky ions condensation remains partial. In this regime, dendrimers deswell. In particular, in the presence of conventional ions, dendrimers collapse into globules, while, for bulky counterions, deswelling is suppressed.

Competitive sorption of monovalent and divalent ions by highly charged globular macromolecules.

When a highly charged globular macromolecule, such as a dendritic polyelectrolyte or charged nanogel, is immersed into a physiological electrolyte solution, monovalent and divalent counterions from the solution bind to the macromolecule in a certain ratio and thereby almost completely electroneutralize it. For charged macromolecules in biological media, the number ratio of bound monovalent vs divalent ions is decisive for the desired function. A theoretical prediction of such a sorption ratio is challenging because of the competition of electrostatic (valency), ion-specific, and binding saturation effects. Here, we devise and discuss a few approximate models to predict such an equilibrium sorption ratio by extending and combining established electrostatic binding theories such as Donnan, Langmuir, Manning, and Poisson-Boltzmann approaches, to systematically study the competitive uptake of monovalent and divalent counterions by the macromolecule. We compare and fit our models to coarse-grained (implicit-solvent) computer simulation data of the globular polyelectrolyte dendritic polyglycerol sulfate (dPGS) in salt solutions of mixed valencies. The dPGS molecule has high potential to serve in macromolecular carrier applications in biological systems and at the same time constitutes a good model system for a highly charged macromolecule. We finally use the simulation-informed models to extrapolate and predict electrostatic features such as the effective charge as a function of the divalent ion concentration for a wide range of dPGS generations (sizes).

The Poisson–Boltzmann–Flory Approach to Charged Dendrimers: Effect of Generation and Spacer Length

Using the Poisson–Boltzmann–Flory approach and a cell model, we examine the properties of dendritic polyelectrolytes and counterions in a broad range of molecular weights under variation of dendrim...

Counterion-Release Entropy Governs the Inhibition of Serum Proteins by Polyelectrolyte Drugs.

Dendritic polyelectrolytes constitute high potential drugs and carrier systems for biomedical purposes. Still, their biomolecular interaction modes, in particular those determining the binding affinity to proteins, have not been rationalized. We study the interaction of the drug candidate dendritic polyglycerol sulfate (dPGS) with serum proteins using isothermal titration calorimetry (ITC) interpreted and complemented with molecular computer simulations. Lysozyme is first studied as a well-defined model protein to verify theoretical concepts, which are then applied to the important cell adhesion protein family of selectins. We demonstrate that the driving force of the strong complexation, leading to a distinct protein corona, originates mainly from the release of only a few condensed counterions from the dPGS upon binding. The binding constant shows a surprisingly weak dependence on dPGS size (and bare charge) which can be understood by colloidal charge-renormalization effects and by the fact that the magnitude of the dominating counterion-release mechanism almost exclusively depends on the interfacial charge structure of the protein-specific binding patch. Our findings explain the high selectivity of P- and L-selectins over E-selectin for dPGS to act as a highly anti-inflammatory drug. The entire analysis demonstrates that the interaction of proteins with charged polymeric drugs can be predicted by simulations with unprecedented accuracy. Thus, our results open new perspectives for the rational design of charged polymeric drugs and carrier systems.

Dendritic polyelectrolytes revisited through the Poisson-Boltzmann-Flory theory and the Debye-Hückel approximation.

The properties of a dendritic polyelectrolyte in equilibrium with a reservoir of monovalent salts are investigated using the cell model and the Poisson-Boltzmann-Flory theory. Within this approach we use the Debye-Hückel approximation to solve the Poisson-Boltzmann equation and minimize the semi-grand potential of the system with respect to the size of the molecule which enables us to inspect its conformations as well as the electric field, the ionic density profile, the overall charge density, the effective charge of the dendrimer and the osmotic pressure based on their response to the salt concentration and the dendrimer charge. The model predicts pronounced trapping of salt ions, a local charge neutrality and a zero electric field in the volume of the molecule as well as oscillations of the density profiles and the electric field in the vicinity of the dendrimer-bulk interface. As a result of ion trapping and screening of Coulomb interactions monovalent salts are found to have a minor effect on the size of the dendrimer. Specifically, the dendrimer exists in slightly swollen states as compared to the neutral molecule which indicates that the conformational properties of the polyelectrolyte depend weakly on monovalent salts. These observations harmonise with the equilibrium behavior of the dendrimer pressure, the internal pressure and the bulk pressure, respectively.

Dendritic polyelectrolytes as seen by the Poisson-Boltzmann-Flory theory.

G3-G9 dendritic polyelectrolytes accompanied by counterions are investigated using the Poisson-Boltzmann-Flory theory. Within this approach we solve numerically the Poisson-Boltzmann equation for the mean electrostatic potential and minimize the Poisson-Boltzmann-Flory free energy with respect to the size of the molecules. Such a scheme enables us to inspect the conformational and electrostatic properties of the dendrimers in equilibrium based on their response to varying the dendrimer generation. The calculations indicate that the G3-G6 dendrimers exist in the polyelectrolyte regime where absorption of counterions into the volume of the molecules is minor. Trapping of ions in the interior region becomes significant for the G7-G9 dendrimers and signals the emergence of the osmotic regime. We find that the behavior of the dendritic polyelectrolytes corresponds with the degree of ion trapping. In particular, in both regimes the polyelectrolytes are swollen as compared to their neutral counterparts and the expansion factor is maximal at the crossover generation G7.

Charge and hydration structure of dendritic polyelectrolytes: molecular simulations of polyglycerol sulphate.

Macromolecules based on dendritic or hyperbranched polyelectrolytes have been emerging as high potential candidates for biomedical applications. Here we study the charge and solvation structure of dendritic polyglycerol sulphate (dPGS) of generations 0 to 3 in aqueous sodium chloride solution by explicit-solvent molecular dynamics computer simulations. We characterize dPGS by calculating several important properties such as relevant dPGS radii, molecular distributions, the solvent accessible surface area, and the partial molecular volume. In particular, as the dPGS exhibits high charge renormalization effects, we address the challenges of how to obtain a well-defined effective charge and surface potential of dPGS for practical applications. We compare implicit- and explicit-solvent approaches in our all-atom simulations with the coarse-grained simulations from our previous work. We find consistent values for the effective electrostatic size (i.e., the location of the effective charge of a Debye-Hückel sphere) within all the approaches, deviating at most by the size of a water molecule. Finally, the excess chemical potential of water insertion into dPGS and its thermodynamic signature are presented and rationalized.

Dendritic polyelectrolyte brushes

The current state of the theory of brushes formed by dendritically branched ionized macromolecules attached by the root segment to a planar substrate and immersed in a polar solvent (water) is discussed. The theory makes it possible to unravel the most distinctive features of such brushes associated with the branched architecture of brush-forming chains and to systematically compare them with the properties of brushes formed by linear polyelectrolyte chains. Owing to their peculiar properties, dendritic polyelectrolyte brushes show promise for designing smart functional polymeric materials.

Regulating plant physiology with organic electronics

The organic electronic ion pump (OEIP) provides flow-free and accurate delivery of small signaling compounds at high spatiotemporal resolution. To date, the application of OEIPs has been limited to delivery of nonaromatic molecules to mammalian systems, particularly for neuroscience applications. However, many long-standing questions in plant biology remain unanswered due to a lack of technology that precisely delivers plant hormones, based on cyclic alkanes or aromatic structures, to regulate plant physiology. Here, we report the employment of OEIPs for the delivery of the plant hormone auxin to induce differential concentration gradients and modulate plant physiology. We fabricated OEIP devices based on a synthesized dendritic polyelectrolyte that enables electrophoretic transport of aromatic substances. Delivery of auxin to transgenic Arabidopsis thaliana seedlings in vivo was monitored in real time via dynamic fluorescent auxin-response reporters and induced physiological responses in roots. Our results provide a starting point for technologies enabling direct, rapid, and dynamic electronic interaction with the biochemical regulation systems of plants.

Simulations of a Grafted Dendritic Polyelectrolyte in Electric Fields

Using Monte Carlo simulations based on the bond fluctuation model, we study the behavior of a charged dendrimer grafted on one of the electrodes of a plate capacitor in an athermal, salt-free solvent. The calculations are performed for the full Coulomb potential in a wide range of parameters determining the strength of the electrostatic interactions between the charges and the magnitude of electric fields between the electrodes. For low temperatures and without an external field the dendrimer is in an osmotic regime where entropy of the trapped counterions controls the size of the molecule. Increasing the field strength leads to gradual removal of trapped counterions being localized at the opposite electrode. At a threshold value of the displacement field, D*, all counterions are stripped from the dendrimer, and the molecule is collapsed on the electrode. The collapse of the extension of the dendrimer in the direction perpendicular to the electrode is very sharp, and a bimodal distribution of monomers in ...

Synthesis of Dendritic Polyglycerol Anions and Their Efficiency Toward L-Selectin Inhibition

A versatile route for the synthesis of highly functionalized, polyanionic macromolecules based on dendritic polyglycerol was applied by means of the Huisgen-Sharpless-Meldal 1,3-dipolar cycloaddition ("click-reaction") of polyglycerolazide precursors and alkyne-functionalized anions such as sulfonates, carboxylates, phosphonates, and bisphosphonates. In addition, the corresponding polyglycerol phosphate has been synthesized via direct hydroxyl interconversion of polyglycerol to the corresponding phosphate with a degree of functionalization >80% by analogy to the synthesis of previously reported polyglycerol sulfates (dPGS). On the basis of the finding that dPGS exhibits high affinity for L- and P-selectin, the potential of these novel polyanionic, multivalent macromolecules of varying anionic nature as L-selectin inhibitors has been evaluated in vitro by means of a competitive concentration dependent binding assay. Affinity of all polyanions toward L-selectin was demonstrated with distinct IC(50) values ranging from the low nanomolar to the high micromolar range. The efficiency of L-selectin inhibition increases in the order carboxylate < phosphate < phosphonate ≈ sulfonate < bisphosphonate < sulfate. Additional DLS and ζ-potential measurements of these polyanions were performed to correlate their binding affinity toward L-selectin with their anionic nature. However, a direct correlation of effective charge and particle size with the determined IC(50) values turned out to require further in-depth studies on the microstructure of the polyanions but clearly indicate an exceptional position of dPGS among the studied dendritic polyelectrolytes.

Simulations of Dendrimers with Flexible Spacer Chains and Explicit Counterions under Low and Neutral pH Conditions

We study the properties of weak dendritic polyelectrolytes of generation G = 5 with flexible spacers of various lengths and explicit counterions in an athermal solvent using Monte Carlo simulations based on the bond fluctuation model. The calculations are performed for molecules under neutral and low pH conditions. At neutral pH we assume that only the terminal groups of the dendrimers bear positive charges, while at low pH both the terminal groups and the branching units are charged. In our study, the full Coulomb potential and the excluded volume interactions are taken into account explicitly with the reduced temperature τ as the main simulation parameter. We observe an interplay of condensation of counterions, trapping of counterions inside the dendrimer’s volume and evaporation of counterions into the surrounding solution giving rise to a nonmonotonous electrostatic swelling of the dendrimer with temperature. Decreasing pH leads to higher swelling and stronger spacer-length dependence. At low pH spacer length-scaling cannot be applied and longer spacers shift the maximum of the swelling to lower temperature. To explain the swelling effect we apply a Flory-type argument where both trapped but noncondensed counterions and uncompensated charges due to evaporation of counterions are taken into account. This model properly reflects the swelling behavior with respect to temperature, pH and spacer-length variation, but quantitatively underestimates the swelling effect. We further investigate the pH-effects on density and charge profiles of the dendrimer.

Conformations of high-generation dendritic polyelectrolytes

We perform monomer-resolved computer simulations of high-generation dendritic molecules, varying the amount of charge and the spacer length between subsequent generations. Charged entities (monomers and counterions) are simulated with the explicit Coulomb interaction, employing the Ewald summation technique. We discover considerable stretching of the molecules with increasing generation number and spacer length, whereas the effects of charging are less pronounced on the overall size of the molecule than those of the former two parameters. For large generations and spacer lengths, charging of the molecules leads to both the opening of large voids within the dendrimer and to charge distributions that are nearly uniform along the molecule's extent. These findings suggest both the possible usage of charge dendrimers as efficient encapsulating agents and their character as realizations of model charged colloids with a uniform charge distribution in their interior.

Field‐theoretic simulations of polyelectrolyte complexation

Field‐theoretic simulations of polyelectrolyte complexation

Graded‐Bandgap Quantum‐ Dot‐Modified Nanotubes: A Sensitive Biosensor for Enhanced Detection of DNA Hybridization

Biosensors containing quantum dots (QDs) as fluorescent markers have been employed for immunoassays, gene expression, genomic analysis, and fluorescence imaging because QDs have superior properties to traditional organic fluorophores, such as higher quantum yield and much sharper emission spectra. Recently, the use of QDs as fluorescence resonance energy transfer (FRET) donors to detect DNA, RNA, or proteins was reported, where an amplification of the detected fluorescent signal was achieved by exploiting FRET. One particularly promising strategy in this context involves funneling energy from strongly light-harvesting species towards a reaction center, because energy is always transferred from a species with a larger bandgap to a species with a smaller bandgap. In this way, a cascaded-energy-transfer structure based on QD assembly has been constructed with a high photoluminescence (PL) intensity originating from the center layer. The use of QDs as biomarkers to functionalize nanotubes (NTs) has been also reported, as a new and active field of research. It is known that the preparation of functionalized NTs, for example, inside an ordered porous alumina membrane, can yield hybrid systems containing a large number of aligned and functionalized channels for biological applications. For example, NTs functionalized with QDs have found promising applications as drug carriers, biomarkers, and biosensors. Hence, taking advantage of the superior properties of QDs described above, we describe in this Communication a novel approach to designing functionalized NTs with a cascaded-energy-transfer architecture by incorporating graded-bandgap QDs into ordered porous alumina membranes (Scheme 1) and their use as highly sensitive biosensor component for the detection of DNA hybridization through energy transfer. The incorporation of QDs into the NTs was performed by the well-known approach of layer-by-layer (LBL) deposition. Mercaptoundecanoic acid (MPA) ligand coated ZnCdSe alloy QDs with luminescence maxima at k= 561 nm (QD) (d = 6.6 nm), 594 nm (QD) (d = 6.1 nm), and 614 nm (QD) (d = 5.5 nm) were used. Their PL emission and UV absorption spectra of aqueous suspensions are shown in Figure 1A and Figure S1 (Supporting Information), respectively. Several advantages of ZnCdSe alloy QDs compared with other types of QDs, for example, core/shell QDs, are summarized here: 1) There are very few surface defects around the luminescent particles owing to the high crystallinity. 2) They have large particle sizes, hardened lattice structures, and decreased interdiffusion. 3) ZnCdSe alloy QDs can produce atomically abrupt jumps in the chemical potential, which can further localize free exciton states in the alloy crystallites. Therefore, the fluorescence stability of ZnCdSe alloy QDs can be greatly improved. As a matrix forming the walls of the NTs we used globular N,N-disubstituted hydrazine phosphorus-containing dendrimers of the fourth generation having 96 terminal groups with either cationic [G4(NH Et2Cl )96] (G4 ) or anionic [G4(CHCOONa)96] (G4 ) character. The two dendrimers possess a controlled shape and well-defined external and internal surfaces. The multilayer structures consisting of the two dendritic polyelectrolytes show a lower degree of interpenetration than multilayer systems composed of common linear polyelectrolytes. Therefore, they are ideal components for constructing compartmentalized NT walls, in which different functional species, such as water-soluble QDs with different size or composition in the case of the alloy particles used in this experiment, can be deposited with high spatial precision. For LBL deposition in an ordered porous alumina membrane, the pore walls were first coated with the positively charged 3-aminopropyl dimethylethoxysilane (3-APS), further allowing the deposition of a negatively charged denC O M M U N IC A IO N

Molecular Dynamics Simulations of Dendritic Polyelectrolytes with Flexible Spacers in Salt Free Solution

We present the results of molecular dynamics simulations of dendritic polyelectrolytes in dilute salt-free solutions. The dendritic polyelectrolytes are modeled as an ensemble of regular-branched bead-spring chains of neutral and charged Lennard-Jones particles with explicit counterions. A wide range of molecular variables of the dendritic polyelectrolytes such as generation number, spacer length, and charge density were considered in the simulations. The effect of dendrimer size on relaxation time, the conformation of spacers, and the size dependence of the dendrimer on molecular variables are discussed and compared with a Flory type theory. The osmotic coefficients of the dilute dendritic polyelectrolyte solutions, as well as the profiles of monomers and counterions, are calculated directly from the simulations. Our simulation results show that the inner spacers of the dendrimers are extensively stretched, and the size dependence on the molecular weight deviates from the scaling prediction that assumes a Gaussian elasticity of the spacer.

Multilayer Films Fabricated from Oppositely Charged Polyphenylene Dendrimers by Electrostatic Layer‐by‐Layer Assembly

AbstractSummary: Assemblies of oppositely charged L‐lysine/carboxylic acid functionalized polyphenylene dendrimers and hybrid multilayers of L‐lysine dendrimers/colloidal gold nanocrystals were fabricated as alternate multilayers on 3‐mercaptopropionic acid coated gold surfaces via layer‐by‐layer deposition. The fabrication of the multilayer films was monitored by kinetic and scan mode surface plasmon resonance spectroscopy. The permeability properties of the dendritic polyelectrolyte layers were characterized by electrochemistry in the presence of [Fe(CN)6]3−/4− as the redox couple. A high interfacial charge‐transfer resistance, originating from the electrostatic repulsion of the negatively charged redox couple against the negatively charged interface was observed and the charge‐transfer resistance found to increase with increasing number of layers.3D‐structure of the investigated polyphenylene dendrimers: a) G2(L‐lysine)8 and b) G2(COOH)16.magnified image3D‐structure of the investigated polyphenylene dendrimers: a) G2(L‐lysine)8 and b) G2(COOH)16.