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

Counterion Release from Macroion Assemblies of Planar Geometry

Macroions such as nanoparticles, polyelectrolytes, ionic gels, and amphiphiles can form condensed, often self-assembled, phases that are embedded in a solvent region. The condensed phase contains not only the partially or fully immobile charges of their macroions but also corresponding counterions that are mobile and thus free to migrate out of their confinement into the solvent region where they benefit from high translational entropy. Based on the nonlinear Poisson-Boltzmann model for monovalent ions, we quantify the corresponding fraction of released counterions for a planar slab geometry of the macroion phase. Slab thickness, extension of the solvent phase, fixed background charge density provided by the macroions, and dielectric constants inside slab and solvent combine into three dimensionless parameters that the fraction of released counterions depends on. We calculate that fraction and analyze the limits of a thin macroion phase, a large solvent phase, and linearized theory, where simple analytic results become available. Of particular interest is the presence of a single-planar interface that separates a bulk macroion phase from an extended solvent region. We calculate the apparent surface charge density that emerges due to the released counterions. Our model yields a comprehensive description of counterion partitioning between a planar macroion phase and a solvent region on the level of mean-field electrostatics in the absence of added salt ions.

Adsorption of Mono- and Divalent Ions onto Dendritic Polyglycerol Sulfate (dPGS) as Studied Using Isothermal Titration Calorimetry

The effective charge of highly charged polyelectrolytes is significantly lowered by a condensation of counterions. This effect is more pronounced for divalent ions. Here we present a study of the counterion condensation to dendritic polyglycerol sulfate (dPGS) that consists of a hydrophilic dendritic scaffold onto which sulfate groups are appended. The interactions between the dPGS and divalent ions (Mg²⁺ and Ca²⁺) were analyzed using isothermal titration calorimetry (ITC) and showed no ion specificity upon binding, but clear competition between the monovalent and divalent ions. Our findings, in line with the latest theoretical studies, demonstrate that a large fraction of the monovalent ions is sequentially replaced with the divalent ions.

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.

Highly Heterogeneous Polarization and Solvation of Gold Nanoparticles in Aqueous Electrolytes

The performance of gold nanoparticles (NPs) in applications depends critically on the structure of the NP-solvent interface, at which the electrostatic surface polarization is one of the key characteristics that affects hydration, ionic adsorption, and electrochemical reactions. Here, we demonstrate significant effects of explicit metal polarizability on the solvation and electrostatic properties of bare gold NPs in aqueous electrolyte solutions of sodium salts of various anions (Cl^-, BF₄^-, PF₆^-, nitrophenolate, and 3- and 4-valent hexacyanoferrate), using classical molecular dynamics simulations with a polarizable core-shell model for the gold atoms. We find considerable spatial heterogeneity of the polarization and electrostatic potentials on the NP surface, mediated by a highly facet-dependent structuring of the interfacial water molecules. Moreover, ion-specific, facet-dependent ion adsorption leads to considerable alterations of the interfacial polarization. Compared to nonpolarizable NPs, surface polarization modifies water local dipole densities only slightly but has substantial effects on the electrostatic surface potentials and leads to significant lateral redistributions of ions on the NP surface. Besides, interfacial polarization effects cancel out in the far field for monovalent ions but not for polyvalent ions, as anticipated from continuum "image-charge" concepts. Far-field effective Debye-Hückel surface potentials change accordingly in a valence-specific fashion. Hence, the explicit charge response of metal NPs is crucial for the accurate description and interpretation of interfacial electrostatics (e.g., for charge transfer and interfacial polarization in catalysis and electrochemistry).

Insights into Interactions between Interleukin-6 and Dendritic Polyglycerols

Interleukin-6 (IL-6) is involved in physiological and pathological processes. Different pharmacological agents have been developed to block IL-6 deleterious effects and to recover homeostatic IL-6 signaling. One of the proposed nanostructures in pre-clinical investigations which reduced IL-6 concentrations is polyglycerol dendrimer, a nano-structure with multiple sulfate groups. The aim of the present study was to uncover the type of binding between critical positions in the human IL-6 structure available for binding dPGS and compare it with heparin sulfate binding. We studied these interactions by performing docking simulations of dPGS and heparins with human IL-6 using AutoDock Vina. These molecular docking analyses indicate that the two ligands have comparable affinities for the positively charged positions on the surface of IL-6. All-atom molecular dynamics simulations (MD) employing Gromacs were used to explore the binding sites and binding strengths. Results suggest two major binding sites and show that the strengths of binding are similar for heparin and dPGS (−5.5–6.4 kcal/ mol). dPGS or its analogs could be used in the therapeutic intervention in sepsis and inflammatory disorders to reduce unbound IL-6 in the plasma or tissues and its binding to the receptors. We propose that analogs of dPGS could specifically block IL-6 binding in the desired signaling mode and would be valuable new probes to establish optimized therapeutic intervention in inflammation.

Understanding the Interaction of Polyelectrolyte Architectures with Proteins and Biosystems

The counterions neutralizing the charges on polyelectrolytes such as DNA or heparin may dissociate in water and greatly influence the interaction of such polyelectrolytes with biomolecules, particularly proteins. In this Review we give an overview of studies on the interaction of proteins with polyelectrolytes and how this knowledge can be used for medical applications. Counterion release was identified as the main driving force for the binding of proteins to polyelectrolytes: Patches of positive charge become multivalent counterions of the polyelectrolyte and lead to the release of counterions from the polyelectrolyte and a concomitant increase in entropy. This is shown from investigations on the interaction of proteins with natural and synthetic polyelectrolytes. Special emphasis is paid to sulfated dendritic polyglycerols (dPGS). The Review demonstrates that we are moving to a better understanding of charge-charge interactions in systems of biological relevance. Research along these lines will aid and promote the design of synthetic polyelectrolytes for medical applications.

How the hydroxylation state of the (110)-rutile TiO2 surface governs its electric double layer properties

The hydroxylation state of an oxide surface is a central property of its solid/liquid interface and its corresponding electrical double layer. This study integrated both a reactive force field (ReaxFF) and a non-reactive potential into a hierarchical framework within molecular dynamics (MD) simulations to reveal how the hydroxylation state of the (110)-rutile TiO2 surface affects the electrical double layer properties. The simulation results obtained in the ReaxFF framework have shown that, while water dissociation occurs only at the under-coordinated Ti5c sites on the pristine TiO2 surface, the presence of point defects on the surface facilitates water dissociation at the oxygen vacancy sites, leading to two protonated oxygen bridge atoms for each vacancy site. As a consequence of enhanced water dissociation at the vacancy sites, water dissociation is quenched at the under-coordinated Ti5c sites resulting in two competitive hydroxylation mechanisms on the (110)-TiO2 surface. Using non-reactive MD simulations with hydroxylation states derived from the ReaxFF analysis, we demonstrate that water dissociation at the vacancy sites is a central mechanism governing the structuring of water near the interface. While the structuring of water near the interface is the main contribution to the electric field, water dissociation at the vacancy site enhances the adsorption of the electrolyte ions at the interface. The adsorbed ions lead to an increase of the effective surface charge as well as surface (zeta) potentials which are in the range of experimental observations. Our work provides a hierarchical multiscale simulation approach, covering a series of results with in-depth discussion for atomic/molecular level understanding of water dissociation and its effect on electric double layer properties of TiO2 to advance water splitting.

Ion-Specific Adsorption on Bare Gold (Au) Nanoparticles in Aqueous Solutions: Double-Layer Structure and Surface Potentials

We study the solvation and electrostatic properties of bare gold (Au) nanoparticles (NPs) of 1-2 nm in size in aqueous electrolyte solutions of sodium salts of various anions with large physicochemical diversity (Cl^-, BF₄^-, PF₆^-, Nip^- (nitrophenolate), 3- and 4-valent hexacyanoferrate (HCF)) using nonpolarizable, classical molecular dynamics computer simulations. We find a substantial facet selectivity in the adsorption structure and spatial distribution of the ions at the AuNPs: while sodium and some of the anions (e.g., Cl^-, HCF^3-) adsorb more at the "edgy" (100) and (110) facets of the NPs, where the water hydration structure is more disordered, other ions (e.g., BF₄^-, PF₆^-, Nip^-) prefer to adsorb strongly on the extended and rather flat (111) facets. In particular, Nip^-, which features an aromatic ring in its chemical structure, adsorbs strongly and perturbs the first water monolayer structure on the NP (111) facets substantially. Moreover, we calculate adsorptions, radially resolved electrostatic potentials as well as the far-field effective electrostatic surface charges and potentials by mapping the long-range decay of the calculated electrostatic potential distribution onto the standard Debye-Hückel form. We show how the extrapolation of these values to other ionic strengths can be performed by an analytical Adsorption-Grahame relation between the effective surface charge and potential. We find for all salts negative effective surface potentials in the range from -10 mV for NaCl down to about -80 mV for NaNip, consistent with typical experimental ranges for the zeta potential. We discuss how these values depend on the surface definition and compare them to the explicitly calculated electrostatic potentials near the NP surface, which are highly oscillatory in the ±0.5 V range.

Probing the protein corona around charged macromolecules: interpretation of isothermal titration calorimetry by binding models and computer simulations

Isothermal titration calorimetry (ITC) is a widely used tool to experimentally probe the heat signal of the formation of the protein corona around macromolecules or nanoparticles. If an appropriate binding model is applied to the ITC data, the heat of binding and the binding stoichiometry as well as the binding affinity per protein can be quantified and interpreted. However, the binding of the protein to the macromolecule is governed by complex microscopic interactions. In particular, due to the steric and electrostatic protein–protein interactions within the corona as well as cooperative, charge renormalization effects of the total complex, the application of standard (e.g., Langmuir) binding models is questionable and the development of more appropriate binding models is very challenging. Here, we discuss recent developments in the interpretation of the Langmuir model applied to ITC data of protein corona formation, exemplified for the well-defined case of lysozyme coating highly charged dendritic polyglycerol sulfate (dPGS), and demonstrate that meaningful data can be extracted from the fits if properly analyzed. As we show, this is particular useful for the interpretation of ITC data by molecular computer simulations where binding affinities can be calculated but it is often not clear how to consistently compare them with the ITC data. Moreover, we discuss the connection of Langmuir models to continuum binding models (where no discrete binding sites have to be assumed) and their possible extensions toward the inclusion of leading order cooperative electrostatic effects.