Polyelectrolytes in Multivalent Salt Solutions: Monomolecular versus Multimolecular Aggregation

Double-hydrophilic block copolymer-metal ion associations: Structures, properties and applications

Hybrid polyionic complexes (HPICs), constructed from double-hydrophilic block copolymers and metal ions, have been largely developed with increasing interest in the past decade in the fields of catalysis, materials science and biological applications. The chemical natures of both blocks are very versatile, but one block should be able to interact with ions, and the second one should be neutral. Many metals have been used to form HPICs, which have, in their simplest architectural form, a core-shell structure of a few tens of nanometers in radius with an external shell made of the neutral block of the copolymer. In this review, we focus our discussion on the stability, shape, size and inner structure of these hybrid micelles. We then describe the most recent applications of HPICs, as reported in the literature, and point out the current challenges, missing structural information and future perspectives for this class of organized structures.

Phase Separation of Aqueous Poly(diisopropylaminoethyl methacrylate) upon Heating

Poly(diisopropylaminoethyl methacrylate) (PDPA) is a pH- and thermally responsive water-soluble polymer. This study deepens the understanding of its phase separation behavior upon heating. Phase separation upon heating was investigated in salt solutions of varying pH and ionic strength. The effect of the counterion on the phase transition upon heating is clearly demonstrated for chloride-, phosphate-, and citrate-anions. Phase separation did not occur in pure water. The buffer solutions exhibited similar cloud points, but phase separation occurred in different pH ranges and with different mechanisms. The solution behavior of a block copolymer comprising poly(dimethylaminoethyl methacrylate) (PDMAEMA) and PDPA was investigated. Since the PDMAEMA and PDPA blocks phase separate within different pH- and temperature ranges, the block copolymer forms micelle-like structures at high temperature or pH.

Influence of Calcium Binding on Conformations and Motions of Anionic Polyamino Acids. Effect of Side Chain Length

Investigation of the effect of CaCl2 salt on conformations of two anionic poly(amino acids) with different side chain lengths, poly-(α-l glutamic acid) (PGA) and poly-(α-l aspartic acid) (PASA), was performed by atomistic molecular dynamics (MD) simulations. The simulations were performed using both unbiased MD and the Hamiltonian replica exchange (HRE) method. The results show that at low CaCl2 concentration adsorption of Ca2+ ions lead to a significant chain size reduction for both PGA and PASA. With the increase in concentration, the chains sizes partially recover due to electrostatic repulsion between the adsorbed Ca2+ ions. Here, the side chain length becomes important. Due to the longer side chain and its ability to distance the charged groups with adsorbed ions from both each other and the backbone, PGA remains longer in the collapsed state as the CaCl2 concentration is increased. The analysis of the distribution of the mineral ions suggests that both poly(amino acids) should induce the formation of mineral with the same structure of the crystal cell.

Parameters influencing the size of chitosan-TPP nano- and microparticles

Chitosan nanoparticles, produced by ionic gelation, are among the most intensely studied nanosystems for drug delivery. However, a lack of inter-laboratory reproducibility and a poor physicochemical understanding of the process of particle formation have been slowing their potential market applications. To address these shortcomings, the current study presents a systematic analysis of the main polymer factors affecting the nanoparticle formation driven by an initial screening using systematic statistical Design of Experiments (DoE). In summary, we found that for a given chitosan to TPP molar ratio, the average hydrodynamic diameter of the particles formed is strongly dependent on the initial chitosan concentration. The degree of acetylation of the chitosan was found to be the second most important factor involved in the system's ability to form particles. Interestingly, viscosimetry studies indicated that the particle formation and the average hydrodynamic diameter of the particles formed were highly dependent on the presence or absence of salts in the medium. In conclusion, we found that by controlling two simple factors of the polymer solution, namely its initial concentration and its solvent environment, it is feasible to control in a reproducible manner the production and characteristics of chitosan particles ranging in size from nano- to micrometres.

Crystallization, Reentrant Melting, and Resolubilization of Virus Nanoparticles

Crystallization is a fundamental and ubiquitous process that is well understood in the case of atoms or small molecules, but its outcome is still hard to predict in the case of nanoparticles or macromolecular complexes. Controlling the organization of virus nanoparticles into a variety of 3D supramolecular architectures is often done by multivalent ions and is of great interest for biomedical applications such as drug or gene delivery and biosensing, as well as for bionanomaterials and catalysis. In this paper, we show that slow dialysis, over several hours, of wild-type Simian Virus 40 (wt SV40) nanoparticle solution against salt solutions containing MgCl₂, with or without added NaCl, results in wt SV40 nanoparticles arranged in a body cubic center crystal structure with Im3m space group, as a thermodynamic product, in coexistence with soluble wt SV40 nanoparticles. The nanoparticle crystals formed above a critical MgCl₂ concentrations. Reentrant melting and resolubilization of the virus nanoparticles took place when the MgCl₂ concentrations passed a second threshold. Using synchrotron solution X-ray scattering we determined the structures and the mass fraction of the soluble and crystal phases as a function of MgCl₂ and NaCl concentrations. A thermodynamic model, which balances the chemical potentials of the Mg²⁺ ions in each of the possible states, explains our observations. The model reveals the mechanism of both the crystallization and the reentrant melting and resolubilization and shows that counterion entropy is the main driving force for both processes.

A review of immune amplification via ligand clustering by self-assembled liquid-crystalline DNA complexes

We examine how the interferon production of plasmacytoid dendritic cells is amplified by the self-assembly of liquid-crystalline antimicrobial peptide/DNA complexes. These specialized dendritic cells are important for host defense because they quickly release large quantities of type I interferons in response to infection. However, their aberrant activation is also correlated with autoimmune diseases such as psoriasis and lupus. In this review, we will describe how polyelectrolyte self-assembly and the statistical mechanics of multivalent interactions contribute to this process. In a more general compass, we provide an interesting conceptual corrective to the common notion in molecular biology of a dichotomy between specific interactions and non-specific interactions, and show examples where one can construct exquisitely specific interactions using non-specific interactions.

A route to self-assemble suspended DNA nano-complexes

Highly charged polyelectrolytes can self-assemble in presence of condensing agents such as multivalent cations, amphiphilic molecules or proteins of opposite charge. Aside precipitation, the formation of soluble micro- and nano-particles has been reported in multiple systems. However a precise control of experimental conditions needed to achieve the desired structures has been so far hampered by the extreme sensitivity of the samples to formulation pathways. Herein we combine experiments and molecular modelling to investigate the detailed microscopic dynamics and the structure of self-assembled hexagonal bundles made of short dsDNA fragments complexed with small basic proteins. We suggest that inhomogeneous mixing conditions are required to form and stabilize charged self-assembled nano-aggregates in large excess of DNA. Our results should help re-interpreting puzzling behaviors reported for a large class of strongly charged polyelectrolyte systems.

Role of salt in the aqueous two-phase copolymerization of acrylamide and cationic monomers: from screening to anion-bridging

Mechanism for the anions effect on the aqueous two-phase copolymerization (ATPP) of acrylamide and cationic monomers in poly(ethylene glycol) (PEG) aqueous solution was proposed.

Load-collapse-release cascades of amphiphilic guest molecules in charged dendronized polymers through spatial separation of noncovalent forces

The ability to pack guest molecules into charged dendronized polymers (denpols) and the possibility to release these guest molecules from subsequently densely aggregated denpols in a load-collapse-release cascade is described. Charged denpols, which constitute molecular objects with a persistent, well-defined envelope and interior, are capable of incorporating large amounts of amphiphilic guest molecules. Simultaneously, multivalent ions can coordinate to the surfaces of charged denpols, leading to counterion-induced aggregation of the already guest-loaded host structures. Thus, although the local guest concentration in denpol-based molecular transport might already be initially high due to the dense guest packing inside the dendritic denpol scaffolding, the "local" guest concentration can nonetheless be further increased by packing (through aggregation) of the host-guest complexes themselves. Subsequent release of guest compounds from densely aggregated dendronized polymers is then possible (e.g., through increasing the solution concentration of imidazolium-based ions). Augmented with this release possibility, the concept of twofold packing of guests, firstly through hosting itself and secondly through aggregation of the hosts, gives rise to a load-collapse-release cascade that strikingly displays the high potential of dendronized macromolecules for future molecular transport applications.

Formation of hybrid colloids by suspension polycondensation in the presence of hydrophilic block copolymers

Double hydrophilic block copolymers were used to control the growth of inorganic particles and directly prepare hybrid colloidal suspensions. Colloids of metal hydrous oxides were obtained by forced hydrolysis of metal ions in presence of the copolymers. The block copolymers contain a metal-complexing polyelectrolyte block and a stabilizing neutral block. The role of the first block is to ensure a controlled growth of the inorganic phase, while simultaneously, the second block ensures the colloidal stabilization. Phase diagrams presenting the conditions under which precipitation is inhibited are established. The nanoparticles are then characterized in terms of sizes, morphologies and surface charges. The main parameters controlling the size were identified: the copolymer-to-metal ratio and the metal prehydrolysis ratio. The synthesis steps were characterized. First, a key step of induced micellization of the hydrophilic copolymers leads to hybrid core-shell assemblies. The second step consists in mineralization of the micellar core. The suspension polycondensation leads to hairy particles whose morphologies depend on the nature of the metal and on synthesis parameters.

Stability of poly(ethylene glycol)-graft-polyethylenimine copolymer/DNA complexes: influences of PEG molecular weight and PEGylation degree

Polyethylenimine (PEI) is one of the most widely investigated cationic polymers for gene delivery. However, PEI/DNA complexes are unstable and tend to aggregate. PEGylation was used to improve the stability. The stability of polymer/DNA complexes was investigated including complexation stability, aggregation stability, sedimentation stability, and nuclease stability. PEI25K/DNA complexes were liable to aggregate to large particles (500-700 nm). The aggregation was proved to be induced by phosphate anion. In the medium without phosphate anion, aggregation was prevented by electrostatic repulsion. Owing to more efficient steric repulsion, PEG2 and PEG5K excelled PEG750 in facilitating copolymers to form stable small polyplexes (below 100 nm) without aggregation regardless of phosphate anion. The steric repulsion predominated over electrostatic repulsion in stabilization.

Salt-induced aggregation of stiff polyelectrolytes

Molecular dynamics simulation techniques are used to study the process of aggregation of highly charged stiff polyelectrolytes due to the presence of multivalent salt. The dominant kinetic mode of aggregation is found to be the case of one end of one polyelectrolyte meeting others at right angles, and the kinetic pathway to bundle formation is found to be similar to that of flocculation dynamics of colloids as described by Smoluchowski. The aggregation process is found to favor the formation of finite bundles of 10-11 filaments at long times. Comparing the distribution of the cluster sizes with the Smoluchowski formula suggests that the energy barrier for the aggregation process is negligible. Also, the formation of long-lived metastable structures with similarities to the raft-like structures of actin filaments is observed within a range of salt concentration.

Molecular simulation study of peptide amphiphile self-assembly

We study the self-assembly of peptide amphiphile (PA) molecules, which is governed by hydrophobic interactions between alkyl tails and a network of hydrogen bonds between peptide blocks. We demonstrate that the interplay between these two interactions results in the formation of assemblies of different morphology, in particular, single beta-sheets connected laterally by hydrogen bonds, stacks of parallel beta-sheets, spherical micelles, micelles with beta-sheets in the corona, and long cylindrical fibers. We characterize the size distribution of the aggregates as a function of the molecular interactions. Our results suggest that the formation of nanofibers of peptide amphiphiles obeys an open association model, which resembles living polymerization.

Aggregation kinetics of stiff polyelectrolytes in the presence of multivalent salt

Using molecular dynamics simulations, the kinetics of bundle formation for stiff polyelectrolytes such as actin is studied in the solution of multivalent salt. The dominant kinetic mode of aggregation is found to be the case of one end of one rod meeting others at a right angle due to electrostatic interactions. The kinetic pathway to bundle formation involves a hierarchical structure of small clusters forming initially and then feeding into larger clusters, which is reminiscent of the flocculation dynamics of colloids. For the first few cluster sizes, the Smoluchowski formula for the time evolution of the cluster size gives a reasonable account of the results of our simulation without a single fitting parameter. The description using the Smoluchowski formula provides evidence for the aggregation time scale to be controlled by diffusion, with no appreciable energy barrier to overcome.

Solvation behavior of short-chain polystyrene sulfonate in aqueous electrolyte solutions: a molecular dynamics study

We analyze the solvation behavior of short-chain polystyrene sulfonate (PSS) in aqueous electrolyte solutions by isothermal-isochoric molecular dynamics simulation to determine the solvation effects on the structure and conformation of the polyelectrolyte as a function of the aqueous environment. To that end, we study these aqueous systems including the explicit atomistic description of water, the PSS chain, and their interactions with all species in solution. In addition, we investigate the effect of the degree of sulfonation and its distribution along the PSS chain on the resulting conformation as well as solvation structure. Moreover, we assess the impact of added salts on the net charge of the PSS backbone, placing emphasis on the valence of the counterion and the extent of the ion-pair formation between the sulfonate group and the counterions. Finally, we present evidence for the so-called like-charge attraction between sulfonate groups through the formation of counterion-mediated interchain sulfonate-sulfonate and water-mediated intrachain sulfonate-sulfonate bridges, as well as between unlike counterion-counterion interactions.

Evolution of growth modes for polyelectrolyte bundles

Multivalent ions induce attractions between polyelectrolytes, but lead to finite-sized bundles rather than macroscopic phase separation. The kinetics of aggregation and bundle formation of actin is tracked using two different fluorescently labeled populations of F-actin. It is found that the growth mode of these bundles evolves with time and salt concentration, varying from an initial lateral growth to a longitudinal one at later stages. The results suggest that kinetics play a role in bundle growth, but not in the lateral size of bundles, which is constant for linear and branched topologies.

A simple phenomenological fix for the dielectric constant within the reference interaction site model approach

The effective interactions among ions immersed in water are studied by means of the effective pair potentials (EPPs) [J. Chem. Phys. 2002, 117, 6133] obtained after contracting (integrating out) the degrees of freedom of the solvent molecules. The dressed interaction site theory (DIST) leads to a simple way of adjusting the effective dielectric constant of the model solvent to its experimental value at standard conditions. The molecular structure of the solvent is mirrored in the structure of the short-ranged component of the induced EPPs, with noticeable differences between the cases with trivial (ideal gas) and nontrivial (experimental) values of the dielectric constant. The shape of these EPPs remains almost invariant over the whole range of salt concentrations considered here. The asymptotic behavior of the EPP between two macroions obtained after contracting the supporting electrolyte (water molecules plus small ions) is also briefly discussed.

Solubility and charge inversion of complexes of DNA and basic proteins

The basic proteins, protamines and histones H1, are known to condense DNA in vivo. We examine here their ability to condense and solubilize in vitro linear DNA [and a synthetic polyanion, Poly(Styrene-Sulfonate) or PSS] at low ionic concentrations by varying the charge concentration ratio. Phase separation is observed in a very narrow range of ratios for short DNA and PSS; on both sides of this range, polydisperse and charged complexes are formed. A charge inversion is detected. For long DNA chains however, a different behavior is observed: the complexes are not soluble in excess of proteins.

Condensation of DNA-actin polyelectrolyte mixtures driven by ions of different valences

Multivalent ions can induce condensation of like-charged polyelectrolytes into compact states, a process that requires different ion valences for different polyelectrolyte species. In this work we examine the condensation behavior in binary anionic polyelectrolyte mixtures consisting of DNA coils and F-actin rods in the presence of monovalent, divalent, and trivalent ions. As expected, monovalent ions do not condense either component and divalent ions selectively condense F-actin rods out of the polyelectrolyte mixture. For trivalent ions, however, we observe a microphase separation between the two polyelectrolytes into coexisting finite-sized F-actin bundles and DNA toroids. Further, by increasing the DNA volume fraction in the mixture, condensed F-actin bundles can be completely destabilized, leading to only DNA condensation within the mixture. We examine a number of possible causes and propose a model based on polyelectrolyte competition for ions.

Linear polyelectrolytes in tetravalent salt solutions

The effect of adding tetravalent salt of different sizes to a solution of linear and flexible polyelectrolytes is investigated by molecular dynamics simulations. Upon the addition of salt, a chain reexpansion takes place, following a well-known collapsed conformation. The degrees of collapse and reexpansion increase with ion size. In the solution, tetravalent counterions replace monovalent ones and condense onto the chains. The condensation for small ions displays a profile different from that for large ones. In a high-salt region, ions can form layering orders around a polyelectrolyte and locally overcompensate the charge inside. Consequently, the integrated charge distribution reveals an oscillatory behavior away from a chain. By studying the radial distribution function between monomers on different polyelectrolytes, like-charge attraction between chains is demonstrated. This attraction is a prerequisite to chain aggregation or precipitation. The results show a strong dependence of salt concentration and ion size on the properties of polyelectrolyte solutions.

Formation of hybrid micelles between poly(ethylene glycol)-block-poly(4-vinylpyridinium) cations and sulfate anions in an aqueous milieu

The SO-induced micellization of poly(ethylene glycol)--poly(4-vinylpyridinium)(PEG-b-P(4-VPH)) in aqueous solution is studied by dynamic and static light scattering, and transmission electron microscopy. The SO anions can act as cross-linkers of the P(4-VPH) blocks through the electrostatic attraction between 4-VPH and SO to induce the micellization of PEG--P(4-VPH). The resultant hybrid micelles are spherical and consist of an ion-complex core of P(4-VPH)/SO and a water-soluble PEG corona and present a density gradient between the core and corona and the core has a higher density. The SO concentrations can affect the structure of the core-corona hybrid micelles. The low SO conentration leads to a loose core while the high SO concentration leads to a compact core.

Equilibrium bundle size of rodlike polyelectrolytes with counterion-induced attractive interactions

Multivalent counterions can induce an effective attraction between like-charged rodlike polyelectrolytes, leading to the formation of polyelectrolyte bundles. In this paper, we calculate the equilibrium bundle size using a simple model in which the attraction between polyelectrolytes (assumed to be pairwise additive) is treated phenomenologically. If the counterions are pointlike, they almost completely neutralize the charge of the bundle, and the equilibrium bundle size diverges. When the counterions are large, however, steric and short-range electrostatic interactions prevent charge neutralization of the bundle, thus forcing the equilibrium bundle size to be finite. We also show that if the attractive interactions between the rods become frustrated as the bundle grows, finite-size bundles can be obtained with pointlike counterions.