Development of the modern theory of polymeric complex coacervation

Saloplastics based on protein-peptides complexes immobilizing organic molecules in gastrointestinal drug delivery for ulcerative colitis treatment

Ulcerative colitis (UC) stands as a chronic inflammatory intestinal disease. This study aimed to explore a sustained-release strategy to alleviate DSS-induced colitis in mice using polyelectrolyte complexes (PECs) encapsulating an alkaloid, isoliensinine (ISO). The drug delivery platform, termed "Saloplastics (SAL)", was prepared by fabrication of PECs through the solid-liquid phase separation of sodium caseinate (SC) and ε-polylysine (EPL), followed by centrifugation to yield compact structures. Coarse-grained molecular dynamics simulations demonstrated that SAL had a nanorod-like structure formation between EPL and SC, which implied that the self-assembly of SAL is driven by hydrophobic aggregation and strong electrostatic attractions. A comprehensive evaluation of SAL was conducted, including characterizations of its physicochemical and biological properties. The results showed SAL had thermal plasticization properties and excellent swelling capacity as well as susceptibility to hydrolysis by pH and proteinase in simulated gastric fluid. Moreover, SAL displayed a porous morphology with high surface area for immobilizing organic molecules. ISO@SAL, formulated by ISO encapsulated in SAL, not only demonstrated high potency in alleviating DSS-induced colitis in mice, but also increased the dosing intervals from one day to three days. In conclusion, SAL is a biocompatible sustained-release oral drug delivery platform for gastrointestinal applications.

Effect of cosolvents on the phase separation of polyelectrolyte complexes

Evidence is shown that cosolvent mixtures control the coacervation of mixtures of oppositely charged polyelectrolytes. Binary and ternary solvent mixtures lead to non-monotonic solubility as a function of the average dielectric constants of the solvent mixtures. These data are rationalized by considering both electrostatic-driven phase separation and solvophobic-driven phase separation using group contribution effects on solubility parameters. These estimates are introduced into an effective Flory-Huggins interaction parameter within the framework of Voorn-Overbeek theory with variable dielectric constants and temperature dependences. Despite its simplicity, the model recovers salient experimental observations not only on their coacervate stabilities, but also on their lower critical solution temperature behaviors. These observations highlight the importance of weak van der Waals interactions in determining the phase behaviors of polyelectrolyte complexes relative to electrostatic correlations.

Theory and quantitative assessment of pH-responsive polyzwitterion-polyelectrolyte complexation

We introduce a theoretical framework to describe the pH-sensitive phase behavior of polyzwitterion-polyelectrolyte complex coacervates that reasonably captures the phenomenon from recent experimental observations. The polyzwitterion is described by a combinatorial sequence of the four states in which each zwitterionic monomer can occupy: dipolar, quasi-cationic, quasi-anionic, and fully neutralized. We explore the effects of various modifiable chemical and physical properties of the polymers-such as, pKa of the pH-active charged group on the zwitterion, equilibrium constant of salt condensation on the permanently charged group on the zwitterion, degrees of polymerization, hydrophobicity (via the Flory-Huggins interaction parameter), and dipole lengths-on the window of complexation across many stoichiometric mixing ratios of polyzwitterion and polyelectrolyte. The properties that determine the net charge of the polyzwitterion have the strongest effect on the pH range in which polyzwitterion-polyelectrolyte complexation occurs. We finish with general guidance for those interested in molecular design of polyzwitterion-polyelectrolyte complex coacervates and opportunities for future investigation.

Coacervate Formation in Dilute Aqueous Solutions of Inorganic Molecular Clusters with Simple Divalent Countercations

We report a complex coacervate formed by a 2.5 nm-diameter, rigid uranyl peroxide molecular cluster (Li68K12(OH)20)[UO2(O2)OH]60, U6060-) and SrCl2 salt in dilute aqueous solutions, including its location in the phase diagram, composition, rheological features, and critical conditions for phase transitions. In this coacervate, the Sr2+ cations are a major building component, and the coacervate phase covers a substantial region of the phase diagram. This coacervate demonstrates features that differ from traditional coacervates formed by oppositely charged long-chain polyelectrolytes, especially in its formation mechanism, dehydration, enhancement of mechanical strength with increasing ionic strength, and the change of salt partition preference into the coacervate and supernatant phases with ionic strength.

Minimal Peptide Sequences That Undergo Liquid-Liquid Phase Separation via Self-Coacervation or Complex Coacervation with ATP

The simple (self-)coacervation of the minimal tryptophan/arginine peptide sequences W2R2 and W3R3 was observed in salt-free aqueous solution. The phase diagrams were mapped using turbidimetry and optical microscopy, and the coacervate droplets were imaged using confocal microscopy complemented by cryo-TEM to image smaller droplets. The droplet size distribution and stability were probed using dynamic light scattering, and the droplet surface potential was obtained from zeta potential measurements. SAXS was used to elucidate the structure within the coacervate droplets, and circular dichroism spectroscopy was used to probe the conformation of the peptides, a characteristic signature for cation-π interactions being present under conditions of coacervation. These observations were rationalized using a simple model for the Rayleigh stability of charged coacervate droplets, along with atomistic molecular dynamics simulations which provide insight into stabilizing π-π stacking interactions of tryptophan as well as arginine-tryptophan cation-π interactions (which modulate the charge of the tryptophan π-electron system). Remarkably, the dipeptide WR did not show simple coacervation under the conditions examined, but complex coacervation was observed in mixtures with ATP (adenosine triphosphate). The electrostatically stabilized coacervation in this case provides a minimal model for peptide/nucleotide membraneless organelle formation. These are among the simplest model peptide systems observed to date able to undergo either simple or complex coacervation and are of future interest as protocell systems.

Two Methods Based on Integral Equation Approaches in Analyzing Polyelectrolyte Solutions: Macrophase Separation

To understand the phase behaviors of polyelectrolyte solutions, we provide two analytical methods to formulate a molecular equation of state for a system of fully charged polyanions (PAs) and polycations (PCs) in a monomeric neutral component, based on integral equation theories. The mixture is treated in a primitive and restricted manner. The first method utilizes Blum's approach to charged hard spheres, incorporating the chain connectivity contribution by charged spheres via Stell's cavity function method. The second method employs Wertheim's multi-density Ornstein-Zernike treatment of charged hard spheres with Baxter's adhesive potential. The pressures derived from these methods are compared to available molecular dynamics simulations data for a solution of PAs and monomeric counterions as a limiting case. Two-phase equilibrium for the system is calculated using both methods to evaluate the relative strength of phase segregation that leads to complex coacervation. Additionally, the scaling exponents for a selected solution near its critical point are examined.

Charge transport in electrospinning of polyelectrolyte solutions

This study elucidates the electrical charge transport during electrospinning of weak polyelectrolyte (poly(acrylic acid) (PAA)) solutions by employing current emission measurements. With pH variation, the PAA ionization degree could be controlled from uncharged at low pH to weakly charged at intermediate solution pH. Electrospinning neutral poly(vinylpyrrolidone) (PVP) as a reference polymer solution confirmed established current-flow rate scaling relationships as shown by De La Mora and Loscertales (1994), I ∼ (γKQ)ν, independent of the applied electric field polarity, where ν = 0.5, K is the conductivity, γ is the surface tension, Q is the flow rate, and I is the current. Similarly, the uncharged PAA did not display any polarity dependence, yet ν ≈ 0.8. Negatively charged PAA, however, showed a marked deviation in the current-flow rate behavior, which was affected by the applied electric field polarity. In the case of negative polarity, ν = 0.99, whereas for a positive polarity ν = 0.68. Similarly, the voltage required for stable cone-jet electrospinning of charged PAA was significantly higher in the negative polarity configuration for all tested flow rates (300-1600 μL h-1). As opposed to merely surface charges typically considered when electrospinning leaky dielectric fluids, as suggested by Melcher and Taylor (1969), our results suggest that the measured current is also affected by volumetric charges from charged PAA in the bulk of the jet. The proposed additional charge transport might affect the orientational order within PE-based nanofibers and their diameter.

Quantitative turbidimetric characterization of stabilized complex coacervate dispersions

Stabilizing complex coacervate microdroplets is desirable due to their various applications, such as bioreactors, drug delivery vehicles, and encapsulants. Here, we present quantitative characterization of complex coacervate dispersion stability inferred by turbidimetry measurements. The stability of the dispersions is shown to be modulated by the concentrations of comb polyelectrolyte (cPE) stabilizers and salt. We demonstrate cPEs as effective stabilizers for complex coacervate dispersions independent of the chemistry or length of the constituent polyelectrolytes, salts, or preparation routes. By monitoring the temporal evolution of dispersion turbidity, we show that cPEs suppress microdroplet coalescence with minimal change in microdroplet sizes over 48 hours, even at salt concentrations up to 300 mM. The number density and average microdroplet size are shown to be controlled by varying the cPE and salt concentrations. Lastly, turbidity maps, akin to binodal phase maps, depict an expansion of the turbid two-phase region and an increase in the salt resistance of the coacervates upon the introduction of cPEs. The coacervate salt resistance is shown to increase by >3×, and this increase is maintained for up to 15 days, demonstrating that cPEs impart higher salt resistance over extended durations.

Biomolecular Condensates in Contact with Membranes

Biomolecular condensates are highly versatile membraneless organelles involved in a plethora of cellular processes. Recent years have witnessed growing evidence of the interaction of these droplets with membrane-bound cellular structures. Condensates' adhesion to membranes can cause their mutual molding and regulation, and their interaction is of fundamental relevance to intracellular organization and communication, organelle remodeling, embryogenesis, and phagocytosis. In this article, we review advances in the understanding of membrane-condensate interactions, with a focus on in vitro models. These minimal systems allow the precise characterization and tuning of the material properties of both membranes and condensates and provide a workbench for visualizing the resulting morphologies and quantifying the interactions. These interactions can give rise to diverse biologically relevant phenomena, such as molecular-level restructuring of the membrane, nano- to microscale ruffling of the condensate-membrane interface, and coupling of the protein and lipid phases.

Pressure Changes Across a Membrane Formed by Coacervation of Oppositely Charged Polymer-Surfactant Systems

We investigate the mass transfer and membrane growth processes during capsule formation by the interaction of the biopolymer xanthan gum with CnTAB surfactants. When a drop of xanthan gum polymer solution is added to the surfactant solution, a membrane is formed by coacervation. It encapsulates the polymer drop in the surfactant solution. The underlying mechanisms and dynamic processes during capsule formation are not yet understood in detail. Therefore, we characterized the polymer-surfactant complex formation during coacervation by measuring the surface tension and surface elasticity at the solution-air interface for different surfactant chain lengths and concentrations. The adsorption behavior of the mixed polymer-surfactant system at the solution-air interface supports the understanding of observed trends during the capsule formation. We further measured the change in capsule pressure over time and simultaneously imaged the membrane growth via confocal microscopy. The cross-linking and shrinkage during the membrane formation by coacervation leads to an increasing tensile stress in the elastic membrane, resulting in a rapid pressure rise. Afterward, the pressure gradually decreases and the capsule shrinks as water diffuses out. This is not only due to the initial capsule overpressure but also due to osmosis caused by the higher ionic strength of the surfactant solution outside the capsule compared to the polymer solution inside the capsule. The influence of polymer concentration and surfactant type and concentration on the pressure changes and the membrane structure are studied in this work, providing detailed insights into the dynamic membrane formation process by coacervation. This knowledge can be used to produce capsules with tailored membrane properties and to develop a suitable encapsulation protocol in technological applications. The obtained insights into the mass transfer of water across the capsule membrane are important for future usage in separation techniques and the food industry and allow us to better predict the capsule time stability.

Multiscale remodeling of biomembranes and vesicles

Biomembranes and vesicles cover a wide range of length scales. Indeed, small nanovesicles have a diameter of a few tens of nanometers whereas giant vesicles can have diameters up to hundreds of micrometers. The remodeling of giant vesicles on the micron scale can be observed by light microscopy and understood by the theory of curvature elasticity, which represents a top-down approach. The theory predicts the formation of multispherical shapes as recently observed experimentally. On the nanometer scale, much insight has been obtained via coarse-grained molecular dynamics simulations of nanovesicles, which provides a bottom-up approach based on the lipid numbers assembled in the two bilayer leaflets and the resulting leaflet tensions. The remodeling processes discussed here include the shape transformations of vesicles, their morphological responses to the adhesion of condensate droplets, the instabilities of lipid bilayers and nanovesicles, as well as the topological transformations of vesicles by membrane fission and fusion. The latter processes determine the complex topology of the endoplasmic reticulum.

Tuning the underwater adhesiveness of antibacterial polysaccharides complex coacervates

HYPOTHESIS

Adjusting the water content and mechanical properties of polyelectrolyte coacervates for optimal underwater adhesion requires simultaneous control of the macromolecular design and the type and concentration of the salt used. Using synthetic or bio-inspired polymers to make coacervates often involves complicated chemistries and large variations in salt concentration. The underwater adhesiveness of simple, bio-sourced coacervates can be tuned with relatively small variations in salt concentration. Bio-sourced polymers can also impart beneficial biological activities to the final material.

EXPERIMENTS

We made complex coacervates from charged chitosan (CHI) and hyaluronic acid (HA) with NaCl as the salt. Their water content and viscoelastic properties were investigated to identify the formulation with optimal underwater adhesion in physiological conditions. The coacervates were also studied in antibacterial and cytotoxicity experiments.

FINDINGS

As predicted by linear rheology, the CHI-HA coacervates at 0.1 and 0.2 M NaCl had the highest pull-off adhesion strengths of 44.4 and 40.3 kPa in their respective supernatants. In-situ physical hardening of the 0.2 M coacervate upon a salt switch in 0.1 M NaCl resulted in a pull-off adhesion strength of 62.9 kPa. This material maintained its adhesive properties in physiological conditions. Finally, the optimal adhesive was found to be non-cytotoxic and inherently antimicrobial through a chitosan release-killing mechanism.

Optical Control over Liquid–Liquid Phase Separation

Liquid-liquid phase separation (LLPS) is responsible for the emergence of intracellular membrane-less organelles and the development of coacervate protocells. Benefitting from the advantages of simplicity, precision, programmability, and noninvasiveness, light has become an effective tool to regulate the assembly dynamics of LLPS, and mediate various biochemical processes associated with LLPS. In this review, recent advances in optically controlling membrane-less organelles within living organisms are summarized, thereby modulating a series of biological processes including irreversible protein aggregation pathologies, transcription activation, metabolic flux, genomic rearrangements, and enzymatic reactions. Among these, the intracellular systems (i.e., optoDroplet, Corelet, PixELL, CasDrop, and other optogenetic systems) that enable the photo-mediated control over biomolecular condensation are highlighted. The design of photoactive complex coacervate protocells in laboratory settings by utilizing photochromic molecules such as azobenzene and diarylethene is further discussed. This review is expected to provide in-depth insights into phase separation-associated biochemical processes, bio-metabolism, and diseases.

Solid-Liquid-Solution Phases in Poly(diallyldimethylammonium)/Poly(acrylic acid) Polyelectrolyte Complexes at Varying Temperatures

The coacervation and complexation of oppositely charged polyelectrolytes are dependent on numerous environmental and preparatory factors, but temperature is often overlooked. Temperature effects remain unclear because the temperature dependence of both the dielectric constant and polymer-solvent interaction parameter can yield lower and/or upper critical solution phase behaviors for PECs. Further, secondary interactions, such as hydrogen bonding, can affect the temperature response of a PEC. That is, mixtures of oppositely charged polyelectrolytes can exhibit phase separation upon lowering and/or increasing the mixture's temperature. Here, the phase behavior of poly(diallylmethylammonium)/poly(acrylic acid) (PDADMA/PAA) complexes under varying KBr ionic strengths, mixing ratios, and temperatures at a fixed pH (in which PAA hydrogen bonding can occur) is examined. At room temperature, the PDADMA/PAA PECs exhibit four different phase states: precipitate, coexisting precipitate and coacervate, solid-like gel, and coacervate. Variable-temperature optical microscopy reveals the upper critical solution temperature (UCST) at which each phase transitioned to a solution state. Interestingly, the UCST value is highly dependent on the original phase of the PEC, in which solid-like precipitates exhibit higher UCST values. Large-scale all-atom molecular dynamics (MD) simulations support that precipitates exhibit kinetic trapping, which may contribute to the higher UCST values observed in the experiment. Taken together, this study highlights the significance of temperature on the phase behavior of PECs, which may play a larger role in stimuli-responsive materials, membraneless organelles, and separations applications.

Assembly of porous filaments by interfacial complexation of nanochitin-based Pickering emulsion and seaweed alginate

Interfacial polyelectrolyte complexation spinning is an all-water, easy-to-operate method for production of composite filaments. Herein, this concept is extended to interfacial polyelectrolyte-emulsion complexation (IPEC) that better encodes structural and functional attributes of biomass substances into the filaments. This allows for formation of composite filaments by drawing contacting oppositely-charged chitin nanofiber-stabilized Pickering emulsion and seaweed alginate solution. The parameters affecting spinnability of the system including water-to-oil ratio, alginate concentration, and pH are comprehensively elucidated to support the design and application of IPEC. The composite filaments exhibit varied diameters and diverse porous structures that are adjustable by properties of Pickering droplets. The droplet diameter of precursor emulsion and pore size in the filaments are well correlated, revealing controllability of the IPEC spinning. The filaments are mechanically robust in dry condition and show stable performance even in wet condition. The release rate of filaments that is pre-loaded with hydrophilic drug is regulated by the internal pore size, showing capability on sustained release. This study offers a new perspective toward dry spinning via interfacial complexation of complicated nanochitin-based structural building blocks, aiming at developing high-performance fiber materials for advanced applications.

Sequestration of Small Ions and Weak Acids and Bases by a Polyelectrolyte Complex Studied by Simulation and Experiment

Mixing of oppositely charged polyelectrolytes can result in phase separation into a polymer-poor supernatant and a polymer-rich polyelectrolyte complex (PEC). We present a new coarse-grained model for the Grand-reaction method that enables us to determine the composition of the coexisting phases in a broad range of pH and salt concentrations. We validate the model by comparing it to recent simulations and experimental studies, as well as our own experiments on poly(acrylic acid)/poly(allylamine hydrochloride) complexes. The simulations using our model predict that monovalent ions partition approximately equally between both phases, whereas divalent ones accumulate in the PEC phase. On a semiquantitative level, these results agree with our own experiments, as well as with other experiments and simulations in the literature. In the sequel, we use the model to study the partitioning of a weak diprotic acid at various pH values of the supernatant. Our results show that the ionization of the acid is enhanced in the PEC phase, resulting in its preferential accumulation in this phase, which monotonically increases with the pH. Currently, this effect is still waiting to be confirmed experimentally. We explore how the model parameters (particle size, charge density, permittivity, and solvent quality) affect the measured partition coefficients, showing that fine-tuning of these parameters can make the agreement with the experiments almost quantitative. Nevertheless, our results show that charge regulation in multivalent solutes can potentially be exploited in engineering the partitioning of charged molecules in PEC-based systems at various pH values.

Design Rules for the Sequestration of Viruses into Polypeptide Complex Coacervates

Encapsulation is a strategy that has been used to facilitate the delivery and increase the stability of proteins and viruses. Here, we investigate the encapsulation of viruses via complex coacervation, which is a liquid-liquid phase separation resulting from the complexation of oppositely charged polymers. In particular, we utilized polypeptide-based coacervates and explored the effects of peptide chemistry, chain length, charge patterning, and hydrophobicity to better understand the effects of the coacervating polypeptides on virus incorporation. Our study utilized two nonenveloped viruses, porcine parvovirus (PPV) and human rhinovirus (HRV). PPV has a higher charge density than HRV, and they both appear to be relatively hydrophobic. These viruses were compared to characterize how the charge, hydrophobicity, and patterning of chemistry on the surface of the virus capsid affects encapsulation. Consistent with the electrostatic nature of complex coacervation, our results suggest that electrostatic effects associated with the net charge of both the virus and polypeptide dominated the potential for incorporating the virus into a coacervate, with clustering of charges also playing a significant role. Additionally, the hydrophobicity of a virus appears to determine the degree to which increasing the hydrophobicity of the coacervating peptides can enhance virus uptake. Nonintuitive trends in uptake were observed with regard to both charge patterning and polypeptide chain length, with these parameters having a significant effect on the range of coacervate compositions over which virus incorporation was observed. These results provide insights into biophysical mechanisms, where sequence effects can control the uptake of proteins or viruses into biological condensates and provide insights for use in formulation strategies.

Coexistence of two coacervate phases of polyglycine in water suggested by polymer reference interaction site model theory

Mixing Gibbs energy and phase equilibria of aqueous solutions of polyglycine were studied theoretically by means of polymer reference interaction site model integral equation theory combined with the Gibbs-Duhem method. In addition to the ordinary liquid-liquid phase separation between dilute and concentrated solutions, the theoretical calculation predicted the coexistence of two coacervate phases, namely, the lower- and higher-density coacervates. The relative thermodynamic stabilities of these two phases change with the polymerization degree of polyglycine. The higher-density coacervate phase was rapidly stabilized by increasing the polymer length, and the lower-density phase became metastable at large polymers. The hydrogen bonds between the peptide chains were strengthened, and water was thermodynamically destabilized in the higher-density coacervate. A possible relation with the formation of amyloid fibril within a liquid droplet is also discussed.

Coacervate Droplets for Synthetic Cells

The design and construction of synthetic cells - human-made microcompartments that mimic features of living cells - have experienced a real boom in the past decade. While many efforts have been geared toward assembling membrane-bounded compartments, coacervate droplets produced by liquid-liquid phase separation have emerged as an alternative membrane-free compartmentalization paradigm. Here, the dual role of coacervate droplets in synthetic cell research is discussed: encapsulated within membrane-enclosed compartments, coacervates act as surrogates of membraneless organelles ubiquitously found in living cells; alternatively, they can be viewed as crowded cytosol-like chassis for constructing integrated synthetic cells. After introducing key concepts of coacervation and illustrating the chemical diversity of coacervate systems, their physicochemical properties and resulting bioinspired functions are emphasized. Moving from suspensions of free floating coacervates, the two nascent roles of these droplets in synthetic cell research are highlighted: organelle-like modules and cytosol-like templates. Building the discussion on recent studies from the literature, the potential of coacervate droplets to assemble integrated synthetic cells capable of multiple life-inspired functions is showcased. Future challenges that are still to be tackled in the field are finally discussed.

Counterion-controlled phase equilibria in a charge-regulated polymer solution

We study phase equilibria in a minimal model of charge-regulated polymer solutions. Our model consists of a single polymer species whose charge state arises from protonation-deprotonation processes in the presence of a dissolved acid, whose anions serve as screening counterions. We explicitly account for variability in the polymers' charge states. Homogeneous equilibria in this model system are characterised by the total concentration of polymers, the concentration of counter-ions and the charge distributions of polymers which can be computed with the help of analytical approximations. We use these analytical results to characterise how parameter values and solution acidity influence equilibrium charge distributions and identify for which regimes uni-modal and multi-modal charge distributions arise. We then study the interplay between charge regulation, solution acidity and phase separation. We find that charge regulation has a significant impact on polymer solubility and allows for non-linear responses to the solution acidity: Re-entrant phase behaviour is possible in response to increasing solution acidity. Moreover, we show that phase separation can yield to the coexistence of local environments characterised by different charge distributions.

Theoretical treatment of complex coacervate core micelles: structure and pH-induced disassembly

Complex coacervate core micelles (C3Ms) are supramolecular soft nanostructures formed by the assembly of a block copolymer and an oppositely charged homopolymer. The coacervation of the charged segments in both macromolecules drives the formation of the core of the C3M, while the neutral block of the copolymer forms the corona. This work introduces a molecular theory (MOLT) that predicts the internal structure and stimuli-responsive properties of C3Ms and explicitly considers the chemical architecture of the polyelectrolytes, their acid-based equilibria and electrostatic and non-electrostatic interactions. In order to accurately predict complex coacervation, the correlations between charged species are incorporated into MOLT as ion-pairing processes, which are modeled using a coupled chemical equilibrium formalism. Very good agreement was observed between the experimental results in the literature and MOLT predictions for the scaling relationships that relate the dimensions of the micelle (aggregation number and sizes of the micelle and the core) to the lengths of the different blocks. MOLT was used to study the disassembly of the micelles when the solution pH is driven away from the value that guarantees the charge stoichiometry of the core. This study reveals that very sharp disassembly transitions can be obtained by tuning the length or architecture of the copolymer component, thereby suggesting potential routes to design C3Ms capable of releasing their components at very precise pH values.

Driving forces of the complex formation between highly charged disordered proteins

Highly disordered complexes between oppositely charged intrinsically disordered proteins present a new paradigm of biomolecular interactions. Here, we investigate the driving forces of such interactions for the example of the highly positively charged linker histone H1 and its highly negatively charged chaperone, prothymosin α (ProTα). Temperature-dependent single-molecule Förster resonance energy transfer (FRET) experiments and isothermal titration calorimetry reveal ProTα-H1 binding to be enthalpically unfavorable, and salt-dependent affinity measurements suggest counterion release entropy to be an important thermodynamic driving force. Using single-molecule FRET, we also identify ternary complexes between ProTα and H1 in addition to the heterodimer at equilibrium and show how they contribute to the thermodynamics observed in ensemble experiments. Finally, we explain the observed thermodynamics quantitatively with a mean-field polyelectrolyte theory that treats counterion release explicitly. ProTα-H1 complex formation resembles the interactions between synthetic polyelectrolytes, and the underlying principles are likely to be of broad relevance for interactions between charged biomolecules in general.

The effect of monomer polarizability on the stability and salt partitioning in model coacervates

Coacervation of charged polymer chains has been a topic of major interest in both polymer and biological sciences, as it is a subset of a phenomenon called liquid-liquid phase separation (LLPS). In this process the polymer-rich phase separates from the polymer-lean supernatant while still maintaining its liquid-like properties. LLPS has been shown to play a crucial role in cellular homeostasis by driving the formation of membraneless organelles. It also has the potential to be harnessed to aid in novel therapeutical applications. Recent studies have demonstrated that there is no one simple mechanism which drives LLPS, which is instead a result of the combined effect of electrostatic, dipolar, hydrophobic, and other weak interactions. Using coarse-grained polymer simulations we investigate the relatively unexplored effects of monomer polarizability and spatially varying dielectric constant on LLPS propensity, and these factors affect the properties of the resulting condensates. In order to produce spatial variations in the dielectric constant, all our simulations include explicit solvent and counterions. We demonstrate that polarizability has only a minor effect on the bulk behaviour of the condensates but plays a major role when ion partitioning and microstructure are considered. We observe that the major contribution comes from the nature of the neutral blocks as endowing them with an induced dipole changes their character from hydrophobic to hydrophilic. We hypothesize that the results of this work can aid in guiding future studies concerned with LLPS by providing a general framework and by highlighting important factors which influence LLPS.

Fluctuations, structure, and size inside coacervates

Aqueous solutions of oppositely charged macromolecules exhibit the ubiquitous phenomenon of coacervation. This subject is of considerable current interest due to numerous biotechnological applications of coacervates and the general premise of biomolecular condensates. Towards a theoretical foundation of structural features of coacervates, we present a field-theoretic treatment of coacervates formed by uniformly charged flexible polycations and polyanions in an electrolyte solution. We delineate different regimes of polymer concentration fluctuations and structural features of coacervates based on the concentrations of polycation and polyanion, salt concentration, and experimentally observable length scales. We present closed-form formulas for correlation length of polymer concentration fluctuations, scattering structure factor, and radius of gyration of a labelled polyelectrolyte chain inside a concentrated coacervate. Using random phase approximation suitable for concentrated polymer systems, we show that the inter-monomer electrostatic interaction is screened by interpenetration of all charged polymer chains and that the screening length depends on the individual concentrations of the polycation and the polyanion, as well as the salt concentration. Our calculations show that the scattering intensity decreases monotonically with scattering wave vector at higher salt concentrations, while it exhibits a peak at intermediate scattering wave vector at lower salt concentrations. Furthermore, we predict that the dependence of the radius of gyration of a labelled chain on its degree of polymerization generally obeys the Gaussian chain statistics. However, the chain is modestly swollen, the extent of which depending on polyelectrolyte composition, salt concentration, and the electrostatic features of the polycation and polyanion such as the degree of ionization.

Phase Behavior and Electrochemical Properties of Highly Asymmetric Redox Coacervates

This work reports the phase behavior and electrochemical properties of liquid coacervates made of ferricyanide and poly(ethylenimine). In contrast to the typical polyanion/polycation pairs used in liquid coacervates, the ferricyanide/poly(ethylenimine) system is highly asymmetric because poly(ethylenimine) has approximately 170 charges per molecule, while ferricyanide has only 3. Two types of phase diagrams were measured and fitted with a theoretical model. In the first type of diagram, the stability of the coacervate was studied in the plane given by the concentration of poly(ethylenimine) versus the concentration of ferricyanide for a fixed concentration of added monovalent salt (NaCl). The second type of diagram involved the plane given by the concentration of poly(ethylenimine) vs the concentration of the added monovalent salt for a fixed poly(ethyleneimine)/ferricyanide ratio. Interestingly, these phase diagrams displayed qualitative similarities to those of symmetric polyanion/polycation systems, suggesting that coacervates formed by a polyelectrolyte and a small multivalent ion can be treated as a specific case of polyelectrolyte coacervate. The characterization of the electrochemical properties of the coacervate revealed that the addition of monovalent salt greatly enhances charge transport, presumably by breaking ion pairs between ferricyanide and poly(ethylenimine). This finding highlights the significant influence of added salt on the transport properties of coacervates. This study provides the first comprehensive characterization of the phase behavior and transport properties of asymmetric coacervates and places these results within the broader context of the better-known symmetric polyelectrolyte coacervates.

Ultrasmall Gold Nanoparticles as Clients of Biomolecular Condensates

Liquid-liquid phase separation (LLPS) of biopolymers to form condensates is a widespread phenomenon in living cells. Agents that target or alter condensation can help uncover elusive physiological and pathological mechanisms. Owing to their unique material properties and modes of interaction with biomolecules, nanoparticles represent attractive condensate-targeting agents. Our work focused on elucidating the interaction between ultrasmall gold nanoparticles (usGNPs) and diverse types of condensates of tau, a representative phase-separating protein associated with neurodegenerative disorders. usGNPs attract considerable interest in the biomedical community due to unique features, including emergent optical properties and good cell penetration. We explored the interaction of usGNPs with reconstituted self-condensates of tau, two-component tau/polyanion and three-component tau/RNA/alpha-synuclein coacervates. The usGNPs were found to concentrate into condensed liquid droplets, consistent with the formation of dynamic client (nanoparticle) - scaffold (tau) interactions, and were observable thanks to their intrinsic luminescence. Furthermore, usGNPs were capable to promote LLPS of a protein domain which is unable to phase separate on its own. Our study demonstrates the ability of usGNPs to interact with and illuminate protein condensates. We anticipate that nanoparticles will have broad applicability as nanotracers to interrogate phase separation, and as nanoactuators controlling the formation and dissolution of condensates.

Condensation Goes Viral: A Polymer Physics Perspective

The past decade has seen a revolution in our understanding of how the cellular environment is organized, where an incredible body of work has provided new insights into the role played by membraneless organelles. These rapid advancements have been made possible by an increasing awareness of the peculiar physical properties that give rise to such bodies and the complex biology that enables their function. Viral infections are not extraneous to this. Indeed, in host cells, viruses can harness existing membraneless compartments or, even, induce the formation of new ones. By hijacking the cellular machinery, these intracellular bodies can assist in the replication, assembly, and packaging of the viral genome as well as in the escape of the cellular immune response. Here, we provide a perspective on the fundamental polymer physics concepts that may help connect and interpret the different observed phenomena, ranging from the condensation of viral genomes to the phase separation of multicomponent solutions. We complement the discussion of the physical basis with a description of biophysical methods that can provide quantitative insights for testing and developing theoretical and computational models.

Competition between β-Sheet and Coacervate Domains Yields Diverse Morphologies in Mixtures of Oppositely Charged Homochiral Polypeptides

Biomolecular assembly processes involving competition between specific intermolecular interactions and thermodynamic phase instability have been implicated in a number of pathological states and technological applications of biomaterials. As a model for such processes, aqueous mixtures of oppositely charged homochiral polypeptides such as poly-l-lysine and poly-l-glutamic acid have been reported to form either β-sheet-rich solid-like precipitates or liquid-like coacervate droplets depending on competing hydrogen bonding interactions. Herein, we report studies of polypeptide mixtures that reveal unexpectedly diverse morphologies ranging from partially coalescing and aggregated droplets to bulk precipitates, as well as a previously unreported re-entrant liquid-liquid phase separation at high polypeptide concentration and ionic strength. Combining our experimental results with all-atom molecular dynamics simulations of folded polypeptide complexes reveals a concentration dependence of β-sheet-rich secondary structure, whose relative composition correlates with the observed macroscale morphologies of the mixtures. These results elucidate a crucial balance of interactions that are important for controlling morphology during coacervation in these and potentially similar biologically relevant systems.

Application of Nanoparticles in the Diagnosis of Gastrointestinal Diseases: A Complete Future Perspective

The diagnosis of gastrointestinal (GI) diseases currently relies primarily on invasive procedures like digestive endoscopy. However, these procedures can cause discomfort, respiratory issues, and bacterial infections in patients, both during and after the examination. In recent years, nanomedicine has emerged as a promising field, providing significant advancements in diagnostic techniques. Nanoprobes, in particular, offer distinct advantages, such as high specificity and sensitivity in detecting GI diseases. Integration of nanoprobes with advanced imaging techniques, such as nuclear magnetic resonance, optical fluorescence imaging, tomography, and optical correlation tomography, has significantly enhanced the detection capabilities for GI tumors and inflammatory bowel disease (IBD). This synergy enables early diagnosis and precise staging of GI disorders. Among the nanoparticles investigated for clinical applications, superparamagnetic iron oxide, quantum dots, single carbon nanotubes, and nanocages have emerged as extensively studied and utilized agents. This review aimed to provide insights into the potential applications of nanoparticles in modern imaging techniques, with a specific focus on their role in facilitating early and specific diagnosis of a range of GI disorders, including IBD and colorectal cancer (CRC). Additionally, we discussed the challenges associated with the implementation of nanotechnology-based GI diagnostics and explored future prospects for translation in this promising field.

Leaflet Tensions Control the Spatio-Temporal Remodeling of Lipid Bilayers and Nanovesicles

Biological and biomimetic membranes are based on lipid bilayers, which consist of two monolayers or leaflets. To avoid bilayer edges, which form when the hydrophobic core of such a bilayer is exposed to the surrounding aqueous solution, a single bilayer closes up into a unilamellar vesicle, thereby separating an interior from an exterior aqueous compartment. Synthetic nanovesicles with a size below 100 nanometers, traditionally called small unilamellar vesicles, have emerged as potent platforms for the delivery of drugs and vaccines. Cellular nanovesicles of a similar size are released from almost every type of living cell. The nanovesicle morphology has been studied by electron microscopy methods but these methods are limited to a single snapshot of each vesicle. Here, we review recent results of molecular dynamics simulations, by which one can monitor and elucidate the spatio-temporal remodeling of individual bilayers and nanovesicles. We emphasize the new concept of leaflet tensions, which control the bilayers' stability and instability, the transition rates of lipid flip-flops between the two leaflets, the shape transformations of nanovesicles, the engulfment and endocytosis of condensate droplets and rigid nanoparticles, as well as nanovesicle adhesion and fusion. To actually compute the leaflet tensions, one has to determine the bilayer's midsurface, which represents the average position of the interface between the two leaflets. Two particularly useful methods to determine this midsurface are based on the density profile of the hydrophobic lipid chains and on the molecular volumes.

The effect of polymer length in liquid-liquid phase separation

Understanding the thermodynamics that drive liquid-liquid phase separation (LLPS) is quite important given the number of diverse biomolecular systems undergoing this phenomenon. Many studies have focused on condensates of long polymers, but very few systems of short-polymer condensates have been observed and studied. Here, we study a short-polymer system of various lengths of poly-adenine RNA and peptides formed by the RGRGG sequence repeats to understand the underlying thermodynamics of LLPS. Using the recently developed COCOMO coarse-grained (CG) model, we predicted condensates for lengths as short as 5-10 residues, which was then confirmed by experiment, making this one of the smallest LLPS systems yet observed. A free-energy model reveals that the length dependence of condensation is driven primarily by entropy of confinement. The simplicity of this system will provide the basis for understanding more biologically realistic systems.

Characterization and stability evaluation of Ca2+ cross-linked soybean protein isolate/chitosan/sodium alginate ternary complex coacervate phase

To improve the stability of the soybean protein isolate/chitosan/sodium alginate ternary complex coacervate phase against environmental pH and ionic strength, the complex ternary phase cross-linked by Ca²⁺ was characterized and evaluated. The viscoelastic properties, thermal properties, microstructure, and texture profile were characterized using rheology, differentia scanning calorimetry as well as thermmogravimetric analysis, scanning electron microscopy as well as transmission electron microscopy, and texture profile analysis, respectively. Compared with the uncross-linked ternary complex coacervate, the complex in situ cross-linked with 1.0 % Ca²⁺ for 1 h still retains its typical solid characteristics, and has a more compact network structure and better stability. Our research results also showed that prolonging the cross-linking time (from 3 h to 5 h) and increasing the concentration of the cross-linking agent (from 1.5 % to 2.0 %) did not further improve the rheological, thermodynamic and textural properties of the complex coacervate. The ternary complex coacervate phase cross-linked in situ under 1.5 % concentration of Ca²⁺ for 3 h showed significantly improved stability at low pH 1.5-3.0, which indicats that the ternary complex coacervate phase cross-linked in situ by Ca²⁺ can be used as a potential delivery platform for the effective delivery of biomolecules under physiological conditions.

Polyelectrolyte Complexes from Oppositely Charged Filamentous Viruses

Here, we present an explorative study on a new type of polyelectrolyte complex made from chemically modified filamentous fd viruses. The fd virus is a semiflexible rod-shaped bacteriophage with a length of 880 nm and a diameter of 6.6 nm, which has been widely used as a well-defined model system of colloidal rods to investigate phase, flow, and other behavior. Here, chemically modified viruses have been prepared to obtain two types with opposite electrical charges in addition to a steric stabilization layer by poly(ethylene glycol) (PEG) grafting. The complex formation of stoichiometric mixtures of these oppositely charged viruses is studied as a function of virus and salt concentration. Furthermore, static light scattering measurements show a varying, strong increase in scattering intensity in some samples without visual macroscopic complex formation. Finally, the results of the complex formation are rationalized by comparing to model calculations on the pair interaction potential between oppositely charged viruses.

Polyelectrolyte-multivalent molecule complexes: physicochemical properties and applications

The complexation of polyelectrolytes with other oppositely charged structures gives rise to a great variety of functional materials with potential applications in a wide spectrum of technological fields. Depending on the assembly conditions, polyelectrolyte complexes can acquire different macroscopic configurations such as dense precipitates, nanosized colloids and liquid coacervates. In the past 50 years, much progress has been achieved to understand the principles behind the phase separation induced by the interaction of two oppositely charged polyelectrolytes in aqueous solutions, especially for symmetric systems (systems in which both polyions have similar molecular weight and concentration). However, in recent years, the complexation of polyelectrolytes with alternative building blocks such as small charged molecules (multivalent inorganic species, oligopeptides, and oligoamines, among others) has gained attention in different areas. In this review, we discuss the physicochemical characteristics of the complexes formed by polyelectrolytes and multivalent small molecules, putting a special emphasis on their similarities with the well-known polycation-polyanion complexes. In addition, we analyze the potential of these complexes to act as versatile functional platforms in various technological fields, such as biomedicine and advanced materials engineering.

Development of engineered probiotics with tailored functional properties and their application in food science

The potential health benefits of probiotics may not be cognized because of the substantial curtailment in their viability during food storage and passage through the gastrointestinal system. Intestinal flora composition, and resistance against pathogens are among the health benefits associated with probiotic consumption. In the gastric environment, pH 2.0, probiotics dramatically lose their viability during the transit through the gastrointestinal system. The challenge remains to maintain cell viability until it reaches the large intestine. In extreme conditions, such as a decrease in pH or an increase in temperature, encapsulation technology can enhance the viability of probiotics. Probiotic bacterial strains can be encapsulated in a variety of ways. The methods are broadly systematized into two categories, liquid and solid delivery systems. This review emphasizes the technology used in the research and commercial sectors to encapsulate probiotic cells while keeping them alive and the food matrix used to deliver these cells to consumers.

Graphical abstract

Remodeling of Biomembranes and Vesicles by Adhesion of Condensate Droplets

Condensate droplets are formed in aqueous solutions of macromolecules that undergo phase separation into two liquid phases. A well-studied example are solutions of the two polymers PEG and dextran which have been used for a long time in biochemical analysis and biotechnology. More recently, phase separation has also been observed in living cells where it leads to membrane-less or droplet-like organelles. In the latter case, the condensate droplets are enriched in certain types of proteins. Generic features of condensate droplets can be studied in simple binary mixtures, using molecular dynamics simulations. In this review, I address the interactions of condensate droplets with biomimetic and biological membranes. When a condensate droplet adheres to such a membrane, the membrane forms a contact line with the droplet and acquires a very high curvature close to this line. The contact angles along the contact line can be observed via light microscopy, lead to a classification of the possible adhesion morphologies, and determine the affinity contrast between the two coexisting liquid phases and the membrane. The remodeling processes generated by condensate droplets include wetting transitions, formation of membrane nanotubes as well as complete engulfment and endocytosis of the droplets by the membranes.

Polyelectrolyte complexation of two oppositely charged symmetric polymers: A minimal theory

Interplay of Coulomb interaction energy, free ion entropy, and conformational elasticity is a fascinating aspect in polyelectrolytes (PEs). We develop a theory for complexation of two oppositely charged PEs, a process known to be the precursor to the formation of complex coacervates in PE solutions, to explore the underlying thermodynamics of complex formation, at low salts. The theory considers general degrees of solvent polarity and dielectricity within an implicit solvent model, incorporating a varying Coulomb strength. Explicit calculation of the free energy of complexation and its components indicates that the entropy of free counterions and salt ions and the Coulomb enthalpy of bound ion-pairs dictate the equilibrium of PE complexation. This helps decouple the self-consistent dependency of charge and size of the uncomplexed parts of the polyions, derive an analytical expression for charge, and evaluate the free energy components as functions of chain overlap. Complexation is observed to be driven by enthalpy gain at low Coulomb strengths, driven by entropy gain of released counterions but opposed by enthalpy loss due to reduction of ion-pairs at moderate Coulomb strengths, and progressively less favorable due to enthalpy loss at even higher Coulomb strengths. The total free energy of the system is found to decrease linearly with an overlap of chains. Thermodynamic predictions from our model are in good quantitative agreement with simulations in literature.

Numerical Techniques for Applications of Analytical Theories to Sequence-Dependent Phase Separations of Intrinsically Disordered Proteins

Biomolecular condensates, physically underpinned to a significant extent by liquid-liquid phase separation (LLPS), are now widely recognized by numerous experimental studies to be of fundamental biological, biomedical, and biophysical importance. In the face of experimental discoveries, analytical formulations emerged as a powerful yet tractable tool in recent theoretical investigations of the role of LLPS in the assembly and dissociation of these condensates. The pertinent LLPS often involves, though not exclusively, intrinsically disordered proteins engaging in multivalent interactions that are governed by their amino acid sequences. For researchers interested in applying these theoretical methods, here we provide a practical guide to a set of computational techniques devised for extracting sequence-dependent LLPS properties from analytical formulations. The numerical procedures covered include those for the determination of spinodal and binodal phase boundaries from a general free energy function with examples based on the random phase approximation in polymer theory, construction of tie lines for multiple-component LLPS, and field-theoretic simulation of multiple-chain heteropolymeric systems using complex Langevin dynamics. Since a more accurate physical picture often requires comparing analytical theory against explicit-chain model predictions, a commonly utilized methodology for coarse-grained molecular dynamics simulations of sequence-specific LLPS is also briefly outlined.

A mini-review on bio-inspired polymer self-assembly: single-component and interactive polymer systems

Biology demonstrates meticulous ways to control biomaterials self-assemble into ordered and disordered structures to carry out necessary bioprocesses. Empowering the synthetic polymers to self-assemble like biomaterials is a hallmark of polymer physics studies. Unlike protein engineering, polymer science demystifies self-assembly by purposely embedding particular functional groups into the backbone of the polymer while isolating others. The polymer field has now entered an era of advancing materials design by mimicking nature to a very large extend. For example, we can make sequence-specific polymers to study highly ordered mesostructures similar to studying proteins, and use charged polymers to study liquid-liquid phase separation as in membraneless organelles. This mini-review summarizes recent advances in studying self-assembly using bio-inspired strategies on single-component and multi-component systems. Sequence-defined techniques are used to make on-demand hybrid materials to isolate the effects of chirality and chemistry in synthetic block copolymer self-assembly. In the meantime, sequence patterning leads to more hierarchical assemblies comprised of only hydrophobic and hydrophilic comonomers. The second half of the review discusses complex coacervates formed as a result of the associative charge interactions of oppositely charged polyelectrolytes. The tunable phase behavior and viscoelasticity are unique in studying liquid macrophase separation because the slow polymer relaxation comes primarily from charge interactions. Studies of bio-inspired polymer self-assembly significantly impact how we optimize user-defined materials on a molecular level.

Bio-inspired adhesive hydrogel for biomedicine-principles and design strategies

The adhesiveness of hydrogels is urgently required in various biomedical applications such as medical patches, tissue sealants, and flexible electronic devices. However, biological tissues are often wet, soft, movable, and easily damaged. These features pose difficulties for the construction of adhesive hydrogels for medical use. In nature, organisms adhere to unique strategies, such as reversible sucker adhesion in octopuses and nontoxic and firm catechol chemistry in mussels, which provide many inspirations for medical hydrogels to overcome the above challenges. In this review, we systematically classify bioadhesion strategies into structure-related and molecular-related ones, which cover almost all known bioadhesion paradigms. We outline the principles of these strategies and summarize the corresponding designs of medical adhesive hydrogels inspired by them. Finally, conclusions and perspectives concerning the development of this field are provided. For the booming bio-inspired adhesive hydrogels, this review aims to summarize and analyze the various existing theories and provide systematic guidance for future research from an innovative perspective.

Self-Defensive Antimicrobial Surfaces Using Polymyxin-Loaded Poly(styrene sulfonate) Microgels

Self-defensive antimicrobial surfaces are of interest because they can inhibit bacterial colonization while minimizing unnecessary antimicrobial release in the absence of a bacterial challenge. One self-defensive approach uses self-assembly to first deposit a submonolayer coating of polyelectrolyte microgels and subsequently load those microgels by complexation with small-molecule antimicrobials. The microgel/antimicrobial complexation strength is a key parameter that controls the ability of the antimicrobial both to remain sequestered within the microgels when exposed to medium and to release in response to a bacterial challenge. Here we study the relative complexation strengths of two FDA-approved cationic antibiotics─colistin (polymyxin E) and polymyxin B─with microgels of poly(styrene sulfonate) (PSS). These polymyxins are similar cyclic polypeptides with +5 charge at pH 7.4. However, polymyxin B substitutes an aromatic ring for a dimethyl moiety in colistin, and this aromaticity can influence complexation via π and hydrophobic interactions. Coarse-grained molecular dynamics shows that the free-energy change associated with polymyxin B/PSS complexation is more negative than that of colistin/PSS complexation. Experimentally, in situ optical microscopy of microgel deswelling shows that both antibiotics load quickly from low-ionic-strength phosphate buffer. The enhanced polymyxin B/PSS complexation strength is then manifested by subsequent exposure to flowing antibiotic-free buffer with varying NaCl concentration. Microgels loaded with polymyxin B remain stably deswollen to higher salt concentrations than do colistin/PSS microgels. Importantly, exposing loaded microgels to E. coli in nutrient-free-flowing phosphate buffer shows that bacteria are killed by physical contact with the loaded microgels consistent with the contact-transfer mechanism of self-defensiveness. In vitro culture experiments show that these same surfaces, nevertheless, support the adhesion, spreading and proliferation of human fetal osteoblasts. These findings suggest a pathway to create a self-defensive antimicrobial surface effective under physiological conditions based on the nonmetabolic bacteria-triggered release of FDA-approved antibiotics.

Driving force and pathway in polyelectrolyte complex coacervation

There is notable discrepancy between experiments and coarse-grained model studies regarding the thermodynamic driving force in polyelectrolyte complex coacervation: experiments find the free energy change to be dominated by entropy, while simulations using coarse-grained models with implicit solvent usually report a large, even dominant energetic contribution in systems with weak to intermediate electrostatic strength. Here, using coarse-grained, implicit-solvent molecular dynamics simulation combined with thermodynamic analysis, we study the potential of mean force (PMF) in the two key stages on the coacervation pathway for symmetric polyelectrolyte mixtures: polycation-polyanion complexation and polyion pair-pair condensation. We show that the temperature dependence in the dielectric constant of water gives rise to a substantial entropic contribution in the electrostatic interaction. By accounting for this electrostatic entropy, which is due to solvent reorganization, we find that under common conditions (monovalent ions, room temperature) for aqueous systems, both stages are strongly entropy-driven with negligible or even unfavorable energetic contributions, consistent with experimental results. Furthermore, for weak to intermediate electrostatic strengths, this electrostatic entropy, rather than the counterion-release entropy, is the primary entropy contribution. From the calculated PMF, we find that the supernatant phase consists predominantly of polyion pairs with vanishingly small concentration of bare polyelectrolytes, and we provide an estimate of the spinodal of the supernatant phase. Finally, we show that prior to contact, two neutral polyion pairs weakly attract each other by mutually induced polarization, providing the initial driving force for the fusion of the pairs.

An Overview of Coacervates: The Special Disperse State of Amphiphilic and Polymeric Materials in Solution

Individual amphiphiles, polymers, and colloidal dispersions influenced by temperature, pH, and environmental conditions or interactions between their oppositely charged pairs in solvent medium often produce solvent-rich and solvent-poor phases in the system. The solvent-poor denser phase found either on the top or the bottom of the system is called coacervate. Coacervates have immense applications in various technological fields. This review comprises a concise introduction, focusing on the types of coacervates, and the influence of different factors in their formation, structures, and stability. In addition, their physicochemical properties, thermodynamics of formation, and uses and multifarious applications are also concisely presented and discussed.

Wetting behavior of polyelectrolyte complex coacervates on solid surfaces

The wetting behavior of complex coacervates underpins their use in many emerging applications of surface science, particularly wet adhesives and coatings. Many factors dictate if a coacervate phase will condense on a solid surface, including solution conditions, the nature of the polymer-substrate interaction, and the underlying supernatant-coacervate bulk phase behavior. In this work, we use a simple inhomogeneous mean-field theory to study the wetting behavior of complex coacervates on solid surfaces both off-coexistence (wetting transitions) and on-coexistence (contact angles). We focus on the effects of salt concentration, the polycation/polyanion surface affinity, and the applied electrostatic potential on the wettability. We find that the coacervate generally wets the surface via a first order wetting transition with second order transitions possible above a surface critical point. Applying an electrostatic potential to a solid surface always improves the surface wettability when the polycation/polyanion-substrate interaction is symmetric. For asymmetric surface affinity, the wettability has a nonmonotonic dependence with the applied potential. We use simple scaling and thermodynamic arguments to explain our results.

How to Predict the Order of Phase Separation of Polyelectrolyte Complexes and Their Miscibility

The mixture of two oppositely charged polyelectrolyte solutions results in complexation that may lead to an associative phase separation, forming a highly concentrated phase in both polyelectrolytes in equilibrium with a dilute phase. In this work, we aim to investigate what controls the order of complexation when more polyelectrolytes of the same charge are present. For this, the effect of the addition of a third oppositely charged polyelectrolyte in a mixture of two polyelectrolytes with the same charge was studied. Our results show that, under certain conditions, the electrostatic complexation takes place selectively, where one polyanion (or polycation) phase separates first, followed by the other phase separation, with both complexes at their 1:1 charge stoichiometry. Infrared analyses of the phase-separated complexes confirmed that, in a mixture of polyanions, poly(styrenesulfonate) is complexed first, followed by poly(acrylate). For polycations, these analyses showed that poly(diallyldimethylammonium) is preferentially complexed over poly(allylamine). These results suggest that electrostatic complexation occurs following the sequence predicted as in an acid/base titration, where the acidic/basic strength of the involved polyions dictates which one is complexed first. In this respect, the order of complexation can be associated with the equivalence pH for each pair, which we propose can be used as a parameter to predict phase separation in polyelectrolyte mixtures. In addition, we have investigated the miscibility of these complex mixtures, confirming that multiphasic complexes are formed whenever the polyions display ionizable groups with different acid/basic strengths and that this can also be related to their equivalence pH.