Driving force and pathway in polyelectrolyte complex coacervation

Spatiotemporal Regulation of Cell Fate in Living Systems Using Photoactivatable Artificial DNA Membraneless Organelles

Coacervates formed by liquid-liquid phase separation emerge as important biomimetic models for studying the dynamic behaviors of membraneless organelles and synchronously motivating the creation of smart architectures with the regulation of cell fate. Despite continuous progress, it remains challenging to balance the trade-offs among structural stability, versatility, and molecular communication for regulation of cell fate and systemic investigation in a complex physiological system. Herein, we present a self-stabilizing and fastener-bound gain-of-function methodology to create a new type of synthetic DNA membraneless organelle (MO) with high stability and controlled bioactivity on the basis of DNA coacervates. Specifically, long single-strand DNA generated by rolling circle amplification (RCA) is selected as the scaffold that assembles into membraneless coacervates via phase separation. Intriguingly, the as-formed DNA MO can recruit RCA byproducts and other components to achieve self-stabilization, nanoscale condensation, and function encoding. As a proof of concept, photoactivatable DNA MO is constructed and successfully employed for time-dependent accumulation and spatiotemporal management of cancer in a mouse model. This study offers new, important insights into synthetic membraneless organelles for the basic understanding and manipulation of important life processes.

Charge Regulation Triggers Condensation of Short Oligopeptides to Polyelectrolytes

Electrostatic interactions between charged macromolecules are ubiquitous in biological systems, and they are important also in materials design. Attraction between oppositely charged molecules is often interpreted as if the molecules had a fixed charge, which is not affected by their interaction. Less commonly, charge regulation is invoked to interpret such interactions, i.e., a change of the charge state in response to a change of the local environment. Although some theoretical and simulation studies suggest that charge regulation plays an important role in intermolecular interactions, experimental evidence supporting such a view is very scarce. In the current study, we used a model system, composed of a long polyanion interacting with cationic oligolysines, containing up to 8 lysine residues. We showed using both simulations and experiments that while these lysines are only weakly charged in the absence of the polyanion, they charge up and condense on the polycations if the pH is close to the pKa of the lysine side chains. We show that the lysines coexist in two distinct populations within the same solution: (1) practically nonionized and free in solution; (2) highly ionized and condensed on the polyanion. Using this model system, we demonstrate under what conditions charge regulation plays a significant role in the interactions of oppositely charged macromolecules and generalize our findings beyond the specific system used here.

Complexation of Poly(ethylene glycol)-(ds)OligoDNA Conjugates with Ionic Liquids

We report the complexation of poly(ethylene glycol) conjugated double-stranded oligoDNA (PEG-(ds)oligoDNA) with imidazolium-based ionic liquids (ILs) to form polyelectrolyte complex aggregates (PCAs). The PEG-(ds)oligoDNA conjugates are prepared following a solution-phase coupling reaction. The binding of PEG-(ds)oligoDNA with either 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]) or 1-hexyl-3-methylimidazolium tetrafluoroborate ([HMIM][BF4]) is confirmed by a fluorescence displacement assay. Both ILs show stronger binding affinity to PEG-(ds)oligoDNA than bare (ds)oligoDNA due to the PEG-assisted increase in IL cation concentration in the vicinity of (ds)oligoDNA. The complex morphology formed at various amine (N) to phosphate (P) ratios is also examined. At high N/P ratios above 4, nanosized PCAs are formed, driven by a counterion-mediated attraction among the IL-bound (ds)oligoDNA segments and stabilized by the conjugated PEG segments. The PCAs exhibit near-neutral surface charges and resistance to DNase degradation, suggesting their potential use in gene delivery applications.

Entropy Drives Interpolymer Association in Water: Insights into Molecular Mechanisms

Interpolymer association in aqueous solutions is essential for many industrial processes, new materials design, and the biochemistry of life. However, our understanding of the association mechanism is limited. Classical theories do not provide molecular details, creating a need for detailed mechanistic insights. This work consolidates previous literature with complementary isothermal titration calorimetry (ITC) measurements and molecular dynamics (MD) simulations to investigate molecular mechanisms to provide such insights. The large body of ITC data shows that intermolecular bonds, such as ionic or hydrogen bonds, cannot drive association. Instead, polymer association is entropy-driven due to the reorganization of water and ions. We propose a unifying entropy-driven association mechanism by generalizing previously suggested polyion association principles to include nonionic polymers, here termed polydipoles. In this mechanism, complementary charge densities of the polymers are the common denominators of association, for both polyions and polydipoles. The association of the polymers results mainly from two processes: charge exchange and amphiphilic association. MD simulations indicate that the amphiphilic assembly alone is enough for the initial association. Our proposed mechanism is a step toward a molecular understanding of the formation of complexes between synthetic and biological polymers under ambient or biological conditions.

Submillisecond Atomistic Molecular Dynamics Simulations Reveal Hydrogen Bond-Driven Diffusion of a Guest Peptide in Protein-RNA Condensate

Liquid-liquid phase separation mediated by proteins and/or nucleic acids is believed to underlie the formation of many distinct condensed phases, or membraneless organelles, within living cells. These condensates have been proposed to orchestrate a variety of important processes. Despite recent advances, the interactions that regulate the dynamics of molecules within a condensate remain poorly understood. We performed accumulated 564.7 μs all-atom molecular dynamics (MD) simulations (system size ∼200k atoms) of model condensates formed by a scaffold RNA oligomer and a scaffold peptide rich in arginine (Arg). These model condensates contained one of three possible guest peptides: the scaffold peptide itself or a variant in which six Arg residues were replaced by lysine (Lys) or asymmetric dimethyl arginine (ADMA). We found that the Arg-rich peptide can form the largest number of hydrogen bonds and bind the strongest to the scaffold RNA in the condensate, relative to the Lys- and ADMA-rich peptides. Our MD simulations also showed that the Arg-rich peptide diffused more slowly in the condensate relative to the other two guest peptides, which is consistent with a recent fluorescence microscopy study. There was no significant increase in the number of cation-π interactions between the Arg-rich peptide and the scaffold RNA compared to the Lys-rich and ADMA-rich peptides. Our results indicate that hydrogen bonds between the peptides and the RNA backbone, rather than cation-π interactions, play a major role in regulating peptide diffusion in the condensate.

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.

Electro-Sorting Create Heterogeneity: Constructing A Multifunctional Janus Film with Integrated Compositional and Microstructural Gradients for Guided Bone Regeneration

Biology remains the envy of flexible soft matter fabrication because it can satisfy multiple functional needs by organizing a small set of proteins and polysaccharides into hierarchical systems with controlled heterogeneity in composition and microstructure. Here, it is reported that controlled, mild electronic inputs (<10 V; <20 min) induce a homogeneous gelatin-chitosan mixture to undergo sorting and bottom-up self-assembly into a Janus film with compositional gradient (i.e., from chitosan-enriched layer to chitosan/gelatin-contained layer) and tunable dense-porous gradient microstructures (e.g., porosity, pore size, and ratio of dense to porous layers). This Janus film performs is shown multiple functions for guided bone regeneration: the integration of compositional and microstructural features confers flexible mechanics, asymmetric properties for interfacial wettability, molecular transport (directional growth factor release), and cellular responses (prevents fibroblast infiltration but promotes osteoblast growth and differentiation). Overall, this work demonstrates the versatility of electrofabrication for the customized manufacturing of functional gradient soft matter.

Effect of counterion size on polyelectrolyte conformations and thermodynamics

We present a theoretical model to study the effect of counterion size on the effective charge, size, and thermodynamic behavior of a single, isolated, and flexible polyelectrolyte (PE) chain. We analyze how altering counterion size modifies the energy and entropy contributions to the system, including the ion-pair free energy, excluded volume interactions, entropy of free and condensed ions, and dipolar attraction among monomer-counterion pairs, which result in competing effects challenging intuitive predictions. The PE self-energy is calculated using the Edwards-Muthukumar Hamiltonian, considering a Gaussian monomer distribution for the PE. The condensed ions are assumed to be confined within a cylindrical volume around the PE backbone. The dipolar and excluded volume interactions are described by the second and third virial coefficients. The assumption of freely rotating dipoles results in a first-order coil-globule transition of the PE chain. A more realistic, weaker dipolar attraction, parameterized in our theory, shifts it to a second-order continuous transition. We calculate the size scaling-exponent of the PE and find exponents according to the relative dominance of the electrostatic, excluded volume, or dipolar effects. We further identify the entropy- and energy-driven regimes of the effective charge and conformation of the PE, highlighting the interplay of free ion entropy and ion-pair energy with varying electrostatic strengths. The crossover strength, dependent on the counterion size, indicates that diminishing sizes favor counterion condensation at the expense of free ion entropy. The predictions of the model are consistent with trends in simulations and generalize the findings of the point-like counterion theories.

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.

Self-Assembling Polypeptides in Complex Coacervation

Intracellular compartmentalization plays a pivotal role in cellular function, with membrane-bound organelles and membrane-less biomolecular "condensates" playing key roles. These condensates, formed through liquid-liquid phase separation (LLPS), enable selective compartmentalization without the barrier of a lipid bilayer, thereby facilitating rapid formation and dissolution in response to stimuli. Intrinsically disordered proteins (IDPs) or proteins with intrinsically disordered regions (IDRs), which are often rich in charged and polar amino acid sequences, scaffold many condensates, often in conjunction with RNA.Comprehending the impact of IDP/IDR sequences on phase separation poses a challenge due to the extensive chemical diversity resulting from the myriad amino acids and post-translational modifications. To tackle this hurdle, one approach has been to investigate LLPS in simplified polypeptide systems, which offer a narrower scope within the chemical space for exploration. This strategy is supported by studies that have demonstrated how IDP function can largely be understood based on general chemical features, such as clusters or patterns of charged amino acids, rather than residue-level effects, and the ways in which these kinds of motifs give rise to an ensemble of conformations.Our laboratory has utilized complex coacervates assembled from oppositely charged polypeptides as a simplified material analogue to the complexity of liquid-liquid phase separated biological condensates. Complex coacervation is an associative LLPS that occurs due to the electrostatic complexation of oppositely charged macro-ions. This process is believed to be driven by the entropic gains resulting from the release of bound counterions and the reorganization of water upon complex formation. Apart from their direct applicability to IDPs, polypeptides also serve as excellent model polymers for investigating molecular interactions due to the wide range of available side-chain functionalities and the capacity to finely regulate their sequence, thus enabling precise control over interactions with guest molecules.Here, we discuss fundamental studies examining how charge patterning, hydrophobicity, chirality, and architecture affect the phase separation of polypeptide-based complex coacervates. These efforts have leveraged a combination of experimental and computational approaches that provide insight into molecular level interactions. We also examine how these parameters affect the ability of complex coacervates to incorporate globular proteins and viruses. These efforts couple directly with our fundamental studies into coacervate formation, as such "guest" molecules should not be considered as experiencing simple encapsulation and are instead active participants in the electrostatic assembly of coacervate materials. Interestingly, we observed trends in the incorporation of proteins and viruses into coacervates formed using different chain length polypeptides that are not well explained by simple electrostatic arguments and may be the result of more complex interactions between globular and polymeric species. Additionally, we describe experimental evidence supporting the potential for complex coacervates to improve the thermal stability of embedded biomolecules, such as viral vaccines.Ultimately, peptide-based coacervates have the potential to help unravel the physics behind biological condensates, while paving the way for innovative methods in compartmentalization, purification, and biomolecule stabilization. These advancements could have implications spanning medicine to biocatalysis.

Toward a Unified Description of the Electrostatic Assembly of Microgels and Nanoparticles

The interplay of soft responsive particles, such as microgels, with nanoparticles (NPs) yields highly versatile complexes that show great potential for applications, ranging from plasmonic sensing to catalysis and drug delivery. However, the microgel-NP assembly process has not been investigated so far at the microscopic level, thus hindering the possibility of designing such hybrid systems a priori. In this work, we combine state-of-the-art numerical simulations with experiments to elucidate the fundamental mechanisms taking place when microgel-NP assembly is controlled by electrostatic interactions and the associated effects on the structure of the resulting complexes. We find a general behavior where, by increasing the number of interacting NPs, the microgel deswells up to a minimum size after which a plateau behavior occurs. This occurs either when NPs are mainly adsorbed to the microgel corona via the folding of the more external chains or when NPs penetrate inside the microgel, thereby inducing a collective reorganization of the polymer network. By varying microgel properties, such as fraction of cross-linkers or charge, as well as NP size and charge, we further show that the microgel deswelling curves can be rescaled onto a single master curve, for both experiments and simulations, demonstrating that the process is entirely controlled by the charge of the whole microgel-NP complex. Our results thus have a direct relevance in fundamental materials science and offer novel tools to tailor the nanofabrication of hybrid devices of technological interest.

Surface-Immobilized Interpolyelectrolyte Complexes Formed by Polyelectrolyte Brushes

A scaling theory of interaction and complex formation between planar polyelectrolyte (PE) brush and oppositely charged mobile linear PEs is developed. Counterion release is found to be the main driving force for the complexation. An interpolyelectrolyte coacervate complex (IPEC) between the brush and oppositely charged mobile PEs is formed at moderate grafting density and low salt concentration. At higher grafting density mobile chains penetrate the brush, but the brush structure is controlled by the balance between entropic elasticity and nonelectrostatic short-range interactions, as happens in a neutral brush. An increase in salt concentration beyond the theoretically predicted threshold leads to the release of the guest polyions from the brush. For brushes with moderate grafting density, complexation with oppositely charged guest polyions is predicted to trigger lateral microphase separation and formation of the finite-size surface IPEC clusters. Power law dependencies for the cluster dimensions on the brush grafting density, PE length, and salt concentration are provided.

Poly(allylamine)-tripolyphosphate Ionic Assemblies as Nanocarriers: Friend or Foe?

Designing effective drug nanocarriers that are easy to synthesize, robust, and nontoxic is a significant challenge in nanomedicine. Polyamine-multivalent molecule nanocomplexes are promising drug carriers due to their simple and all-aqueous manufacturing process. However, these systems can present issues of colloidal instability over time and cellular toxicity due to the cationic polymer. In this study, we finely modulate the formation parameters of poly(allylamine-tripolyphosphate) complexes to jointly optimize the robustness and safety. Polyallylamine was ionically assembled with tripolyphosphate anions to form liquid-like nanocomplexes with a size of around 200 nm and a zeta potential of -30 mV. We found that nanocomplexes exhibit tremendous long-term stability (9 months of storage) in colloidal dispersion and that they are suitable as protein-loading agents. Moreover, the formation of nanocomplexes induced by tripolyphosphate anions produces a switch-off in the toxicity of the system by altering the overall charge from positive to negative. In addition, we demonstrate that nanocomplexes can be internalized by bone-marrow-derived macrophage cells. Altogether, these nanocomplexes have attractive and promising properties as delivery nanoplatforms for potential therapies based on the immune system activation.

Global control of cellular physiology by biomolecular condensates through modulation of electrochemical equilibria

Control of the electrochemical environment in living cells is typically attributed to ion channels. Here we show that the formation of biomolecular condensates can modulate the electrochemical environment in cells, which affects processes globally within the cell and interactions of the cell with its environment. Condensate formation results in the depletion or enrichment of certain ions, generating intracellular ion gradients. These gradients directly affect the electrochemical properties of a cell, including the cytoplasmic pH and hyperpolarization of the membrane potential. The modulation of the electrochemical equilibria between the intra- and extra-cellular environments by biomolecular condensates governs charge-dependent uptake of small molecules by cells, and thereby directly influences bacterial survival under antibiotic stress. The shift of the intracellular electrochemical equilibria by condensate formation also drives a global change of the gene expression profile. The control of the cytoplasmic environment by condensates is correlated with their volume fraction, which can be highly variable between cells due to the stochastic nature of gene expression at the single cell level. Thus, condensate formation can amplify cell-cell variability of the environmental effects induced by the shift of cellular electrochemical equilibria. Our work reveals new biochemical functions of condensates, which extend beyond the biomolecules driving and participating in condensate formation, and uncovers a new role of biomolecular condensates in cellular regulation.

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.

Using Implicit-Solvent Potentials to Extract Water Contributions to Enthalpy-Entropy Compensation in Biomolecular Associations

Biomolecular assembly typically exhibits enthalpy-entropy compensation (EEC) behavior whose molecular origin remains a long-standing puzzle. While water restructuring is believed to play an important role in EEC, its contribution to the entropy and enthalpy changes, and how these changes relate to EEC, remains poorly understood. Here, we show that water reorganization entropy/enthalpy can be obtained by exploiting the temperature dependence in effective, implicit-solvent potentials. We find that the different temperature dependencies in the hydrophobic interaction, rooted in water reorganization, result in substantial variations in the entropy/enthalpy change, which are responsible for EEC. For lower-critical-solution-temperature association, water reorganization entropy dominates the free-energy change at the expense of enthalpy; for upper-critical-solution-temperature association, water reorganization enthalpy drives the process at the cost of entropy. Other effects, such as electrostatic interaction and conformation change of the macromolecules, contribute much less to the variations in entropy/enthalpy.

Re-entrant transitions of locally stiff RNA chains in the presence of polycations leads to gelated architectures

The liquid-liquid phase separation of protein and nucleic acid mixtures drives the formation of numerous membraneless compartments in cells. Temperature variation is commonly used for mapping condensate phase diagrams, which often display unique upper critical temperatures. Recent report on peptide-RNA mixtures has shown the existence of lower and upper critical solution temperatures, highlighting the importance of temperature-dependent solvent and ion-mediated forces. In the present work, we employ residue-level coarse-grained models of RNA and polycation peptide chains for simulating temperature-induced re-entrant transitions and shedding light on the role played by mobile ions, temperature-dependent dielectric permittivity, and local chain stiffness. We show that differences in bending rigidity can significantly modulate condensate topology leading to the formation of gelated or fibril like architectures. The study also finds that temperature dependence of water permittivity is generally sufficient for recapitulating experimentally observed closed loop and LCST phase diagrams of highly charged protein-RNA mixtures. However, we find that similar-looking closed-loop phase diagrams can correspond to vastly different condensate topologies.

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.

Structure and Dynamics of Hybrid Colloid-Polyelectrolyte Coacervates

We develop a scaling theory for the structure and dynamics of "hybrid" complex coacervates formed from linear polyelectrolytes (PEs) and oppositely charged spherical colloids, such as globular proteins, solid nanoparticles, or spherical micelles of ionic surfactants. At low concentrations, in stoichiometric solutions, PEs adsorb at the colloids to form electrically neutral finite-size complexes. These clusters attract each other through bridging between the adsorbed PE layers. Above a threshold concentration, macroscopic phase separation sets in. The coacervate internal structure is defined by (i) the adsorption strength and (ii) the ratio of the resulting shell thickness to the colloid radius, H/R. A scaling diagram of different coacervate regimes is constructed in terms of the colloid charge and its radius for Θ and athermal solvents. For high charges of the colloids, the shell is thick, H ≫ R, and most of the volume of the coacervate is occupied by PEs, which determine its osmotic and rheological properties. The average density of hybrid coacervates exceeds that of their PE-PE counterparts and increases with nanoparticle charge, Q. At the same time, their osmotic moduli remain equal, and the surface tension of hybrid coacervates is lower, which is a consequence of the shell's inhomogeneous density decreasing with the distance from the colloid surface. When charge correlations are weak, hybrid coacervates remain liquid and follow Rouse/reptation dynamics with a Q-dependent viscosity, η _Rouse ∼ Q ^4/5 and η _rep ∼ Q ^28/15 for a Θ solvent. For an athermal solvent, these exponents are equal to 0.89 and 2.68, respectively. The diffusion coefficients of colloids are predicted to be strongly decreasing functions of their radius and charge. Our results on how Q affects the threshold coacervation concentration and colloidal dynamics in condensed phases are consistent with experimental observations for in vitro and in vivo studies of coacervation between supercationic green fluorescent proteins (GFPs) and RNA.

Applicability of the Generalized Stokes-Einstein Equation of Mode-Coupling Theory to Near-Critical Polyelectrolyte Complex Solutions

We examine whether the mode-coupling theory of Kawasaki and Ferrell (KF) [Kawasaki, K. Kinetic Equations and Time Correlation Functions of Critical Fluctuations. Ann. Phys. 1970, 61 (1), 1-56; Ferrell, R. A. Decoupled-Mode Dynamical Scaling Theory of the Binary-Liquid Phase Transition. Phys. Rev. Lett. 1970, 24 (21), 1169-1172] can describe dynamic light scattering (DLS) measurements of the dynamic structure factor of near-critical polyelectrolyte complex (PC) solutions that have been previously shown to exhibit a theoretically unanticipated lower critical solution temperature type phase behavior, i.e., phase separation upon heating, and a conventional pattern of static critical properties (low angle scattering intensity and static correlation, ξ_s) as a function of reduced temperature. Good qualitative accord is observed between our DLS measurements and the KF theory. In particular, we observe that the collective diffusion coefficient D_c of the PC solutions obeys the generalized Stokes-Einstein equation (GSE), D_c = k_BT/6πηξ_s, where ξ_s is specified from our previous measurements and where η is measured by capillary rheometry under the same thermodynamic conditions as in our previous study of these solutions, allowing for a no-free-parameter test of the GSE. We also find that even the wavevector (q)-dependent collective diffusion coefficient D_c(q), measured by varying the scattering angle in the DLS measurements over a large range, is also well-described by the mean-field version of the KF theory. We find it remarkable that the KF theory provides such a robust description of collective diffusion in these complex charged polyelectrolyte blends under near-critical conditions given that charge fluctuations and association of the polymers might be expected to lead to physical complications that would invalidate the standard model of uncharged fluid mixtures.

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.

Structure and Flocculation of Ion Associates of Carrageenan and Poly(diallyldimethylammonium chloride) Depending on the Component Ratio

Carrageenan is a polysaccharide of a plant origin, commonly used as a thickening and gelling agent in the food, pharmaceutical, and cosmetic industries. Due to the negative charges of its sulfate groups, carrageenan macromolecules strongly interact with oppositely charged polyions. The ionic complexes of carrageenan with poly(diallyldimethylammonium chloride) were obtained at the molar ratios 4:1, 2;1, 1:1, 1:2, and 1:4. The structure and characteristics of the polyanion-polycation associates were studied by XRD, IR, optical microscopy, and via sedimentation and particle size measurements. It was found that the suspended particles flocculate and settle fastest when the molar ratio of the polyions is near 1:1. Turbidimetric titration experiments enabled us to measure the molar ratio of cationic to anionic groups at the onset of flocculation, and the value in question was found to be 1:1.32. In other words, a mass of 511 mg carrageenan corresponds to one millimole of ester sulfate (monobasic) groups. The measurement of the onset of flocculation has been employed for the accurate determination of carrageenan in real samples of food products. The color and turbidity of the sample do not interfere with the determination results.