Salt Partitioning in Complex Coacervation of Symmetric Polyelectrolytes

Effects of charge asymmetry on the liquid-liquid phase separation of polyampholytes and their condensate properties

Liquid-liquid phase separation (LLPS) is the mechanism underlying the formation of bio-molecular condensates which are important compartments regulating intra- and extra-cellular functions. Electrostatic interactions are some of the important driving forces of the LLPS behaviors of biomolecules. However, the understanding of the electrostatic interactions is still limited, especially in the mixtures of biomolecules with different charge patterns. Here, we focus on the electrostatic interactions in mixtures of charge-asymmetric and charge-symmetric polyampholytes and their roles in the phase separation behaviors. We build charge-asymmetric and charge-symmetric model proteins consisting of both glutamic acid (E, negatively charged) and lysine (K, positively charged), i.e. polyampholytes of E35K15 (charge asymmetric) and E25K25 (charge symmetric). Pure E25K25 can undergo LLPS. To investigate the effects of charge-asymmetric polyampholytes on the mixtures of E25K25/E35K15, we perform coarse-grained simulations to determine their phase separation. The charge-asymmetric polyampholyte E35K15 is resistant to the LLPS of the mixtures of E25K25/E35K15. The condensate density decreases with the molar fraction of E35K15 increasing to 0.4, and no LLPS occurs at the molar fraction of 0.5 and above. This can be attributed to the electrostatic repulsion between the negatively charged E35K15 polymers. We further investigate the effects of charge asymmetry on the conformations and properties of the condensates. The E35K15 polymers in the condensates exhibit a more collapsed state as the molar fraction of E35K15 increases. However, the conformation of E25K25 polymers changes slightly across different condensates. The surface tensions of condensates decline with the increase of the molar fraction of E35K15 polymers, while the diffusivity of polymers in the condensed phases is enhanced. This work elucidates the role of charge-asymmetric polyampholytes in determining the LLPS behaviours of binary mixtures of charge-symmetric and charge-asymmetric proteins as well as the properties of condensed phases.

Biomolecular condensates can function as inherent catalysts

We report the discovery that chemical reactions such as ATP hydrolysis can be catalyzed by condensates formed by intrinsically disordered proteins (IDPs), which themselves lack any intrinsic ability to function as enzymes. This inherent catalytic feature of condensates derives from the electrochemical environments and the electric fields at interfaces that are direct consequences of phase separation. The condensates we studied were capable of catalyzing diverse hydrolysis reactions, including hydrolysis and radical-dependent breakdown of ATP whereby ATP fully decomposes to adenine and multiple carbohydrates. This distinguishes condensates from naturally occurring ATPases, which can only catalyze the dephosphorylation of ATP. Interphase and interfacial properties of condensates can be tuned via sequence design, thus enabling control over catalysis through sequence-dependent electrochemical features of condensates. Incorporation of hydrolase-like synthetic condensates into live cells enables activation of transcriptional circuits that depend on products of hydrolysis reactions. Inherent catalytic functions of condensates, which are emergent consequences of phase separation, are likely to affect metabolic regulation in cells.

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.

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.

Low-Viscous, Dilute Phase Adhesive from Dense Polyphenolic Coacervates of Poly(vinyl alcohol) and Tannic acid

This study explores a polyphenolic coacervate, named VATA, formed by poly(vinyl alcohol) (PVA) and tannic acid (TA). Distinct from conventional studies that have focused on the bottom, dense phase of coacervates, this research emphasizes the top, dilute phase, low-viscous coacervate liquid termed liquid-VATA (l-VATA). Due to TA's capability of intermolecular association as well as adhesiveness, phenomena not typically observed in the upper dilute phase of standard polyelectrolyte-based coacervates are revealed. At first glance, the dilute phase l-VATA coacervate resembles a water-like, low-viscous mixture solution of PVA, TA, and PVA/TA complexes. However, analysis shows that nearly all of the TA molecules associate with PVA chains, forming PVA/TA complexes. Furthermore, supraparticular association was observed between PVA/TA complex nanoparticles upon applying external shear force. A broad survey of shear rate and strain showed that the solution exhibited sequential shear-thickening, followed by shear-thinning behavior. The water-like, low viscosity of l-VATA unexpectedly reveals robust adhesiveness and thus able to lift an entire mouse using just a single human hair strand. Even in cases of failure, no interfacial failure was detected between mouse and human hair. In addition to enabling hair-to-hair bonding, our study also showcases the efficacy of l-VATA in facilitating hair-to-skin adhesion. The results illustrate how the lower viscosity of l-VATA can be exploited for a wide range of industrial and cosmetic applications, allowing the formulation of thin, uniform adhesive layers, something unachievable with the dense, viscous VATA glue. Thus, this study highlights the importance of investigating the top dilute phase of coacervates, shedding light on an area often underestimated compared to the bottom dense phase reported in prevalent coacervate studies.

Coacervate or precipitate? Formation of non-equilibrium microstructures in coacervate emulsions

Non-equilibrium processing of aqueous polyelectrolyte complex (PEC) coacervates is critical to many applications. In particular, many coacervate-forming systems are known to become trapped in out-of-equilibrium states (e.g., precipitation). The mechanism and conditions under which these states form, and whether they age, is not clearly understood. Here, we elucidate the influence of processing on the PEC coarsening mechanism as it varies with flow during mixing for a model system of poly(allylamine hydrochloride) and poly(acrylic acid sodium salt) in water. We demonstrate that flow conditions can be used to toggle the formation of rough, precipitate-like aggregates of micron-scale PEC structures. These structures form at compositions with viscous-dominant equilibrium rheology, and observations of their formation via optical microscopy suggest that they comprise colloidal aggregates of PEC coacervate droplets. We further show that these aggregates exhibit micron-scale coarsening, with a mixing time-dependent characteristic aging time scale. The results show that the formation of precipitate-like structures is not solely determined by composition, but is instead highly sensitive to mass transport and colloidal instability effects. Our observations suggest that the details of mixing flow can provide non-equilibrium structural control of a broad range of PEC coacervate materials orthogonally to structure-property inspired polymeric design. We anticipate that these findings will open the door for future studies on the control of non-equilibrium PEC formation and structure.

A molecularly informed field-theoretic study of the complexation of polycation PDADMA with mixed micelles of sodium dodecyl sulfate and ethoxylated surfactants

The self-assembly and phase separation of mixtures of polyelectrolytes and surfactants are important to a range of applications, from formulating personal care products to drug encapsulation. In contrast to systems of oppositely charged polyelectrolytes, in polyelectrolyte-surfactant systems the surfactants micellize into structures that are highly responsive to solution conditions. In this work, we examine how the morphology of micelles and degree of polyelectrolyte adsorption dynamically change upon varying the mixing ratio of charged and neutral surfactants. Specifically, we consider a solution of the cationic polyelectrolyte polydiallyldimethylammonium, anionic surfactant sodium dodecyl sulfate, neutral ethoxylated surfactants (C[Formula: see text]EO[Formula: see text]), sodium chloride salt, and water. To capture the chemical specificity of these species, we leverage recent developments in constructing molecularly informed field theories via coarse-graining from all-atom simulations. Our results show how changing the surfactant mixing ratios and the identity of the nonionic surfactant modulates micelle size and surface charge, and as a result dictates the degree of polyelectrolyte adsorption. These results are in semi-quantitative agreement with experimental observations on the same system.

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.

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.

Phase Behavior of Ion-Containing Polymers in Polar Solvents: Predictions from a Liquid-State Theory with Local Short-Range Interactions

The thermodynamic phase behavior of charged polymers is a crucial property underlying their role in biology and various industrial applications. A complete understanding of the phase behaviors of such polymer solutions remains challenging due to the multi-component nature of the system and the delicate interplay among various factors, including the translational entropy of each component, excluded volume interactions, chain connectivity, electrostatic interactions, and other specific interactions. In this work, the phase behavior of partially charged ion-containing polymers in polar solvents is studied by further developing a liquid-state (LS) theory with local shortrange interactions. This work is based on the LS theory developed for fully-charged polyelectrolyte solutions. Specific interactions between charged groups of the polymer and counterions, between neutral segments of the polymer, and between charged segments of the polymer are incorporated into the LS theory by an extra Helmholtz free energy from the perturbed-chain statistical associating fluid theory (PC-SAFT). The influence of the sequence structure of the partially charged polymer is modeled by the number of connections between bonded segments. The effects of chain length, charge fraction, counterion valency, and specific short-range interactions are explored. A computational App for salt-free polymer solutions is developed and presented, which allows easy computation of the binodal curve and critical point by specifying values for the relevant model parameters.

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.

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.

Salt-Induced Transitions in the Conformational Ensembles of Intrinsically Disordered Proteins

Salts modulate the behavior of intrinsically disordered proteins (IDPs) and influence the formation of membraneless organelles through liquid-liquid phase separation (LLPS). In low ionic strength solutions, IDP conformations are perturbed by the screening of electrostatic interactions, independent of the salt identity. In this regime, insight into the IDP behavior can be obtained using the theory for salt-induced transitions in charged polymers. However, salt-specific interactions with the charged and uncharged residues, known as the Hofmeister effect, influence IDP behavior in high ionic strength solutions. There is a lack of reliable theoretical models in high salt concentration regimes to predict the salt effect on IDPs. We propose a simulation methodology using a coarse-grained IDP model and experimentally measured water to salt solution transfer free energies of various chemical groups that allowed us to study the salt-specific transitions induced in the IDPs conformational ensemble. We probed the effect of three different monovalent salts on five IDPs belonging to various polymer classes based on charged residue content. We demonstrate that all of the IDPs of different polymer classes behave as self-avoiding walks (SAWs) at physiological salt concentration. In high salt concentrations, the transitions observed in the IDP conformational ensembles are dependent on the salt used and the IDP sequence and composition. Changing the anion with the cation fixed can result in the IDP transition from a SAW-like behavior to a collapsed globule. An important implication of these results is that a suitable salt can be identified to induce condensation of an IDP through LLPS.

On the nature of screening in Voorn–Overbeek type theories

By using a recently formulated Legendre transform approach to the thermodynamics of charged systems, we explore the general form of the screening length in the Voorn–Overbeek-type theories, which remains valid also in the cases where the entropy of the charged component(s) is not given by the ideal gas form as in the Debye–Hückel theory. The screening length consistent with the non-electrostatic terms in the free energy ansatz for the Flory–Huggins and Voorn–Overbeek type theories, derived from the local curvature properties of the Legendre transform, has distinctly different behavior than the often invoked standard Debye screening length, though it reduces to it in some special cases.

Coacervation between two positively charged poly(ionic liquid)s

Complex coacervates are usually formed through electrostatic attraction between oppositely charged polyelectrolytes, with a few of exceptions such as coacervates of like-charge proteins and polyelectrolytes, both in vivo and in vitro. Understanding of the preparation and mechanism of these coacervates is limited. Here we design a positively charged poly(ionic liquid) poly(1-vinyl-3-benzylimidazolium chloride) (PILben) that bears benzene rings in repeating units. Fluidic coacervates were prepared by mixing the PILben aqueous solution with a like-charge poly(ionic liquid) named poly(dimethyl diallyl ammonium chloride) (PDDA). The effects of polymer concentration, temperature and ionic strength in the PILben-PDDA coacervate were studied. Raman spectroscopy and two-dimensional ¹ H-¹³ C heteronuclear single quantum coherence (¹ H-¹³ C HSQC) characterizations verify that the coacervate formation benefits from the cation-π interaction between PILben and PDDA. This work provides principles and understandings of designing coacervates derived from like-charge poly(ionic liquids) with high charge density. This article is protected by copyright. All rights reserved.

Valence-induced jumps in coacervate properties

Spontaneous phase separation, or coacervation, of oppositely charged macromolecules is a powerful and ubiquitous mechanism for the assembly of natural and synthetic materials. Two critical triggering phenomena in coacervation science and technology are highlighted here. The first is the transition from one (mixed) to two (separated) phases of polyelectrolytes coacervated with small molecules upon the addition of one or two charges per molecule. The second is a large jump in coacervate modulus and viscosity mediated by the addition of just one additional charge to a three-charged system. This previously unknown viscoelastic transition is relevant to those aspects of disease states that are characterized by abnormal mechanical properties and irreversible assembly.

On the stability and layered organization of protein-DNA condensates

Multi-component phase separation is emerging as a key mechanism for the formation of biological condensates that play essential roles in signal sensing and transcriptional regulation. The molecular factors that dictate these condensates' stability and spatial organization are not fully understood, and it remains challenging to predict their microstructures. Using a near-atomistic, chemically accurate force field, we studied the phase behavior of chromatin regulators that are crucial for heterochromatin organization and their interactions with DNA. Our computed phase diagrams recapitulated previous experimental findings on different proteins. They revealed a strong dependence of condensate stability on the protein-DNA mixing ratio as a result of balancing protein-protein interactions and charge neutralization. Notably, a layered organization was observed in condensates formed by mixing HP1, histone H1, and DNA. This layered organization may be of biological relevance, as it enables cooperative DNA packaging between the two chromatin regulators: histone H1 softens the DNA to facilitate the compaction induced by HP1 droplets. Our study supports near-atomistic models as a valuable tool for characterizing the structure and stability of biological condensates.

The critical Transition from Soluble Complexes to Colloidal Aggregates of Polyelectrolyte Complexes at Non-stoichiometric Charge Ratios

The transition from soluble to colloidal polyelectrolyte complex normally occurs at a critical non-stoichiometric charge ratio. Here, we demonstrated that the conventional batch mixing produces heterogeneous binding and complexation, which could easily mask this soluble-colloidal complex transition (sol-col transition) even for weakly binding polyelectrolytes like polyacrylic acid (PAA) and poly(diallyldimethylammonium chloride) (PDADMAC). When mixed efficiently using multi-inlet vortex mixer (MIVM), the sol-col transition occurs beyond a critical charge ratio (n-/n+) and the large colloidal complexes are formed through the aggregation of small primary complexes (as revealed by atomic force microscopy). Moreover, the sol-col transition occurs at a constant charge ratio below the overlapping concentration (c*) of the long host polyelectrolyte, but at lower charge ratios above c* due to chain entanglement. When adding NaCl to the solution, the sol-col transition charge ratio first decreases, then remained stable for a period and finally increased and vanished at high ionic strength. When replacing NaCl with chaotropic salts, the sol-col transition occurs at lower charge ratios, while kosmotropes had little impact. The solvent quality and polymer hydrophobicity effects are also discussed. With the assistance of rapid mixing, this study provides a more reliable way of studying the sol-col transition of polyelectrolyte complexes. This article is protected by copyright. All rights reserved.

A simple simulation model for complex coacervates

When oppositely charged polyelectrolytes mix in an aqueous solution, associative phase separation gives rise to coacervates. Experiments reveal the phase diagram for such coacervates, and determine the impact of charge density, chain length and added salt. Simulations often use hybrid MC-MD methods to produce such phase diagrams, in support of experimental observations. We propose an idealized model and a simple simulation technique to investigate coacervate phase behavior. We model coacervate systems by charged bead-spring chains and counterions with short-range repulsions, of size equal to the Bjerrum length. We determine phase behavior by equilibrating a slab of concentrated coacervate with respect to swelling into a dilute phase of counterions. At salt concentrations below the critical point, the counterion concentration in the coacervate and dilute phases are nearly the same. At high salt concentrations, we find a one-phase region. Along the phase boundary, the total concentration of beads in the coacervate phase is nearly constant, corresponding to a "Bjerrum liquid''. This result can be extended to experimental phase diagrams by assigning appropriate volumes to monomers and salts.

Transfer Matrix Model of pH Effects in Polymeric Complex Coacervation

Oppositely charged polyelectrolytes can undergo an associative phase separation, in a process known as polymeric complex coacervation. This phenomenon is driven by the electrostatic attraction between polyanion and polycation species, leading to the formation of a polymer-dense coacervate phase and a coexisting polymer-dilute supernatant phase. There has been significant recent interest in the physical origin and features of coacervation; yet notably, experiments often use weak polyelectrolytes the charge state of which depends on solution pH, while theoretical or computational efforts typically assume strong polyelectrolytes that remain fully charged. There have been only a few efforts to address this limitation, and thus there has been little exploration of how pH can affect complex coacervation. In this paper, we modify a transfer matrix theory of coacervation to account for acid-base equilibria, taking advantage of its ability to directly account for some local ion correlations that will affect monomer charging. We show that coacervation can stabilize the charged state of a weak polyelectrolyte via the proximity of oppositely charged monomers, and can lead to asymmetric phase diagrams where the positively and negatively charged polyelectrolytes exhibit different behaviors near the pK_a of either chain. Specifically, there is a partitioning of one of the salt species to a coacervate to maintain electroneutrality when one of the polyelectrolytes is only partially charged. This results in the depletion of the same salt species in the supernatant, and overall can suppress phase separation. We also demonstrate that, when one of the species is only partially charged, mixtures that are off-stoichiometric in volume fraction but stoichiometric in charge exhibit the greatest propensity to form coacervate phases.

Polyelectrolyte Complex Coacervation across a Broad Range of Charge Densities

Polyelectrolyte complex coacervates of homologous (co)polyelectrolytes with a near-ideally random distribution of a charged and neutral ethylene oxide comonomer were synthesized. The unique platform provided by these building blocks enabled an investigation of the phase behavior across charge fractions 0.10 ≤ f ≤ 1.0. Experimental phase diagrams for f = 0.30-1.0 were obtained from thermogravimetric analysis of complex and supernatant phases and contrasted with molecular dynamics simulations and theoretical scaling laws. At intermediate to high f, a dependence of polymer weight fraction in the salt-free coacervate phase (w P,c) of w P,c ∼ f 0.37±0.01 was extracted; this trend was in good agreement with accompanying simulation predictions. Below f = 0.50, w P,c was found to decrease more dramatically, qualitatively in line with theory and simulations predicting an exponent of 2/3 at f ≤ 0.25. Preferential salt partitioning to either coacervate or supernatant was found to be dictated by the chemistry of the constituent (co)polyelectrolytes.

The effects of protein charge patterning on complex coacervation

The complex coacervation of proteins with other macromolecules has applications in protein encapsulation and delivery and for determining the function of cellular coacervates. Theoretical or empirical predictions for protein coacervates would enable the design of these coacervates with tunable and predictable structure-function relationships; unfortunately, no such theories exist. To help establish predictive models, the impact of protein-specific parameters on complex coacervation were probed in this study. The complex coacervation of sequence-specific, polypeptide-tagged, GFP variants and a strong synthetic polyelectrolyte was used to evaluate the effects of protein charge patterning on phase behavior. Phase portraits for the protein coacervates demonstrated that charge patterning dictates the protein's binodal phase boundary. Protein concentrations over 100 mg mL-1 were achieved in the coacervate phase, with concentrations dependent on the tag polypeptide sequence covalently attached to the globular protein domain. In addition to shifting the binodal phase boundary, polypeptide charge patterning provided entropic advantages over isotropically patterned proteins. Together, these results show that modest changes of only a few amino acids in the tag polypeptide sequence alter the coacervation thermodynamics and can be used to tune the phase behavior of polypeptides or proteins of interest.

Nonelectrostatic Adsorption of Polyelectrolytes and Mediated Interactions between Solid Surfaces

Polymer-mediated interaction between two solid surfaces is directly connected to the properties of the adsorbed polymer layers. Nonelectrostatic interactions with a surface can significantly impact the adsorption of polyelectrolytes to charged surfaces. We use a classical density functional theory to study the effect of various polyelectrolyte solution properties on the adsorption and interaction between two like-charged surfaces. Our results show that nonelectrostatic interactions not only enhance polyelectrolyte adsorption but can also result in qualitatively different salt effects with respect to the adsorbed amount. In particular, we observe decreasing, increasing, and a previously unreported nonmonotonic behavior in the adsorbed amount of polymer with added salt under the conditions studied, although the nonmonotonic regime only occurs for a narrow range in the parameter space. With sufficient nonelectrostatic adsorption, the adsorbed polymer layers produce a long-range repulsive barrier that is strong enough to overcome dispersive interactions that cause surfaces to attract. Concurrently, a short-range bridging attraction is observed when the two polyelectrolyte layers span both the surfaces. Both the repulsive barrier and bridging attraction depend on the charge density of the polymer backbone and the bulk salt concentration but not on the chain length in the semidilute regime studied.

Pressure Effects on Self-Assembly in Mixtures Containing Zwitterionic Amphiphiles

To understand the responses of self-assembly in mixtures containing zwitterionic amphiphilic chains to high pressure, we introduce a self-consistent field theory in combination with a molecular equation-of-state model for them in a primitive way. The free energy density for those in the bulk state is first formulated. Its locally equilibrated excess part is then incorporated into Edwards Hamiltonian along with the electrostatic energy contributions to elicit the saddle point approximation to the partition function with proper self-consistent field equations. It is shown that charge-charge correlations enhance self-assembling tendency for the amphiphiles with the opposite charges on one component side, as the medium dielectric constant ε_r decreases. Those with the opposite charges at the two chain ends respond in a more complicated way to ε_r. Densification by applied pressure strengthens the self-assembly for both at a moderate ε_r, similar to typical phospholipids, but pressure effects are strongly dependent on the position of charges along the chains at a lower ε_r. It is argued that the manipulation of the dielectric environment and disparity in component dispersion interactions can yield useful materials exhibiting various types of baroresponsivity or thermoresponsivity with re-entrant self-assembly.

Dynamic Coupling in Unentangled Liquid Coacervates Formed by Oppositely Charged Polyelectrolytes

We develop a scaling theory that predicts the dynamics of symmetric and asymmetric unentangled liquid coacervates formed by solutions of oppositely-charged polyelectrolytes. Symmetric coacervates made from oppositely-charged polyelectrolytes consist of polycations and polyanions with equal and opposite charge densities along their backbones. These symmetric coacervates can be described as mixtures of polyelectrolytes in the quasi-neutral regime with a single correlation length. Asymmetric coacervates are made from polycations and polyanions with unequal charge densities. The difference in charge densities results in a double semidilute structure of asymmetric coacervates with two correlation lengths, one for the high-charge-density and the other for the low-charge-density polyelectrolytes. We predict that the double-semidilute structure in asymmetric coacervates results in a dynamic coupling which increases the friction of the high-charge-density polyelectrolyte. This dynamic coupling increases the contribution to the zero-shear viscosity of the high-charge-density polyelectrolyte. The diffusion coefficient of the high-charge-density polyelectrolyte is predicted to depend on the concentration and degree of polymerization of the low-charge-density polyelectrolyte in the coacervate if the size of the low-charge-density polymer is smaller than the correlation length of the high-charge-density polymer. We also predict a non-monotonic salt concentration dependence of the zero-shear viscosity of asymmetric coacervates.

RNA-Mediated Feedback Control of Transcriptional Condensates

Regulation of biological processes typically incorporates mechanisms that initiate and terminate the process and, where understood, these mechanisms often involve feedback control. Regulation of transcription is a fundamental cellular process where the mechanisms involved in initiation have been studied extensively, but those involved in arresting the process are poorly understood. Modeling of the potential roles of RNA in transcriptional control suggested a non-equilibrium feedback control mechanism where low levels of RNA promote condensates formed by electrostatic interactions whereas relatively high levels promote dissolution of these condensates. Evidence from in vitro and in vivo experiments support a model where RNAs produced during early steps in transcription initiation stimulate condensate formation, whereas the burst of RNAs produced during elongation stimulate condensate dissolution. We propose that transcriptional regulation incorporates a feedback mechanism whereby transcribed RNAs initially stimulate but then ultimately arrest the process.

Ion Pairing and the Structure of Gel Coacervates

A scaling model for the structure of coacervates is presented for mixtures of oppositely-charged polyelectrolytes of both symmetric and asymmetric charge-densities for different degrees of electrostatic strength and levels of added salt. At low electrostatic strengths, weak coacervates, with the energy of electrostatic interactions between charges less than the thermal energy, k B T, are liquid. At higher electrostatic strengths, strong coacervates are gels with crosslinks formed by ion pairs of opposite charges bound to each other with energy higher than k B T. Charge-symmetric coacervates are formed for mixtures of oppositely-charged polyelectrolytes with equal and opposite charge-densities. While charge-symmetric weak coacervates form a semidilute polymer solution with a correlation length equal to the electrostatic blob size, charge-symmetric strong coacervates form reversible gels with a correlation length on the order of the distance between bound ion pairs. Charge-asymmetric coacervates are formed from mixtures of oppositely-charged polyelectrolytes with different charge-densities. While charge-asymmetric weak coacervates form double solutions with two correlation lengths and qualitatively different chain conformations of polycations and polyanions, charge-asymmetric strong coacervates form bottlebrush and star-like gels. Unlike liquid coacervates, for which an increase in the concentration of added salt screens electrostatic interactions, causing structural rearrangement and eventually leads to their dissolution, the salt does not affect the structure of strong coacervates until ion pairs dissociate and the gel disperses.

Emerging trends in the dynamics of polyelectrolyte complexes

Polyelectrolyte complexes (PECs) are highly tunable materials that result from the phase separation that occurs upon mixing oppositely charged polymers. Over the years, they have gained interest due to their broad range of applications such as drug delivery systems, protective coatings, food packaging, and surface adhesives. In this review, we summarize the structure, phase transitions, chain dynamics, and rheological and thermal properties of PECs. Although most literature focuses upon the thermodynamics and application of PECs, this review highlights the fundamental role of salt and water on mechanical and thermal properties impacting the PEC's dynamics. A special focus is placed upon experimental results and techniques. Specifically, the review examines phase behaviour and salt partitioning in PECs, as well as different techniques used to measure diffusion coefficients, relaxation times, various superpositioning principles, glass transitions, and water microenvironments in PECs. This review concludes with future areas of opportunity in fundamental studies and best practices in reporting.

Liquid Phase Separation Controlled by pH

We present a minimal model to study the effects of pH on liquid phase separation of macromolecules. Our model describes a mixture composed of water and macromolecules that exist in three different charge states and have a tendency to phase separate. This phase separation is affected by pH via a set of chemical reactions describing protonation and deprotonation of macromolecules, as well as self-ionization of water. We consider the simple case in which interactions are captured by Flory-Huggins interaction parameters corresponding to Debye screening lengths shorter than a nanometer, which is relevant to proteins inside biological cells under physiological conditions. We identify the conjugate thermodynamic variables at chemical equilibrium and discuss the effective free energy at fixed pH. First, we study phase diagrams as a function of macromolecule concentration and temperature at the isoelectric point of the macromolecules. We find a rich variety of phase diagram topologies, including multiple critical points, triple points, and first-order transition points. Second, we change the pH relative to the isoelectric point of the macromolecules and study how phase diagrams depend on pH. We find that these phase diagrams as a function of pH strongly depend on whether oppositely charged macromolecules or neutral macromolecules have a stronger tendency to phase separate. One key finding is that we predict the existence of a reentrant behavior as a function of pH. In addition, our model predicts that the region of phase separation is typically broader at the isoelectric point. This model could account for both in vitro phase separation of proteins as a function of pH and protein phase separation in yeast cells for pH values close to the isoelectric point of many cytosolic proteins.