Polyelectrolyte complex coacervation by electrostatic dipolar interactions

Emergent microenvironments of nucleoli

In higher eukaryotes, the nucleolus harbors at least three sub-phases that facilitate multiple functionalities including ribosome biogenesis. The three prominent coexisting sub-phases are the fibrillar center (FC), the dense fibrillar component (DFC), and the granular component (GC). Here, we review recent efforts in profiling sub-phase compositions that shed light on the types of physicochemical properties that emerge from compositional biases and territorial organization of specific types of macromolecules. We highlight roles played by molecular grammars which refers to protein sequence features including the substrate binding domains, the sequence features of intrinsically disordered regions, and the multivalence of these distinct types of domains / regions. We introduce the concept of a barcode of emergent physicochemical properties of nucleoli. Although our knowledge of the full barcode remains incomplete, we hope that the concept prompts investigations into undiscovered emergent properties and engenders an appreciation for how and why unique microenvironments control biochemical reactions.

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.

Beyond monopole electrostatics in regulating conformations of intrinsically disordered proteins

Conformations and dynamics of an intrinsically disordered protein (IDP) depend on its composition of charged and uncharged amino acids, and their specific placement in the protein sequence. In general, the charge (positive or negative) on an amino acid residue in the protein is not a fixed quantity. Each of the ionizable groups can exist in an equilibrated distribution of fully ionized state (monopole) and an ion-pair (dipole) state formed between the ionizing group and its counterion from the background electrolyte solution. The dipole formation (counterion condensation) depends on the protein conformation, which in turn depends on the distribution of charges and dipoles on the molecule. Consequently, effective charges of ionizable groups in the IDP backbone may differ from their chemical charges in isolation-a phenomenon termed charge-regulation. Accounting for the inevitable dipolar interactions, that have so far been ignored, and using a self-consistent procedure, we present a theory of charge-regulation as a function of sequence, temperature, and ionic strength. The theory quantitatively agrees with both charge reduction and salt-dependent conformation data of Prothymosin-alpha and makes several testable predictions. We predict charged groups are less ionized in sequences where opposite charges are well mixed compared to sequences where they are strongly segregated. Emergence of dipolar interactions from charge-regulation allows spontaneous coexistence of two phases having different conformations and charge states, sensitively depending on the charge patterning. These findings highlight sequence dependent charge-regulation and its potential exploitation by biological regulators such as phosphorylation and mutations in controlling protein conformation and function.

Theory of thermoreversible gelation and anomalous concentration fluctuations in polyzwitterion solutions

We present a theoretical framework to investigate thermoreversible phase transitions within polyzwitterion systems, encompassing macrophase separations (MPS) and gelation. In addition, we explore concentration fluctuations near critical points associated with MPS, as well as tricritical and bicritical points at the intersection of MPS and gelation. By utilizing mean-field percolation theory and field theory formalism, we derive the Landau free energy in terms of polyzwitterion concentration with fixed dipole strengths and other experimental variables, such as temperatures and salt concentrations. As the temperature decreases, the dipoles can form cross-links, resulting in polyzwitterion associations. The associations can grow to a gel network and enhance the propensity for MPS, including liquid-liquid, liquid-gel, and gel-gel phase separations. Remarkably, the associations also impact critical behaviors. Using the renormalization group technique, we find that the critical exponents of the polyzwitterion concentration correlation functions significantly deviate from those in the Ising universality class due to the presence of polyzwitterion associations, leading to crossover critical behaviors.

3D Printing of Aqueous Two-Phase Systems with Linear and Bottlebrush Polyelectrolytes

We formed core-shell-like polyelectrolyte complexes (PECs) from an anionic bottlebrush polymer with poly (acrylic acid) side chains with a cationic linear poly (allylamine hydrochloride). By varying the pH, the number of side chains of the polyanionic BB polymers (Nbb), the charge density of the polyelectrolytes, and the salt concentration, the phase separation behavior and salt resistance of the complexes could be tuned by the conformation of the BBs. By combining the linear/bottlebrush polyelectrolyte complexation with all-liquid 3D printing, flow-through tubular constructs were produced that showed selective transport across the PEC membrane comprising the walls of the tubules. These tubular constructs afford a new platform for flow-through delivery systems.

Adsorption of semiflexible wormlike polymers to a bar and their double-chain complex formation

We theoretically study pairing (double-strand complexation) of semiflexible wormlike chains (WLC) due to their side-to-side attraction. Considering binding of two WLCs of high stiffness we start with the case of infinite stiffness of one chain which is replaced with a straight bar. A combination of the quantitative transfer matrix approach with scaling arguments in terms of trains, loops of different sizes, tails and supertrains allowed us to characterize all the regimes of semiflexible chain adsorption on a bar. In particular, we predict a self-similar monomer concentration profile c(r) ∝ r-10/3 near the bar (at distances r below the chain Kuhn length l) at the critical point for adsorption. Such localized critical profile leads to a sharp adsorption transition. Furthermore, we found that supertrains serve as the basic structural elements in WLC complexes leading to bridging, network formation and condensation of semiflexible polymers in dilute solutions. Polymer collapse (precipitation) and redissolution on increasing attraction strength are predicted in qualitative agreement with experiments on aqueous solutions of DNA and F-actin.

Solutes unmask differences in clustering versus phase separation of FET proteins

Phase separation and percolation contribute to phase transitions of multivalent macromolecules. Contributions of percolation are evident through the viscoelasticity of condensates and through the formation of heterogeneous distributions of nano- and mesoscale pre-percolation clusters in sub-saturated solutions. Here, we show that clusters formed in sub-saturated solutions of FET (FUS-EWSR1-TAF15) proteins are affected differently by glutamate versus chloride. These differences on the nanoscale, gleaned using a suite of methods deployed across a wide range of protein concentrations, are prevalent and can be unmasked even though the driving forces for phase separation remain unchanged in glutamate versus chloride. Strikingly, differences in anion-mediated interactions that drive clustering saturate on the micron-scale. Beyond this length scale the system separates into coexisting phases. Overall, we find that sequence-encoded interactions, mediated by solution components, make synergistic and distinct contributions to the formation of pre-percolation clusters in sub-saturated solutions, and to the driving forces for phase separation.

Biomolecular condensates form spatially inhomogeneous network fluids

The functions of biomolecular condensates are thought to be influenced by their material properties, and these will be determined by the internal organization of molecules within condensates. However, structural characterizations of condensates are challenging, and rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that are formed by macromolecules from nucleolar granular components (GCs). We show that these minimal facsimiles of GCs form condensates that are network fluids featuring spatial inhomogeneities across different length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights suggest that condensates formed by multivalent proteins share features with network fluids formed by systems such as patchy or hairy colloids.

Macromolecular condensation organizes nucleolar sub-phases to set up a pH gradient

Nucleoli are multicomponent condensates defined by coexisting sub-phases. We identified distinct intrinsically disordered regions (IDRs), including acidic (D/E) tracts and K-blocks interspersed by E-rich regions, as defining features of nucleolar proteins. We show that the localization preferences of nucleolar proteins are determined by their IDRs and the types of RNA or DNA binding domains they encompass. In vitro reconstitutions and studies in cells showed how condensation, which combines binding and complex coacervation of nucleolar components, contributes to nucleolar organization. D/E tracts of nucleolar proteins contribute to lowering the pH of co-condensates formed with nucleolar RNAs in vitro. In cells, this sets up a pH gradient between nucleoli and the nucleoplasm. By contrast, juxta-nucleolar bodies, which have different macromolecular compositions, featuring protein IDRs with very different charge profiles, have pH values that are equivalent to or higher than the nucleoplasm. Our findings show that distinct compositional specificities generate distinct physicochemical properties for condensates.

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.

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.

Biomolecular condensates form spatially inhomogeneous network fluids

The functions of biomolecular condensates are thought to be influenced by their material properties, and these will be determined by the internal organization of molecules within condensates. However, structural characterizations of condensates are challenging, and rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that are formed by macromolecules from nucleolar granular components (GCs). We show that these minimal facsimiles of GCs form condensates that are network fluids featuring spatial inhomogeneities across different length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights suggest that condensates formed by multivalent proteins share features with network fluids formed by systems such as patchy or hairy colloids.

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.

Polyzwitterion fast and slow mode behavior are coupled to phase separation as observed by dynamic laser light scattering

A model zwitterionic polysulfobetaine, poly(3-(acrylamidopropyl-dimethyl-ammonium) propyl-1-sulfonate) (pAPAPS), phase separates upon cooling and exhibits an upper critical solution temperature (UCST) behavior with no added salt in deuterium oxide solutions. Dynamic light scattering measurements indicate the presence of distinct fast and slow diffusive modes, where the fast mode is interpreted as a collective diffusion coefficient and the slow mode is attributed to the diffusion of multi-chain dynamic clusters. The relative population of fast and slow modes varies systematically with temperature and concentration. A clustering temperature (T*) was assigned when the slow mode first appeared upon cooling. The slow mode then increases in relative scattering amplitude as the phase boundary is approached. The fast mode exhibits a concentration dependence above T* consistent with the virial expansion in the collective diffusion. The sign of the virial coefficient (kd) is negative, even in the good solvent region above the expected Flory temperature (Θ ≈ 39 °C), a behavior distinct from synthetic neutral polymers in organic solvents. The onset of multi-chain clustering at T < T* coincides with the poor solvent regime (T < Θ). Attractive dipolar interactions due to the zwitterionic sulfobetaine groups in pAPAPS are suggested as the origin of the multi-chain clusters with no salt. Upon the addition of 100 mM NaCl, the slow mode is suppressed, and the hydrodynamic radius is consistent with polyzwitterion chain dimensions in a dilute solution. We find that concentration dependent diffusion is highly linked to the theta temperature and the emergence of dynamic clusters as the polymer goes from good to poor solvent on approach to the UCST. The slow mode in the semidilute regime is reported along with preliminary small-angle neutron scattering data that show salt reduces clustering and leads to predominantly chain scattering.

Phase separation of protein mixtures is driven by the interplay of homotypic and heterotypic interactions

Prion-like low-complexity domains (PLCDs) are involved in the formation and regulation of distinct biomolecular condensates that form via phase separation coupled to percolation. Intracellular condensates often encompass numerous distinct proteins with PLCDs. Here, we combine simulations and experiments to study mixtures of PLCDs from two RNA-binding proteins, hnRNPA1 and FUS. Using simulations and experiments, we find that 1:1 mixtures of A1-LCD and FUS-LCD undergo phase separation more readily than either of the PLCDs on their own due to complementary electrostatic interactions. Tie line analysis reveals that stoichiometric ratios of different components and their sequence-encoded interactions contribute jointly to the driving forces for condensate formation. Simulations also show that the spatial organization of PLCDs within condensates is governed by relative strengths of homotypic versus heterotypic interactions. We uncover rules for how interaction strengths and sequence lengths modulate conformational preferences of molecules at interfaces of condensates formed by mixtures of proteins.

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.

Theory of self-coacervation in semi-dilute and concentrated zwitterionic polymer solutions

Based on the random phase approximation, we develop a molecular theory of self-coacervation in zwitterionic polymer solutions. We show that the interplay between the volume interactions of the monomeric units and electrostatic correlations of charged groups on a polymer backbone can result in liquid-liquid phase separation (self-coacervation). We analyse the behavior of the coacervate phase polymer concentration depending on the electrostatic interaction strength - the ratio of the Bjerrum length to the bond length of the chain. We establish that in a wide range of polymer concentration values - from a semi-dilute to a rather concentrated solution - the chain connectivity and excluded volume interaction of the monomeric units have an extremely weak effect on the contribution of the electrostatic interactions of the dipolar monomeric units to the total free energy. We show that for rather weak electrostatic interactions, the electrostatic correlations manifest themselves as Keesom interactions of point-like freely rotating dipoles (Keesom regime), while in the region of strong electrostatic interactions the electrostatic free energy is described by the Debye-Hückel limiting law (Debye regime). We show that for real zwitterionic coacervates the Keesom regime is realized only for sufficiently small polymer concentrations of the coacervate phase, while the Debye regime is approximately realized for rather dense coacervates. Using the mean-field variant of the density functional theory, we calculate the surface tension (surface free energy) of the "coacervate-solvent" interface as a function of the bulk polymer concentration. Obtained results can be used to estimate the parameters of the polymer chains needed for practical applications such as drug encapsulation and delivery, as well as the design of adhesive materials.

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.

Dipole-driven interlude of mesomorphism in polyelectrolyte solutions

Uniformly charged polyelectrolyte molecules disperse uniformly in aqueous electrolyte solutions, due to electrostatic repulsion between them. In stark contrast to this well-established result of homogeneous polyelectrolyte solutions, we report a phenomenon where an aqueous solution of positively charged poly(L-lysine) (PLL) exhibits precipitation of similarly charged macromolecules at low ionic strength and a homogeneous solution at very high ionic strength, with a stable mesomorphic state of spherical aggregates as an interlude between these two limits. The precipitation at lower ionic strengths that is orthogonal to the standard polyelectrolyte behavior and the emergence of the mesomorphic state are triggered by the presence of a monovalent small organic anion, acrylate, in the electrolyte solution. Using light scattering, we find that the hydrodynamic radius R_h of isolated PLL chains shrinks upon a decrease in electrolyte (NaBr) concentration, exhibiting the "anti-polyelectrolyte effect." In addition, R_h of the aggregates in the mesomorphic state depends on PLL concentration c_p according to the scaling law, [Formula: see text]. Furthermore, at higher PLL concentration, the mesomorphic aggregates disassemble by a self-poisoning mechanism. We conjecture that all these findings can be attributed to both intra- and interchain dipolar interactions arising from the transformation of polycationic PLL into a physical polyzwitterionic PLL at higher concentrations of acrylate. The reported phenomenon of PLL exhibiting dipole-directed assembly of mesomorphic states and the anti-polyelectrolyte effect are of vital importance toward understanding more complex situations such as coacervation and formation of biomolecular condensates.

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.

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.

Coacervation in polyzwitterion-polyelectrolyte systems and their potential applications for gastrointestinal drug delivery platforms

Traditionally, complex coacervation is regarded as a process whereby two oppositely charged polyelectrolytes self-assemble into spherical droplets. Here, we introduce the polyzwitterionic complex, “pZC”, formed by the liquid-liquid phase separation of a polyzwitterion and a polyelectrolyte, and elucidate a mechanism by which such complexes can assemble using theory and experimental evidence. This system exhibits orthogonal phase behavior-it remains intact in acidic conditions, but disassembles as the pH increases, a process governed by the acid-base equilibria of the constituent chains. We relate the observed phase behavior to physiological conditions within the gastrointestinal tract with a simulation of the gastroduodenal junction, and demonstrate using video microscopy the viability of polyzwitterionic coacervates as technologies for the pH-triggered release of cargo. Such a system is envisaged to tackle imminent problems of drug transport via the oral route and serve as a packaging solution to increase uptake efficiency.

Coacervation is widely studied as potential drug delivery platform, but formation of coacervates at lower pH ranges, such as found in the gastrointestinal tract, remains challenging. Here, using theory and experimental methods, the authors demonstrate the formation of a polyzwitterionic complex, formed by coacervation of a polyzwitterion and a polyelectrolyte, exhibiting orthogonal phase behavior under physiological low pH conditions.

Temperature-dependent reentrant phase transition of RNA-polycation mixtures

Liquid-liquid phase separation (LLPS) of multivalent biopolymers is a ubiquitous process in biological systems and is of importance in bio-mimetic soft matter design. The phase behavior of biomolecules, such as proteins and nucleic acids, is typically encoded by the primary chain sequence and regulated by solvent properties. One of the most important physical modulators of LLPS is temperature. Solutions of proteins and/or nucleic acids have been shown to undergo liquid-liquid phase separation either upon cooling (with an upper critical solution temperature, UCST) or upon heating (with a lower critical solution temperature, LCST). However, many theoretical frameworks suggest the possibility of more complex temperature-dependent phase behaviors, such as an hourglass or a closed-loop phase diagram with concurrent UCST and LCST transitions. Here, we report that RNA-polyamine mixtures undergo a reentrant phase separation with temperature. Specifically, at low temperatures, RNA-polyamine mixtures form a homogenous phase. Increasing the temperature leads to the formation of RNA-polyamine condensates. A further increase in temperature leads to the dissolution of condensates, rendering a reentrant homogenous phase. This dual-response phase separation of RNA is not unique to polyamines but also observed with short cationic peptides. The immiscibility gap is controlled by the charge of the polycation, salt concentration, and mixture composition. Based on the existing theories of complex coacervation, our results point to a complex interplay between desolvation entropy, ion-pairing, and electrostatic interactions in dictating the closed-loop phase behavior of RNA-polycation mixtures.

Multiphase Coacervates Driven by Electrostatic Correlations

The liquid-liquid phase separation of a polyelectrolyte solution containing one type of negatively and two types of positively charged polymers with different charge densities is studied theoretically by random phase approximation (RPA). It is predicted that multicoacervate phases could coexist, driven purely by electrostatic correlations. The asymmetry of the linear charge density could induce an effective immiscibility between two positively charged polyelectrolytes, leading to the multiphase separation. Adding salt will induce the disappearance of the dilute phase, forming two coexisting complex phases, instead of fusion between coacervates. Raising temperature could either induce a two coexisting complex phase, or a dilute phase coexisting with a coacervate phase, depending on the bulk concentration. Our predictions are in good agreement with experiments and provide insights in the further designing of the multiphase coacervation system.

Looping-in complexation and ion partitioning in nonstoichiometric polyelectrolyte mixtures

A wide variety of intracellular membraneless compartments are formed via liquid-liquid phase separation of charged proteins and nucleic acids. Understanding the stability of these compartments, while accounting for the compositional heterogeneity intrinsic to cellular environments, poses a daunting challenge. We combined experimental and theoretical efforts to study the effects of nonstoichiometric mixing on coacervation behavior and accurately measured the concentrations of polyelectrolytes and small ions in the coacervate and supernatant phases. For synthetic polyacrylamides and polypeptides/DNA, with unequal mixing stoichiometry, we report a general "looping-in" phenomenon found around physiological salt concentrations, where the polymer concentrations in the coacervate initially increase with salt addition before subsequently decreasing. This looping-in behavior is captured by a molecular model that considers reversible ion binding and electrostatic interactions. Further analysis in the low-salt regime shows that the looping-in phenomenon originates from the translational entropy of counterions that are needed to neutralize nonstoichiometric coacervates.

The effect of ion pairs on coacervate-driven self-assembly of block polyelectrolytes

The incorporation of oppositely charged polyelectrolytes into a block copolymer system can lead to formation of microphase separated nanostructures driven by the electrostatic complex between two oppositely charged blocks. It is a theoretical challenge to build an appropriate model to handle such coacervate-driven self-assembly, which should capture the strong electrostatic correlations for highly charged polymers. In this paper, we develop the self-consistent field theory considering the ion paring effect to predict the phase behavior of block polyelectrolytes. In our model, two types of ion pairs, the binding between two oppositely charged monomers and the binding between charged monomers and counterions, are included. Their strength of formation is controlled by two parameters K_aa and K_ac, respectively. We give a detailed analysis about how the binding strength K_ac and K_aa and salt concentration affect the self-assembled nanostructure of diblock polyelectrolyte systems. The results show that the binding between two oppositely charged blocks provides driven force for microphase separation, while the binding between charged monomers and counterions competes with the polyion pairing and thus suppresses the microphase separation. The addition of salt has a shielding effect on the charges of polymers, which is a disadvantage to microphase separation. The phase diagrams as a function of polymer concentration and salt concentration at different situations are constructed, and the influence of K_aa, K_ac, and charged block composition f_a is analyzed in depth. The obtained phase diagrams are in good agreement with currently existing experimental and theoretical results.

Liquid-Liquid Phase Separation As the Second Step of Complex Coacervation

Liquid-liquid phase separation (LLPS) between tyrosine- and arginine-rich peptides are of biological importance. To understand the interactions between proteins in the condensed phase in close analogy to complex coacervation, we run multiple umbrella calculations between oligomers containing tyrosine (pY) and arginine (pR). We find pR-pY complexation to be energetically driven. Metadynamics simulations on monomers suggest that this energy of complexation is correlated with the number of π-cation bonds. Free energy calculations for the binding between pairs of poly glutamate-pR dimers show striking similarities between this process and LLPS. These calculations suggest that proteins containing arginine and tyrosine residues do not undergo complexation followed by coacervation. The mechanism, rather, is akin to phase separation of neutral polyion pairs.

Sequence-encoded and composition-dependent protein-RNA interactions control multiphasic condensate morphologies

Multivalent protein-protein and protein-RNA interactions are the drivers of biological phase separation. Biomolecular condensates typically contain a dense network of multiple proteins and RNAs, and their competing molecular interactions play key roles in regulating the condensate composition and structure. Employing a ternary system comprising of a prion-like polypeptide (PLP), arginine-rich polypeptide (RRP), and RNA, we show that competition between the PLP and RNA for a single shared partner, the RRP, leads to RNA-induced demixing of PLP-RRP condensates into stable coexisting phases-homotypic PLP condensates and heterotypic RRP-RNA condensates. The morphology of these biphasic condensates (non-engulfing/ partial engulfing/ complete engulfing) is determined by the RNA-to-RRP stoichiometry and the hierarchy of intermolecular interactions, providing a glimpse of the broad range of multiphasic patterns that are accessible to these condensates. Our findings provide a minimal set of physical rules that govern the composition and spatial organization of multicomponent and multiphasic biomolecular condensates.

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.

Distinct Cation-Anion Interactions in the UCST and LCST Behavior of Polyelectrolyte Complex Aqueous Solutions

Polyelectrolyte complexes (PECs) are recently observed to possess diversified thermoresponsive phase transition behaviors in aqueous solutions. Herein, by adjusting the initial polymer concentrations (C_pi) of poly(styrenesulfonate) (PSS)/poly(diallyldimethylammonium) (PDADMA) PEC in the same saline solution, in addition to previously reported lower critical solution temperature (LCST), we experimentally observed the upper critical solution temperature (UCST)-type phase transition behavior of PSS/PDADMA PECs at a lower polymer concentration. As elucidated by temperature-dependent Raman spectroscopy and two-dimensional correlation analysis, at temperatures lower than UCST, more hydrophobic polyelectrolyte chains lead to a high proportion of contact ion pairs (CIPs), contributing to UCST-type solid-liquid phase transition; however, at higher concentrations of PEC, the less hydrophobic polyelectrolyte chains correspond to a higher proportion of solvent-separated ion pairs (SIPs), which enables the occurrence of LCST-type liquid-liquid phase transition. With the spectroscopic indicator of CIPs/SIPs peak ratio and monitoring the hydration state of polymer chains, the complex interplays of PSS/PDADMA PECs are hereby interpreted at the molecular level, which lays the mechanistic foundation for designing other thermoresponsive PEC assemblies.