Development of the modern theory of polymeric complex coacervation

Polyelectrolyte complex coacervation by electrostatic dipolar interactions

We address complex coacervation, the liquid-liquid phase separation of a solution of oppositely charged polyelectrolyte chains into a polyelectrolyte rich complex coacervate phase and a dilute aqueous phase, based on the general premise of spontaneous formation of polycation-polyanion complexes even in the homogeneous phase. The complexes are treated as flexible chains made of dipolar segments and uniformly charged segments. Using a mean field theory that accounts for the entropy of all dissociated ions in the system, electrostatic interactions among dipolar and charged segments of complexes and uncomplexed polyelectrolytes, and polymer-solvent hydrophobicity, we have computed coacervate phase diagrams in terms of polyelectrolyte composition, added salt concentration, and temperature. For moderately hydrophobic polyelectrolytes in water at room temperature, neither hydrophobicity nor electrostatics alone is strong enough to cause phase separation, but their combined effect results in phase separation, arising from the enhancement of effective hydrophobicity by dipolar attractions. The computed phase diagrams capture key experimental observations including the suppression of complex coacervation due to increases in salt concentration, temperature, and polycation-polyanion composition asymmetry, and its promotion by increasing the chain length, and the preferential partitioning of salt into the polyelectrolyte dilute phase. We also provide new predictions such as the emergence of loops of instability with two critical points.

Interfacial properties of polymeric complex coacervates from simulation and theory

Polymeric complex coacervation occurs when two oppositely charged polyelectrolytes undergo an associative phase separation in aqueous salt solution, resulting in a polymer-dense coacervate phase and a polymer-dilute supernatant phase. This phase separation process represents a powerful way to tune polymer solutions using electrostatic attraction and is sensitive to environmental conditions such as salt concentration and valency. One area of particular research interest is using this to create nanoscale polymer assemblies, via (for example) block copolymers with coacervate-forming blocks. The key to understanding coacervate-driven assembly is the formation of the interface between the coacervate and supernatant phases and its corresponding thermodynamics. In this work, we use recent advances in coacervate simulation and theory to probe the nature of the coacervate-supernatant interface. First, we show that self-consistent field theory informed by either Monte-Carlo simulations or transfer matrix theories is capable of reproducing interfacial features present in large-scale molecular dynamics simulations. The quantitative agreement between all three methods gives us a way to efficiently explore interfacial thermodynamics. We show how salt affects the interface, and we find qualitative agreement with literature measurements of interfacial tension. We also explore the influence of neutral polymers, which we predict to drastically influence the phase behavior of coacervates. These neutral polymers can significantly alter the interfacial tension in coacervates; this has a profound effect on the design and understanding of coacervate-driven self-assembly, where the equilibrium structure is tied to interfacial properties.

Phase Separation of Intrinsically Disordered Proteins

There is growing interest in the topic of intracellular phase transitions that lead to the formation of biologically regulated biomolecular condensates. These condensates are membraneless bodies formed by phase separation of key protein and nucleic acid molecules from the cytoplasmic or nucleoplasmic milieus. The drivers of phase separation are referred to as scaffolds whereas molecules that preferentially partition into condensates formed by scaffolds are known as clients. Recent advances have shown that it is possible to generate physical and functional facsimiles of many biomolecular condensates in vitro. This is achieved by titrating the concentration of key scaffold proteins and solution parameters such as salt concentration, pH, or temperature. The ability to reproduce phase separation in vitro allows one to compare the relationships between information encoded in the sequences of scaffold proteins and the driving forces for phase separation. Many scaffold proteins include intrinsically disordered regions whereas others are entirely disordered. Our focus is on comparative assessments of phase separation for different scaffold proteins, specifically intrinsically disordered linear multivalent proteins. We highlight the importance of coexistence curves known as binodals for quantifying phase behavior and comparing driving forces for sequence-specific phase separation. We describe the information accessible from full binodals and highlight different methods for-and challenges associated with-mapping binodals. In essence, we provide a wish list for in vitro characterization of phase separation of intrinsically disordered proteins. Fulfillment of this wish list through key advances in experiment, computation, and theory should bring us closer to being able to predict in vitro phase behavior for scaffold proteins and connect this to the functions and features of biomolecular condensates.

Role of Associative Charging in the Entropy-Energy Balance of Polyelectrolyte Complexes

Polyelectrolytes may be classified into two primary categories (strong and weak) depending on how their charge state responds to the local environment. Both of these find use in many applications, including drug delivery, gene therapy, layer-by-layer films, and fabrication of ion filtration membranes. The mechanism of polyelectrolyte complexation is, however, still not completely understood, though experimental investigations suggest that entropy gain due to release of counterions is the key driving force for strong polyelectrolyte complexation. Here we perform a comprehensive thermodynamic investigation through coarse-grained molecular simulations permitting us to calculate the free energy of complex formation. Importantly, our expanded-ensemble methods permit the explicit separation of energetic and entropic contributions to the free energy. Our investigations indicate that entropic contributions indeed dominate the free energy of complex formation for strong polyelectrolytes, but are less important than energetic contributions when weak electrostatic coupling or weak polyelectrolytes are present. Our results provide a new view of the free energy of polyelectrolyte complex formation driven by polymer association, which should also arise in systems with large charge spacings or bulky counterions, both of which act to weaken ion-polymer binding.

Liquid-liquid phase separation in artificial cells

Liquid-liquid phase separation (LLPS) in biology is a recently appreciated means of intracellular compartmentalization. Because the mechanisms driving phase separations are grounded in physical interactions, they can be recreated within less complex systems consisting of only a few simple components, to serve as artificial microcompartments. Within these simple systems, the effect of compartmentalization and microenvironments upon biological reactions and processes can be studied. This review will explore several approaches to incorporating LLPS as artificial cytoplasms and in artificial cells, including both segregative and associative phase separation.

Theory of polyelectrolyte complexation-Complex coacervates are self-coacervates

The complexation of mixtures of cationic and anionic polymers to produce complex-coacervate phases is a subject of fundamental importance to colloid and polymer science as well as to applications including drug delivery, sensing technologies, and bio-inspired adhesives. Unfortunately the theoretical underpinnings of complex coacervation are widely misunderstood and conceptual mistakes have propagated in the literature. Here, a simple symmetric polyelectrolyte mixture model in the absence of salt is used to discuss the salient features of the phase diagram, including the location of the critical point, binodals, and spinodals. It is argued that charge compensation by dimerization in the dilute region renders the phase diagram of an oppositely charged polyelectrolyte mixture qualitatively and quantitatively similar to that of a single-component symmetric diblock polyampholyte solution, a system capable of "self-coacervation." The theoretical predictions are verified using fully fluctuating field-theoretic simulations for corresponding polyelectrolyte and diblock polyampholyte models. These represent the first comprehensive, approximation-free phase diagrams for coacervate and self-coacervate systems to appear in the literature.

The different faces of mass action in virus assembly

The spontaneous encapsulation of genomic and non-genomic polyanions by coat proteins of simple icosahedral viruses is driven, in the first instance, by electrostatic interactions with polycationic RNA binding domains on these proteins. The efficiency with which the polyanions can be encapsulated in vitro, and presumably also in vivo, must in addition be governed by the loss of translational and mixing entropy associated with co-assembly, at least if this co-assembly constitutes a reversible process. These forms of entropy counteract the impact of attractive interactions between the constituents and hence they counteract complexation. By invoking mass action-type arguments and a simple model describing electrostatic interactions, we show how these forms of entropy might settle the competition between negatively charged polymers of different molecular weights for co-assembly with the coat proteins. In direct competition, mass action turns out to strongly work against the encapsulation of RNAs that are significantly shorter, which is typically the case for non-viral (host) RNAs. We also find that coat proteins favor forming virus particles over nonspecific binding to other proteins in the cytosol even if these are present in vast excess. Our results rationalize a number of recent in vitro co-assembly experiments showing that short polyanions are less effective at attracting virus coat proteins to form virus-like particles than long ones do, even if both are present at equal weight concentrations in the assembly mixture.

Reentrant Phase Transitions and Non-Equilibrium Dynamics in Membraneless Organelles

Compartmentalization of biochemical components, interactions, and reactions is critical for the function of cells. While intracellular partitioning of molecules via membranes has been extensively studied, there has been an expanding focus in recent years on the critical cellular roles and biophysical mechanisms of action of membraneless organelles (MLOs) such as the nucleolus. In this context, a substantial body of recent work has demonstrated that liquid-liquid phase separation plays a key role in MLO formation. However, less is known about MLO dissociation, with phosphorylation being the primary mechanism demonstrated thus far. In this Perspective, we focus on another mechanism for MLO dissociation that has been described in recent work, namely a reentrant phase transition (RPT). This concept, which emerges from the polymer physics field, provides a mechanistic basis for both formation and dissolution of MLOs by monotonic tuning of RNA concentration, which is an outcome of cellular processes such as transcription. Furthermore, the RPT model also predicts the formation of dynamic substructures (vacuoles) of the kind that have been observed in cellular MLOs. We end with a discussion of future directions in terms of open questions and methods that can be used to answer them, including further exploration of RPTs in vitro, in cells, and in vivo using ensemble and single-molecule methods as well as theory and computation. We anticipate that continued studies will further illuminate the important roles of reentrant phase transitions and associated non-equilibrium dynamics in the spatial patterning of the biochemistry and biology of the cell.

Relaxation Behavior by Time-Salt and Time-Temperature Superpositions of Polyelectrolyte Complexes from Coacervate to Precipitate

Complexation between anionic and cationic polyelectrolytes results in solid-like precipitates or liquid-like coacervate depending on the added salt in the aqueous medium. However, the boundary between these polymer-rich phases is quite broad and the associated changes in the polymer relaxation in the complexes across the transition regime are poorly understood. In this work, the relaxation dynamics of complexes across this transition is probed over a wide timescale by measuring viscoelastic spectra and zero-shear viscosities at varying temperatures and salt concentrations for two different salt types. We find that the complexes exhibit time-temperature superposition (TTS) at all salt concentrations, while the range of overlapped-frequencies for time-temperature-salt superposition (TTSS) strongly depends on the salt concentration (Cs) and gradually shifts to higher frequencies as Cs is decreased. The sticky-Rouse model describes the relaxation behavior at all Cs. However, collective relaxation of polyelectrolyte complexes gradually approaches a rubbery regime and eventually exhibits a gel-like response as Cs is decreased and limits the validity of TTSS.

50th Anniversary Perspective: A Perspective on Polyelectrolyte Solutions

From the beginning of life with the information-containing polymers until the present era of a plethora of water-based materials in health care industry and biotechnology, polyelectrolytes are ubiquitous with a broad range of structural and functional properties. The main attribute of polyelectrolyte solutions is that all molecules are strongly correlated both topologically and electrostatically in their neutralizing background of charged ions in highly polarizable solvent. These strong correlations and the necessary use of numerous variables in experiments on polyelectrolytes have presented immense challenges toward fundamental understanding of the various behaviors of charged polymeric systems. This Perspective presents the author's subjective summary of several conceptual advances and the remaining persistent challenges in the contexts of charge and size of polymers, structures in homogeneous solutions, thermodynamic instability and phase transitions, structural evolution with oppositely charged polymers, dynamics in polyelectrolyte solutions, kinetics of phase separation, mobility of charged macromolecules between compartments, and implications to biological systems.

Microphase Separation in Oil-Water Mixtures Containing Hydrophilic and Hydrophobic Ions

We develop a lattice-based Monte Carlo simulation method for charged mixtures capable of treating dielectric heterogeneities. Using this method, we study oil-water mixtures containing an antagonistic salt, with hydrophilic cations and hydrophobic anions. Our simulations reveal several phases with a spatially modulated solvent composition, in which the ions partition between water-rich and water-poor regions according to their affinity. In addition to the recently observed lamellar phase, we find tubular and droplet phases, reminiscent of those found in block copolymers and surfactant systems. Interestingly, these structures stem from ion-mediated interactions, which allows for tuning of the phase behavior via the concentrations, the ionic properties, and the temperature.

Sequence and entropy-based control of complex coacervates

Biomacromolecules rely on the precise placement of monomers to encode information for structure, function, and physiology. Efforts to emulate this complexity via the synthetic control of chemical sequence in polymers are finding success; however, there is little understanding of how to translate monomer sequence to physical material properties. Here we establish design rules for implementing this sequence-control in materials known as complex coacervates. These materials are formed by the associative phase separation of oppositely charged polyelectrolytes into polyelectrolyte dense (coacervate) and polyelectrolyte dilute (supernatant) phases. We demonstrate that patterns of charges can profoundly affect the charge–charge associations that drive this process. Furthermore, we establish the physical origin of this pattern-dependent interaction: there is a nuanced combination of structural changes in the dense coacervate phase and a 1D confinement of counterions due to patterns along polymers in the supernatant phase.

Monomer sequence is an emerging tool to precisely encode information (and thus structure and function) into polymer systems. Here the authors use sequence-control in complex coacervates to understand how monomer sequence translates to physical material properties.

Complex coacervates based on recombinant mussel adhesive proteins: their characterization and applications

Complex coacervates are a dense liquid phase of oppositely charged polyions formed by the associative separation of a mixture of polyions. Coacervates have been widely employed in many fields including the pharmaceutical, cosmetic, and food industries due to their intriguing interfacial and bulk material properties. More recently, attempts to develop an effective underwater adhesive have been made using complex coacervates that are based on recombinant mussel adhesive proteins (MAPs) due to the water immiscibility of complex coacervates and the adhesiveness of MAPs. MAP-based complex coacervates contribute to our understanding of the physical nature of complex coacervates and they provide a promising alternative to conventional invasive surgical repairs. Here, this review provides an overview of recombinant MAP-based complex coacervations, with an emphasis on their characterization and the uses of such materials for applications in the fields of biomedicine and tissue engineering.

Transfer matrix theory of polymer complex coacervation

Oppositely charged polyelectrolytes can undergo a macroscopic, associative phase separation in solution, via a process known as complex coacervation. Significant recent effort has gone into providing a clear, physical picture of coacervation; most work has focused on improving the field theory picture that emerged from the classical Voorn-Overbeek theory. These methods have persistent issues, however, resolving the molecular features that have been shown to play a major role in coacervate thermodynamics. In this paper, we outline a theoretical approach to coacervation based on a transfer matrix formalism that is an alternative to traditional field-based approaches. We develop theoretical arguments informed by experimental observation and simulation, which serve to establish an analytical expression for polymeric complex coacervation that is consistent with the molecular features of coacervate phases. The analytical expression provided by this theory is in a form that can be incorporated into more complicated theoretical or simulation formalisms, and thus provides a starting point for understanding coacervate-driven self-assembly or biophysics.

Sequence-encoded material properties dictate the structure and function of nuclear bodies

Concomitant with packaging the genome, the cell nucleus must also spatially organize the nucleoplasm. This complex mixture of proteins and nucleic acids partitions into a variety of phase-separated, membraneless organelles called nuclear bodies. Significant progress has been made in understanding the relationship between the material properties of nuclear bodies and their structural and functional consequences. Furthermore, the molecular basis of these condensed phases is beginning to emerge. Here, I review the latest work in this exciting field, highlighting recent advances and new challenges.

The effect of comb architecture on complex coacervation

Complex coacervation is a widely utilized technique for effecting phase separation, though predictive understanding of molecular-level details remains underdeveloped.

Explicit description of complexation between oppositely charged polyelectrolytes as an advantage of the random phase approximation over the scaling approach

Formation of single globules via 1 : 1 complexation of oppositely charged linear chains occurs prior to coacervation. F_corr is proved to be negative which is the difference between the random phase approximation (RPA) correction term and the self-energy of the chains.