Interfacial Structure and Tension of Polyelectrolyte Complex Coacervates

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.

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.

RNA regulates cohesiveness and porosity of a biological condensate

Biological condensates have emerged as key elements of a biological cell function, concentrating disparate biomolecules to accomplish specific biological tasks. RNA was identified as a key ingredient of such condensates, however, its effect on the physical properties of the condensate was found to depend on the condensate's composition while its effect on the microstructure has remained elusive. Here, we characterize the physical properties and the microstructure of a protein-RNA condensate by means of large-scale coarse-grained (CG) molecular dynamics simulations. By developing a custom CG model of RNA compatible with a popular CG model of proteins, we systematically investigate the structural, thermodynamic, and kinetic properties of condensate droplets containing thousands of individual protein and RNA molecules over a range of temperatures. While we find RNA to increase the condensate's cohesiveness, its effect on the condensate's fluidity is more nuanced with longer molecules compacting the condensate and making it less fluid. We show that a biological condensate has a sponge-like morphology of interconnected channels of size that increases with temperature and decreases in the presence of RNA. Our results suggest that longer RNA form a dynamic scaffold within a condensate, regulating not only its fluidity but also permeability to intruder molecules.

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

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

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

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

Structure and Dynamics of Hybrid Colloid-Polyelectrolyte Coacervates: Insights from Molecular Simulations

Electrostatic interactions in polymeric systems are responsible for a wide range of liquid-liquid phase transitions that are of importance for biology and materials science. Such transitions are referred to as complex coacervation, and recent studies have sought to understand the underlying physics and chemistry. Most theoretical and simulation efforts to date have focused on oppositely charged linear polyelectrolytes, which adopt nearly ideal-coil conformations in the condensed phase. However, when one of the coacervate components is a globular protein, a better model of complexation should replace one of the species with a spherical charged particle or colloid. In this work, we perform coarse-grained simulations of colloid-polyelectrolyte coacervation using a spherical model for the colloid. Simulation results indicate that the electroneutral cell of the resulting (hybrid) coacervates consists of a polyelectrolyte layer adsorbed on the colloid. Power laws for the structure and the density of the condensed phase, which are extracted from simulations, are found to be consistent with the adsorption-based scaling theory of hybrid coacervation. The coacervates remain amorphous (disordered) at a moderate colloid charge, Q, while an intra-coacervate colloidal crystal is formed above a certain threshold, at Q > Q*. In the disordered coacervate, if Q is sufficiently low, colloids diffuse as neutral nonsticky nanoparticles in the semidilute polymer solution. For higher Q, adsorption is strong and colloids become effectively sticky. Our findings are relevant for the coacervation of polyelectrolytes with proteins, spherical micelles of ionic surfactants, and solid organic or inorganic nanoparticles.

Electroresponse of weak polyelectrolyte brushes

End-tethered polyelectrolytes are widely used to modify substrate properties, particularly for lubrication or wetting. External stimuli, such as pH, salt concentration, or an electric field, can induce profound structural responses in weak polyelectrolyte brushes, which can be utilized to further tune substrate properties. We study the structure and electroresponsiveness of weak polyacid brushes using an inhomogeneous theory that incorporates both electrostatic and chain connectivity correlations at the Debye-Hückel level. Our calculation shows that a weak polyacid brush swells under the application of a negative applied potential, in agreement with recent experimental observation. We rationalize this behavior using a scaling argument that accounts for the effect of the surface charge. We also show that the swelling behavior has a direct influence on the differential capacitance, which can be modulated by the solvent quality, pH, and salt concentration.

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.

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.