Unlocking the electrochemical functions of biomolecular condensates.

Biomolecular condensation is a key mechanism for organizing cellular processes in a spatiotemporal manner. The phase-transition nature of this process defines a density transition of the whole solution system. However, the physicochemical features and the electrochemical functions brought about by condensate formation are largely unexplored. We here illustrate the fundamental principles of how the formation of condensates generates distinct electrochemical features in the dilute phase, the dense phase and the interfacial region. We discuss the principles by which these distinct chemical and electrochemical environments can modulate biomolecular functions through the effects brought about by water, ions and electric fields. We delineate the potential impacts on cellular behaviors due to the modulation of chemical and electrochemical environments through condensate formation. This Perspective is intended to serve as a general road map to conceptualize condensates as electrochemically active entities and to assess their functions from a physical chemistry aspect.

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.

Robust Oxidase-Mimetic Supramolecular Nanocatalyst for Lignin Biodegradation.

Enzymatic catalysis presents an eco-friendly, energy-efficient method for lignin degradation. However, challenges arise due to the inherent incompatibility between enzymes and native lignin. In this work, we introduce a supramolecular catalyst composed of fluorenyl-modified amino acids and Cu2+, designed based on the aromatic stacking of the fluorenyl group, which can operate in ionic liquid environments suitable for the dissolution of native lignin. Amino acids and halide anions of ionic liquids shape the copper site's coordination sphere, showcasing remarkable catechol oxidase-mimetic activity. The catalyst exhibits thermophilic property, and maintains oxidative activity up to 75 °C, which allows the catalyzed degradation of the as-dissolved native lignin with high efficiency even without assistance of the electron mediator. In contrast, at this condition, the native copper-dependent oxidase completely lost its activity. This catalyst with superior stability and activity offer promise for sustainable lignin valorization through biocatalytic routes compatible with ionic liquid pretreatment, addressing limitations in native enzymes for industrially relevant conditions.

Adsorption Isotherm and Mechanism of Ca2+ Binding to Polyelectrolyte.

Polyelectrolytes, such as poly(acrylic acid) (PAA), can effectively mitigate CaCO3 scale formation. Despite their success as antiscalants, the underlying mechanism of binding of Ca2+ to polyelectrolyte chains remains unresolved. Through all-atom molecular dynamics simulations, we constructed an adsorption isotherm of Ca2+ binding to sodium polyacrylate (NaPAA) and investigated the associated binding mechanism. We find that the number of calcium ions adsorbed [Ca2+]ads to the polymer saturates at moderately high concentrations of free calcium ions [Ca2+]aq in the solution. This saturation value is intricately connected with the binding modes accessible to Ca2+ ions when they bind to the polyelectrolyte chain. We identify two dominant binding modes: the first involves binding to at most two carboxylate oxygens on a polyacrylate chain, and the second, termed the high binding mode, involves binding to four or more carboxylate oxygens. As the concentration of free calcium ions [Ca2+]aq increases from low to moderate levels, the polyelectrolyte chain undergoes a conformational transition from an extended coil to a hairpin-like structure, enhancing the accessibility to the high binding mode. At moderate concentrations of [Ca2+]aq, the high binding mode accounts for at least one-third of all binding events. The chain's conformational change and its consequent access to the high binding mode are found to increase the overall Ca2+ ion binding capacity of the polyelectrolyte chain.

A model for zwitterionic polymers and their capacitance applications.

Zwitterions have been shown experimentally to enhance the dielectric constant of ionic media, owing to their large molecular dipole. Many studies since explored the enhancement of ionic conductivity with zwitterion additives as well as bulk behavior of zwitterions. Here, we examine the capacitance behavior of zwitterions between charged parallel plates using a mean-field theory. Employing only chain connectivity of a cation and anion with neutral monomers in between with mean-field electrostatics, we show that our model captures the high-dielectric behavior of zwitterions. We also predict an optimum in the capacitance of zwitterionic media as a function of chain length. To address the issue of zwitterion screening near charged surfaces, we demonstrate that zwitterions simultaneously partially screen charged walls and act as a pure dielectric that propagates the electric field far from the surface. Moreover, we show that salt solutions with zwitterionic additives outperform the energy density of both salt-only and zwitterion-only capacitors. We find that salt-only capacitors perform better at low applied potential, whereas salt capacitors with zwitterionic additives perform better at high applied potential.

A Jacobian-free pseudo-arclength continuation method for phase transitions in inhomogeneous thermodynamic systems.

Developing phase diagrams for inhomogeneous systems in thermodynamics is difficult, in part, due to the large phase space and the possibility of unstable and metastable solutions arising from first-order phase transitions. Pseudo-arclength continuation (PAC) is a method that allows one to trace out stable and unstable solutions of nonlinear systems. Typically, PAC utilizes the Jacobian in order to implement Newton (or quasi-Newton) steps. In this work, we present a Jacobian-free PAC method that is amenable to the usual workflows in inhomogeneous thermodynamics. We demonstrate our method in systems that have first-order phase transitions, including a novel example of polyelectrolyte complex coacervation in confinement, where multiple surface phase transitions occur and can overlap with one another.

Image-charge effects on ion adsorption near aqueous interfaces.

Electrostatic interactions near surfaces and interfaces are ubiquitous in many fields of science. Continuum electrostatics predicts that ions will be attracted to conducting electrodes but repelled by surfaces with lower dielectric constant than the solvent. However, several recent studies found that certain "chaotropic" ions have similar adsorption behavior at air/water and graphene/water interfaces. Here we systematically study the effect of polarization of the surface, the solvent, and solutes on the adsorption of ions onto the electrode surfaces using molecular dynamics simulation. An efficient method is developed to treat an electrolyte system between two parallel conducting surfaces by exploiting the mirror-expanded symmetry of the exact image-charge solution. With neutral surfaces, the image interactions induced by the solvent dipoles and ions largely cancel each other, resulting in no significant net differences in the ion adsorption profile regardless of the surface polarity. Under an external electric field, the adsorption of ions is strongly affected by the surface polarization, such that the charge separation across the electrolyte and the capacitance of the cell is greatly enhanced with a conducting surface over a low-dielectric-constant surface. While the extent of ion adsorption is highly dependent on the electrolyte model (the polarizability of solvent and solutes, as well as the van der Waals radii), we find the effect of surface polarization on ion adsorption is consistent throughout different electrolyte models.

Histidine-Based Supramolecular Nanoassembly Exhibiting Dual Enzyme-Mimetic Functions: Altering the Tautomeric Preference of Histidine to Tailor Oxidative/Hydrolytic Catalysis.

Challenges persist in replicating enzyme-like active sites with functional group arrangements in supramolecular catalysis. In this study, we present a supramolecular material comprising Fmoc-modified histidine and copper. We also investigated the impact of noncanonical amino acids (δmH and εmH), isomers of histidine, on the catalytic process. The Fmoc-δmH-based nanoassembly exhibits an approximately 15-fold increase in oxidative activity and an ∼50-fold increase in hydrolytic activity compared to Fmoc-εmH (kcat/Km). This distinction arises from differences in basicity and ligation properties between the ε- and δ-nitrogen of histidine. The addition of guanosine monophosphate further enhances the oxidative activity of the histidine- and methylated histidine-based catalysts. The Fmoc-δmH/Cu2+-based nanoassembly catalyzes the oxidation/hydrolysis cascade of 2',7'-dichlorofluorescein diacetate, benefiting from the synergistic effect between the copper center and the nonligating ε-nitrogen of histidine. These findings advance the biomimetic catalyst design and provide insights into the mechanistic role of essential residues in natural systems.

Charge Asymmetry Suppresses Coarsening Dynamics in Polyelectrolyte Complex Coacervation.

Mixing solutions of oppositely charged macromolecules can result in liquid-liquid phase separation into a polymer-rich coacervate phase and a polymer-poor supernatant phase. Here, we show that charge asymmetry in the constituent polymers can slow down the coarsening dynamics, with an apparent growth exponent that deviates from the well-known 1/3 for neutral systems and decreases with increasing degrees of charge asymmetry. Decreasing solvent quality accelerates the coarsening dynamics for asymmetric mixtures but slows down the coarsening dynamics for symmetric mixtures. We rationalize these results by examining the interaction potential between merging droplets.

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.

Cofactor-free oxidase-mimetic nanomaterials from self-assembled histidine-rich peptides.

Natural oxidases mainly rely on cofactors and well-arranged amino acid residues for catalysing electron-transfer reactions but suffer from non-recovery of their activity upon externally induced protein unfolding. However, it remains unknown whether residues at the active site can catalyse similar reactions in the absence of the cofactor. Here, we describe a series of self-assembling, histidine-rich peptides, as short as a dipeptide, with catalytic function similar to that of haem-dependent peroxidases. The histidine residues of the peptide chains form periodic arrays that are able to catalyse H2O2 reduction reactions efficiently through the formation of reactive ternary complex intermediates. The supramolecular catalyst exhibiting the highest activity could be switched between inactive and active states without loss of activity for ten cycles of heating/cooling or acidification/neutralization treatments, demonstrating the reversible assembly/disassembly of the active residues. These findings may aid the design of advanced biomimetic catalytic materials and provide a model for primitive cofactor-free enzymes.

Surfactant in a Polyol-CO2 Mixture: Insights from a Classical Density Functional Theory Study.

Silicone-polyether (SPE) surfactants, made of a polydimethyl-siloxane (PDMS) backbone and polyether branches, are commonly used as additives in the production of polymeric foams with improved properties. A key step in the production of polymeric foams is the nucleation of gas bubbles in the polymer matrix upon supersaturation of dissolved gas. However, the role of SPE surfactants in the nucleation of gas bubbles is not well understood. In this study, we use classical density functional theory to investigate the effect of an SPE surfactant on the nucleation of CO2 bubbles in a polyol foam formulation. We find that the addition of an SPE surfactant leads to a ∼3-fold decrease in the polyol-CO2 interfacial tension at the surfactant's critical micelle concentration. Additionally, the surfactant is found to reduce the free energy barrier and affect the minimum free energy pathway (MFEP) associated with CO2 bubble nucleation. In the absence of a surfactant, a CO2-rich bubble nucleates from a homogeneous CO2-supersaturated polyol solution by following an MFEP characterized by a single nucleation barrier. Adding a surfactant results in a two-step nucleation process with reduced free energy barriers. The first barrier corresponds to the formation of a spherical aggregate with a liquid-like CO2 core. This spherical aggregate then grows into a CO2-rich bubble (spherical aggregate with a vapor-like CO2 core) of a critical size representing the second barrier. We hypothesize that the stronger affinity of CO2 for PDMS (than polyether) stabilizes the spherical aggregate with the liquid-like CO2 core, leading to a lower free energy barrier for CO2 bubble nucleation. Stabilization of such an aggregate during the early stages of the nucleation may lead to foams with more, smaller bubbles, which can improve their microstrustural features and insulating abilities.

Enzyme-Mimicking Materials from Designed Self-Assembly of Lysine-Rich Peptides and G-Quadruplex DNA/Hemin DNAzyme: Charge Effect of the Key Residues on the Catalytic Functions.

In enzymatic active sites, the essential functional groups are spatially arranged as a result of the enzyme three-dimensional folding, which leads to remarkable catalytic properties. We are inspired to self-assemble the polylysine peptides with guanine-rich DNA and hemin as cofactor to fabricate the peroxidase-mimicking catalytic nanomaterials. The DNA can fold into G-quadruplex to provide a supramolecular scaffold and a nucleobase for supporting and coordinating hemin, and the polylysine provides amine as distal groups to promote the H2O2 adsorption to the iron of hemin. The polylysine and DNA components synergistically accelerated the hemin-catalyzed reactions, and the complex containing ε-polylysine exhibited higher activity than α-polylysine. This activity difference is attributed to the higher pKa value and more susceptible protonation of amine of ε-polylysine than α-polylysine. The ε-polylysine/DNA/hemin had similar coordination states of hemin and conformations of the components to α-polylysine/DNA/hemin but accelerated the formation of the intermediate compound I faster than α-polylysine. Theoretical simulation reveals that the unprotonated NH2 behaved like a base catalyst, similar to His-42 residue in the natural heme pocket, while the protonated NH3+ acted as an acid, which indicated that the base catalyst on the distal side of the hemin pocket is more active than the acid. This work provides an avenue to control the distribution of the catalytic residues in an enzyme-like active site and to understand the roles of the key residues of native enzymes.

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.

Effects of dilution in ionic liquid supercapacitors.

Room-temperature ionic liquids (RTILs) are synthetic electrolytes that have a large electrochemical stability window, making them attractive candidates for electric double-layer capacitor (EDLC) applications. Due to their high viscosities and low ionic conductivities, RTILs are often diluted with organic solvent for practical use. We study the effects of dilution on the performance of RTIL EDLCs using a simple mean-field model. We find that dilution diminishes the unfavorable hysteresis that results from a spontaneous surface charge separation (SSCS). As a result, the RTIL concentration can be used to modulate the proximity to the SSCS transition, and maximize capacitance. The interplay between the concentration and the correlation strength gives rise to complex zero-potential phase behavior, including a tricritical point and a λ-line, very similar to the Blume-Capel dilute Ising model. Additionally, electrodes that are solvophilic aid in the prevention of SSCS by drawing solvent molecules to the electrode and displacing ions. Solvophilic electrodes give rise to a phase transition at finite potential where the surface charge rapidly increases with a small increase in potential, leading to a substantial increase in capacitance and energy storage.

A coarse-grained model of room-temperature ionic liquids between metal electrodes: a molecular dynamics study.

Recent mean-field theories predict that room-temperature ionic liquid (RTIL) electric double-layer capacitors (EDLCs) undergo a spontaneous surface charge separation (SSCS) with no applied potential. In this study, we construct a coarse-grained molecular model that corresponds to the mean-field models to directly simulate the behavior of RTILs without invoking mean-field approximations. In addition to observing the SSCS transition, we highlight the importance of the image charge interactions and explore the enhanced in-plane ordering on the electrodes, two effects not accounted for by the mean-field theories. By calculating and comparing the differential capacitance for RTILs confined between perfectly conducting and non-metal electrodes, we show that the image charge interactions drastically improve the energy storage properties of RTIL EDLCs.

Thermodynamics of electrolyte solutions near charged surfaces: Constant surface charge vs constant surface potential.

Electric double layers are ubiquitous in science and engineering and are of current interest, owing to their applications in the stabilization of colloidal suspensions and as supercapacitors. While the structure and properties of electric double layers in electrolyte solutions near a charged surface are well characterized, there are subtleties in calculating thermodynamic properties from the free energy of a system with charged surfaces. These subtleties arise from the difference in the free energy between systems with constant surface charge and constant surface potential. In this work, we present a systematic, pedagogical framework to properly account for the different specifications on charged bodies in electrolyte solutions. Our approach is fully variational-that is, all free energies, boundary conditions, relevant electrostatic equations, and thermodynamic quantities are systematically derived using variational principles of thermodynamics. We illustrate our approach by considering a simple electrolyte solution between two charged surfaces using the Poisson-Boltzmann theory. Our results highlight the importance of using the proper thermodynamic potential and provide a general framework for calculating thermodynamic properties of electrolyte solutions near charged surfaces. Specifically, we present the calculation of the pressure and the surface tension between two charged surfaces for different boundary conditions, including mixed boundary conditions.

Semiflexible polymer solutions. II. Fluctuations and Frank elastic constants.

We study the collective elastic behavior of semiflexible polymer solutions in a nematic liquid-crystalline state using polymer field theory. Our polymer field-theoretic model of semiflexible polymer solutions is extended to include second-order fluctuation corrections to the free energy, permitting the evaluation of the Frank elastic constants based on orientational order fluctuations in the nematic state. Our exact treatment of wormlike chain statistics permits the evaluation of behavior from the nematic state, thus accurately capturing the impact of single-chain behavior on collective elastic response. Results for the Frank elastic constants are presented as a function of aligning field strength and chain length, and we explore the impact of conformation fluctuations and hairpin defects on the twist, splay, and bend moduli. Our results indicate that the twist elastic constant Ktwist is smaller than both bend and splay constants (Kbend and Ksplay, respectively) for the entire range of polymer rigidity. Splay and bend elastic constants exhibit regimes of dominance over the range of chain stiffness, where Ksplay > Kbend for flexible polymers (large-N limit) while the opposite is true for rigid polymers. Theoretical analysis also suggests the splay modulus tracks exactly to that of the end-to-end distance in the transverse direction for semiflexible polymers at intermediate to large-N. These results provide insight into the role of conformation fluctuations and hairpin defects on the collective response of polymer solutions.

Salt-Induced Liquid-Liquid Phase Separation: Combined Experimental and Theoretical Investigation of Water-Acetonitrile-Salt Mixtures.

Salt-induced liquid-liquid phase separation in liquid mixtures is a common phenomenon in nature and in various applications, such as in separation and extraction of chemicals. Here, we present results of a systematic investigation of the phase behaviors in water-acetonitrile-salt mixtures using a combination of experiment and theory. We obtain complete ternary phase diagrams for nine representative salts in water-acetonitrile mixtures by cloud point and component analysis. We construct a thermodynamic free energy model by accounting for the nonideal mixing of the liquids, ion hydration, electrostatic interactions, and Born energy. Our theory yields phase diagrams in good agreement with the experimental data. By comparing the contributions due to the electrostatic interaction, Born energy, and hydration, we find that hydration is the main driving force for the liquid-liquid separation and is a major contributor to the specific ion effects. Our theory highlights the important role of entropy in the hydration driving force. We discuss the implications of our findings in the context of salting-out assisted liquid-liquid extraction and make suggestions for selecting salt ions to optimize the separation performance.

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.