Investigating the Impact of Network Functionalization on Protein Adsorption to Polymer Nanogels

This study explores the impact of network functionalization and chemical composition on the pH-responsive behavior of polymer nanogels and their adsorption of proteins. Using a thermodynamic theory informed by a molecular model, this work evaluates the interactions of three proteins with varying isoelectric points (insulin, myoglobin, and cytochrome c) and pH-responsive nanogels based on methacrylic acid or allylamine motifs. Three different functionalization strategies are considered, with pH-responsive segments distributed randomly, at the center, or on the surface of the polymer network. Our results show that the spatial distribution of functional units affects both the nanogels' mechanical response to pH changes and the level and localization of adsorbed proteins. The dependence of protein adsorption on the salt concentration is also investigated, with the conclusion that it is best to encapsulate proteins at low salt concentrations and aim for release at high salt concentrations. These results provide valuable information for the design of pH-responsive nanogels as vehicles for protein encapsulation, transport, and administration.

Induced phase transformation in ionizable colloidal nanoparticles

Acid-base equilibria directly influence the functionality and behavior of particles in a system. Due to the ionizing effects of acid-base functional groups, particles will undergo charge exchange. The degree of ionization and their intermolecular and electrostatic interactions are controlled by varying the pH and salt concentration of the solution in a system. Although the pH can be tuned in experiments, it is hard to model this effect using simulations or theoretical approaches. This is due to the difficulty in treating charge regulation and capturing the cooperative effects in a colloidal suspension with Coulombic interaction. In this work, we analyze a suspension of ionizable colloidal particles via molecular dynamics (MD) simulations, along with Monte Carlo simulations for charge regulation (MC-CR) and derive a phase diagram of the system as a function of pH. It is observed that as pH increases, particles functionalized with acid groups change their arrangement from face-centered cubic (FCC) packing to a disordered state. We attribute these transitions to an increase in the degree of charge polydispersity arising from an increase in pH. Our work shows that charge regulation leads to amorphous solids in colloids when the mean nanoparticle charge is sufficiently high.

Interactions of variants of human apolipoprotein A-I with biopolymeric model matrices. Effect of collagen and heparin

BACKGROUND

The extracellular matrix (ECM) is a complex tridimensional scaffold that actively participates in physiological and pathological events. The objective of this study was to test whether structural proteins of the ECM and glycosaminoglycans (GAGs) may favor the retention of human apolipoprotein A-I (apoA-I) variants associated with amyloidosis and atherosclerosis.

METHODS

Biopolymeric matrices containing collagen type I (Col, a main macromolecular component of the ECM) with or without heparin (Hep, a model of GAGs) were constructed and characterized, and used to compare the binding of apoA-I having the native sequence (Wt) or Arg173Pro, a natural variant inducing cardiac amyloidosis. Protein binding was observed by fluorescence microscopy and unbound proteins quantified by a colorimetric assay.

RESULTS

Both, Wt and Arg173Pro bound to the scaffolds containing Col, but the presence of Hep diminished the binding efficiency. Col-Hep matrices retained Arg173Pro more than the Wt. The retained protein was only partially removed from the matrices with saline solutions, indicating that electrostatic interactions may occur but are not the main driving force. Using in addition thermodynamic molecular simulations and size exclusion chromatography approaches, we suggest that the binding of apoA-I variants to the biopolymeric matrices is driven by many low affinity interactions.

CONCLUSIONS

Under this scenario Col-Hep scaffolds contribute to the binding of Arg173Pro, as a cooperative platform which could modify the native protein conformation affecting protein folding.

GENERAL SIGNIFICANCE

We show that the composition of the ECM is key to the protein retention, and well characterized biosynthetic matrices offer an invaluable in vitro model to mimic the hallmark of pathologies with interstitial infiltration such as cardiac amyloidosis.

Explaining Giant Apparent pK_{a} Shifts in Weak Polyelectrolyte Brushes

Recent experiments on weak polyelectrolyte brushes found marked shifts in the effective pK_{a} that are linear in the logarithm of the salt concentration. Comparing explicit-particle simulations with mean-field calculations we show that for high grafting densities the salt concentration effect can be explained using the ideal Donnan theory, but for low grafting densities the full shift is due to a combination of the Donnan effect and the polyelectrolyte effect. The latter originates from electrostatic correlations that are neglected in the Donnan picture and that are only approximately included in the mean-field theory. Moreover, we demonstrate that the magnitude of the polyelectrolyte effect is almost invariant with respect to salt concentration but depends on the grafting density of the brush. This invariance is due to a complex cancellation of multiple effects. Based on our results, we show how the experimentally determined pK_{a} shifts may be used to infer the grafting density of brushes, a parameter that is difficult to measure directly.

Theoretical treatment of complex coacervate core micelles: structure and pH-induced disassembly

Complex coacervate core micelles (C3Ms) are supramolecular soft nanostructures formed by the assembly of a block copolymer and an oppositely charged homopolymer. The coacervation of the charged segments in both macromolecules drives the formation of the core of the C3M, while the neutral block of the copolymer forms the corona. This work introduces a molecular theory (MOLT) that predicts the internal structure and stimuli-responsive properties of C3Ms and explicitly considers the chemical architecture of the polyelectrolytes, their acid-based equilibria and electrostatic and non-electrostatic interactions. In order to accurately predict complex coacervation, the correlations between charged species are incorporated into MOLT as ion-pairing processes, which are modeled using a coupled chemical equilibrium formalism. Very good agreement was observed between the experimental results in the literature and MOLT predictions for the scaling relationships that relate the dimensions of the micelle (aggregation number and sizes of the micelle and the core) to the lengths of the different blocks. MOLT was used to study the disassembly of the micelles when the solution pH is driven away from the value that guarantees the charge stoichiometry of the core. This study reveals that very sharp disassembly transitions can be obtained by tuning the length or architecture of the copolymer component, thereby suggesting potential routes to design C3Ms capable of releasing their components at very precise pH values.

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.

Fluids and Electrolytes under Confinement in Single-Digit Nanopores

Confined fluids and electrolyte solutions in nanopores exhibit rich and surprising physics and chemistry that impact the mass transport and energy efficiency in many important natural systems and industrial applications. Existing theories often fail to predict the exotic effects observed in the narrowest of such pores, called single-digit nanopores (SDNs), which have diameters or conduit widths of less than 10 nm, and have only recently become accessible for experimental measurements. What SDNs reveal has been surprising, including a rapidly increasing number of examples such as extraordinarily fast water transport, distorted fluid-phase boundaries, strong ion-correlation and quantum effects, and dielectric anomalies that are not observed in larger pores. Exploiting these effects presents myriad opportunities in both basic and applied research that stand to impact a host of new technologies at the water-energy nexus, from new membranes for precise separations and water purification to new gas permeable materials for water electrolyzers and energy-storage devices. SDNs also present unique opportunities to achieve ultrasensitive and selective chemical sensing at the single-ion and single-molecule limit. In this review article, we summarize the progress on nanofluidics of SDNs, with a focus on the confinement effects that arise in these extremely narrow nanopores. The recent development of precision model systems, transformative experimental tools, and multiscale theories that have played enabling roles in advancing this frontier are reviewed. We also identify new knowledge gaps in our understanding of nanofluidic transport and provide an outlook for the future challenges and opportunities at this rapidly advancing frontier.

Surface charge regulation using classical density functional theory: the effect of divalent potential determining ions

The charge regulation approach has been used to describe the charge of surfaces susceptible to the presence of protons and other ions. Conventionally, this model is used with the Poisson-Boltzmann equation, which generally neglects the finite size of the ions and the electrostatic correlations. Recently, progress has been made by coupling charge regulation with classical density functional theory (DFT), which explicitly includes these correlations. However, little is known about charge regulation at surfaces with both acid-base equilibria and complexation with multivalent ions. The main purpose of this work is to investigate the role divalent ions play in charge regulation. Using DFT, we show that the size of the divalent ion has significant consequences on the surface charge density and it should not be neglected. For the surface reactions investigated, the larger the size of the divalent cation, the greater the charge on the surface due to higher divalent concentration there. At low divalent concentration, the ion correlations play a second-order but non-negligible role; using Poisson-Boltzmann theory with point ions cannot recover the DFT surface charge. At high concentrations, ion correlations play a dominant role by creating charge inversion.

Competitive protein adsorption on charge regulating silica-like surfaces: the role of protonation equilibrium

We develop a molecular thermodynamic theory to study the interaction of some proteins with a charge regulating silica-like surface under a wide range of conditions, including pH, salt concentration and protein concentration. Proteins are modeled using their three dimensional structure from crystallographic data and the average experimental pKa of amino acid residues. As model systems, we study single-protein and binary solutions of cytochrome c, green fluorescent protein, lysozyme and myoglobin. Our results show that protonation equilibrium plays a critical role in the interactions of proteins with these type of surfaces. The terminal hydroxyl groups on the surface display considerable extent of charge regulation; protein residues with titratable side chains increase protonation according to changes in the local environment and the drop in pH near the surface. This behavior defines protein-surface interactions and leads to the emergence of several phenomena: (i) a complex non-ideal surface charge behavior; (ii) a non-monotonic adsorption of proteins as a function of pH; and (iii) the presence of two spatial regions, a protein-rich and a protein-depleted layer, that occur simultaneously at different distances from the surface when pH is slightly above the isoelectric point of the protein. In binary mixtures, protein adsorption and surface-protein interactions cannot be predicted from single-protein solution considerations.

Effects of Non-Ionic Micelles on the Acid-Base Equilibria of a Weak Polyelectrolyte

Weak polyelectrolytes (WPEs) are widely used as pH-responsive materials, pH modulators and charge regulators in biomedical and technological applications that involve multi-component fluid environments. In these complex fluids, coupling between (often weak) interactions induced by micelles, nanoparticles and molecular aggregates modify the pKa as compared to that measured in single component solutions. Here we investigated the effect of coupling between hydrogen bonding and excluded volume interactions on the titration curves and pKa of polyacrylic acid (PAA) in solutions comprising PEO-based micelles (Pluronics and Brij-S20) of different size and volume fraction. Titration experiments of dilute, salt-free solutions of PAA (5 kDa, 30 kDa and 100 kDa) at low degree of polymer ionization (α < 0.25) drive spatial re-organization of the system, reduce the degree of ionization and consequentially increase the pKa by up to ~0.7 units. These findings indicate that the actual degree of ionization of WPEs measured in complex fluids is significantly lower (at a given pH) than that measured in single-component solutions.

Acid-Base Equilibrium and Dielectric Environment Regulate Charge in Supramolecular Nanofibers

Peptide amphiphiles are a class of molecules that can self-assemble into a variety of supramolecular structures, including high-aspect-ratio nanofibers. It is challenging to model and predict the charges in these supramolecular nanofibers because the ionization state of the peptides are not fixed but liable to change due to the acid-base equilibrium that is coupled to the structural organization of the peptide amphiphile molecules. Here, we have developed a theoretical model to describe and predict the amount of charge found on self-assembled peptide amphiphiles as a function of pH and ion concentration. In particular, we computed the amount of charge of peptide amphiphiles nanofibers with the sequence C₁₆ − V₂A₂E₂. In our theoretical formulation, we consider charge regulation of the carboxylic acid groups, which involves the acid-base chemical equilibrium of the glutamic acid residues and the possibility of ion condensation. The charge regulation is coupled with the local dielectric environment by allowing for a varying dielectric constant that also includes a position-dependent electrostatic solvation energy for the charged species. We find that the charges on the glutamic acid residues of the peptide amphiphile nanofiber are much lower than the same functional group in aqueous solution. There is a strong coupling between the charging via the acid-base equilibrium and the local dielectric environment. Our model predicts a much lower degree of deprotonation for a position-dependent relative dielectric constant compared to a constant dielectric background. Furthermore, the shape and size of the electrostatic potential as well as the counterion distribution are quantitatively and qualitatively different. These results indicate that an accurate model of peptide amphiphile self-assembly must take into account charge regulation of acidic groups through acid–base equilibria and ion condensation, as well as coupling to the local dielectric environment.

Proteins Adsorbing onto Surface-Modified Nanoparticles: Effect of Surface Curvature, pH, and the Interplay of Polymers and Proteins Acid-Base Equilibrium

Protein adsorption onto nanomaterials is a process of vital significance and it is commonly controlled by functionalizing their surface with polymers. The efficiency of this strategy depends on the design parameters of the nanoconstruct. Although significant amount of work has been carried out on planar surfaces modified with different types of polymers, studies investigating the role of surface curvature are not as abundant. Here, we present a comprehensive and systematic study of the protein adsorption process, analyzing the effect of curvature and morphology, the grafting of polymer mixtures, the type of monomer (neutral, acidic, basic), the proteins in solution, and the conditions of the solution. The theoretical approach we employed is based on a molecular theory that allows to explicitly consider the acid-base reactions of the amino acids in the proteins and the monomers on the surface. The calculations showed that surface curvature modulates the molecular organization in space, but key variables are the bulk pH and salt concentration (in the millimolar range). When grafting the NP with acidic or basic polymers, the surface coating could disfavor or promote adsorption, depending on the solution's conditions. When NPs are in contact with protein mixtures in solution, a nontrivial competitive adsorption process is observed. The calculations reflect the balance between molecular organization and chemical state of polymers and proteins, and how it is modulated by the curvature of the underlying surface.

Structure and dynamics of nanoconfined water and aqueous solutions

This review is devoted to discussing recent progress on the structure, thermodynamic, reactivity, and dynamics of water and aqueous systems confined within different types of nanopores, synthetic and biological. Currently, this is a branch of water science that has attracted enormous attention of researchers from different fields interested to extend the understanding of the anomalous properties of bulk water to the nanoscopic domain. From a fundamental perspective, the interactions of water and solutes with a confining surface dramatically modify the liquid's structure and, consequently, both its thermodynamical and dynamical behaviors, breaking the validity of the classical thermodynamic and phenomenological description of the transport properties of aqueous systems. Additionally, man-made nanopores and porous materials have emerged as promising solutions to challenging problems such as water purification, biosensing, nanofluidic logic and gating, and energy storage and conversion, while aquaporin, ion channels, and nuclear pore complex nanopores regulate many biological functions such as the conduction of water, the generation of action potentials, and the storage of genetic material. In this work, the more recent experimental and molecular simulations advances in this exciting and rapidly evolving field will be reported and critically discussed.

Regulation of oligonucleotide adsorption by a thermo and pH dual-responsive copolymer layer

Oligonucleotides hold great promise as therapeutic agents to specifically and selectively inhibit gene expression. In order to achieve better targeting efficiency and treatment efficacy, nanocarriers that are dual-responsive to both temperature and pH are more attractive and suitable due to the fact that certain malignancies can cause a slight increase of local temperature and a minor decrease in extracellular pH around the tumor site at the same time. Here, we systematically study oligonucleotide adsorption on the poly(ethyleneimine)-b-poly(N-isopropylacrylamide) (PEI-b-PNIPAm) copolymer layer grafted on a planar surface and nanoparticles with various radii, where the single effect of temperature or pH alone on oligonucleotide adsorption has been extensively investigated, but the combined effect of temperature and pH is less discussed. The theoretical results show that the surface density of the adsorbed oligonucleotides exhibits thermo and pH dual-responsive behavior, in which temperature and pH exhibit a combined effect on the loading capacity of the oligonucleotides. The underlying molecular mechanism of the dual-responsive behavior is revealed. Besides, the effect of important but coupled parameters in nanocarrier design such as polymer surface coverage and length, salt concentration as well as surface curvature (inverse nanoparticle radius) that may influence the dual-responsive behavior of oligonucleotide adsorption is further discussed, which is of great significance to direct the optimal design of PNIPAm/PEI-based nanocarriers to improve the transfection efficiency by achieving the maximal loading capacity of oligonucleotides at different temperatures and pH values.

Transfer Matrix Model of pH Effects in Polymeric Complex Coacervation

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

Molecular Basis for the Morphological Transitions of Surfactant Wormlike Micelles Triggered by Encapsulated Nonpolar Molecules

Surfactant wormlike micelles are prone to experience morphological changes, including the transition to spherical micelles, upon the addition of nonpolar additives. These morphological transitions have profound implications in diverse technological areas, such as the oil and personal-care industries. In this work, additive-induced morphological transitions in wormlike micelles were studied using a molecular theory that predicts the equilibrium morphology and internal molecular organization of the micelles as a function of their composition and the molecular properties of their components. The model successfully captures the transition from wormlike to spherical micelles upon the addition of a nonpolar molecule. Moreover, the predicted effects of the concentration, molecular structure, and degree of hydrophobicity of the nonpolar additive on the wormlike-to-sphere transition are shown to be in good agreement with experimental trends in the literature. The theory predicts that the location of the additive in the micelle (core or hydrophobic-hydrophilic interface) depends on the additive hydrophobicity and content, and the morphology of the micelles. Based on the results of our model, simple molecular mechanisms were proposed to explain the morphological transitions of wormlike micelles upon the addition of nonpolar molecules of different polarities.

On the distribution of hydrophilic polyelectrolytes and their counterions around zwitterionic micelles: the possible impact on the charge density in solution

Despite their charge neutrality, micelles composed of surfactants with zwitterionic headgroups selectively accumulate anions at their hydrophobic core/solution interphase due to electrostatic interactions if headgroup positive moieties are the innermost. This tendency may be markedly enhanced if polyions substitute simple ions. To investigate this possibility, solutions composed of zwitterionic micelles and hydrophilic polyanions have been investigated with Monte Carlo simulations representing the studied systems via primitive electrolyte models. Structural and energetic properties are obtained to highlight the impact of connecting simple ions into polyions on the interactions between electrolytes and micelles. Despite the latter, polyanions conserve their conformational properties. A marked increase in the concentration of charged species inside the micellar corona is, instead, found when polyions are present independently of their charge sign or the headgroup structure. Thus, polyelectrolytes act as "shuttle" for all charged species, with the potential of increasing reactions rates involving the latter due to mass effects. Besides, results for the polyions/micelles mixing free energy and Helmholtz energy profiles indicate that the critical micelle concentration is impacted minimally by hydrophilic polyelectrolytes, an outcome agreeing with experiments. This finding is entirely due to weak enthalpic effects while mixing hydrophilic polyions and micelles. A strong reduction in the screening of the micelle negative charge, acquired following the adsorption of anions in the corona and due to counterions layering just outside it (the so called "chameleon effect"), is forecasted when polyanions substitute monovalent anions.

Topology and Molecular Architecture of Polyelectrolytes Determine Their pH-Responsiveness When Assembled on Surfaces

Polymer composition and topology of surface-grafted polyacids determine the amplitude of their pH-induced swelling transition. The intrinsic steric constraints characterizing cyclic poly(2-carboxypropyl-2-oxazoline) (c-PCPOXA) and poly(2-carboxyethyl-2-oxazoline) (c-PCEOXA) forming brushes on Au surfaces induce an enhancement in repulsive interactions between charged polymer segments upon deprotonation, leading to an amplified expansion and a significant increment in swelling with respect to their linear analogues of similar molar mass. On the other hand, it is the composition of polyacid grafts that governs their hydration in both undissociated and ionized forms, determining the degree of swelling during their pH-induced transition.

Ionization behavior of nanoporous polyamide membranes

Escalating global water scarcity necessitates high-performance desalination membranes, for which fundamental understanding of structure-property-performance relationships is required. In this study, we comprehensively assess the ionization behavior of nanoporous polyamide selective layers in state-of-the-art nanofiltration (NF) membranes. In these films, residual carboxylic acids and amines influence permeability and selectivity by imparting hydrophilicity and ionizable moieties that can exclude coions. We utilize layered interfacial polymerization to prepare physically and chemically similar selective layers of controlled thickness. We then demonstrate location-dependent ionization of carboxyl groups in NF polyamide films. Specifically, only surface carboxyl groups ionize under neutral pH, whereas interior carboxyl ionization requires pH >9. Conversely, amine ionization behaves invariably across the film. First-principles simulations reveal that the low permittivity of nanoconfined water drives the anomalous carboxyl ionization behavior. Furthermore, we report that interior carboxyl ionization could improve the water-salt permselectivity of NF membranes over fourfold, suggesting that interior charge density could be an important tool to enhance the selectivity of polyamide membranes. Our findings highlight the influence of nanoconfinement on membrane transport properties and provide enhanced fundamental understanding of ionization that could enable novel membrane design.

Microphase separation and aggregate self-assembly in brushes of oppositely charged polyelectrolytes triggered by ion pairing

This work applies a molecular theory to study the formation of lateral self-assembled aggregates in mixed brushes composed of polyanion and polycation chains. In order to overcome the well-known limitations of mean-field electrostatics to capture polyelectrolyte complexation, the formation of ion pairs between anionic and cationic groups in the polyelectrolytes is explicitly modeled in our theory as an association reaction. This feature is essential to capture the microphase separation of the mixed brush and the formation of lateral aggregates triggered by polyelectrolyte complexation. The effects of solution pH and ionic strength, surface coverage, and chain length on the morphology of the mixed brush are systematically explored. It is shown that increasing salt concentration leads to the rupture of polyelectrolyte complexes and the stabilization of the homogeneous, non-aggregated brush, providing that the formation of ion pairs between the polyelectrolytes and the salt ions in solution is explicitly accounted for by the theory. The inclusion of ion-pairing association reactions between oppositely charged polyelectrolytes within a mean-field description of electrostatics emerges from this work as a useful and simple theoretical approach to capture the formation of polyelectrolyte complexes and their responsiveness to solution ionic strength and pH.

Charge regulation mechanism in end-tethered weak polyampholytes

Weak polyampholytes, containing oppositely charged dissociable groups, are expected to be responsive to changes in ionic conditions. Here, we determine structural and thermodynamic properties, including the charged groups' degrees of dissociation, of end-tethered weak polyampholyte layers as a function of salt concentration, pH, and the solvent quality. For diblock weak polyampholytes grafted by their acidic blocks, we find that the acidic monomers increase their charge while the basic monomers decrease their charge with decreasing salt concentration for pH values less than the pKa value of both monomers and vice versa when the pH > pKa. This complex charge regulation occurs because the electrostatic attraction between oppositely charged blocks is stronger than the repulsion between monomers with the same charge in both good and poor solvents when the screening by salt ions is weak. This is evidenced by the retraction of the top block into the bottom layer. In the case of poor solvent conditions to the basic block (the top block), we find lateral segregation of basic monomers into micelles, forming a two-dimensional hexagonal pattern on the surface at intermediate and high pH values for monovalent salt concentrations from 0.01 to 0.1 M. When the solvent is poor to both blocks, we find lateral segregation of the grafted acidic block into lamellae with longitudinal undulations of low and high acidic monomer density. By exploiting weak block polyampholytes, our work expands the parameter space for creating responsive surfaces stable over a wide range of pH and salt concentration.

Theoretical Modeling of Chemical Equilibrium in Weak Polyelectrolyte Layers on Curved Nanosystems

Surface functionalization with end-tethered weak polyelectrolytes (PE) is a versatile way to modify and control surface properties, given their ability to alter their degree of charge depending on external cues like pH and salt concentration. Weak PEs find usage in a wide range of applications, from colloidal stabilization, lubrication, adhesion, wetting to biomedical applications such as drug delivery and theranostics applications. They are also ubiquitous in many biological systems. Here, we present an overview of some of the main theoretical methods that we consider key in the field of weak PE at interfaces. Several applications involving engineered nanoparticles, synthetic and biological nanopores, as well as biological macromolecules are discussed to illustrate the salient features of systems involving weak PE near an interface or under (nano)confinement. The key feature is that by confining weak PEs near an interface the degree of charge is different from what would be expected in solution. This is the result of the strong coupling between structural organization of weak PE and its chemical state. The responsiveness of engineered and biological nanomaterials comprising weak PE combined with an adequate level of modeling can provide the keys to a rational design of smart nanosystems.

Liquid Phase Separation Controlled by pH

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

Triggering doxorubicin release from responsive hydrogel films by polyamine uptake

Polyamines such as putrescine, spermidine and spermine are required in many inter- and intra-cellular processes. There is, however, evidence of anomalously high concentrations of these polyamines around cancer cells. Furthermore, high polyamine concentrations play a key role in accelerating the speed of cancer proliferation. Some current therapies target the reduction of the polyamine concentration to delay the cancer advance. In this study, we use a molecular theory to prove the concept that poly(methacrylic acid) (PMAA) hydrogels can play the dual role of incorporating and retaining polyamines as well as releasing preloaded drugs in response. Towards such a goal, we have developed a molecular model for each of the chemical species, which includes the shape, size, charge, protonation state, and configuration. Our results indicate that PMAA hydrogel films can incorporate significant amounts of polyamines; this absorption increases with the solution concentration of the polyamines. Doxorubicin was chosen as a model drug for this study, which can be successfully incorporated within the film; the optimal encapsulation conditions occur at low salt concentrations and pH values near neutral. Polyamine absorption within the film results in the desorption of the drug from the hydrogel. An increase in the concentration of the polyamines enhances the drug release. To validate our theoretical findings, poly(methacrylic acid) hydrogel thin films were synthesized by atom transfer radical polymerization. Absorption/desorption experiments followed by UV-Vis spectroscopy demonstrate doxorubicin encapsulation within these films and polyamine-dependent drug release.

Modeling the nucleoporins that form the hairy pores

Sitting on the nuclear envelope, nuclear pore complexes (NPCs) control the molecular transport between the nucleus and the cytoplasm. Without definite open or close states, the NPC uses a family of intrinsically disordered nucleoporins called FG-Nups to construct a selective permeability barrier whose functional structure is unclear. Experimental advances have offered high-resolution molecular knowledge of the NPC scaffold and docking of the unfolded FG-Nups, however, the ‘hairy’ barrier structure still appears as blurred lobes even under the state-of-the-art microscopy. Without accurate experimental visualization, the molecular mechanism for the NPC-mediated transport remains a matter of debate. Modeling provides an alternative way to resolve this long-standing mystery. Here, we briefly review different methods employed in modeling the FG-Nups, arranging from all-atom molecular dynamics to mean-field theories. We discuss the advantage and limit of each modeling technique, and summarize the theoretical insights that, despite certain controversy, deepened our understanding of the hairy pore.

The Phase Behavior of Nanoparticle Superlattices in the Presence of a Solvent

Superlattices of nanoparticles coated by alkyl-chain ligands are usually prepared from a stable solution by evaporation, therefore the pathway of superlattice self-assembly critically depends on the amount of solvent present within it. This work addresses the role of the solvent on the structure and the relative stability of the different supercrystalline phases of single-component superlattices (simple cubic, body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed). The study is performed with a molecular theory for nanoparticle superlattices introduced in this work, which predicts the structure and thermodynamics of the supercrystals explicitly treating the presence and molecular details of the solvent and the ligands. The theory predicts a FCC-BCC transition with decreasing solvent content due to the competition between the translational entropy of the solvent and the entropy and internal energy of the ligands. This result provides an explanation for recent experimental observations by in situ X-ray scattering, which reported a FCC-BCC transition during solvent evaporation. The theory also predicts the effects of the length and surface coverage of the ligands and the radius of the core on the phase behavior in agreement with experimental evidence and previous molecular dynamics simulations. These results validate the use of the dimensionless softness parameter λ (ratio of ligand length to core radius) to predict the phase behavior of wet superlattices. Our results stress the importance of explicitly considering the presence of the solvent in order to reach a complete picture of the mechanisms that mediate the self-assembly of nanoparticle superlattices.

Fabrication and in situ functionalisation of mesoporous silica films by the physical entrapment of functional and responsive block copolymer structuring agents

Stimuli-responsive mesoporous silica films were prepared by evaporation-induced self-assembly through the physical entrapment of a functional block copolymer structuring agent, which simultaneously serves to functionalise the mesopore. These polymer-silica hybrid materials exhibit remarkable ionic permselectivity under highly filled conditions, and offer the potential for local polymer functionalisation for enhanced and tunable ionic permselectivity. This innovative and simple approach for the in situ functionalisation of mesoporous silica has the potential to improve how we approach the design of complex architectures at the nanoscale for enhanced transport, and is thus relevant for a variety of technologies based on molecular transport in nanoscale pores including separation, sensing, catalysis, and energy conversion.

Simulations of ionization equilibria in weak polyelectrolyte solutions and gels

This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels. We start out by reviewing the essential thermodynamics of ionization and show how the weak polyelectrolyte ionization differs from the ionization of simple weak acids and bases. Next, we describe simulation methods for ionization reactions, focusing on two methods: the constant-pH ensemble and the reaction ensemble. After discussing the advantages and limitations of both methods, we review the existing simulation literature. We discuss coarse-grained simulations of weak polyelectrolytes with respect to ionization equilibria, conformational properties, and the effects of salt, both in good and poor solvent conditions. This is followed by a discussion of branched star-like weak polyelectrolytes and weak polyelectrolyte gels. At the end we touch upon the interactions of weak polyelectrolytes with other polymers, surfaces, nanoparticles and proteins. Although proteins are an important class of weak polyelectrolytes, we explicitly exclude simulations of protein ionization equilibria, unless they involve protein-polyelectrolyte interactions. Finally, we try to identify gaps and open problems in the existing simulation literature, and propose challenges for future development.

Explicit Ion Effects on the Charge and Conformation of Weak Polyelectrolytes

The titration behavior of weak polyelectrolytes is of high importance, due to their uses in new technologies including nanofiltration and drug delivery applications. A comprehensive picture of polyelectrolyte titration under relevant conditions is currently lacking, due to the complexity of systems involved in the process. One must contend with the inherent structural and solvation properties of the polymer, the presence of counterions, and local chemical equilibria enforced by background salt concentration and solution acidity. Moreover, for these cases, the systems of interest have locally high concentrations of monomers, induced by polymer connectivity or confinement, and thus deviate from ideal titration behavior. This work furthers knowledge in this limit utilizing hybrid Monte Carlo⁻Molecular Dynamics simulations to investigate the influence of salt concentration, pK a , pH, and counterion valence in determining the coil-to-globule transition of poorly solvated weak polyelectrolytes. We characterize this transition at a range of experimentally relevant salt concentrations and explicitly examine the role multivalent salts play in determining polyelectrolyte ionization behavior and conformations. These simulations serve as an essential starting point in understanding the complexation between weak polyelectrolytes and ion rejection of self-assembled copolymer membranes.

Electrostatically Driven Protein Adsorption: Charge Patches versus Charge Regulation

The mechanisms of electrostatically driven adsorption of proteins on charged surfaces are studied with a new theoretical framework. The acid-base behavior, charge distribution, and electrostatic contributions to the thermodynamic properties of the proteins are modeled in the presence of a charged surface. The method is validated against experimental titration curves and apparent p K_as. The theory predicts that electrostatic interactions favor the adsorption of proteins at their isoelectric points on charged surfaces despite the fact that the protein has no net charge in solution. Two known mechanisms explain adsorption under these conditions: (i) charge regulation (the charge of the protein changes due to the presence of the surface) and (ii) charge patches (the protein orients to place charged amino acids near opposite surface charges). This work shows that both mechanisms contribute to adsorption at low ionic strengths, whereas only the charge-patch mechanism operates at high ionic strength. Interestingly, the contribution of charge regulation is insensitive to protein orientation under all conditions, which validates the use of constant-charge simulations to determine the most stable orientation of adsorbed proteins. The present study also shows that the charged surface can induce large shifts in the apparent p K_as of individual amino acids in adsorbed proteins. Our conclusions are valid for all proteins studied in this work (lysozyme, α-amylase, ribonuclease A, and β-lactoglobulin), as well as for proteins that are not isoelectric but have instead a net charge in solution of the same sign as the surface charge, i.e. the problem of protein adsorption on the "wrong side" of the isoelectric point.

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.