Orientational Pathways during Protein Translocation through Polymer-Modified Nanopores.

Protein translocation through nanopores holds significant promise for applications in biotechnology, biomolecular analysis, and medicine. However, the interpretation of signals generated by the translocation of the protein remains challenging. In this way, it is crucial to gain a comprehensive understanding on how macromolecules translocate through a nanopore and to identify what are the critical parameters that govern the process. In this study, we investigate the interplay between protein charge regulation, orientation, and nanopore surface modifications using a theoretical framework that allows us to explicitly take into account the acid-base reactions of the titrable amino acids in the proteins and in the polyelectrolytes grafted to the nanopore surface. Our goal is to thoroughly characterize the translocation process of different proteins (GFP, ß-lactoglobulin, lysozyme, and RNase) through nanopores modified with weak polyacids. Our calculations show that the charge regulation mechanism exerts a profound effect on the translocation process. The pH-dependent interactions between proteins and charged polymers within the nanopore lead to diverse free energy landscapes with barriers, wells, and flat regions dictating translocation efficiency. Comparison of different proteins allows us to identify the significance of protein isoelectric point, size, and morphology in the translocation behavior. Taking advantage of these insights, we propose pH-responsive nanopores that can load proteins at one pH and release them at another, offering opportunities for controlled protein delivery, separation, and sensing applications.

Solvent Isotherms and Structural Transitions in Nanoparticle Superlattice Assembly.

We introduce a Molecular Theory for Compressible Fluids (MOLT-CF) that enables us to compute free energies and other thermodynamic functions for nanoparticle superlattices with any solvent content, including the dry limit. Quantitative agreement is observed between MOLT-CF and united-atom molecular dynamics simulations performed to assess the reliability and precision of the theory. Among other predictions, MOLT-CF shows that the amount of solvent within the superlattice decreases approximately linearly with its vapor pressure and that in the late stages of drying, solvent-filled voids form at lattice interstitials. Applied to single-component superlattices, MOLT-CF predicts fcc-to-bcc Bain transitions for decreasing vapor pressure and for increasing ligand length, both in agreement with experimental results. We explore the stability of other single-component phases and show that the C14 Frank-Kasper phase, which has been reported in experiments, is not a global free-energy minimum. Implications for precise assembly and prediction of multicomponent nanoparticle systems are discussed.

Phase Behavior and Electrochemical Properties of Highly Asymmetric Redox Coacervates.

This work reports the phase behavior and electrochemical properties of liquid coacervates made of ferricyanide and poly(ethylenimine). In contrast to the typical polyanion/polycation pairs used in liquid coacervates, the ferricyanide/poly(ethylenimine) system is highly asymmetric because poly(ethylenimine) has approximately 170 charges per molecule, while ferricyanide has only 3. Two types of phase diagrams were measured and fitted with a theoretical model. In the first type of diagram, the stability of the coacervate was studied in the plane given by the concentration of poly(ethylenimine) versus the concentration of ferricyanide for a fixed concentration of added monovalent salt (NaCl). The second type of diagram involved the plane given by the concentration of poly(ethylenimine) vs the concentration of the added monovalent salt for a fixed poly(ethyleneimine)/ferricyanide ratio. Interestingly, these phase diagrams displayed qualitative similarities to those of symmetric polyanion/polycation systems, suggesting that coacervates formed by a polyelectrolyte and a small multivalent ion can be treated as a specific case of polyelectrolyte coacervate. The characterization of the electrochemical properties of the coacervate revealed that the addition of monovalent salt greatly enhances charge transport, presumably by breaking ion pairs between ferricyanide and poly(ethylenimine). This finding highlights the significant influence of added salt on the transport properties of coacervates. This study provides the first comprehensive characterization of the phase behavior and transport properties of asymmetric coacervates and places these results within the broader context of the better-known symmetric polyelectrolyte coacervates.

Revisiting the Mechanisms of Charge Transport in Solutions of Redox-Active Molecules Using Computer Simulations: When and Why Do Analytical Theories Fail?

Understanding charge transport is essential for the development of energy-storage applications. This work introduces a new theoretical methodology to model diffusive charge transport in solutions of redox-active molecules by combining Langevin dynamics for the spatial degrees of freedom and a master-equation formalism to describe the electron-hopping events between redox molecules. The model is used to analyze the effects of the concentration of the redox molecules and the strength of the intermolecular interactions on the charge-transport mechanism. In the past, the rate of charge transport has been modeled with the analytical Dahms-Ruff equation; however, this is a mean-field equation, whose range of validity has not been tested with less approximate theories. We show that the Dahms-Ruff equation fails to quantitatively predict the diffusion coefficient for charge transport for large concentrations of the redox species and high bimolecular electron-transfer rates, i.e., the most relevant conditions for energy-storage applications. Under these conditions, the diffusion coefficient for charge transport obtained from simulations is larger than that predicted from the Dahm-Ruff equation because of the formation of transient clusters of redox molecules. Also, intermolecular interactions, which are not taken into account by the Dahms-Ruff equation, play a central role in the charge transport of redox species. We show that the apparent diffusion coefficient experiences a maximum with respect to the strength of the intermolecular attractions. This maximum is traced back to the formation of clusters and their two opposite effects on the diffusion coefficient: electron hopping is fast within a cluster but inefficient between neighboring clusters.

Polyelectrolyte-multivalent molecule complexes: physicochemical properties and applications.

The complexation of polyelectrolytes with other oppositely charged structures gives rise to a great variety of functional materials with potential applications in a wide spectrum of technological fields. Depending on the assembly conditions, polyelectrolyte complexes can acquire different macroscopic configurations such as dense precipitates, nanosized colloids and liquid coacervates. In the past 50 years, much progress has been achieved to understand the principles behind the phase separation induced by the interaction of two oppositely charged polyelectrolytes in aqueous solutions, especially for symmetric systems (systems in which both polyions have similar molecular weight and concentration). However, in recent years, the complexation of polyelectrolytes with alternative building blocks such as small charged molecules (multivalent inorganic species, oligopeptides, and oligoamines, among others) has gained attention in different areas. In this review, we discuss the physicochemical characteristics of the complexes formed by polyelectrolytes and multivalent small molecules, putting a special emphasis on their similarities with the well-known polycation-polyanion complexes. In addition, we analyze the potential of these complexes to act as versatile functional platforms in various technological fields, such as biomedicine and advanced materials engineering.

Molecular Theory: A Tool for Predicting the Outcome of Self-Assembly of Polymers, Nanoparticles, Amphiphiles, and Other Soft Materials.

The supramolecular organization of soft materials, such as colloids, polymers, and amphiphiles, results from a subtle balance of weak intermolecular interactions and entropic forces. This competition can drive the self-organization of soft materials at the nano-/mesoscale. Modeling soft-matter self-assembly requires, therefore, considering a complex interplay of forces at the relevant length scales without sacrificing the molecular details that define the chemical identity of the system. This mini-review focuses on the application of a tool known as molecular theory to study self-assembly in different types of soft materials. This tool is based on extremizing an approximate free energy functional of the system, and, therefore, it provides a direct, computationally affordable estimation of the stability of different self-assembled morphologies. Moreover, the molecular theory explicitly incorporates structural details of the chemical species in the system, accounts for their conformational degrees of freedom, and explicitly includes their chemical equilibria. This mini-review introduces the general ideas behind the theoretical formalism and discusses its advantages and limitations compared with other theoretical tools commonly used to study self-assembled soft materials. Recent application examples are discussed: the self-patterning of polyelectrolyte brushes on planar and curved surfaces, the formation of nanoparticle (NP) superlattices, and the self-organization of amphiphiles into micelles of different shapes. Finally, prospective methodological improvements and extensions (also relevant for related theoretical tools) are analyzed.

Mechanisms of Enzymatic Transduction in Nanochannel Biosensors.

The immobilization of enzymes in solid-state nanochannels is a new avenue for the design of biosensors with outstanding selectivity and sensitivity. This work reports the first theoretical model of an enzymatic nanochannel biosensor. The model is applied to the system previously experimentally studied by Lin, et al. (Anal. Chem. 2014, 86, 10546): a hourglass nanochannel modified by glucose oxidase for the detection of glucose. Our predictions are in good agreement with experimental observations as a function of the applied potential, pH and glucose concentration. The sensing mechanism results from the combination of three processes: i) the establishment of a steady-state proton concentration gradient due to a reaction-diffusion mechanism, ii) the effect of that gradient on the charge of the adsorbed enzymes and native surface groups, and iii) the effect of the resulting surface charge on the ionic current. Strategies to improve the sensor performance based on this mechanism are identified and discussed.

Body centered tetragonal nanoparticle superlattices: why and when they form?

Body centered tetragonal (BCT) phases are structural intermediates between body centered cubic (BCC) and face centered cubic (FCC) structures. However, BCC ↔ FCC transitions may or may not involve a stable BCT intermediate. Interestingly, nanoparticle superlattices usually crystallize in BCT structures, but this phase is much less frequent for colloidal crystals of micrometer-sized particles. Two origins have been proposed for the formation of BCT NPSLs: (i) the influence of the substrate on which the nanoparticle superlattice is deposited, and (ii) non-spherical nanoparticle shapes, combined with the fact that different crystal facets have different ligand organizations. Notably, none of these two mechanisms alone is able to explain the set of available experimental observations. In this work, these two hypotheses were independently tested using a recently developed molecular theory for nanoparticle superlattices that explicitly captures the degrees of freedom associated with the ligands on the nanoparticle surface and the crystallization solvent. We show that the presence of a substrate can stabilize the BCT structure for spherical nanoparticles, but only for very specific combinations of parameters. On the other hand, a truncated-octahedron nanoparticle shape strongly stabilizes BCT structures in a wide region of the phase diagram. In the latter case, we show that the stabilization of BCT results from the geometry of the system and it does not require different crystal facets to have different ligand properties, as previously proposed. These results shed light on the mechanisms of BCT stabilization in nanoparticle superlattices and provide guidelines to control its formation.

Scission energies of surfactant wormlike micelles loaded with nonpolar additives.

HYPOTHESIS: The previously observed effects of nonpolar additives on the scission energy and rheological properties of surfactant wormlike micelles can be explained in terms of the spatial distribution of the additive within the micelles. The dependence of the scission energy with the molecular organization of the system can be analyzed with a molecular theory capable of describing the thermodynamics and structure of the micelles. THEORY: A new theoretical method to determine the scission energy of surfactant wormlike micelles is introduced. This methodology is based on a molecular theory that explicitly considers molecular details of all components of the micelles, and their inter- and intramolecular interactions without the use of fitting and/or empirical macroscopic parameters. FINDINGS: The predicted effects of the concentration, molecular structure and hydrophobicity of the additive on the scission energy of cetyltrimethylammonium bromide (CTAB) wormlike micelles are found to be in qualitative agreement with previous experimental observations. In particular, our theory captures the decrease of micellar length with increasing content of highly hydrophobic additives and the non-monotonic dependence of the viscosity with additive hydrophobicity. The latter effect arises because highly and mildly hydrophobic additives affect the scission energy of wormlike micelles via markedly different molecular mechanisms.

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.

Nanopore gates via reversible crosslinking of polymer brushes: a theoretical study.

Polymer-brush-modified nanopores are synthetic structures inspired by the gated transport exhibited by their biological counterparts. This work theoretically analyzes how the reversible crosslinking of a polymer network by soluble species can be used to control transport through nanochannels and pores. The study was performed with a molecular theory that allows inhomogeneities in the three spatial dimensions and explicitly takes into account the size, shape and conformations of all molecular species, considers the intermolecular interactions between the polymers and the soluble crosslinkers and includes the presence of a translocating particle inside the pore. It is shown than increasing the concentration of the soluble crosslinkers in bulk solution leads to a gradual increase of its number within the pore until a critical bulk concentration is reached. At the critical concentration, the number of crosslinkers inside the pore increases abruptly. For long chains, this sudden transition triggers the collapse of the polymer brush to the center of the nanopore. The resulting structure increases the free-energy barrier that a translocating particle has to surmount to go across the pore and modifies the route of translocation from the axis of the pore to its walls. On the other hand, for short polymer chains the crosslinkers trigger the collapse of the brush to the pore walls, which reduces the translocation barrier.

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.

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.

Redox-active polyamine-salt aggregates as multistimuli-responsive soft nanoparticles.

Polyamine-salt aggregates have become promising soft materials in nanotechnology due to their easy preparation process and pH-responsiveness. Here, we report the use of hexacyanoferrate(ii) and hexacyanoferrate(iii) as electroactive crosslinking agents for the formation of nanometer-sized redox-active polyamine-redox-salt aggregates (rPSA) in bulk suspension. This nanoplatform can be selectively assembled or disassembled under different stimuli such as redox environment, pH and ionic strength. By changing the charge of the building blocks, external triggers allow switching the system between two phase states: aggregate-free solution or colloidal rPSA dispersion. The stimuli-activated modulation of the assembly/disassembly processes opens a path to exploit rPSA in technologies based on smart nanomaterials.

Twisting of Charged Nanoribbons to Helicoids Driven by Electrostatics.

Charged amphiphiles in solution usually self-assemble into flat nanoribbons that spontaneously twist into different shapes. The role of electrostatics in this process is still under strong debate. This work studies the electrostatic free energy of twisting a nanoribbon at the level of the nonlinear Poisson-Boltzmann approximation. It is shown that helicoid-shaped ribbons are more stable than flat ribbons, while other shapes under consideration (cylindrical helixes and bent ribbons) are always less stable than the flat ribbon. The unexpected electrostatics-driven twisting of the ribbon into a helicoid is ascribed to the increase in its perimeter with increasing degree of twisting, as charges near the edge of the ribbon are electrostatically more stable than those near its center. This argument successfully explains the effects of salt concentration and the width of the ribbon on the optimal twisting period and allows us to approximately describe the problem of ribbon twisting in terms of two dimensionless variables that combine the helicoid twisting period, the Debye length of the solution, and the width of the ribbon. The magnitude of the electrostatic twisting energy predicted by our calculations is comparable to that of restoring elastic forces for typical ribbons of self-assembled amphiphiles, which indicates that electrostatics plays an important role in determining the equilibrium shape of charged nanoribbons.

Insulin Delivery from Glucose-Responsive, Self-Assembled, Polyamine Nanoparticles: Smart "Sense-and-Treat" Nanocarriers Made Easy.

Polyamine-salt aggregates (PSA) are biomimetic soft materials that have attracted great attention due to their straightforward fabrication methods, high drug-loading efficiencies, and attractive properties for pH-triggered release. Herein, a simple and fast multicomponent self-assembly process was used to construct cross-linked poly(allylamine hydrochloride)/phosphate PSAs (hydrodynamic diameter of 360 nm) containing glucose oxidase enzyme, as a glucose-responsive element, and human recombinant insulin, as a therapeutic agent for the treatment of diabetes mellitus (GI-PSA). The addition of increasing glucose concentrations promotes the release of insulin due to the disassembly of the GI-PSAs triggered by the catalytic in situ formation of gluconic acid. Under normoglycemia, the GI-PSA integrity remained intact for at least 24 h, whereas hyperglycemic conditions resulted in 100 % cargo release after 4 h of glucose addition. This entirely supramolecular strategy presents great potential for the construction of smart glucose-responsive delivery nanocarriers.

Multitasking polyamine/ferrioxalate nano-sized assemblies: thermo-, photo-, and redox-responsive soft materials made easy.

Responsive nanomaterials have emerged as key components in materials sciences. Herein, we report the one-step preparation of multi-stimuli responsive polyamine-salt aggregates (PSA) by ionically crosslinking polyethylenimine with potassium ferrioxalate (FeOx). The unique properties of FeOx enables a novel class of soft nanomaterial that disassembles by exposure to light, reducing environments and temperature.

Interpolymer complexes of poly(sulfonic acid)s and poly(ethylene oxide): an unexpected association.

The formation of novel interpolymer complexes (IPCs) between poly(sulfonic acid)s and poly(ethylene oxide) (PEO) is reported. The complexes were precipitated from polymer mixtures in aqueous solution and deposited on surfaces as layer-by-layer films. Based on evidence from infrared spectroscopy, the interpolymer association in poly(sulfonic acid)/PEO IPCs is ascribed to hydrogen bonding between the sulfonic acid and the ether in PEO. This interaction is not anticipated because sulfonic acids are fully dissociated in aqueous solutions due to their strong acidity. Theoretical calculations suggest that the unexpected association of PEO and poly(sulfonic acid)s results from the formation of very strong sulfonic-acid/ether hydrogen bonds, which increase the apparent pKas of the poly(sulfonic acid)s and, therefore, decrease the net charge of these polymers. It is shown that while poly(styrene sulfonic acid) (PSSA) and Nafion form IPCs with PEO, poly(vinyl sulfonic acid) (PVSA) does not. This result is explained in terms of the hydrodrophobic nature of PSSA and Nafion, which stabilizes their IPCs, and the fact that hydrogen bonds in PSSA/PEO IPCs are predicted to be stronger than in PVSA/PEO IPCs.

Polyamine Colloids Cross-Linked with Phosphate Ions: Towards Understanding the Solution Phase Behavior.

Ionically crosslinked poly(allylamine)/phosphate (PAH/Pi) colloids consist of self-assembled nanostructures stabilized by supramolecular interactions. Under physiological conditions, these interactions should be present at high ionic strength and only in a narrow pH window to be effective as drug delivery agents. In this work we study the effect of the pH and ionic strength in the chemical behaviour of inorganic phosphate (Pi), poly(allylamine hydrochloride) (PAH) and their mixture in aqueous solution (PAH-Pi). By combination of experimental measurements and a theoretical model, we demonstrate that the driving force that leads to the formation of colloids is the electrostatic pairing between the positively charged amino groups in PAH and negatively charged HPO42- ions. Increasing the ionic strength of the system by addition of KCl weakens the PAH-Pi interactions and narrows the pH stability window from 4 to 1.8 pH units. In addition, a fully reversible system was obtained in which the colloids assemble and disassemble by changing the pH between 6.8 and 7.1 at high ionic strength, making them suitable for use as pH-responsive nanocarriers.

Charge percolation in redox-active thin membrane hybrids of mesoporous silica and poly(viologens).

This work reports the fabrication of redox-active films of oligomeric and molecular viologens and mesoporous silica via the infiltration method. Pore-ellipsometry and UV-vis confirm that low-molecular-weight poly(viologens) in solution are able to enter the mesoporous structure, in contrast to high-molecular weight polymers that adsorb only on top of the film. Cyclic voltammetry shows that viologens are able to reach the bottom of the pores and access the electrode/film interface. However, the number of viologen sites that can be accessed by cyclic voltammetry at 50 mV s-1 is only a tenth of the total viologen population determined by UV-vis and pore-ellipsometry. The effect is ascribed to the very small apparent diffusion coefficient for charge transport within the film (Dapp < 10-12 cm2 s-1). A theoretical model is put forward to describe charge transport via the electron-hopping mechanism for redox sites randomly adsorbed on the inner walls of the pores. Our model predicts that the threshold of charge percolation occurs for viologen surface coverages close to those observed in our experiments; therefore, the low fraction of electrochemically addressable viologens is ascribed to inefficient charge percolation via the electron-hopping mechanism.