3D Printing of Aqueous Two-Phase Systems with Linear and Bottlebrush Polyelectrolytes.

We formed core-shell-like polyelectrolyte complexes (PECs) from an anionic bottlebrush polymer with poly (acrylic acid) side chains with a cationic linear poly (allylamine hydrochloride). By varying the pH, the number of side chains of the polyanionic BB polymers (Nbb), the charge density of the polyelectrolytes, and the salt concentration, the phase separation behavior and salt resistance of the complexes could be tuned by the conformation of the BBs. By combining the linear/bottlebrush polyelectrolyte complexation with all-liquid 3D printing, flow-through tubular constructs were produced that showed selective transport across the PEC membrane comprising the walls of the tubules. These tubular constructs afford a new platform for flow-through delivery systems.

Electro-osmotic flow in nanoconfinement: Solid-state and protein nanopores.

Electro-osmotic flow (EOF) is a phenomenon where fluid motion occurs in porous materials or micro/nano-channels when an external electric field is applied. In the particular example of single-molecule electrophoresis using single nanopores, the role of EOF on the translocation velocity of the analyte molecule through the nanopore is not fully understood. The complexity arises from a combination of effects from hydrodynamics in restricted environments, electrostatics emanating from charge decorations and geometry of the pores. We address this fundamental issue using the Poisson-Nernst-Planck and Navier-Stokes (PNP-NS) equations for cylindrical solid-state nanopores and three representative protein nanopores (α-hemolysin, MspA, and CsgG). We present the velocity profiles inside the nanopores as a function of charge decoration and geometry of the pore and applied electric field. We report several unexpected results: (a) The apparent charges of the protein nanopores are different from their net charge and the surface charge of the whole protein geometry, and the net charge of inner surface is consistent with the apparent charge. (b) The fluid velocity depends non-monotonically on voltage. The three protein nanopores exhibit unique EOF and velocity-voltage relations, which cannot be simply deduced from their net charge. Furthermore, effective point mutations can significantly change both the direction and the magnitude of EOF. The present computational analysis offers an opportunity to further understand the origins of the speed of transport of charged macromolecules in restricted space and to design desirable nanopores for tuning the speed of macromolecules through nanopores.

Stability of sectored morphologies of polymer lamellae.

When a solution of interpenetrating and entangled long flexible polymer chains is cooled to low enough temperatures, the chains crystallize into thin lamellae of nanoscopic thickness and microscopic lateral dimensions. Depending on the nature of the solvent and growth conditions, the lamellae exhibit several sectors that have differing growth kinetics and melting temperatures. Remarkably, these lamellae can spontaneously form tentlike morphology. The experimentally well-documented phenomenology of lamellar sectorization and tent formation has so far eluded a fundamental understanding of their origins. We present a theoretical model to explain this longstanding challenge and derive conditions for the relative stabilities of planar, sectored, and tent morphologies for polymer lamellae in terms of their elastic constants and interfacial tensions. While the present model offers an explanation of the origin of the spontaneous formation of sectored tentlike morphology as well as sectored planar morphology, in contrast to planar unsectored morphology, predictions are made for morphology transformations based on the materials properties of the polymeric lamellae.

Fluctuations, structure, and size inside coacervates.

Aqueous solutions of oppositely charged macromolecules exhibit the ubiquitous phenomenon of coacervation. This subject is of considerable current interest due to numerous biotechnological applications of coacervates and the general premise of biomolecular condensates. Towards a theoretical foundation of structural features of coacervates, we present a field-theoretic treatment of coacervates formed by uniformly charged flexible polycations and polyanions in an electrolyte solution. We delineate different regimes of polymer concentration fluctuations and structural features of coacervates based on the concentrations of polycation and polyanion, salt concentration, and experimentally observable length scales. We present closed-form formulas for correlation length of polymer concentration fluctuations, scattering structure factor, and radius of gyration of a labelled polyelectrolyte chain inside a concentrated coacervate. Using random phase approximation suitable for concentrated polymer systems, we show that the inter-monomer electrostatic interaction is screened by interpenetration of all charged polymer chains and that the screening length depends on the individual concentrations of the polycation and the polyanion, as well as the salt concentration. Our calculations show that the scattering intensity decreases monotonically with scattering wave vector at higher salt concentrations, while it exhibits a peak at intermediate scattering wave vector at lower salt concentrations. Furthermore, we predict that the dependence of the radius of gyration of a labelled chain on its degree of polymerization generally obeys the Gaussian chain statistics. However, the chain is modestly swollen, the extent of which depending on polyelectrolyte composition, salt concentration, and the electrostatic features of the polycation and polyanion such as the degree of ionization.

Substantial Slowing of Electrophoretic Translocation of DNA through a Nanopore Using Coherent Multiple Entropic Traps.

One of the major challenges in the technology of sequencing DNA using single-molecule electrophoresis through a nanopore is to control the translocation of the macromolecule across the pore in order to allow sufficient time for accurate sequence reading at limited recording bandwidths. If the translocation speed is too fast, the signatures of the bases passing through the sensing region of the nanopore overlap in time, presenting difficulties in accurately identifying the bases in a sequential manner. Even though several strategies, such as enzyme ratcheting, have been implemented to reduce the translocation speed, the challenge to achieve a substantial reduction in the translocation speed continues to be of paramount significance. Toward achieving this goal, we have fabricated a nonenzymatic hybrid device that can reduce the translocation speed of long DNAs by more than 2 orders of magnitude, in comparison with the current status of the art. This device is made of a tetra-PEG hydrogel that is chemically anchored to the donor side of a solid-state nanopore. The idea behind this device is based on the recent discovery of the topologically frustrated dynamical state of confined polymers, whereby the front hydrogel matter of the hybrid device provides multiple entropic traps for a single DNA molecule holding it back against the electrophoretic driving force that pulls the DNA through the solid-state nanopore portion of the device. As a demonstration of slowing DNA translocation by a factor of about 500, we find the average translocation time realized in the present hybrid device for 3 kbp DNA as 23.4 ms, whereas the corresponding time for the bare solid-state nanopore under otherwise identical conditions is 0.047 ms. Our measurements on 1 kbp DNA and λ-DNA show that such a slowing down of DNA translocation with our hybrid device is general. An additional feature of our hybrid device is its incorporation of all features of the conventional gel electrophoresis to separate different DNA sizes in a clump of DNAs and to streamline them in an orderly and slow manner into the nanopore. Our results suggest the high potential of our hydrogel-nanopore hybrid device in further advancing the single-molecule electrophoresis technology to accurately sequence very large biological polymers.

Dipole-driven interlude of mesomorphism in polyelectrolyte solutions.

Uniformly charged polyelectrolyte molecules disperse uniformly in aqueous electrolyte solutions, due to electrostatic repulsion between them. In stark contrast to this well-established result of homogeneous polyelectrolyte solutions, we report a phenomenon where an aqueous solution of positively charged poly(L-lysine) (PLL) exhibits precipitation of similarly charged macromolecules at low ionic strength and a homogeneous solution at very high ionic strength, with a stable mesomorphic state of spherical aggregates as an interlude between these two limits. The precipitation at lower ionic strengths that is orthogonal to the standard polyelectrolyte behavior and the emergence of the mesomorphic state are triggered by the presence of a monovalent small organic anion, acrylate, in the electrolyte solution. Using light scattering, we find that the hydrodynamic radius Rh of isolated PLL chains shrinks upon a decrease in electrolyte (NaBr) concentration, exhibiting the "anti-polyelectrolyte effect." In addition, Rh of the aggregates in the mesomorphic state depends on PLL concentration cp according to the scaling law, [Formula: see text]. Furthermore, at higher PLL concentration, the mesomorphic aggregates disassemble by a self-poisoning mechanism. We conjecture that all these findings can be attributed to both intra- and interchain dipolar interactions arising from the transformation of polycationic PLL into a physical polyzwitterionic PLL at higher concentrations of acrylate. The reported phenomenon of PLL exhibiting dipole-directed assembly of mesomorphic states and the anti-polyelectrolyte effect are of vital importance toward understanding more complex situations such as coacervation and formation of biomolecular condensates.

Coacervation in polyzwitterion-polyelectrolyte systems and their potential applications for gastrointestinal drug delivery platforms.

Traditionally, complex coacervation is regarded as a process whereby two oppositely charged polyelectrolytes self-assemble into spherical droplets. Here, we introduce the polyzwitterionic complex, "pZC", formed by the liquid-liquid phase separation of a polyzwitterion and a polyelectrolyte, and elucidate a mechanism by which such complexes can assemble using theory and experimental evidence. This system exhibits orthogonal phase behavior-it remains intact in acidic conditions, but disassembles as the pH increases, a process governed by the acid-base equilibria of the constituent chains. We relate the observed phase behavior to physiological conditions within the gastrointestinal tract with a simulation of the gastroduodenal junction, and demonstrate using video microscopy the viability of polyzwitterionic coacervates as technologies for the pH-triggered release of cargo. Such a system is envisaged to tackle imminent problems of drug transport via the oral route and serve as a packaging solution to increase uptake efficiency.

Zwitterionic Ammonium Sulfonate Polymers: Synthesis and Properties in Fluids.

Polymer zwitterions continue to emerge as useful materials for numerous applications, ranging from hydrophilic and antifouling coatings to electronic materials interfaces. While several polymer zwitterion compositions are now well established, interest in this field of soft materials science has grown rapidly in recent years due to the introduction of new structures that diversify their chemistry and architecture. Nonetheless, at present, the variation of the chemical composition of the anionic and cationic components of zwitterionic structures remains relatively limited to a few primary examples. In this article, the versatility of 4-vinylbenzyl sultone as a precursor to ammonium sulfonate zwitterionic monomers, which are then used in controlled free radical polymerization chemistry to afford "inverted sulfobetaine" polymer zwitterions, is highlighted. An evaluation of the solubility, interfacial activity, and solution configuration of the resultant polymers reveals the dependence of properties on the selection of tertiary amines used for nucleophilic ring-opening of the sultone precursor, as well as useful properties comparisons across different zwitterionic compositions.

Theory of ionic conductivity with morphological control in polymers.

We present a general theory of ionic conductivity in polymeric materials consisting of percolated ionic pathways. Identifying two key length scales corresponding to inter-path permeation distance ξ and one-dimensional hopping conduction path length mλ, we have derived closed-form formulas in terms of the energy U required to unbind a conductive ion from its bound state and the partition ratio ξ/mλ between the three-dimensional permeation and one-dimensional hopping pathways. The results provide design strategies to significantly enhance ionic conductivity in single-ion conductors. For large barriers to dissociate an ion, corrections to the Arrhenius law are presented. The predicted dependence of ionic conductivity on the unbinding time is in agreement with results in the literature based on simulations and experiments. This theory is generally applicable to conductive systems where the two mechanisms of permeation and hopping occur concurrently.

Investigating the Atomic and Mesoscale Interactions that Facilitate Spider Silk Protein Pre-Assembly.

Black widow spider dragline silk is one of nature's high-performance biological polymers, exceeding the strength and toughness of most man-made materials including high tensile steel and Kevlar. Major ampullate (Ma), or dragline silk, is primarily comprised of two spidroin proteins (Sp) stored within the Ma gland. In the native gland environment, the MaSp1 and MaSp2 proteins self-associate to form hierarchical 200-300 nm superstructures despite being intrinsically disordered proteins (IDPs). Here, dynamic light scattering (DLS), three-dimensional (3D) triple resonance solution NMR, and diffusion NMR is utilized to probe the MaSp size, molecular structure, and dynamics of these protein pre-assemblies diluted in 4 M urea and identify specific regions of the proteins important for silk protein pre-assembly. 3D NMR indicates that the Gly-Ala-Ala and Ala-Ala-Gly motifs flanking the poly(Ala) runs, which comprise the ß-sheet forming domains in fibers, are perturbed by urea, suggesting that these regions may be important for silk protein pre-assembly stabilization.

Entropic barrier of topologically immobilized DNA in hydrogels.

The single most intrinsic property of nonrigid polymer chains is their ability to adopt enormous numbers of chain conformations, resulting in huge conformational entropy. When such macromolecules move in media with restrictive spatial constraints, their trajectories are subjected to reductions in their conformational entropy. The corresponding free energy landscapes are interrupted by entropic barriers separating consecutive spatial domains which function as entropic traps where macromolecules can adopt their conformations more favorably. Movement of macromolecules by negotiating a sequence of entropic barriers is a common paradigm for polymer dynamics in restrictive media. However, if a single chain is simultaneously trapped by many entropic traps, it has recently been suggested that the macromolecule does not undergo diffusion and is localized into a topologically frustrated dynamical state, in apparent violation of Einstein's theorem. Using fluorescently labeled λ-DNA as the guest macromolecule embedded inside a similarly charged hydrogel with more than 95% water content, we present direct evidence for this new state of polymer dynamics at intermediate confinements. Furthermore, using a combination of theory and experiments, we measure the entropic barrier for a single macromolecule as several tens of thermal energy, which is responsible for the extraordinarily long extreme metastability. The combined theory-experiment protocol presented here is a determination of single-molecule entropic barriers in polymer dynamics. Furthermore, this method offers a convenient general procedure to quantify the underlying free energy landscapes behind the ubiquitous phenomenon of movement of single charged macromolecules in crowded environments.

Theory of Charged Gels: Swelling, Elasticity, and Dynamics.

The fundamental attributes of charged hydrogels containing predominantly water and controllable amounts of low molar mass electrolytes are of tremendous significance in biological context and applications in healthcare. However, a rigorous theoretical formulation of gel behavior continues to be a challenge due to the presence of multiple length and time scales in the system which operate simultaneously. Furthermore, chain connectivity, the electrostatic interaction, and the hydrodynamic interaction all lead to long-range interactions. In spite of these complications, considerable progress has been achieved over the past several decades in generating theories of variable complexity. The present review presents an analytically tractable theory by accounting for correlations emerging from topological, electrostatic, and hydrodynamic interactions. Closed-form formulas are derived for charged hydrogels to describe their swelling equilibrium, elastic moduli, and the relationship between microscopic properties such as gel diffusion and macroscopic properties such as elasticity. In addition, electrostatic coupling between charged moieties and their ion clouds, which significantly modifies the elastic diffusion coefficient of gels, and various scaling laws are presented. The theoretical formulas summarized here are useful to adequately capture the essentials of the physics of charged gels and to design new hydrogels with specified elastic and dynamical properties.

Electrostatically Driven Topological Freezing of Polymer Diffusion at Intermediate Confinements.

Breaking the paradigm that polymers in crowded aqueous media obey Einstein's law of diffusion, we report a localized nondiffusive hierarchical metastable state at intermediate confinements. Combining electrostatic and topological effects, we can tune the propensity of this new universality class in a quasicoacervate gel system consisting of guest polyamino acid chains inside an oppositely charged host hydrogel. Our observations offer strategies for controlled release and retention of macromolecules in aqueous crowded media, while opening a new direction for understanding topologically frustrated dynamics in polymers and other soft matter systems.

Surface Tension of Dielectric-Air Interfaces.

Analytical and semianalytical expressions for the surface tension of dielectric-air interfaces are presented after considering local and nonlocal dielectric effects near interfaces. It is shown that the nonlocal effects of dielectrics are significant for highly polar dielectric fluids such as water. Far from the interface, nonlocal dielectric effects are shown to cause not only the oscillatory potential of the mean force but also a reversal of sign at intermediate distances.

Characterization of silk-hyaluronic acid composite hydrogels towards vitreous humor substitutes.

Multiple ophthalmic pathologies, such as retinal detachment and diabetic retinopathy, require the removal and replacement of the vitreous humor. Clinical tamponades such as silicone oil and fluorinated gases are utilized but limited due to complications and toxicity. Therefore, there is a need for biocompatible, stable, vitreous humor substitutes. In this study, enzymatically crosslinked silk-hyaluronic acid (HA) hydrogels formed using horseradish peroxidase and H2O2 were characterized for use as vitreous humor substitutes. The composite network structure was characterized with dynamic light scattering. In addition, the rheological, optical, and swelling properties of hydrogels with varying silk to HA ratios and crosslinking densities controlled via H2O2 were determined over time. Hydrogels had refractive indexes of 1.336 and were clear with 75-91% light transmission. Hydrogel shear storage modulus ranged between ~6 and 240 Pa where increased H2O2 increased the modulus. After 1 month of aging, there were no changes in modulus for hydrogels with lower silk ratios, while those with higher silk ratios exhibited a significant increase in modulus. Decreasing H2O2 concentration in the reactions led to increased hydrogel volume during swelling, with higher silk ratios returning to their original size after 15 days. Dynamic light scattering results show three diffusive modes, revealing the possible structures of the hydrogel composite and are consistent with the mechanical properties and swelling results. The normalized intraocular pressure of ex vivo porcine eyes after injecting hydrogels were comparable with those treated with silicone oil showing the potential clinical utility of the hydrogels as vitreous substitutes. The versatility of the silk-HA hydrogel system, the tunable swelling properties, and the stability of hydrogels with lower silk ratios show the benefit of utilizing silk-HA hydrogels as vitreous substitutes.

Interlude of metastability in the melting of polymer crystals.

We have studied the process of melting of polymer crystals using Langevin dynamics simulations with a coarse-grained united atom model. We have considered two ideal situations: one in which a single crystal melts and the other in which a multichain crystal melts. We show that the melting of the single crystal proceeds through a globular metastable state, which is followed by expansion to a more random coil-like state. Similarly, the melting of the multichain crystal reveals a special mechanism comprising two steps: one in which a long-lived partially molten metastable state is formed, followed by a second step in which the chains peel off from the crystalline core to a free state. We elucidate the nature of the metastable state close to the equilibrium melting temperature and show that the multichain crystals equilibrate to states of intermediate order, with the extent of ordering decreasing as we increase the melting temperature. We quantify the kinetics of melting by estimating a free energy landscape using parallel tempering Langevin dynamics simulations. These simulations reveal a metastable state in the single molecule systems, allowing us to estimate the free energy barriers. Additionally, the melting of the multichain crystals reveals the existence of two barriers, with the preference for the intermediate state reducing with increasing temperature. We compare our findings to the existing experimental evidence and find qualitative agreements.

Theory of statistics of ties, loops, and tails in semicrystalline polymers.

Polymer crystals grown from melts consist of alternating lamellar crystalline regions and amorphous regions. We study the statistics of ties: chains which bridge the adjacent lamellae, loops: chains which come out of one lamella and enter back into the same lamella before reaching the other lamellae, and tails: chains which end in an amorphous region. We develop a theory to calculate the probabilities of formation of ties, loops, and tails with consideration of finite chain length and cooperative incorporation of a chain into multiple lamellae. The results of our numerical calculations based on a field-theoretic formalism show that the fraction of ties increases with increasing chain length, and it decreases with increasing interlamellar separation. In the limiting case of an infinite chain confined between only two walls, we recover the classical results of the gambler's ruin model. We show that the density anomaly encountered in previous theories is avoided naturally in the present theory without forcing the majority of stems to form tight loops. The derived results on the probability of tie chains in the amorphous regions are pertinent to the mechanical properties of semicrystalline polymers.

Conformational fluctuations of a DNA electrophoretically translocating through a nanopore under the action of a motor protein.

Single-file single-molecule electrophoresis through a nanopore has emerged as one of the successful methods in DNA sequencing. In gaining sufficient accuracy in the readout of the sequence, it is essential to position every nucleotide of the sequence with great accuracy and precision at the interrogation point of the nanopore. A combination of a ratcheting enzyme and a threaded DNA across a protein pore under an electric field is experimentally shown to be a viable method for DNA sequencing within the single-molecule electrophoresis technique. Using coarse-grained models of the enzyme and the protein nanopore, and Langevin dynamics simulations, we have characterized the conformational fluctuations of the DNA inside the nanopore. We show that the conformational fluctuations of DNA are significant for slowly operating enzymes such as phi29 DNA polymerase. Our results imply that there is considerable uncertainty in precisely positioning a nucleotide at the interrogation point of the nanopore. The discrepancy between the results of coarse-grained simulations and the experimentally successful accurate sequencing suggests that additional features of the experiments, such as explicit treatment of electrolyte ions and hydrodynamics, must be incorporated in the simulations to accurately model experimental constructs.

Effect of Salt on the Ordinary-Extraordinary Transition in Solutions of Charged Macromolecules.

Using dynamic light scattering technique, we address the role of added salt at higher concentrations on the "ordinary-extraordinary" transition in solutions of charged macromolecules. The "ordinary" behavior has previously been associated with a "fast" diffusion coefficient which is independent of salt concentration Cs and polymer concentration Cp if the ratio Cp/ Cs is above a threshold value. The "extraordinary" transition is associated with formation of aggregates, with a "slow" diffusion coefficient, formed from similarly charged macromolecules. By investigating aqueous solutions of sodium poly(styrenesulfonate) and sodium chloride with variations in Cp, Cs, and polymer molecular weight, Mw, we report the emergence of a new diffusive "fast" relaxation mode at higher values of Cp, Cs, and Mw, in addition to the previously known "fast" and "slow" relaxation modes. Furthermore, we find that Mw plays a crucial role on the collective dynamics of polyelectrolyte solutions with salt, instead of just the Cp/ Cs ratio as previously postulated. As Mw is progressively decreased, the salty solution exhibits dynamical transitions from three modes to two modes and then to one mode of relaxation. The emergence of the new fast mode and the dynamical transitions are in marked departure from the general premise of the ordinary-extraordinary transition developed over several decades. In an effort to rationalize our experimental findings we present a theory for the collective dynamics of polyelectrolyte solutions with salt by addressing the coupling between the relaxations of polyelectrolyte chains, counterions from the polymer and added salt, and co-ions from the salt. The predictions are in qualitative agreement with experimental findings. The present combined work of experiments and theory forms the basis for accurately characterizing dynamics of charged macromolecules in salty solutions, which are ubiquitous in biological systems and polyelectrolyte-based technologies.