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.

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.

Theory of thermoreversible gelation and anomalous concentration fluctuations in polyzwitterion solutions.

We present a theoretical framework to investigate thermoreversible phase transitions within polyzwitterion systems, encompassing macrophase separations (MPS) and gelation. In addition, we explore concentration fluctuations near critical points associated with MPS, as well as tricritical and bicritical points at the intersection of MPS and gelation. By utilizing mean-field percolation theory and field theory formalism, we derive the Landau free energy in terms of polyzwitterion concentration with fixed dipole strengths and other experimental variables, such as temperatures and salt concentrations. As the temperature decreases, the dipoles can form cross-links, resulting in polyzwitterion associations. The associations can grow to a gel network and enhance the propensity for MPS, including liquid-liquid, liquid-gel, and gel-gel phase separations. Remarkably, the associations also impact critical behaviors. Using the renormalization group technique, we find that the critical exponents of the polyzwitterion concentration correlation functions significantly deviate from those in the Ising universality class due to the presence of polyzwitterion associations, leading to crossover critical behaviors.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Ordinary-extraordinary transition in dynamics of solutions of charged macromolecules.

The occurrence of the ubiquitous and intriguing "ordinary-extraordinary" behavior of dynamics in solutions of charged macromolecules is addressed theoretically by explicitly considering counterions around the macromolecules. The collective and coupled dynamics of macromolecules and their counterion clouds in salt-free conditions are shown to lead to the "ordinary" behavior (also called the "fast" mode) where diffusion coefficients are independent of molar mass and polymer concentration and are comparable to those of isolated metallic ions in aqueous media, in agreement with experimental facts observed repeatedly over the past four decades. The dipoles arising from adsorbed counterions on polymer backbones can form many pairwise physical cross-links, leading to microgel-like aggregates. Balancing the swelling from excluded volume effects and counterion pressure with elasticity of the microgel, we show that there is a threshold value of a combination of polymer concentration and electrolyte concentration for the occurrence of the "extraordinary" phase (also called the "slow" mode) and the predicted properties of diffusion coefficient for this phase are in qualitative agreement with well-known experimental data.

Size-dependent forced PEG partitioning into channels: VDAC, OmpC, and α-hemolysin.

Nonideal polymer mixtures of PEGs of different molecular weights partition differently into nanosize protein channels. Here, we assess the validity of the recently proposed theoretical approach of forced partitioning for three structurally different ß-barrel channels: voltage-dependent anion channel from outer mitochondrial membrane VDAC, bacterial porin OmpC (outer membrane protein C), and bacterial channel-forming toxin α-hemolysin. Our interpretation is based on the idea that relatively less-penetrating polymers push the more easily penetrating ones into nanosize channels in excess of their bath concentration. Comparison of the theory with experiments is excellent for VDAC. Polymer partitioning data for the other two channels are consistent with theory if additional assumptions regarding the energy penalty of pore penetration are included. The obtained results demonstrate that the general concept of "polymers pushing polymers" is helpful in understanding and quantification of concrete examples of size-dependent forced partitioning of polymers into protein nanopores.

Electrostatic effects in collagen fibril formation.

Using light scattering and Atomic Force Microscopy techniques, we have studied the kinetics and equilibrium scattering intensity of collagen association, which is pertinent to the vitreous of the human eye. Specifically, we have characterized fibrillization dependence on pH, temperature, and ionic strength. At higher and lower pH, collagen triple helices remain stable in solution without fibrillization. At physiological pH, fibrillization occurs and the fibril growth is slowed upon either an increase in ionic strength or a decrease in temperature. The total light scattering with respect to ionic strength is non-monotonic in these conditions as a result of a competing dependence of fibril concentration and size on ionic strength. Fibril concentration is the highest at lower ionic strengths and rapidly decays for higher ionic strengths. On the other hand, fibril size is larger in solutions with higher ionic strength. We present a theoretical model, based on dipolar interactions in solutions, to describe the observed electrostatic nature of collagen assembly. At extreme pH values, either very low or very high, collagen triple helices carry a large net charge of the same sign preventing their assembly into fibrils. At intermediate pH values, fluctuations in the charge distribution of the collagen triple helices around roughly zero net charge lead to fibrillization. The growth kinetics of fibrils in this regime can be adequately described by dipolar interactions arising from charge fluctuations.

Langevin dynamics simulation of crystallization of ring polymers.

We have studied the crystallization of ring polymers using Langevin dynamics simulations with a coarse-grained united atom model. We show that there are marked differences in the crystallization of single ring polymers in comparison to single linear polymers. Contrary to expectations from equilibrium thermodynamics, ring polymers melt at lower temperatures than linear polymers. An analysis of the early stage crystallization mechanism shows that ring and linear polymers crystallize through the birth of baby nuclei with their coarsening depending uniquely on their topology. The single ring polymers nucleate faster than the single linear analogs and into several metastable lamellar thicknesses, although the motion of the monomers in both cases is comparable. Additionally, using multiple polymer molecules, we find that the secondary nucleation of ring polymers proceeds with free energy barriers, as opposed to linear polymers where no barriers are found. Our results are in qualitative agreement with some experiments, while in disagreement with some other experiments, indicating additional roles by chemistries of ring and linear polymers. Our simulations are designed to explore only the topological effects without any consideration of non-universal chemical effects for our particular model.

Polyelectrolyte complex coacervation by electrostatic dipolar interactions.

We address complex coacervation, the liquid-liquid phase separation of a solution of oppositely charged polyelectrolyte chains into a polyelectrolyte rich complex coacervate phase and a dilute aqueous phase, based on the general premise of spontaneous formation of polycation-polyanion complexes even in the homogeneous phase. The complexes are treated as flexible chains made of dipolar segments and uniformly charged segments. Using a mean field theory that accounts for the entropy of all dissociated ions in the system, electrostatic interactions among dipolar and charged segments of complexes and uncomplexed polyelectrolytes, and polymer-solvent hydrophobicity, we have computed coacervate phase diagrams in terms of polyelectrolyte composition, added salt concentration, and temperature. For moderately hydrophobic polyelectrolytes in water at room temperature, neither hydrophobicity nor electrostatics alone is strong enough to cause phase separation, but their combined effect results in phase separation, arising from the enhancement of effective hydrophobicity by dipolar attractions. The computed phase diagrams capture key experimental observations including the suppression of complex coacervation due to increases in salt concentration, temperature, and polycation-polyanion composition asymmetry, and its promotion by increasing the chain length, and the preferential partitioning of salt into the polyelectrolyte dilute phase. We also provide new predictions such as the emergence of loops of instability with two critical points.

Preface: Special Topic on Chemical Physics of Charged Macromolecules.

This special topic highlights recent advances in experiments, theory, and coarse-grained modeling on charged macromolecular systems involving synthetic and biological polymers and membranes. The behaviors of the charged systems are very complex and are qualitatively different from those of uncharged polymers. The results presented in this special topic provide deep insights into the fundamentals of how the coupling between the long-ranged electrostatic and topological correlations of charged macromolecules controls their conformations, assembly, dynamics, and transport. There are many insights into the creation and design of new materials based on ionic interactions.