We have performed Langevin dynamics simulations of single polyzwitterion chains by accounting for the combined effects of the hydrophobic interactions from the nonpolar chain backbone and the dipolar interactions among all zwitterionic groups attached to the chain backbone. In the present coarse-grained united atom model of polyzwitterions, the solvent quality is represented as the hydrophobicity parameter and in terms of a change in temperature, and the dipolar interactions in terms of orientations of the zwitterionic groups and the dielectric constant of the medium, which is taken as a constant. By extracting the size exponent of a chain under different temperatures, we have deduced the Theta-temperature and its variation with respect to the dipole moment and distribution of dipolar units. The Theta-temperature of a polymer chain, whose every monomer is explicitly zwitterionic, shows a quadratic dependence on the dipole moment of the zwitterionic group, which is buttressed by theoretical considerations. These results from simulations show that the ansatz of randomly oriented zwitterionic groups determining polyzwitterion solution behaviors is inapplicable. Furthermore, for polymer chains with half zwitterionic monomers and the other half with nonpolar monomers, we find that the Theta-temperature is lower for a more homogeneous distribution of dipoles. The obtained results provide a rough estimate of the location of the critical temperature of polyzwitterion phase separation and its sequence-dependent modification.

Controlling diffusion and retention of biomacromolecules in congested aqueous media is vital for various living processes. When charged macromolecules are trapped inside a hydrogel, the molecules undergo diffusion only if the degree of confinement is either weak or very strong; for intermediate confinements, the center of mass of the macromolecules does not diffuse, but the molecules exhibit glass-like hierarchical dynamics even though the medium is essentially water. Using dynamic light scattering on poly(styrenesulfonate) embedded inside Tetra-PEG hydrogels, we have investigated this enigmatic nonmonotonic diffusion behavior and present a comprehensive dynamical state diagram. After determining the nature of the nondiffusive state at intermediate confinements, we have determined the confinement thresholds for its transition into diffusion when the degree of confinement is either decreased or increased away from the initial confinement. After crossing the higher confinement threshold, the molecules are diffusive, with the coexistence of two populations obeying Rouse dynamics and reptation dynamics. The other threshold condition to fully switch off the nondiffusive state is when the chain size is smaller than the gel mesh size. Our experimental findings are buttressed by the theoretical calculation of the free energy barrier for localizing the nondiffusive state at intermediate confinements. The presented results on the transitions from diffusion to nondiffusion to diffusion again as the degree of confinement progressively increases may reveal the mechanism of how biomacromolecules move toward the targets in the congested aqueous media and provide strategies to design scaffolds for controlled retention and release of macromolecular cargos in crowded aqueous media.

Gels comprised of dynamic bonds are important candidates for the emerging 'intelligent' gels due to their unique characteristics. We report a universal law of hierarchical gel dynamics arising from association-dissociation of physical crosslinks, as discerned from dynamic light scattering (DLS) on diverse sets of complex gels. It is the first experimental evidence of a stretched exponential decay with a universal exponent 1/3 in DLS for all the physical gels, complementing more than five decades of DLS studies on conventional chemical gels. Here we show that diversely different chemistries of dynamic bonds map into the observed unifying law for large-scale collective dynamical properties of physical gels. This discovery allows identification of whether physical or chemical bonds dominate the crosslinks in complex gels, as well as extraction of local energetics of the constituent physical crosslinks by their characteristic relaxation times. It also elicits large-scale functional properties applicable in smart gels.

Response of polar and neutral monomers in macromolecules to an electric field in their crowded aqueous solutions remains as an unchartered area of research, in contrast with well understood behavior of ionized groups. Wondering whether such monomers impart merely frictional resistance or cooperate with the other ionic groups in their electrophoretic mobility, we investigate single-molecule electrophoresis of a couple of neutral polyzwitterions which have charge-neutrality with strong acidic group and permanent positive charge within their repeat units. Combining experiments and theory, we study the roles of dipole orientation of zwiterionic monomers and salt identity. Here, we report that charge-neutral polyzwitterions exhibit mobility with rectification in their direction of movement because of charge symmetry breaking arising from differential counterion bindings due to gradients in the local dielectric constant around chain backbone, and thus opening a new avenue to understand dipolar polymers of broad interest and applications.

We present a theory of melting kinetics of semicrystalline polymers at temperatures above the equilibrium melting temperature, by accounting for conformational entropy of chains during melting. We have derived free energy landscapes for escape of individual chains from a lamella into the amorphous phase as a function of the characteristics of the initial lamella, such as the lamellar thickness, number of chain folds, fold‐ and lateral‐surface free energies, and mean energy of a monomer inside the lamella. We show that melting of lamellae is always accompanied by a free energy barrier which is entirely entropic in origin. In terms of the parameters characterizing the lamellae and the extent of superheating, closed‐form formulas are presented for the equilibrium melting temperature, driving force for crystallization, free energy barrier height, average expulsion time of a single chain from a lamella, and the melting velocity of lamellae. The present entropic barrier theory predicts that the dependence of melting velocity on superheating is nonlinear and non‐Arrhenius, in qualitative agreement with experimental observations reported in the literature. The derived formulas open an opportunity to further explore the role of various molecular features of semicrystalline polymers on their melting kinetics.

Direct translocation of RNA with secondary structures using single-molecule electrophoresis through protein nanopores shows significant fluctuations in the measured ionic current, in contrast to unstructured single-stranded RNA or DNA. We developed a multiscale model combining the oxRNA model for RNA with the 3-dimensional Poisson-Nernst-Planck formalism for electric fields within protein pores, aiming to map RNA conformations to ionic currents as RNA translocates through three protein nanopores: α-hemolysin, CsgG, and MspA. Our findings reveal three distinct stages of translocation (pseudoknot, melting, and molten globule) based on contact maps and current values. Two translocation modes emerge: fast and slow. In the fast mode, the speed is determined by the electric field, independent of pore geometry. In the slow mode, the molten globule stage is the rate-determining factor in slowing the translocation, instead of the previous paradigm of melting of the base pairs. Using these insights, we propose a neural network framework to identify and reconstruct RNA secondary structures from ionic current windows. We find that the electric field distribution, not the nanopore geometry, drives the molten globule stage. Our results explain the large current fluctuations. These results provide a fundamental understanding of the role of secondary and tertiary structures in the translocation of RNA in direct RNA translocation platforms based on single-molecule electrophoresis. This work offers design rules for new protein pores and real-time imaging of the secondary structures of RNA.

We study the role of active coupling on the transport properties of homogeneously charged macromolecules in an infinitely dilute solution. An enzyme becomes actively bound to a segment of the macromolecule, exerting an electrostatic force on it. Eventually, thermal fluctuations cause it to become unbound, introducing active coupling into the system. We study the mean-squared displacement (MSD) and find a new scaling regime compared to the thermal counterpart in the presence of hydrodynamic and segment-segment electrostatic interactions. Furthermore, the study of segment-segment equal-time correlation reveals the swelling of the macromolecule. Further, we derive the concentration equation of the macromolecule with active binding and study how the cooperative diffusivity of the macromolecules get modified by its environment, including the macromolecules itself. It turns out that these active fluctuations enhance the effective diffusivity of the macromolecules. The derived closed-form expression for diffusion constant is pertinent to the accurate interpretation of light scattering data in multi-component systems with binding-unbinding equilibria.

We introduce a theoretical framework to describe the pH-sensitive phase behavior of polyzwitterion-polyelectrolyte complex coacervates that reasonably captures the phenomenon from recent experimental observations. The polyzwitterion is described by a combinatorial sequence of the four states in which each zwitterionic monomer can occupy: dipolar, quasi-cationic, quasi-anionic, and fully neutralized. We explore the effects of various modifiable chemical and physical properties of the polymers-such as, pKa of the pH-active charged group on the zwitterion, equilibrium constant of salt condensation on the permanently charged group on the zwitterion, degrees of polymerization, hydrophobicity (via the Flory-Huggins interaction parameter), and dipole lengths-on the window of complexation across many stoichiometric mixing ratios of polyzwitterion and polyelectrolyte. The properties that determine the net charge of the polyzwitterion have the strongest effect on the pH range in which polyzwitterion-polyelectrolyte complexation occurs. We finish with general guidance for those interested in molecular design of polyzwitterion-polyelectrolyte complex coacervates and opportunities for future investigation. We introduce a theoretical framework to describe the pH-sensitive phase behavior of polyzwitterion-polyelectrolyte complex coacervates that reasonably captures the phenomenon from recent experimental observations.

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.

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.

For semidilute polyelectrolyte solutions, it is generally assumed that topological, electrostatic, and hydrodynamic interactions are screened (called triple screening). Despite a large body of research focused on polyelectrolyte solutions, the concept of triple screening has never been rigorously verified. In this work, we test the concept by probing concentration fluctuations in aqueous solutions containing a well-studied polyelectrolyte, sodium poly(styrenesulfonate) (NaPSS) with neutron scattering, theory, and molecular dynamics simulations. Neutron spin-echo (NSE) and small-angle neutron scattering (SANS) data from semidilute solutions of NaPSS are presented at different polymer and salt (NaCl) concentrations. A combined theory for structure (J. Chem. Phys. 105, 5183 (1996)) and dynamics (J. Chem. Phys. 107, 2619 (1997)), which captures effects of hydrodynamic, topological, and electrostatic screening, is used to interpret the experimental results. The theory quantitatively predicts the decay rate obtained from the NSE measurements while capturing the shape and concentration dependencies of the polyelectrolyte peak observed in the SANS spectra. Detailed comparisons of the theory and the experiments reveal that the wavevector-dependent decay rate of concentration fluctuations in semidilute solutions of polyelectrolytes is dictated by the screening of hydrodynamic, topological, and electrostatic interactions. This conclusion is corroborated by coarse-grained molecular dynamics simulations, executed without any hydrodynamic interactions, which fail to capture the correct wavevector dependence of the decay rate. These results highlight that the theories based on the concept of triple screening provide a quantitative framework for predicting a relation between the structure and dynamics of polyelectrolyte solutions.

While the translocation of linear polymers through nanopores is well-understood, the underlying mechanism of transport of branched polymers through nanopores is yet to be fully developed. In this general premise, we have investigated the translocation of multiarm star-like polyethylene glycols (PEGs) through single solid-state nanopores, using single-molecule electrophoresis. Our experiments reveal the conformational trajectories of multiarm-PEGs during their sojourn inside the nanopore in exquisite detail. We quantify these pathways in terms of the number of leading arms (f(in)) and the number of lagging arms (f(out)), which depend on the pore diameter (d) and the total number of arms (f). We have measured the average translocation time (tau), polymer capture rate (R-c), and polymer conformations during translocation in terms of d, f, and applied voltage (V-m). We find a direct proportionality between R-c and fV(m), and between tau and f/V-m. Interestingly, star polymers with more arms inside the nanopore (f(in)) than outside (f(out)) also translocate successfully, in contrast with previous suggestions of f(in) < f(out). As the pore size increases, the optimal f(in) shifts from 0.25f to 0.5f. In addition to gaining insight into the mechanism of translocation of star-like polymers, the present experimental strategy opens new opportunities to characterize and separate polymers with different branching architectures.

The behavior of polyzwitterions, constituted by dipole-like zwitterionic monomers, is significantly different from that of uniformly charged polyelectrolytes. The origin of this difference lies in the intrinsic capacity of polyzwitterions to self-associate intramolecularly and associate with interpenetrating chains driven by dominant dipolar interactions. Earlier attempts to treat polyzwitterions implicitly assume that the dipoles of zwitterion monomers are randomly oriented. At ambient temperatures, the dipolar zwitterion monomers can readily align with each other generating quadrupoles and other multipoles and thus generating heterogeneous structures even in homogeneous solutions. Towards an attempt to understand the role of such dipolar associations, we present a mean field theory of solutions of polyzwitterions. Generally, we delineate a high-temperature regime where the zwitterion dipoles are randomly oriented from a low-temperature regime where quadrupole formation is significantly prevalent. We present closed-form formulas for: (1) Coil-globule transition in the low-temperature regime, the anti-polyelectrolyte effect of chain expansion upon addition of low molar mass salt, and chain relaxation times in dilute solutions. (2) Spontaneous formation of a mesomorphic state at the borderline between the high-temperature and low-temperature regimes and its characteristics. A universal law is presented for the radius of gyration of the microgel, as a proportionality to one-sixth power of the polymer concentration. (3) Swelling equilibrium of chemically cross-linked polyzwitterion gels in both the high temperature and low-temperature regimes. Addressing the hierarchical internal dynamics of polyzwitterion gels, we present a general stretched exponential law for the time-correlation function of gel displacement vector, that can be measured in dynamic light scattering experiments. The present theory is of direct experimental relevance and additional theoretical developments to all polyzwitterion systems, and generally to biological macromolecular systems such as intrinsically disordered proteins.

Conformations and dynamics of an intrinsically disordered protein (IDP) depend on its composition of charged and uncharged amino acids, and their specific placement in the protein sequence. In general, the charge (positive or negative) on an amino acid residue in the protein is not a fixed quantity. Each of the ionizable groups can exist in an equilibrated distribution of fully ionized state (monopole) and an ion-pair (dipole) state formed between the ionizing group and its counterion from the background electrolyte solution. The dipole formation (counterion condensation) depends on the protein conformation, which in turn depends on the distribution of charges and dipoles on the molecule. Consequently, effective charges of ionizable groups in the IDP backbone may differ from their chemical charges in isolation-a phenomenon termed charge-regulation. Accounting for the inevitable dipolar interactions, that have so far been ignored, and using a self-consistent procedure, we present a theory of charge-regulation as a function of sequence, temperature, and ionic strength. The theory quantitatively agrees with both charge reduction and salt-dependent conformation data of Prothymosin-alpha and makes several testable predictions. We predict charged groups are less ionized in sequences where opposite charges are well mixed compared to sequences where they are strongly segregated. Emergence of dipolar interactions from charge-regulation allows spontaneous coexistence of two phases having different conformations and charge states, sensitively depending on the charge patterning. These findings highlight sequence dependent charge-regulation and its potential exploitation by biological regulators such as phosphorylation and mutations in controlling protein conformation and function.

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 (N bb ), 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.

Polyampholyte gel is a perfect physics model to mimic condensed state of proteins. We have studied the hierarchical dynamics of polyampholyte gels by dynamic light scattering. In addition to the normal gel mode, which indicates the gel elasticity, we also discovered a new mode with a stretched exponential decay with the stretched exponent β = 1/3, and a diffusive exponential decay, which indicates the coupled motion between counterion and the polyampholyte backbone. After dialysis to low salt concentration, the coupled motion of the counterion will go away, so that there are only two modes. Combined with a newly developed theory, we attribute this stretched exponential mode to hierarchical dynamics of the segments between two crosslinking junctions, whose segmental distribution obeys Poisson distribution. As salt concentration inside the gel increases, β decreases from 0.38 to 0.33, which is consistent with theoretical results. The gel with the molar charge ratio R=1, which is at the charge balance point, has the highest value β = 0.38. As long as R deviates further away from the charge balance point from either side, the β values decrease. When the gel is 100% positive charged, their dynamic light scattering results will go back to that of the normal polyelectrolyte gels. ### Competing Interest Statement The authors have declared no competing interest.

When very long polymers are trapped into multiple entropic traps created by the meshes of host hydrogels, our recent discovery shows that the guest polymer chains are entropically frozen into a nondiffusive topologically frustrated dynamical state (TFDS) at intermediate confinements. Outside the confinement boundaries of the TFDS, the guest molecules diffuse, whereas in the TFDS regime, the center of mass diffusion coefficient is essentially zero due to the macromolecule being localized into long-lived metastable states with extreme free-energy barriers for the escape of the macromolecule. However, the segmental dynamics of the macromolecule is active with hierarchical dynamics. A key assumption to explain this hierarchical segmental dynamics of the macromolecule in the TFDS regime has been that the number of monomers in the various entropic traps is polydisperse. The validity of this assumption is tested in the present paper by experimentally investigating the segmental dynamics using the ideal tetra-PEG hydrogel as the host matrix and sodium poly-(styrene sulfonate) as the guest macromolecule. We find that all features of TFDS previously observed using poly-(acrylamide-co-acrylate) hydrogels with the polydisperse distribution of mesh size are recovered in the present system of uniform mesh size as well. Thus, the present study, with the chemical details different from those of our previous systems, adds credence to the universality of the phenomenon of TFDS. Furthermore, the present finding suggests that the polydispersity in the number of monomers in the various entropic traps must arise from conformational fluctuations emanating from the local exchange dynamics of segments among neighboring meshes.

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.