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

Translocation frequency of double-stranded DNA through a solid-state nanopore.

Solid-state nanopores are single-molecule sensors that measure changes in ionic current as charged polymers such as DNA pass through. Here, we present comprehensive experiments on the length, voltage, and salt dependence of the frequency of double-stranded DNA translocations through conical quartz nanopores with mean opening diameter 15 nm. We observe an entropic barrier-limited, length-dependent translocation frequency at 4M LiCl salt concentration and a drift-dominated, length-independent translocation frequency at 1M KCl salt concentration. These observations are described by a unifying convection-diffusion equation, which includes the contribution of an entropic barrier for polymer entry.This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevE.93.02240

Electroosmotic flow reversal outside glass nanopores.

We report observations of a striking reversal in the direction of electroosmotic flow (EOF) outside a conical glass nanopore as a function of salt concentration. At high ionic strengths (>100 mM), we observe EOF in the expected direction as predicted by classical electrokinetic theory, while at low salt concentrations (<1 mM) the direction of the flow is reversed. The critical crossover salt concentration depends on the pore diameter. Finite-element simulations indicate a competition between the EOF generated from the inner and outer walls of the pore, which drives flows in opposite directions. We have developed a simple analytical model which reveals that, as the salt concentration is reduced, the flow rates inside the pore are geometrically constrained, whereas there is no such limit for flows outside the pore. This model captures all of the essential physics of the system and explains the observed data, highlighting the key role the external environment plays in determining the overall electroosmotic behavior

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

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

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