Elasticity at Swelling Equilibrium of Ultrasoft Polyelectrolyte Gels: Comparisons of Theory and Experiments

The coupling of rotational and translational dynamics for rapid diffusion of nanorods in macromolecular networks

The rod-like viruses show anomalously rapid diffusion in bio-tissue networks originated from the rotation-facilitated transportation; however, the experimental investigation of the correlation of the rotational and translational dynamics is still in blank. Herein, typical rod-like and spherical gold nanoparticles (NPs) are dispersed in the classical Tetra-PEG gels, respectively, as model systems for light scattering studies. The contributions from translational and rotational diffusive dynamics, and network fluctuation dynamics can be well-resolved and the stretch exponent of rotational dynamics at 0.25 is proven to be the fingerprint for the coupled rotational and translational dynamics of nanorods. The rotation facilitated re-orientation finally leads to the fast transportation of nanorods. The discoveries are confirmed to be valid for rod-like biomacromolecule systems by studying the diffusive dynamics of Tobacco mosaic virus in gels. The work can be inspiring for the development of protocols to prevent infection of microorganism and regulate the transportation of nano-medicines.

Effect of Polymer Gel Elasticity on Complex Coacervate Phase Behavior

Gels are key materials in biological systems such as tissues and may control biocondensate formation and structure. To further understand the effects of elastic environments on biomacromolecular assembly, we have investigated the phase behavior and radii of complex coacervate droplets in polyacrylamide (PAM) networks as a function of gel modulus. Poly-l-lysine (PLL) and sodium hyaluronate (HA) complex coacervate phases were prepared in PAM gels with moduli varying from 0.035 to 15.0 kPa. The size of the complex coacervate droplets is reported from bright-field microscopy and confocal fluorescence microscopy. Overall, the complex coacervate droplet volume decreases inversely with the modulus. Fluorescence microscopy is also used to determine the phase behavior and concentration of fluorescently tagged HA in the complex coacervate phases as a function of ionic strength (100-270 mM). We find that the critical ionic strength and complex coacervate stability are nonmonotonic as a function of the network modulus and that the local gel concentration can be used to control phase behavior and complex coacervate droplet size scale. By understanding how elastic environments influence simple electrostatic assembly, we can further understand how biomacromolecules exist in complex, crowded, and elastic cellular environments.

Network Viscoelasticity from Brillouin Spectroscopy

Even though the physical nature of shear and longitudinal moduli are different, empirical correlations between them have been reported in several biological systems. This correlation is of fundamental interest and immense practical value in biomedicine due to the importance of the shear modulus and the possibility to map the longitudinal modulus at high-resolution with all-optical spectroscopy. We investigate the origin of such a correlation in hydrogels. We hypothesize that both moduli are influenced in the same direction by underlying physicochemical properties, which leads to the observed material-dependent correlation. Matching theoretical models with experimental data, we quantify the scenarios in which the correlation holds. For polymerized hydrogels, a correlation was found across different hydrogels through a common dependence on the effective polymer volume fraction. For hydrogels swollen to equilibrium, the correlation is valid only within a given hydrogel system, as the moduli are found to have different scalings on the swelling ratio. The observed correlation allows one to extract one modulus from another in relevant scenarios.

In situ forming, mechanically resilient hydrogels prepared from 4a-[PEG-b-PTMC-Ac] and thiolated chondroitin sulfate for nucleus pulposus cell delivery

Intervertebral disk degeneration (IVDD) is a common condition that causes severe back pain and affects patients' mobility and life quality considerably. IVDD originates within the central region of the disk called the nucleus pulposus (NP). Removing the damaged tissue and replacing it with NP cells (NPCs) delivered within an in situ forming hydrogel is a promising treatment approach. Herein we describe a hydrogel formulation based on 4-arm [poly(ethylene glycol)-b-poly(trimethylene carbonate)-acrylate] (4a[PEG-b-PTMC-Ac]) crosslinked with thiolated chondroitin sulfate via Michael-type reaction for this purpose. A library of hydrogels based on 15 kDa 4a-[PEG] with PTMC blocks of varying molecular weight were prepared and characterized. The instantaneous moduli of the hydrogels were adjustable from 24 to 150 kPa depending on the length of the PTMC block and the polymer volume fraction. The influence of each of these parameters was effectively explained using both scaling or mean field theories of polyelectrolyte hydrogels. The hydrogels were resistant to cyclic compressive loading and degraded gradually over 70 days in vitro. A hydrogel formulation with an instantaneous modulus at the high end of the range of values reported for human NP tissue was chosen to assess the ability of these hydrogels for delivering NPCs. The prepolymer solution was injectable and formed a hydrogel within 30 minutes at 37 °C. Bovine NPCs were encapsulated within this hydrogel with high viability and proliferated throughout a 28 day, hypoxic culture period. The encapsulated NPCs formed clusters and deposited collagen type II but no collagen type I within the hydrogels. Despite an initial gradual decrease, a steady-state modulus was reached at the end of the 28 day culture period that was within the range reported for healthy human NP tissue. This in situ forming hydrogel formulation is a promising approach and with further development could be a viable clinical treatment for IVDD.

In situ forming macroporous biohybrid hydrogel for nucleus pulposus cell delivery

Degenerative intervertebral disc disease is a common source of chronic pain and reduced quality of life in people over the age of 40. While degeneration occurs throughout the disc, it most often initiates in the nucleus pulposus (NP). Minimally invasive delivery of NP cells within hydrogels that can restore and maintain the disc height while regenerating the damaged NP tissue is a promising treatment strategy for this condition. Towards this goal, a biohybrid ABA dimethacrylate triblock copolymer was synthesized, possessing a lower critical solution temperature below 37 °C and which contained as its central block an MMP-degradable peptide flanked by poly(trimethylene carbonate) blocks bearing pendant oligoethylene glycol groups. This triblock prepolymer was used to form macroporous NP cell-laden hydrogels via redox initiated (ammonium persulfate/sodium bisulfite) crosslinking, with or without the inclusion of thiolated chondroitin sulfate. The resulting macroporous hydrogels had water and mechanical properties similar to those of human NP tissue and were mechanically resilient. The hydrogels supported NP cell attachment and growth over 28 days in hypoxic culture. In hydrogels prepared with the triblock copolymer but without the chondroitin sulfate the NP cells were distributed homogeneously throughout in clusters and deposited collagen type II and sulfated glycosaminoglycans but not collagen type I. This hydrogel formulation warrants further investigation as a cell delivery vehicle to regenerate degenerated NP tissue. STATEMENT OF SIGNIFICANCE: The intervertebral disc between the vertebral bones of the spine consists of three regions: a gel-like central nucleus pulposus (NP) within the annulus fibrosis, and bony endplates. Degeneration of the intervertebral disc is a source of chronic pain in the elderly and most commonly initiates in the NP. Replacement of degenerated NP tissue with a NP cell-laden hydrogel is a promising treatment strategy. Herein we demonstrate that a crosslinkable polymer with a lower critical solution temperature below 37 °C can be used to form macroporous hydrogels for this purpose. The hydrogels are capable of supporting NP cells, which deposit collagen II and sulfated glycosaminoglycans, while also possessing mechanical properties matching those of human NP tissue.

Neutralization and Salt Effect on the Structure and Mechanical Properties of Polyacrylic Acid Gels under Equivolume Conditions

The effects of neutralization and salt on the structure and mechanical properties of polyacrylic acid (PAA) gels under equivolume conditions were investigated by small-angle X-ray scattering (SAXS) measurements and tensile tests. We attained the equivolume condition by immersing a piece of PAA gel sample in an ion reservoir containing linear PAA, NaOH, and NaCl at prescribed concentrations (post-ion-tuning). The volume fraction of the linear polymer was set to be the same as that of the gel so as to satisfy the iso-osmotic pressure at the reference state. Various types of reservoirs were prepared by adding NaOH and/or NaCl with different concentrations to the reference reservoir, followed by immersing a PAA gel piece. In the SAXS measurements, a scattering peak appeared, and the scattering intensity at q = 0 decreased by neutralization, while the addition of salt increased the scattering intensity. On the other hand, Young’s modulus measured with the tensile test decreased with neutralization; however, it scarcely changed with the addition of salt. The newly developed equivolume post-ion-tuning technique may serve as a new standard scheme to study polyelectrolyte gels.

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.

Experimental Verification of the Balance between Elastic Pressure and Ionic Osmotic Pressure of Highly Swollen Charged Gels

The equilibrium swelling degree of a highly swollen charged gel has been thought to be determined by the balance between its elastic pressure and ionic osmotic pressure. However, the full experimental verification of this balance has not previously been conducted. In this study, we verified the balance between the elastic pressure and ionic osmotic pressure of charged gels using purely experimental methods. We used tetra-PEG gels created using the molecular stent method (St-tetra-PEG gels) as the highly swollen charged gels to precisely and separately control their network structure and charge density. The elastic pressure of the gels was measured through the indentation test, whereas the ionic osmotic pressure was determined by electric potential measurement without any strong assumptions or fittings. We confirmed that the two experimentally determined pressures of the St-tetra-PEG gels were well balanced at their swelling equilibrium, suggesting the validity of the aforementioned relationship. Furthermore, from single-strand level analysis, we investigated the structural requirements of the highly swollen charged gels in which the elasticity and ionic osmosis are balanced at their swelling equilibrium.

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.

pH-Dependent Gelation of a Stiff Anionic Polysaccharide in the Presence of Metal Ions

Cross-linking of polysaccharides by metal ions provides polymer gels highly required by industrial applications. In this article, we study the rheological properties and microstructure of solutions of a stiff anionic polysaccharide xanthan cross-linked by chromium (III) ions, and we demonstrate that their properties are highly sensitive to the preparation pH. Stable gels are obtained in a wide range of pH from 2.4 to 7.8. The maximum elastic modulus is observed for the gels made at pH 6.3, and by freeze-fracture transmission electron microscopy it is shown that they are characterized by the most dense network structure. However, out of this pH interval, no gelation is observed. At low pH (< 2.4) it is due to high protonation of carboxylic groups of xanthan preventing their interaction with chromium ions, and to the disappearance of oligomeric ions, which are effective in cross-linking. At high pH (> 7.8) the absence of gelation is caused by the transformation of reactive chromium ions into insoluble chromium hydroxide. At the same time, for the gels initially formed at pH 6.3, subsequent change of pH to strongly acidic (1.4) or basic (8.9) medium does not affect appreciably their properties, meaning that chromium cross-links are stable once they are formed. These observations open a reliable route to produce polysaccharide gels with required mechanical properties in a wide pH range where they initially cannot be prepared. It is also shown that the increase of pH to 6.3 of the initially ungelled solution prepared at pH 1.5 results in gelation. This effect offers a facile way for delayed gelation of polysaccharides, which is especially required by oil industry.

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.

Effect of ionic strength and seawater cations on hagfish slime formation

The defensive slime of hagfish consists of a polyanionic mucin hydrogel that synergistically interacts with a fiber network forming a coherent and elastic hydrogel in high ionic strength seawater. In seawater, the slime deploys in less than a second entrapping large quantities of water by a well-timed thread skein unravelling and mucous gel swelling. This rapid and vast hydrogel formation is intriguing, as high ionic strength conditions generally counteract the swelling speed and ratio of polyelectrolyte hydrogels. In this work we investigate the effect of ionic strength and seawater cations on slime formation dynamics and functionality. In the absence of ionic strength skeins swell radially and unravel uncontrolled, probably causing tangling and creating a confined thread network that entraps limited water. At high ionic strength skeins unravel, but create a collapsed and dense fiber network. High ionic strength conditions therefore seem crucial for controlled skein unraveling, however not sufficient for water retention. Only the presence of naturally occurring Ca2+ or Mg2+-ions allowed for an expanded network and full water retention probably due to Ca2+-mediated vesicle rupture and cross-linking of the mucin. Our study demonstrates that hagfish slime deployment is a well-timed, ionic-strength, and divalent-cation dependent dynamic hydrogel formation process.

Topologically frustrated dynamics of crowded charged macromolecules in charged hydrogels

Movement of charged macromolecules in crowded aqueous environments is a ubiquitous phenomenon vital to the various living processes and formulations of materials for health care. While study of diffusion of tracer amounts of probe macromolecules trapped inside concentrated solutions, gels, or random media has led to an enhanced understanding of this complex process, the collective dynamics of charged macromolecules embedded inside congested charge-bearing matrices still remains to be fully explored. Here we report a frustrated dynamics of DNA and synthetic polyelectrolytes inside a charged host hydrogel where the guest molecules do not diffuse. Instead, they exhibit a family of relaxation processes arising from a combination of conformational entropy and local chain dynamics, which are frustrated by the confinement from the gel. We also have developed a model explaining this new universality class of non-diffusive topologically frustrated dynamics of charged macromolecules.

Diffusion of molecules in crowded environment is important for various living systems, but the dynamics of charged molecules in charged matrices remains still unexplored. Here the authors report a dynamics of DNA and polyelectrolytes in a charged hydrogel where the guest molecules do not diffuse but experience topologically frustrated dynamics.