Systematic investigation of synthetic polyelectrolyte bottlebrush solutions by neutron and dynamic light scattering, osmometry, and molecular dynamics simulation

Cartilage extracellular matrix polymers: hierarchical structure, osmotic properties, and function

Proteoglycans are hierarchically organized structures that play an important role in the hydration and the compression resistance of cartilage matrix. In this study, the static and dynamic properties relevant to the biomechanical function of cartilage are determined at different levels of the hierarchical structure, using complementary osmotic pressure, neutron scattering (SANS) and light scattering (DLS) measurements. In cartilage proteoglycans (PGs), two levels of bottlebrush structures can be distinguished: the aggrecan monomer, which consists of a core protein to which are tethered charged glycosaminoglycan (GAG) chains, and complexes formed of the aggrecan monomers attached around a linear hyaluronic acid backbone. The principal component of GAG, chondroitin sulfate (CS), is used as a baseline in this comparison. The osmotic modulus, measured as a function of the proteoglycan concentration, follows the order CS < aggrecan < aggrecan-HA complex. This order underlines the benefit of the increasing complexity at each level of the molecular architecture. The hierarchical bottlebrush configuration, which prevents interpenetration among the bristles of the aggrecan monomers, enhances both the mechanical properties and the osmotic resistance. The osmotic pressure of the collagen solution is notably smaller than in the proteoglycan systems. This is consistent with its known primary role to provide tensile strength to the cartilage and to confine the aggrecan-HA complexes, as opposed to load bearing. The collective diffusion coefficient D governs the rate of recovery of biological tissue after compressive load. In CS solutions the diffusion process is fast, D ≈ 3 × 10-6 cm2 s-1 at concentrations comparable with that of the GAG chains inside the aggrecan molecule. In CS solutions D is a weakly decreasing function of calcium ion concentration, while in aggrecan and its complexes with HA, the relaxation rate is insensitive to the presence of calcium.

Coexistence of Crumpling and Flat Sheet Conformations in Two-Dimensional Polymer Networks: An Understanding of Aggrecan Self-Assembly

We investigate the conformational properties of self-avoiding two-dimensional (2D) ideal polymer networks with tunable mesh sizes as a model of self-assembled structures formed by aggrecan. Polymer networks having few branching points and large enough mesh tend to crumple, resulting in a fractal dimension of d_{f}≈2.7. The flat sheet behavior (d_{f}=2) emerges in 2D polymer networks having more branching points at large length scales; however, it coexists with crumpling conformations at intermediate length scales, a feature found in scattering profiles of aggrecan solutions. Our findings bridge the long-standing gap between theories and simulations of polymer sheets.

Conformation of a Comb-like Chain in Solution: Effect of Backbone Rigidity

We study the effect of backbone rigidity on the conformation of comb-like chains in dilute solution by using Brownian dynamics simulations. Our results demonstrate that the backbone rigidity can control the effect of side chains on the conformation of comb-like chains; that is, the relative strength of the excluded-volume interactions from backbone monomer-graft and graft-graft to backbone monomer-monomer gradually weakens with the increase of backbone rigidity. Only when the rigidity of the backbone tends to be flexible and the grafting density is high is the effect of excluded volume of graft-graft on the conformation of comb-like chains significant enough, and other cases can be ignored. Our results show that the radius of gyration of comb-like chains and the persistence length of the backbone are exponentially related to the stretching factor, where the power exponent exhibits an increase with the increase of the strength of bending energy. These finds provide new insights for characterizing the structure properties of comb-like chains.

Swelling, collapse and ordering of rod-like microgels in solution: Computer simulation studies

Polymer microgels have proven to be highly promising macromolecular objects for a wide variety of applications. In particular, the soft particles of an anisotropic (rod-like) shape are of special interest because of their potential use in tissue engineering or materials design. However, a little is known about the physical behavior of such microgels in solution, which inspired us to study them using mesoscopic computer simulations. For single networks, depending on the solvent quality, the dimensional characteristics were obtained for microgels of different molecular weight, crosslinking density and aspect ratio. In particular, the conditions for the rod-to-rod (preserving the nonspherical shape) and rod-to-sphere collapse were found. In addition, the effect of the liquid-crystalline (LC) ordering was demonstrated for the ensemble of rod-like microgels at different swelling ratios, and the influence of microgel aspect ratio on the volume fraction of the LC transition was shown.

Perineuronal nets restrict transport near the neuron surface: A coarse-grained molecular dynamics study

Perineuronal nets (PNNs) are mesh-like extracellular matrix structures that wrap around certain neurons in the central nervous system. They are hypothesized to stabilize memories in the brain and act as a barrier between cell and extracellular space. As a means to study the impact of PNNs on diffusion, the nets were approximated by negatively charged polymer brushes and simulated by coarse-grained molecular dynamics. Diffusion constants of single neutral and single charged particles were obtained in directions parallel and perpendicular to the brush substrate. The results for the neutral particle were compared to different theories of diffusion in a heuristic manner. Diffusion was found to be considerably reduced for brush spacings smaller than 10 nm, with a pronounced anisotropy for dense brushes. The exact dynamics of the chains was found to have a negligible impact on particle diffusion. The resistance of the brush proved small compared to typical values of the membrane resistance of a neuron, indicating that PNNs likely contribute little to the total resistance of an enwrapped neuron.

Influence of network defects on the conformational structure of nanogel particles: From "closed compact" to "open fractal" nanogel particles

We propose an approach to generate a wide range of randomly branched polymeric structures to gain general insights into how polymer topology encodes a configurational structure in solution. Nanogel particles can take forms ranging from relatively symmetric sponge-like compact structures to relatively anisotropic open fractal structures observed in some nanogel clusters and in some self-associating polymers in solutions, such as aggrecan solutions under physiologically relevant conditions. We hypothesize that this broad "spectrum" of branched polymer structures derives from the degree of regularity of bonding in the network defining these structures. Accordingly, we systematically introduce bonding defects in an initially perfect network having a lattice structure in three and two topological dimensions corresponding to "sponge" and "sheet" structures, respectively. The introduction of bonding defects causes these "closed" and relatively compact nanogel particles to transform near a well-defined bond percolation threshold into "open" fractal objects with the inherent anisotropy of randomly branched polymers. Moreover, with increasing network decimation, the network structure of these polymers acquires other configurational properties similar to those of randomly branched polymers. In particular, the mass scaling of the radius of gyration and its eigenvalues, as well as hydrodynamic radius, intrinsic viscosity, and form factor for scattering, all undergo abrupt changes that accompany these topological transitions. Our findings support the idea that randomly branched polymers can be considered to be equivalent to perforated sheets from a "universality class" standpoint. We utilize our model to gain insight into scattering measurements made on aggrecan solutions.

Evidence of Many-Body Interactions in the Virial Coefficients of Polyelectrolyte Gels

Simulation studies of aqueous polymer solutions, and heuristic arguments by De Gennes for aqueous polyethylene oxide polymer solutions, have suggested that many-body interactions can give rise to the ‘anomalous’ situation in which the second osmotic virial coefficient is positive, while the third virial coefficient is negative. This phenomenon was later confirmed in analytic calculations of the phase behavior and the osmotic pressure of complex fluids exhibiting cooperative self-assembly into extended dynamic polymeric structures by Dudowicz et al. In the present study, we experimentally confirm the occurrence of this osmotic virial sign inversion phenomenon for several highly charged model polyelectrolyte gels (poly(acrylic acid), poly(styrene sulfonate), DNA, hyaluronic acid), where the virial coefficients are deduced from osmotic pressure measurements. Our observations qualitatively accord with experimental and simulation studies indicating that polyelectrolyte materials exhibit supramolecular assembly in solution, another symptomatic property of fluids exhibiting many-body interactions. We also find that the inversion in the variation of the second (A₂) and third (A₂) virial coefficients upon approach to phase separation does not occur in uncharged poly(vinyl acetate) gels. Finally, we briefly discuss the estimation of the osmotic compressibility of swollen polyelectrolyte gels from neutron scattering measurements as an alternative to direct, time-consuming and meticulous osmotic pressure measurements. We conclude by summarizing some general trends and suggesting future research directions of natural and synthetic polyelectrolyte hydrogels.

Hybrid polarizable simulations of a conventional hydrophobic polyelectrolyte. Toward a theoretical tool for green science innovation

Hybrid modeling approaches based on all-atom force fields to handle a solute and coarse-grained models to account for the solvent are promising numerical tools that can be used to understand the properties of large and multi-components solutions and thus to speed up the development of new industrial products that obey the standard of green and sustainable chemistry. Here, we discuss the ability of a full polarizable hybrid approach coupled to a standard molecular dynamics scheme to model the behavior in the aqueous phase and at infinite dilution conditions of a standard hydrophobic polyelectrolyte polymer whose charge is neutralized by explicit counterions. Beyond the standard picture of a polyelectrolyte behavior governed by an interplay between opposite intra-polyelectrolyte and inter-polyelectrolyte/counterion Coulombic effects, our simulations show the key role played by both intra-solute polarization effects and long range solute/solvent electrostatics to stabilize compact globular conformations of that polyelectrolyte. Our full polarizable hybrid modeling approach is thus a new theoretical tool well suited to be used in digital strategies for accelerating innovation for green science, for instance.

Comparative experimental and computational study of synthetic and natural bottlebrush polyelectrolyte solutions

We systematically investigate model synthetic and natural bottlebrush polyelectrolyte solutions through an array of experimental techniques (osmometry and neutron and dynamic light scattering) along with molecular dynamics simulations to characterize and contrast their structures over a wide range of spatial and time scales. In particular, we perform measurements on solutions of aggrecan and the synthetic bottlebrush polymer, poly(sodium acrylate), and simulations of solutions of highly coarse-grained charged bottlebrush molecules having different degrees of side-branch density and inclusion of an explicit solvent and ion hydration effects. While both systems exhibit a general tendency toward supramolecular organization in solution, bottlebrush poly(sodium acrylate) solutions exhibit a distinctive "polyelectrolyte peak" in their structure factor, but no such peak is observed in aggrecan solutions. This qualitative difference in scattering properties, and thus polyelectrolyte solution organization, is attributed to a concerted effect of the bottlebrush polymer topology and the solvation of the polymer backbone and counterions. The coupling of the polyelectrolyte topological structure with the counterion distribution about the charged polymer molecules along with direct polymer segmental hydration makes their solution organization and properties "tunable," a phenomenon that has significant ramifications for biological function and disease as well as for numerous materials applications.