Ion Partition in Polyelectrolyte Gels and Nanogels.

Polyelectrolyte gels provide a load-bearing structural framework for many macroscopic biological tissues, along with the organelles within the cells composing tissues and the extracellular matrices linking the cells at a larger length scale than the cells. In addition, they also provide a medium for the selective transportation and sequestration of ions and molecules necessary for life. Motivated by these diverse problems, we focus on modeling ion partitioning in polyelectrolyte gels immersed in a solution with a single type of ionic valence, i.e., monovalent or divalent salts. Specifically, we investigate the distribution of ions inside the gel structure and compare it with the bulk, i.e., away from the gel structure. In this first exploratory study, we neglect solvation effects in our gel by modeling the gels without an explicit solvent description, with the understanding that such an approach may be inadequate for describing ion partitioning in real polyelectrolyte gels. We see that this type of model is nonetheless a natural reference point for considering gels with solvation. Based on our idealized polymer network model without explicit solvent, we find that the ion partition coefficients scale with the salt concentration, and the ion partition coefficient for divalent ions is higher than for monovalent ions over a wide range of Bjerrum length (lB) values. For gels having both monovalent and divalent salts, we find that divalent ions exhibit higher ion partition coefficients than monovalent salt for low divalent salt concentrations and low lB. However, we also find evidence that the neglect of an explicit solvent, and thus solvation, provides an inadequate description when compared to experimental observations. Thus, in future work, we must consider both ion and polymer solvation to obtain a more realistic description of ion partitioning in polyelectrolyte gels.

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.

Ion-induced changes in DNA gels.

Small angle neutron scattering (SANS) measurements are reported for DNA gels under near physiological conditions in which the concentration of monovalent and divalent counter-ions and the pH are varied. The scattering intensity I(q) is described by a two-term equation, one due to osmotic concentration fluctuations and the other coming from static inhomogeneities frozen in by the cross-links. SANS in the low q range indicates the presence of large clusters and the size of which exceeds the resolution of the experiment. In the intermediate q-range, the intensity increases with the CaCl2 concentration and the slope approaches -1, corresponding to linear (rod-like) scatterers. In the highest q region, the scattering response is governed by the local chain geometry. Screening of electrostatic interactions by sodium chloride causes a moderate increase in the SANS intensity that is accompanied by an increase in the mesh size L of the network. Addition of calcium chloride, or a decrease in pH, produces similar trends, and ultimately leads to phase separation. The scattering intensity at q = 0, estimated from independent measurements of the osmotic pressure Π, is in excellent agreement with I(0) from the SANS measurements. Anomalous small angle X-ray scattering (ASAXS) measurements on the uncross-linked DNA show that the monovalent ion cloud is only weakly influenced by the addition of divalent ions. Conversely, the divalent counter-ion cloud tightly follows the contour of polymer chains.

Influence of solvent quality on the swelling and deswelling and the shear modulus of semi-dilute solution cross-linked poly(vinyl acetate) gels.

We systematically examine the influence of varying temperature (T) over a large range in model poly(vinyl acetate) gels swollen in isopropyl alcohol. The theta temperature Θ, at which the second virial coefficient A2 vanishes, is found to be equal to within numerical uncertainty to the corresponding high molecular mass polymer solution value without cross-links, and we quantify the swelling and deswelling of our model gels relative to their size at T = Θ, as customary for individual flexible polymer chains in solutions. We also quantify the "solvent quality" dependence of the shear modulus G relative to G(T = Θ) and compare to the hydrogel swelling factor, α. We find that all our network swelling and deswelling data can be reduced to a scaling equation of the same general form as derived from renormalization group theory for flexible linear polymer chains in solutions so that it is not necessary to invoke either the Flory-Huggins mean field theory or the Flory-Rehner hypothesis that the elastic and mixing contributions to the free energy of network swelling are separable to describe our data. We also find that changes of G relative to G(T = Θ) are directly related to α. At the same time, we find that classical rubber elasticity theory describes many aspects of these semi-dilute solution cross-linked networks, regardless of the solvent quality, although the prefactor clearly reflects the existence of network defects whose concentration depends on the initial polymer concentration of the polymer solution from which the networks were synthesized.

Prestressed Composite Polymer Gels as a Model of the Extracellular-Matrix of Cartilage.

Articular cartilage is a composite hydrogel found in animal and human joints, which exhibits unique load-bearing properties that have been challenging to reproduce in synthetic materials and model in molecular dynamics (MD) simulations. We computationally investigate a composite hydrogel that mimics key functional properties of articular cartilage as a potential biomimetic model to investigate its unique load-bearing properties. Specifically, we find that the emergence of prestress in composite gels derives primarily from the stiffness of the polymer matrix and the asymmetry in the enthalpic interactions of the embedded particles and polymer matrix. Our MD simulations of the development of prestress agree qualitatively with osmotic pressure measurements observed in our model composite hydrogel material.

Molecular dynamics study of the swelling and osmotic properties of compact nanogel particles.

Owing to their great importance in materials science and other fields, we investigate the solution and osmotic properties of uncharged compact nanogel particles over a wide range of solvent quality and particle concentration by molecular dynamics (MD) simulations. We characterize the osmotic pressure by estimating the second and third virial coefficients, and by extension, we identify the θ-point where the second virial coefficient vanishes. Calculations of the structure factor indicate that these particles are similar to macrogels in that the particle-like scattering profile disappears at moderate concentrations. We also find that improving the solvent quality enhances the spatial segmental uniformity, while significant heterogeneous structure arises near the θ-point. Well below the θ-point where the second osmotic virial coefficient vanishes, these heterogeneous structures become less prevalent as the particles tend to collapse. We also investigate the degree of swelling and structure of compact nanogel particles with a variable excluded volume interaction and gel particle concentration. The osmotic modulus and the scaling exponents in good and θ-point conditions of these gels are characteristic of interacting randomly branched polymers, i.e., "lattice animals".

Hydrogel composite mimics biological tissues.

A novel composite hydrogel was developed that shows remarkable similarities to load bearing biological tissues. The composite gel consisting of a poly(vinyl alcohol (PVA) matrix filled with poly(acrylic acid) (PAA) microgel particles exhibits osmotic and mechanical properties that are qualitatively different from regular gels. In the PVA/PAA system the swollen PAA particles "inflate" the PVA network. The swelling of the PAA is limited by the tensile stress Pel developing in the PVA matrix. Pel increases with increasing swelling degree, which is opposite to the decrease of the elastic pressure observed in regular gels. The maximum tensile stress Pmaxel can be identified as a quantity that defines the load bearing ability of the composite gel. Systematic osmotic swelling pressure measurements have been made on PVA/PAA gels to determine the effects of PVA stiffness, PAA crosslink density, and Ca2+ ion concentration on Pmaxel. It is found that Pmaxel increases with the stiffness of the PVA matrix, and decreases with (i) increasing crosslink density of the PAA and (ii) increasing Ca2+ ion concentration. Small angle neutron scattering (SANS) measurements indicate only a weak interaction between the PVA and PAA gels. It is demonstrated that the osmotic swelling pressure of PVA/PAA composite gels reproduces the osmotic behavior of healthy and osteoarthritic cartilage.

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.

"Turtle cage" method in the cardiac surgical treatment of constrictive pericarditis ­ our short-term results / "Turtle cage" módszer a pericarditis constrictiva szívsebészeti kezelésében - rövid távú eredményeink.

Összefoglaló. Bevezetés: A pericarditis constrictiva egy krónikus gyulladásos folyamat révén kialakuló betegség, melynek során a pericardium elveszíti rugalmasságát, gátolja a szív muködését, végso soron szívelégtelenséghez vezet. Egyetlen oki terápiája sebészi. A mutéti megoldásként legelterjedtebben alkalmazott teljes pericardiectomia hosszú idotartamú mutét, amely akár 18%-os mutéti kockázattal járhat, és amelyhez az esetek jelentos részében szívmotor alkalmazása szükséges. Célkituzés: Egy, az irodalomból már ismert, de csak ritkán és a legtöbbször csak a hagyományos pericardiectomia kiegészítéseként alkalmazott mutéti eljárás, a "turtle cage" pericardiectomia hatásosságának, eredményeinek, lehetséges elonyeinek vizsgálata. Módszer: 2008 és 2021 között Klinikánkon 33 "turtle cage" mutétet végeztünk pericarditis constrictiva miatt. A posztoperatív 30 napos idoszak eredményeit több, a nemzetközi irodalomban megjelent közlemény adataival hasonlítottuk össze. Eredmények: Az intraoperatív kép alapján minden esetben sikeres volt a beavatkozás, a 33 beteg egyikénél sem volt szükség szívmotor alkalmazására (0%), szemben a vizsgált közleményekkel. A 33 beavatkozás során 1 beteget veszítettünk el (3%), valamint 1 páciensnél volt szükség vérzés miatti reoperációra (3%), 4 betegnél dialízisre (12,1%). Ezen eredményeink összevethetok a nagy esetszámot felvonultató közleményekkel, és szignifikánsan jobbak az egyik megjelenített európai centrum eredményeinél. Következtetés: Az általunk alkalmazott "turtle cage" pericardiectomia önmagában is megfelelo eljárás a pericarditis constrictiva szívsebészeti kezelésére. Alkalmazásával minimalizálható a szívmotor használatának szükségessége, ezáltal a mutéti kockázat. Eredményeink a technikának köszönhetoen még a nagy esetszámú, sok tapasztalattal rendelkezo centrumok eredményeivel is összevethetok, azokkal megegyezok. Orv Hetil. 2022; 163(10): 393-399. INTRODUCTION: Constrictive pericarditis is a disease caused by a chronic inflammatory process, which is characterized by the pericardium's loss of flexibility, inhibiting the function of the heart, ultimately causing heart failure. The only definitive therapy is surgical. Total pericardiectomy, which is the most common surgical approach, is a lengthy procedure with up to 18% operative risk, and it often requires the use of cardiopulmonary bypass. OBJECTIVE: The evaluation of the effectiveness, results and possible advantages of a surgical technique, "turtle cage" pericardiectomy, which is described in the literature, although rarely used, mainly in addition to conventional pericardiectomy. METHOD: Between 2008 and 2021, we performed 33 "turtle cage" procedures on patients with constrictive pericarditis in our Institute. We compared the results of the 30-day postoperative period with internationally published data from multiple sources. RESULTS: Based on intraoperative findings, the procedure was successful in all cases, there were no instances when the use of cardiopulmonary bypass was required (0%). During the 33 procedures, we lost 1 patient (3%), reoperation was necessary for postoperative bleeding in 1 case (3%), and postoperative dialysis was necessary in 4 cases (12.1%). These results are comparable to those published by high-volume centres, and significantly better than those of one of the European centres published. CONCLUSION: The "turtle cage" pericardiectomy, as performed in our Institute, is suitable for the treatment of constrictive pericarditis on its own. With its use, we were able to minimize the use of cardiopulmonary bypass and the operative risk. Our results with this technique are comparable to those of the high-volume, highly experienced centres. Orv Hetil. 2022; 163(10): 393-399.

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.

Structure and conformational properties of ideal nanogel particles in athermal solutions.

We investigate the conformational properties of "ideal" nanogel particles having a lattice network topology by molecular dynamics simulations to quantify the influence of polymer topology on the solution properties of this type of branched molecular architecture. In particular, we calculate the mass scaling of the radius of gyration (Rg), the hydrodynamic radius, as well as the intrinsic viscosity with the variation of the degree of branching, the length of the chains between the branched points, and the average mesh size within these nanogel particles under good solvent conditions. We find competing trends between the molecular characteristics, where an increase in mesh size or degree of branching results in the emergence of particle-like characteristics, while an increase in the chain length enhances linear polymer-like characteristics. This crossover between these limiting behaviors is also apparent in our calculation of the form factor, P(q), for these structures. Specifically, a primary scattering peak emerges, characterizing the overall nanogel particle size. Moreover, a distinct power-law regime emerges in P(q) at length scales larger than the chain size but smaller than Rg of the nanogel particle, and the Rg mass scaling exponent progressively approaches zero as the mesh size increases, the same scaling as for an infinite network of Gaussian chains. The "fuzzy sphere" model does not capture this feature, and we propose an extension to this popular model. These structural features become more pronounced for values of molecular parameters that enhance the localization of the branching segments within the nanogel particle.

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.

Polyelectrolyte Gels: A Unique Class of Soft Materials.

The objective of this article is to introduce the readers to the field of polyelectrolyte gels. These materials are common in living systems and have great importance in many biomedical and industrial applications. In the first part of this paper, we briefly review some characteristic properties of polymer gels with an emphasis on the unique features of this type of soft material. Unsolved problems and possible future research directions are highlighted. In the second part, we focus on the typical behavior of polyelectrolyte gels. Many biological materials (e.g., tissues) are charged (mainly anionic) polyelectrolyte gels. Examples are shown to illustrate the effect of counter-ions on the osmotic swelling behavior and the kinetics of the swelling of model polyelectrolyte gels. These systems exhibit a volume transition as the concentration of higher valence counter-ions is gradually increased in the equilibrium bath. A hierarchy is established in the interaction strength between the cations and charged polymer molecules according to the chemical group to which the ions belong. The swelling kinetics of sodium polyacrylate hydrogels is investigated in NaCl solutions and in solutions containing both NaCl and CaCl2. In the presence of higher valence counter-ions, the swelling/shrinking behavior of these gels is governed by the diffusion of free ions in the swollen network, the ion exchange process and the coexistence of swollen and collapsed states.

Ion-Induced Volume Transition in Gels and Its Role in Biology.

Incremental changes in ionic composition, solvent quality, and temperature can lead to reversible and abrupt structural changes in many synthetic and biopolymer systems. In the biological milieu, this nonlinear response is believed to play an important functional role in various biological systems, including DNA condensation, cell secretion, water flow in xylem of plants, cell resting potential, and formation of membraneless organelles. While these systems are markedly different from one another, a physicochemical framework that treats them as polyelectrolytes, provides a means to interpret experimental results and make in silico predictions. This article summarizes experimental results made on ion-induced volume phase transition in a polyelectrolyte model gel (sodium polyacrylate) and observations on the above-mentioned biological systems indicating the existence of a steep response.

Disappearance of the polyelectrolyte peak in salt-free solutions.

We investigate the nature of the polyelectrolyte peak in salt-free solutions by molecular dynamics simulations using a minimal model of polyelectrolyte solutions that includes an explicit solvent and counterions and small angle scattering experiments. It is found that the polyelectrolyte peak progressively disappears as the strength of solvation for the charged species is increased and the scattering profiles start to resemble those of neutral polymer solutions. The disappearance of the polyelectrolyte peak coincides with the emergence of attractive interchain interactions over a wide range of length scales. These findings provide insights into the microscopic origin of the polyelectrolyte peak.

Screening lengths and osmotic compressibility of flexible polyelectrolytes in excess salt solutions.

We report results of small angle neutron scattering measurements made on sodium polystyrene sulfonate in aqueous salt solutions. The correlation length (ξ) and osmotic compressibility are measured as a function of polymer (c) and added salt (cS) concentrations, and the results are compared with scaling predictions and the random-phase approximation (RPA). In Dobrynin et al.'s scaling model the osmotic pressure consists of a counter-ion contribution and a polymer contribution. The polymer contribution is found to be two orders of magnitude smaller than expected from the scaling model, in agreement with earlier observations made on neutral polymers in good solvent condition. RPA allows the determination of single-chain dimensions in semidilute solutions at high polymer and added salt concentrations, but fails for cS≤ 2 M. The χ parameter can be modelled as the sum of an intrinsic contribution (χ0) and an electrostatic term: χ∼χ0 + K'/√cS, where χ0 > 0.5 is consistent with the hydrophobic nature of the backbone of NaPSS. The dependence of χelec∼ 1/√cS disagrees with the random-phase approximation (χelec∼ 1/cs), but agrees with the light scattering results in dilute solution and Dobrynin et al.'s scaling treatment of electrostatic excluded volume.

Composite Hydrogel Model of Cartilage Predicts Its Load-Bearing Ability.

Articular cartilage is a load-bearing tissue found in animal and human joints. It is a composite gel-like material in which a fibrous collagen network encapsulates large proteoglycan assemblies that imbibe fluid and "inflate" the network. Here we describe a composite hydrogel consisting of a cross-linked polyvinyl alcohol matrix filled with poly(acrylic acid) microparticles that mimics functional properties and biomechanical behavior of cartilage. The swelling and mechanical behaviors of this biomimetic model system are strikingly similar to that of human cartilage. The development of synthetic composite gel-based articular cartilage analog suggests new avenues to explore material properties, and their change in disease and degeneration, as well as novel strategies for developing composite tissue-engineered cartilage constructs for regenerative medicine applications.

Outcomes After Left Main Coronary Artery Revascularization by Percutaneous Coronary Intervention or Coronary Artery Bypass Grafting According to Smoking Status.

Cigarette smoking is a well-known risk factor for coronary artery disease (CAD). However, the impact of smoking on outcomes after coronary revascularization, especially in patients with left main CAD (LMCAD) is less well understood. The EXCEL trial randomized 1,905 patients with LMCAD and visually assessed low or intermediate anatomical complexity (SYNTAX score ≤32) to PCI with everolimus-eluting stents or CABG. Patients were categorized according to smoking status (current, former, or never), and their outcomes at 5 years were compared by logistic regression with follow-up time included as a log-transformed offset variable. The primary endpoint was a composite of death, myocardial infarction, or stroke. Among 1893 patients with known smoking status at baseline, 416 (22%) were current smokers and 774 (41%) were former smokers. The crude rates of the primary endpoint were 19.5% for never smokers, 20.5% for former smokers (p = 0.61 vs never smokers), and 23.1% for smokers (p = 0.15 vs never smokers). Compared with never smokers, the adjusted risk of the primary endpoint was higher for current smokers (adjOR 1.82, 95% confidence interval [CI] 1.126 to 2.63; p = 0.001), but not for former smokers (adjOR 1.00, 95% CI 0.75 to 1.33, p = 0.10). The relative efficacy of PCI versus CABG for the 5-year primary endpoint was similar irrespective of smoking status (Pinteraction = 0.22). In conclusion, current smokers in the EXCEL trial had a higher adjusted 5-year risk of the primary composite endpoint of death, myocardial infarction, or stroke than never smokers, whereas former smokers were not at increased risk. Active smoking was a risk factor after LMCAD revascularization irrespective of revascularization method.

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

There is a great interest in the synthesis and characterization of polyelectrolytes that mimic naturally occurring bottlebrush polyelectrolytes to capitalize on the unique properties of this class of macromolecules. Charged bottlebrush polymers form the protective mucus layer in the lungs, stomach, and orifices of animals and provide osmotic stabilization and lubrication to joints. In the present work, we systematically investigate bottlebrush poly(sodium acrylates) through a combination of measurements of solution properties (osmometry, small-angle neutron scattering, and dynamic light scattering) and molecular dynamics simulations, where the bottlebrush properties are compared in each case to their linear polymer counterparts. These complementary experimental and computational methods probe vastly different length- and timescales, allowing for a comprehensive characterization of the supermolecular structure and dynamics of synthetic polyelectrolyte bottlebrush molecules in solution.

Experimental Evidence for Universal Behavior of Ion-Induced Volume Phase Transition in Sodium Polyacrylate Gels.

Introduction of high valence counterions into polyelectrolyte gels results in a reversible volume phase transition. In the present work new experimental results are reported for the volume transition induced by calcium/sodium exchange in sodium polyacrylate gels. The effects of cross-link density, concentration of ionized groups on the network chains, composition of the equilibrium salt solution containing both mono- and divalent cations, and temperature on the swelling degree of these gels are systematically investigated. It is demonstrated that the normalized swelling data fall on a master curve, indicating that the ion-exchange-induced volume transition exhibits universal behavior in sodium polyacrylate gels. Model calculations made on the basis of the classical Flory-Rehner theory are in reasonable agreement with the measured dependencies.