Precision measurements of osmotic pressure in concentrated polymer solutions

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.

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.

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.

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 P_el developing in the PVA matrix. P_el 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.

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.

Control of nuclear size by osmotic forces in Schizosaccharomyces pombe

The size of the nucleus scales robustly with cell size so that the nuclear-to-cell volume ratio (N/C ratio) is maintained during cell growth in many cell types. The mechanism responsible for this scaling remains mysterious. Previous studies have established that the N/C ratio is not determined by DNA amount but is instead influenced by factors such as nuclear envelope mechanics and nuclear transport. Here, we developed a quantitative model for nuclear size control based upon colloid osmotic pressure and tested key predictions in the fission yeast Schizosaccharomyces pombe. This model posits that the N/C ratio is determined by the numbers of macromolecules in the nucleoplasm and cytoplasm. Osmotic shift experiments showed that the fission yeast nucleus behaves as an ideal osmometer whose volume is primarily dictated by osmotic forces. Inhibition of nuclear export caused accumulation of macromolecules in the nucleoplasm, leading to nuclear swelling. We further demonstrated that the N/C ratio is maintained by a homeostasis mechanism based upon synthesis of macromolecules during growth. These studies demonstrate the functions of colloid osmotic pressure in intracellular organization and size control.

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.

Universal Equation of State Describes Osmotic Pressure throughout Gelation Process

The equation of state of the osmotic pressure for linear-polymer solutions in good solvents is universally described by a scaling function. We experimentally measure the osmotic pressure of the gelation process via osmotic deswelling. We find that the same scaling function for linear-polymer solutions also describes the osmotic pressure throughout the gelation process involving both the sol and gel states. Furthermore, we reveal that the osmotic pressure of polymer gels is universally governed by the semidilute scaling law of linear-polymer solutions.

Jones R, Lou J, Xia Y. 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.

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.

Structure, dynamics and phase behavior of short rod inclusions dissolved in a colloidal membrane

Inclusions dissolved in an anisotropic quasi-2D membrane acquire new types of interactions that can drive assembly of complex structures and patterns. We study colloidal membranes composed of a binary mixture of long and short rods, such that the length ratio of the long to short rods is approximately two. At very low volume fractions, short rods dissolve in the membrane of long rods by strongly anchoring to the membrane polymer interface. At higher fractions, the dissolved short rods phase separate from the background membrane, creating a composite structure comprised of bilayer droplets enriched in short rods that coexist with the background monolayer membrane. These results demonstrate that colloidal membranes serve as a versatile platform for assembly of soft materials, while simultaneously providing new insight into universal membrane-mediated interactions.

Equation of state of colloidal membranes

In the presence of a non-adsorbing polymer, monodisperse rod-like colloids assemble into one-rod-length thick liquid-like monolayers, called colloidal membranes. The density of the rods within a colloidal membrane is determined by a balance between the osmotic pressure exerted by the enveloping polymer suspension and the repulsion between the colloidal rods. We developed a microfluidic device for continuously observing an isolated membrane while dynamically controlling the osmotic pressure of the polymer suspension. Using this technology we measured the membrane rod density over a range of osmotic pressures than is wider that what is accessible in equilibrium samples. With increasing density we observed a first-order phase transition, in which the in-plane membrane order transforms from a 2D fluid into a 2D solid. In the limit of low osmotic pressures, we measured the rate at which individual rods evaporate from the membrane. The developed microfluidic technique could have wide applicability for in situ investigation of various soft materials and how their properties depend on the solvent composition.

Colloid osmotic parameterization and measurement of subcellular crowding

Crowding of the subcellular environment by macromolecules is thought to promote protein aggregation and phase separation. A challenge is how to parameterize the degree of crowding of the cell interior or artificial solutions that is relevant to these reactions. Here I review colloid osmotic pressure as a crowding metric. This pressure is generated by solutions of macromolecules in contact with pores that are permeable to water and ions but not macromolecules. It generates depletion forces that push macromolecules together in crowded solutions and thus promotes aggregation and phase separation. I discuss measurements of colloid osmotic pressure inside cells using the nucleus, the cytoplasmic gel, and fluorescence resonant energy transfer (FRET) biosensors as osmometers, which return a range of values from 1 to 20 kPa. I argue for a low value, 1-2 kPa, in frog eggs and perhaps more generally. This value is close to the linear range on concentration-pressure curves and is thus not crowded from an osmotic perspective. I discuss the implications of a low crowding pressure inside cells for phase separation biology, buffer design, and proteome evolution. I also discuss a pressure-tension model for nuclear shape, where colloid osmotic pressure generated by nuclear protein import inflates the nucleus.

Effects of mono- and divalent cations on the structure and thermodynamic properties of polyelectrolyte gels

Measurements are reported on the effect of monovalent and divalent salts on the swelling behavior and supramolecular structure of sodium polyacrylate gels (NaPA) made by osmotic swelling pressure and small angle neutron scattering measurements. The swelling response of the gels in solutions of ten different monovalent salts is found to be practically identical indicating that the principal effect of monovalent ions is screening the electrostatic repulsion among the charged groups on the polyelectrolyte chains; i.e., chemical differences between the monovalent ions do not play a significant role. Introducing Ca2+ ions into the equilibrium NaCl solution results in a sharp volume transition of the gels. The threshold Ca2+ ion concentration at which the transition occurs increases with increasing NaCl concentration in the surrounding bath. It is demonstrated that the swelling behavior of NaPA gels exhibits universal properties in solutions containing both NaCl and CaCl2. Osmotic swelling pressure measurements reveal that both the second and third virial coefficients decrease with increasing CaCl2 concentration until the volume transition is reached. The macroscopic measurements are complemented by small angle neutron scattering that reveals the variation of the thermodynamic length scales as the volume transition is approached. The thermodynamic correlation length L increases with increasing CaCl2 concentration.

Thermodynamics of the Water-Retaining Properties of Cellulose-Based Networks

Noncrystalline cellulose-based gel beads were used as a model material to investigate the effect of osmotic stress on a cellulosic network. The gel beads were exposed to osmotic stress by immersion in solutions with different concentrations of high molecular mass dextran and the equilibrium dimensional change of the gel beads was studied using optical microscopy. The volume fraction of cellulose was calculated from the volume of the gel beads in dextran solutions and their dry content and the relation between the cellulose volume fraction and the total osmotic pressure was thus obtained. The results show that the contribution to the osmotic pressure from counterions increases the water-retaining capacity of the beads at high osmotic pressures but also that the main factor controlling the gel bead collapse at high osmotic strains is the resistance to the deformation of the polymer chain network within the beads. Furthermore, the osmotic pressure associated with the deformation of the polymer network, which counteracts the deswelling of the beads, could be fitted to the Wall model indicating that the response of the cellulose polymer networks was independent of the charge of the cellulose. The best fit to the Wall model was obtained when the Flory-Huggins interaction parameter (χ) of the cellulose-water system was set to 0.55-0.60, in agreement with the well-established insolubility of high molecular mass β-(1,4)-d-glucan polymers in water.

Three cooperative diffusion coefficients describing dynamics of polymer gels

Cooperative diffusion coefficient (Dcoop) describes the dynamics of a polymer network in a gel, and is estimated by three independent methods. We measured three Dcoop's of a model polymer network system (Tetra-PEG gels), and obtained the experimental evidence to fundamentally understand the dynamics of polymer gels.

Radial stiffness characteristics of the overlap regions of sarcomeres in isolated skeletal myofibrils in pre-force generating state

We have studied the stiffness of myofilament lattice in sarcomeres in the pre-force generating state, which was realized by a relaxing reagent, BDM (butane dione monoxime). First, the radial stiffness for the overlap regions of sarcomeres of isolated single myofibrils was estimated from the resulting decreases in diameter by osmotic pressure applied with the addition of Dextran. Then, the radial stiffness was also estimated from force-distance curve measurements with AFM technology. The radial stiffness for the overlap regions thus obtained was composed of a soft and a rigid component. The soft component visco-elastically changed in a characteristic fashion depending on the physiological conditions of myofibrils, suggesting that it comes from cross-bridge structures. BDM treatments significantly affected the soft radial component of contracting myofibrils depending on the approach velocity of cantilever: It was nearly equal to that in the contracting state at high approach velocity, whereas as low as that in the relaxing state at low approach velocity. However, comparable BDM treatments greatly suppressed the force production and the axial stiffness in contracting glycerinated muscle fibers and also the sliding velocity of actin filaments in the in vitro motility assay. Considering that BDM shifts the cross-bridge population from force generating to pre-force generating states in contracting muscle, the obtained results strongly suggest that cross-bridges in the pre-force generating state are visco-elastically attached to the thin filaments in such a binding manner that the axial stiffness is low but the radial stiffness significantly high similar to that in force generating state.

Structure and Properties of Cartilage Proteoglycans

The most abundant cartilage proteoglycan is aggrecan, a bottlebrush shaped molecule that possesses over 100 glycosaminoglycan (chondroitin sulfate and keratan sulfate) chains. The side-chains are linear sulfated polysaccharides that are negatively charged under physiological conditions. Aggrecan interacts with hyaluronic acid (HA) to form large aggregates. Osmotic pressure measurements and rheological measurements are used to study the static and dynamic behavior of aggrecan assemblies at the macroscopic length scales. The microscopic properties of aggrecan solutions are determined by small angle neutron scattering (SANS), and static and dynamic light scattering (SLS and DLS). In dilute solutions aggrecan forms microgels with a diffuse boundary, composed of loosely connected clusters. The osmotic pressure of the aggrecan-HA system decreases with increasing HA content. DLS yields a relaxation rate that varies as q3, arising from internal modes in the microgel. The relaxation rate in the solutions of the aggrecan-HA complex is slightly greater than in the pure aggrecan solution.

Effect of calcium/sodium ion exchange on the osmotic properties and structure of polyelectrolyte gels

We discuss the main findings of a long-term research program exploring the consequences of sodium/calcium ion exchange on the macroscopic osmotic and elastic properties, and the microscopic structure of representative synthetic polyelectrolyte (sodium polyacrylate, (polyacrylic acid)) and biopolymer gels (DNA). A common feature of these gels is that above a threshold calcium ion concentration, they exhibit a reversible volume phase transition. At the macroscopic level, the concentration dependence of the osmotic pressure shows that calcium ions influence primarily the third-order interaction term in the Flory-Huggins model of polymer solutions. Mechanical tests reveal that the elastic modulus is practically unaffected by the presence of calcium ions, indicating that ion bridging does not create permanent cross-links. At the microscopic level, small-angle neutron scattering shows that polyacrylic acid and DNA gels exhibit qualitatively similar structural features in spite of important differences (e.g. chain flexibility and chemical composition) between the two polymers. The main effect of calcium ions is that the neutron scattering intensity increases due to the decrease in the osmotic modulus. At the level of the counterion cloud around dissolved macroions, anomalous small-angle X-ray scattering measurements made on DNA indicate that divalent ions form a cylindrical sheath enveloping the chain, but they are not localized. Small-angle neutron scattering and small-angle X-ray scattering provide complementary information on the structure and interactions in polymer solutions and gels.

Impact of confining 3-D polymer networks on dynamics of bacterial ingress and self-organisation

Alignment of microbial colonies along with polymeric cell wall.

Accurate calibration and control of relative humidity close to 100% by X-raying a DOPC multilayer

In this study, we have designed a compact sample chamber that can achieve accurate and continuous control of the relative humidity (RH) in the vicinity of 100%. A 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) multilayer can be used as a humidity sensor by measuring its inter-layer repeat distance (d-spacing) via X-ray diffraction. We convert from DOPC d-spacing to RH according to a theory given in the literature and previously measured data of DOPC multilamellar vesicles in polyvinylpyrrolidone (PVP) solutions. This curve can be used for calibration of RH close to 100%, a regime where conventional sensors do not have sufficient accuracy. We demonstrate that this control method can provide RH accuracies of 0.1 to 0.01%, which is a factor of 10-100 improvement compared to existing methods of humidity control. Our method provides fine tuning capability of RH continuously for a single sample, whereas the PVP solution method requires new samples to be made for each PVP concentration. The use of this cell also potentially removes the need for an X-ray or neutron beam to pass through bulk water if one wishes to work close to biologically relevant conditions of nearly 100% RH.

Osmocapsules for direct measurement of osmotic strength

Monodisperse microcapsules with ultra-thin membranes are microfluidically designed to be highly sensitive to osmotic pressure, thereby providing a tool for the direct measurement of the osmotic strength. To make such osmocapsules, water-in-oil-in-water double-emulsion drops with ultra-thin shells are prepared as templates through emulsification of core-sheath biphasic flow in a capillary microfluidic device. When photocurable monomers are used as the oil phase, the osmocapsules are prepared by in-situ photopolymerization of the monomers, resulting in semipermeable membranes with a relatively large ratio of membrane thickness to capsule radius, approximately 0.02. These osmocapsules are buckled by the outward flux of water when they are subjected to a positive osmotic pressure difference above 125 kPa. By contrast, evaporation-induced consolidation of middle-phase containing polymers enables the production of osmocapsules with a small ratio of membrane thickness to capsule radius of approximately 0.002. Such an ultra-thin membrane with semi-permeability makes the osmocapsules highly sensitive to osmotic pressure; a positive pressure as small as 12.5 kPa induces buckling of the capsules. By employing a set of distinct osmocapsules confining aqueous solutions with different osmotic strengths, the osmotic strength of unknown solutions can be estimated through observation of the capsules that are selectively buckled. This approach provides the efficient measurement of the osmotic strength using only a very small volume of liquid, thereby providing a useful alternative to other measurement methods which use complex setups. In addition, in-vivo measurement of the osmotic strength can be potentially accomplished by implanting these biocompatible osmocapsules into tissue, which is difficult to achieve using conventional methods.

Thick-to-thin filament surface distance modulates cross-bridge kinetics in Drosophila flight muscle

The demembranated (skinned) muscle fiber preparation is widely used to investigate muscle contraction because the intracellular ionic conditions can be precisely controlled. However, plasma membrane removal results in a loss of osmotic regulation, causing abnormal hydration of the myofilament lattice and its proteins. We investigated the structural and functional consequences of varied myofilament lattice spacing and protein hydration on cross-bridge rates of force development and detachment in Drosophila melanogaster indirect flight muscle, using x-ray diffraction to compare the lattice spacing of dissected, osmotically compressed skinned fibers to native muscle fibers in living flies. Osmolytes of different sizes and exclusion properties (Dextran T-500 and T-10) were used to differentially alter lattice spacing and protein hydration. At in vivo lattice spacing, cross-bridge attachment time (t(on)) increased with higher osmotic pressures, consistent with a reduced cross-bridge detachment rate as myofilament protein hydration decreased. In contrast, in the swollen lattice, t(on) decreased with higher osmotic pressures. These divergent responses were reconciled using a structural model that predicts t(on) varies inversely with thick-to-thin filament surface distance, suggesting that cross-bridge rates of force development and detachment are modulated more by myofilament lattice geometry than protein hydration. Generalizing these findings, our results suggest that cross-bridge cycling rates slow as thick-to-thin filament surface distance decreases with sarcomere lengthening, and likewise, cross-bridge cycling rates increase during sarcomere shortening. Together, these structural changes may provide a mechanism for altering cross-bridge performance throughout a contraction-relaxation cycle.

Interactions of Cartilage Extracellular Matrix Macromolecules

Articular cartilage is a low-friction, load-bearing tissue located at joint surfaces. The extracellular matrix (ECM) of cartilage consists of a fibrous collagen network, which is pre-stressed by the osmotic swelling pressure exerted by negatively charged proteoglycan aggregates embedded in the collagen network. The major proteoglycan is the bottlebrush shaped aggrecan, which forms complexes with linear hyaluronic acid chains. We quantify microscopic and macroscopic changes resulting from self-assembly between aggrecan and hyaluronic acid using a complementary set of physical measurements to determine structure and interactions by combining scattering techniques, including small-angle X-ray scattering, small-angle neutron scattering, and dynamic light scattering with macroscopic osmotic pressure measurements. It is demonstrated that the osmotic pressure that defines the load bearing ability of cartilage is primarily governed by the main macromolecular components (aggrecan and collagen) of the ECM. Knowledge of the interactions between the macromolecular components of cartilage ECM is essential to understand biological function and to develop successful tissue engineering strategies for cartilage repair.

Controlling interactions in supported bilayers from weak electrostatic repulsion to high osmotic pressure

Understanding interactions between membranes requires measurements on well-controlled systems close to natural conditions, in which fluctuations play an important role. We have determined, by grazing incidence X-ray scattering, the interaction potential between two lipid bilayers, one adsorbed on a solid surface and the other floating close by. We find that interactions in this highly hydrated model system are two orders of magnitude softer than in previously reported work on multilayer stacks. This is attributed to the weak electrostatic repulsion due to the small fraction of ionized lipids in supported bilayers with a lower number of defects. Our data are consistent with the Poisson-Boltzmann theory, in the regime where repulsion is dominated by the entropy of counter ions. We also have unique access to very weak entropic repulsion potentials, which allowed us to discriminate between the various models proposed in the literature. We further demonstrate that the interaction potential between supported bilayers can be tuned at will by applying osmotic pressure, providing a way to manipulate these model membranes, thus considerably enlarging the range of biological or physical problems that can be addressed.

Thermodynamic Analysis of the Selectivity Enhancement Obtained by Using Smart Hydrogels That Are Zwitterionic When Detecting Glucose With Boronic Acid Moieties

Because the boronic acid moiety reversibly binds to sugar molecules and has low cytotoxicity, boronic acid-containing hydrogels are being used in a variety of implantable glucose sensors under development, including sensors based on optical, fluorescence, and swelling pressure measurements. However, some method of glucose selectivity enhancement is often necessary, because isolated boronic acid molecules have a binding constant with glucose that is some forty times smaller than their binding constant with fructose, the second most abundant sugar in the human body. In many cases, glucose selectivity enhancement is obtained by incorporating pendant tertiary amines into the hydrogel network, thereby giving rise to a hydrogel that is zwitterionic at physiological pH. However, the mechanism by which incorporation of tertiary amines confers selectivity enhancement is poorly understood. In order to clarify this mechanism, we use the osmotic deswelling technique to compare the thermodynamic interactions of glucose and fructose with a zwitterionic smart hydrogel containing boronic acid moieties. We also investigate the change in the structure of the hydrogel that occurs when it binds to glucose or to fructose using the technique of small angle neutron scattering.

Hierarchical organization of cartilage proteoglycans

The hierarchical organization of cartilage proteoglycans is investigated on different length and time scales using osmotic pressure measurements, small angle neutron scattering (SANS), small angle X-ray scattering (SAXS), static and dynamic light scattering and neutron spin echo techniques. Osmotic pressure measurements reveal association of aggrecan bottlebrushes into microgel-like assemblies. SAXS, SANS and light scattering results indicate weak interpenetration between neighboring aggrecan molecules. As opposed to DNA and many synthetic polyelectrolytes, which display great sensitivity to ion valence, aggrecan exhibits exceptional insensitivity to calcium ions in the physiological ion concentration range and beyond. This property allows aggrecan to play a role of ion reservoir that can mediate calcium metabolism in cartilage and bone.

Regulatory light chain phosphorylation and N-terminal extension increase cross-bridge binding and power output in Drosophila at in vivo myofilament lattice spacing

The N-terminal extension and phosphorylation of the myosin regulatory light chain (RLC) independently improve Drosophila melanogaster flight performance. Here we examine the functional and structural role of the RLC in chemically skinned fibers at various thick and thin filament lattice spacings from four transgenic Drosophila lines: rescued null or control (Dmlc2(+)), truncated N-terminal extension (Dmlc2(Δ2-46)), disrupted myosin light chain kinase phosphorylation sites (Dmlc2(S66A,S67A)), and dual mutant (Dmlc2(Δ2-46; S66A,S67A)). The N-terminal extension truncation and phosphorylation sites disruption mutations decreased oscillatory power output and the frequency of maximum power output in maximally Ca(2+)-activated fibers compressed to near in vivo inter-thick filament spacing, with the phosphorylation sites disruption mutation having a larger affect. The diminished power output parameters with the N-terminal extension truncation and phosphorylation sites disruption mutations were due to the reduction of the number of strongly-bound cross-bridges and rate of myosin force production, with the larger parameter reductions in the phosphorylation sites disruption mutation additionally related to reduced myosin attachment time. The phosphorylation and N-terminal extension-dependent boost in cross-bridge kinetics corroborates previous structural data, which indicate these RLC attributes play a complementary role in moving and orienting myosin heads toward actin target sites, thereby increasing fiber and whole fly power generation.

Structural, mechanical and osmotic properties of injectable hyaluronan-based composite hydrogels

The osmotic and scattering properties of hyaluronan-based composite hydrogels composed of stiff biopolymer chains (carboxymethylated thiolated hyaluronan (CMHA-S)) crosslinked by a flexible polymer (polyethylene glycol diacrylate (PEGDA)) are investigated and analyzed in terms of the scaling theory. The total pre-gel polymer weight concentration is varied between 0.5 wt.% and 3.2 wt.%, while the mole ratio between the reactive PEG chain ends and the thiolated HA moieties is changed between 0.15 and 1.0. The shear modulus G of the fully swollen gels exhibits a stronger dependence on pre-gel concentration than on the crosslink density. Osmotic deswelling measurements reveal that the osmotic mixing pressure depends on the weight ratio CMHA-S/PEGDA, and is practically unaffected by the pre-gel concentration. Small-angle neutron scattering observations indicate that the thermodynamic properties of these composite gels are governed by total polymer concentration, i.e., specific interactions between the two polymeric components do not play a significant role.

Counterion and pH-Mediated Structural Changes in Charged Biopolymer Gels

DNA solutions and gels exhibit a wide range of phenomena, many of which have not yet been fully understood. In the presence of multivalent counterions, attraction between charged DNA strands occurs. Increasing the concentration of multivalent ions leads to a decrease of the osmotic pressure, and a sufficiently high ion concentration results in the precipitation of the polymer. Replacing the monovalent counterions by hydrogen ions (decreasing the pH) also produces a marked decrease of the osmotic pressure, and at low pH a phase transition takes place. In this paper we analyze osmotic swelling pressure measurements and small-angle neutron scattering (SANS) measurements made on chemically cross-linked DNA gels swollen in near physiological salt solutions. The effect of calcium ions is compared with that of decreasing the pH of the equilibrium salt solution. We demonstrate that both the concentration dependence of the osmotic pressure and the SANS response of DNA gels display significant differences in the two cases.

Mapping the local osmotic modulus of polymer gels

Polymer gels undergo volume phase transition in a thermodynamically poor solvent as a result of changes in molecular interactions. The osmotic pressure of gels, both synthetic and biological in nature, induces swelling and imparts the materials with the capacity to resist compressive loads. We have investigated the mechanical and swelling properties of poly(vinyl alcohol) (PVA) gels brought into the unstable state by changing the composition of the solvent. Chemically cross-linked PVA gels were prepared and initially swollen in water at 25 degrees C, and then n-propyl alcohol (nonsolvent) was gradually added to the equilibrium liquid. AFM imaging and force-indentation measurements were made in water/n-propyl alcohol mixtures of different composition. It has been found that the elastic modulus of the gels exhibits simple scaling behavior as a function of the polymer concentration in each solvent mixture over the entire concentration range investigated. The power law exponent n obtained for the concentration dependence of the shear modulus increases from 2.3 (in pure water) to 7.4 (in 35% (v/v) water + 65% (v/v) n-propyl alcohol mixture). In the vicinity of the theta-solvent composition (59% (v/v) water + 41% (v/v) n-propyl alcohol) n approximately 2.9. Shear and osmotic modulus maps of the phase separating gels have been constructed. It is demonstrated that the latter sensitively reflects the changes both in the topography and thermodynamic interactions occurring in the course of volume phase transition.

Ionic and pH effects on the osmotic properties and structure of polyelectrolyte gels

We investigate the effects of salt concentration and pH on neutralized poly(acrylic acid) (PAA) gels in near physiological salt solutions. Either adding calcium ions or decreasing the pH are found to induce reversible volume transitions but the nature of these transitions seems to be different. For example, the osmotic pressure exhibits a simple power law dependence on the concentration as the transition is approached in both systems, but the power law exponent n is substantially different in the two cases. On decreasing the pH the value of n gradually increases from 2.1 (at pH = 7) to 3.2 (at pH = 1). By contrast, n decreases with increasing calcium ion concentration from 2.1 (in 100 mM NaCl solution) to 1.6 (0.8 mM CaCl(2) in 100 mM NaCl solution). In both systems, a strong increase of the small-angle neutron scattering intensity (SANS) is observed near the volume transition. The SANS results reveal that calcium ions favor the formation of linearly aligned regions in PAA gels.

Molecular simulation of the swelling of polyelectrolyte gels by monovalent and divalent counterions

Permanently crosslinked polyelectrolyte gels are known to undergo discontinuous first-order volume phase transitions, the onset of which may be caused by a number of factors. In this study we examine the volumetric properties of such polyelectrolyte gels in relation to the progressive substitution of monovalent counterions by divalent counterions as the gels are equilibrated in solvents of different dielectric qualities. We compare the results of coarse-grained molecular dynamics simulations of polyelectrolyte gels with previous experimental measurements by others on polyacrylate gels. The simulations show that under equilibrium conditions there is an approximate cancellation between the electrostatic contribution and the counterion excluded-volume contribution to the osmotic pressure in the gel-solvent system; these two contributions to the osmotic pressure have, respectively, energetic and entropic origins. The finding of such a cancellation between the two contributions to the osmotic pressure of the gel-solvent system is consistent with experimental observations that the swelling behavior of polyelectrolyte gels can be described by equations of state for neutral gels. Based on these results, we show and explain that a modified form of the Flory-Huggins model for nonionic polymer solutions, which accounts for neither electrostatic effects nor counterion excluded-volume effects, fits both experimental and simulated data for polyelectrolyte gels. The Flory-Huggins interaction parameters obtained from regression to the simulation data are characteristic of ideal polymer solutions, whereas the experimentally obtained interaction parameters, particularly that associated with the third virial coefficient, exhibit a significant departure from ideality, leading us to conclude that further enhancements to the simulation model, such as the inclusion of excess salt, the allowance for size asymmetric electrolytes, or the use of a distance-dependent solvent dielectricity model, may be required. Molecular simulations also reveal that the condensation of divalent counterions onto the polyelectrolyte network backbone occurs preferentially over that of monovalent counterions.