Elsevier

Polymer

Volume 50, Issue 7, 20 March 2009, Pages 1805-1813
Polymer

Effect of the counterion behavior on the frictional–compressive properties of chondroitin sulfate solutions

https://doi.org/10.1016/j.polymer.2009.01.066Get rights and content

Abstract

Chondroitin sulfate is a major constituent of articular cartilage, which is known to affect in a decisive way the mobility and flexibility of our joints. A deviation from the physiological conditions, like e.g. a deficiency of water and salt content, in the cartilage tissue has long been suspected to be a possible trigger for rheumatoid diseases. Progresses in understanding the frictional–compressive behavior on the molecular level have been hindered due to the lack of reliable experimental data and the multitude of controlling parameters, influencing the structure and properties of cartilage tissue in its natural environment. In this paper we study the thermodynamic response of aqueous chondroitin sulfate solutions to changes in the monomer and added salt concentrations, using a recently developed field-theoretic approach beyond the mean field (MF) level of approximation. Our approach relies on the method of Gaussian equivalent representation, which has recently been shown to provide reliable thermodynamic information for polyelectrolyte solutions without and with added salt over the whole range of monomer concentrations. We compare our calculation results to experimental as well as molecular modeling data, and demonstrate that it provides useful estimates for important thermodynamic properties. Moreover, we obtain conclusive insights about the hydration effects and counterion behavior under various conditions, which show that, at the physiological salt concentration, CS solutions have optimal compressive and tribological properties. Finally, our work provides support for the possibility that a long-term deviation from the physiological conditions may trigger rheumatoid diseases.

Introduction

Articular cartilage is a hydrated soft tissue composed of negatively charged proteoglycans fixed within a collagen matrix, whose primary function is to provide low friction and wear in the synovial joints. A charge gradient causes the tissue to absorb water and swell, creating a net osmotic pressure that is counteracted by the resistance of the network of collagen fibers [1]. This confers cartilage its characteristic mechanical properties of being able to resist high loads and tensile strains. Joint loading is known to be a combination of cartilage compression and shear, including all transversal and frictional forces [2]. It is primarily controlled by large proteoglycan molecules called aggrecans, which interact with a long hyaluronic acid carbohydrate to form aggregates of very high molecular weight. A single aggrecan molecule is composed of a protein backbone of 210–250 kDa, to which are attached long negatively charged polysaccharide molecules, so-called glycosaminoglycans (GAGs), with a molecular weight ranging from 10 to 40 kDa. A schematic representation of an aggrecan monomer and its aggregate is shown in Fig. 1. The predominant type of GAG in aggrecan is chondroitin sulfate (CS). It is a linear polysaccharide with alternating disaccharide units of glucuronic acid and N-acetylgalactosamine [3], whose chemical composition can vary, depending on the state of health or disease of the cartilage tissue [1], [4], [5]. The physiologically important CS's are in particular chondroitin 4-sulfate (C4S) and chondroitin 6-sulfate (C6S), for which the sulfate group is either located at the C4- or C6-position of the galactosamine residue, respectively.

Systems composed of CS have been the subject of various experimental as well as theoretical investigations, both in solution [1], [3], [5], [6], [7] as well as in cartilage [3]. Extensive thermodynamic investigations on aqueous CS solutions have recently been presented by Chahine et al. [1], who performed direct experimental measurements of the osmotic pressure using membrane osmometry. Their experiments were conducted with solutions of CS-C (89.6% C6S and 10.3% C4S) and CS-A (39% C6S and 61% C4S). They concluded from their study that the osmotic pressure grows nonlinearly with increasing CS concentration and decreasing ionic strength of the NaCl bath. Moreover, they found that the differences in the osmotic pressure of the CS-C and CS-A solutions are negligible. From the theoretical side, Bathe et al. [5] carried out molecular modeling investigations using a Metropolis Monte Carlo algorithm, to determine the osmotic pressure of C4S and C6S solutions at various monomer concentrations and reservoir ionic strengths. To represent their data, Bathe et al. used a virial expansion, which allowed them to quantify the extent of nonideality in the dilute and semidilute regimes for different chain lengths. They compared their predictions to the experimental results of Ehrlich et al. [8] and various theoretical models, including the Donnan theory [9] and the Poisson–Boltzmann cylindrical cell model [10]. A major conclusion from their work is that their modeling predictions only agree qualitatively with the experimental results of Ehrlich et al. and Chahine et al., as well as with the results from the theoretical models mentioned previously. Another important outcome is that the steric excluded volume plays a negligible role in the CS osmotic pressure at the physiological ionic strength. This relates to the dominance of the repulsive electrostatic interactions that maintain the chains in this regime maximally spaced, whereas at high-ionic strengths the steric interactions dominate due to electrostatic screening. Finally, they found, in agreement with the experimental measurements of Chahine et al. on CS-C and CS-A solutions, that the position of the sulfate group in C4S and C6S solutions has only a minor effect on the osmotic pressure. In a concerted experimental and theoretical investigation of the mechanical behavior of cartilage Jin and Grodzinsky discovered that the electrostatic interactions between the GAG molecules have a major influence on the shear properties of the cartilage tissue in the extracellular matrix [11]. In a recent work Basalo et al. [3] found that CS decreases the friction coefficient of articular cartilage by performing frictional tests and concluded that the underlying mechanism is neither mediated by viscosity nor osmotic pressure. Based on these findings, they suggested that a direct injection of CS into the joints may be beneficial for their tribological properties.

In the present study our goal is to understand the role and assess the influence of CS on the frictional–compressive properties of articular cartilage. To this end, we investigate the response of the thermodynamic properties of aqueous CS solutions to changes in the monomer as well as salt concentrations. We put a particular focus on the central issue of counterion condensation onto the CS chains, which we suspect to be responsible for the reduction of the friction coefficient in articular cartilage [3]. The counterion condensation phenomenon is commonly described by Manning's theory [12], which assumes that counterions can condense onto the polyions until the charged density between neighboring monomer charges along the polyion chain is reduced below a certain critical value. In the model the real polyion chain is replaced by an idealized line charge, where the polyion is represented by a uniformly charged thread of zero radius, infinite length and finite charge density, and the condensed counterion layer is assumed to be in physical equilibrium with the ionic atmosphere surrounding the polyion. The uncondensed mobile ions in the ionic atmosphere are treated within the Debye–Hückel (DH) approximation. The phenomenon of counterion condensation now takes place when the dimensionless Coulomb coupling strength Γ = λB/lcharge > 1, where λB represents the Bjerrum length and lcharge the distance between neighboring charged monomers [13]. In this case the Coulomb interactions dominate over the thermal interactions and counterion condensation is favored. For many standard polyelectrolytes, this phenomenon is relevant, since the distance between neighboring monomer charges typically ranges between 2 and 3 Å and λB  7 Å in water. In the case of CS systems Γ = 1.4, which implies that counterion condensation should take place. However, Bathe et al. [7] have recently performed simulations with fully ionized CS chains. They validated their approach by noting that CS systems are a borderline case and Manning's theory does not take into account the molecular details of real polyion chains, like e.g. local solvation effects or atomic partial charge distributions.

In the present paper our goal is to investigate the counterion condensation phenomenon in CS solutions at different monomer and salt concentrations and study the influence of solvation effects on the frictional–compressive properties of CS polyelectrolytes in solution and cartilage. Our investigations are carried out, using the field-theoretic approach for flexible polyelectrolyte chains introduced by us in Ref. [14]. In the latter work we employed the tadpole renormalization procedure making use of the method of Gaussian equivalent representation (GER) for functional integrals [14], [15], [16], which goes beyond the MF level of approximation. In particular, we demonstrated that the GER methodology provides useful osmotic pressure results for polyelectrolyte solutions composed of sodium poly(styrene-sulfonate) (NaPSS) without and with added salt over the whole range of monomer concentrations.

Our paper is organized in the following way. In Section 2 we review the basic derivation of the field theory for flexible polymer chains, followed by the derivation of our GER theory. Then, we demonstrate the applicability of the method on systems of polyelectrolyte chains, where the monomers interact via the electrostatic part of the Derjaguin–Landau–Verwey–Overbeek (DLVO) pair potential [17], [18], and develop the corresponding formulas, employed to calculate the structural and thermodynamic quantities considered in this work. In Section 3 we present and discuss the results of our calculations on the example of aqueous C4S solutions at various monomer and salt concentrations by comparing them to the osmotic pressure measurements of Chahine et al. [1] and the molecular modeling data of Bathe et al. [5].

Section snippets

Field theory for flexible polymer chains

In this work we treat the aqueous polyelectrolyte solutions within the standard continuum model of Edwards for flexible polymer chains, dissolved in a good solvent [19]. The macromolecules are assumed to be linear homopolymers of uniform length with statistical properties, described by the continuous Gaussian chain model. The solvent degrees of freedom are not explicitly taken into account in the statistical mechanical description, but will be introduced a posteriori in a coarse-grained

Results and discussion

In the following we present GER0 calculations for aqueous CS solutions at different NaCl concentrations and compare the results to the osmotic pressure measurements of Chahine et al. [1], as well as the molecular modeling data of Bathe et al. [5]. For comparison, we considered only C4S solutions, because the differences in the osmotic pressure of the C4S and C6S solutions, as well as of their mixtures, were found to be negligible. Note that we did not take into account the osmotic pressure

Conclusions and outlook

In the present work we have studied the thermodynamic response of aqueous chondroitin sulfate solutions to changes in the monomer and added salt concentrations, using a recently developed field-theoretic approach beyond the mean field level of approximation. We have compared our calculation results to data from experiments as well as molecular dynamics calculations, and demonstrated that our method provides reliable information for the osmotic pressure and entropy. By adjusting the osmotic

Acknowledgments

We gratefully acknowledge the support of Prof. Dr. Buchner for offering helpful suggestions and encouragements.

References (30)

  • N.O. Chahine et al.

    Biophys J

    (2005)
  • L. Han et al.

    Biophys J

    (2007)
  • I.M. Basalo et al.

    J Biomech

    (2007)
  • M. Bathe et al.

    Biophys J

    (2005)
  • M. Bathe et al.

    Biophys J

    (2005)
  • S. Ehrlich et al.

    Biorheology

    (1998)
  • S.A. Baeurle et al.

    Polymer

    (2007)
  • L. Han et al.

    Biophys J

    (2008)
  • J. Seog et al.

    J Biomechanics

    (2005)
  • V.C. Hascall et al.

    Proteoglycans

  • A. Papagiannopoulos et al.

    Biomacromolecules

    (2006)
  • F.G. Donnan

    Chem Rev

    (1924)
  • M. Fixman

    J Chem Phys

    (1979)
  • M. Jin et al.

    Macromolecules

    (2001)
  • G.S. Manning

    J Chem Phys

    (1969)
  • Cited by (73)

    • Determination of glycosaminoglycans in biological matrices using a simple and sensitive reversed-phase HPLC method with fluorescent detection

      2021, Journal of Chromatography B: Analytical Technologies in the Biomedical and Life Sciences
    • ChondroGELesis: Hydrogels to harness the chondrogenic potential of stem cells

      2021, Materials Science and Engineering C
      Citation Excerpt :

      Another commonly used GAG in cartilage tissue engineering is chondroitin sulfate (CS). CS is a naturally abundant structural component of cartilage that plays a significant role in its resistance to compression [39]. It has also been shown to inhibit cell attachment to adhesive ECM proteins by directly interacting with them and masking their adhesive sites from cells [40–42].

    View all citing articles on Scopus
    View full text