Can Modern Statistical Mechanics Unravel Some Practical Problems . . .
67 [185, 164]. However other research has shown that staining after Trypsin digestion demon-
strates an inhomogeneous pattern, where the penetration wavefront of Trypsin does not result in complete depletion of proteoglycans but instead a decrease in stain intensity. Fol-
lowing these results, it could be argued that Trypsin penetrates the layers of cartilage at a faster rate than its rate of proteoglycan digestion along its path. That is, proteoglycans
remain within the matrix following Trypsin passage. This has implication for mechanical experiments that are intended to test biomechanical characteristics especially.
The two modes of Trypsin penetration mentioned above raise important questions. What is the exact action of Trypsin on proteoglycans, and how is its effect altered by differ-
ent parameters such as enzyme concentration, medium and initial cartilage physical prop- erties? These questions require attention if the accuracy of in vitro modelling of cartilage
degeneration for biomechanicalchemical assessment is to have sufficient scientific merit and data integrity. Despite the vast body of work that has been done in this area, there
is no protocol for the use of Trypsin as to the optimum Trypsin concentration, or the re- quired length of time of exposure to the enzyme necessary to produce a consistent loss in
proteoglycan along the cartilage thickness.
The above included informations about biomechanics and biochemistry of the AC seem to be necessary to get a deeply realistic view of the object modeled. In what follows one
shall see how can we “slightly” abstract from this very reality focusing the modeling on certain relevant elements of the AC, selected for the purpose of the modeling.
3.2. AC at Equilibrium
Joint lubrication by AC: Conceptual background - AC can be viewed as a multilayer of micromolecular components that overlays the ends of the bones in articulation joints of
mammals. During physiological function it can experience peak stresses of over 20 MPa in magnitude. Structurally, its major component are proteoglycans PG which occupy
3-10, collagen which exist as 10-30, water, which is present to between 60-80 of the wet weight of the tissue [199]. It is contains some intramatrix cells and lipids while
its surface is covered by multilayered three dimensional-lamellar sheets of surface active phospholipid which tend to present a cushioning structure Fig. 25 [199, 200]. The exposed
face of AC to the load bearing joint interface is phospholipid-based and phospholipid PL molecules bind amino acid groups that contain the protein chains of glycoprotein, namely
lubricin [201]. Lubricin has been proposed by researchers as the lubricant in the joint [202, 203], however, a new school of thought that is based on thorough understanding
is fast replacing this viewpoint. This is that the lubricant in the joint is phospholipids- based. The most compelling argument supporting this notion of PLs as the main lubricant
in the joint is consequent on the fact that lubricin, would need to be adsorbed to the surface as a hydrophilic molecule and yet act as an effective lubricant, which is difficult if not
impossible to achieve. In our opinion, the lubrication of mammalian joints is provided by PLs, in chemical association with lubricin, acting as large water-soluble molecules.
Biolubrication between cartilage surfaces is provided by a complex interaction of SF, pressurized exuded matrix water, surface active phospholipids various glycoproteins and
hyaluronan. Using a surface force apparatus see Ref. [122] the friction coefficient on three surfaces using lubricin glicoprotein with 12 PL was measured at a pressure of
68 A. Gadomski, I. Santamaria-Holek, N. Kruszewska et al.
6 atm according to CA framework usually applied in such a case. The surfaces investigated were, negatively charged mica, f
= 0.038, positively charged poly-lysine surface, f = 0.22, and hydrophobic alkanethiol monolayers surface, f
= 0.40 [201]. On all these surfaces lubricin forms dense adsorbed layers of thickness 60
− 100 nm. Lubricin molecular weight is 227
, 000, at pH = 7.2 − 7.6 of the SF, the macromolecule has a small net positive charge, the isoelectric point being in the range 7
.8 − 8.1 [202, 203].
Figure 25. Schematic drawing of a typical AC surface covered by three bilayer of PLs “cushion”, with cholesterol and glycoprotein contributing to the solubilization process
of ions and water, macromolecules of PLs bilayers to support lubrication to maintain a frictionless and wear resisting AC surface.
A negatively charged hyaluronan as polylectrolyte molecule, hyaluronic acid HA, in aqueous solution does not adsorb onto negatively charged surfaces of mica or AC. HA did
not lubricate the mica surfaces, and under relatively low loads and low sliding velocities exhibited a high friction coefficient [201]. Consequently, it can be argued that the role of
HA in joint lubrication might be in helping to immobilize the surface-active PLs dispersed in the SF during loading. In their immobilised state, the PLs will potentially be capable of
acting as reverse micelles, thereby leading to the conceptual deduction that HA might act as the agent which enables the formation of PLs into reverse micelles, where the functional
mechanism is facilitated by a mostly water-assisted mutual replacement between the PLs and lubricin molecules. The latter molecules are then adsorbed at the solid surfaces of the
AC, thus causing the biolubrication to proceed efficiently [201].
Joint lubrication mechanism - The biolubrication mechanism between PL bilayers lo-
cated on the articular surfaces has been studied for decades [202], however, a further insight into the molecular interactions taking place at the joint interface as the PL layers contact
under load delivering biolubrication is still required for us to fully understand the mech- anisms involved in the process. Using electron microscopy and fixation procedures PLs
have been identified in both AC oligolamellar surface active and intramatrix PLs and SF [123, 204]. More specifically, a study has shown that when the PLs bilayers are removed by
a lipid solvent, the surface of AC becomes very hydrophobic [205], leading, according to CA, to an increase in friction of 150 [204]. An analysis of the fluid extracted from rinsing
the surface of AC with a solvent further reveals that joint surfactant consists of about 61 PLs with major sub-fraction of phosphatidycholine [156]. It has also been proposed that the
components of the SF namely, lubricin a glycoprotein, hyaluronan which are “held” on cartilage via their interaction with the proteoglycans, in association with the PL molecules
are responsible for the almost frictionless CA-departing [12] biolubrication of the mam- malian joint [206]. We hypothesize here that biolubrication of joint surfaces is enabled by
Can Modern Statistical Mechanics Unravel Some Practical Problems . . .
69 the interactions between water the solvent which is normally under pressure during phys-
iological function, “additives” i.e., ionic salts and other macromolecular components, and the nature of the acid-base equilibrium occurring in the joint space. Note also that the ions
may, due to the electrostatic Debye screening cause additionally a formation of nuclei containing PL, which in the confined aqueous ambient phase may cause crystallization to
be switched on; its thorough emergence can then be hampered by means of friction out of the classical CA regime. Some undissolved nuclei may also contribute to facilitate the
biolubrication [207].
It can be argued that the hydration of ions and macromolecular polyelectrolytes is fun- damental to the ability of two charged PL bilayers to function as a lubrication agent on
the surfaces of contacting AC layers. The contacting bilayer phospholipidic articular sur- faces in the joint are hydrophilic and it has recently been proposed that their physiological
function can be explained thoroughly using the principles of core reverse micelles [207]. In this regard, we note that the charged core of the reverse micelle is able to solubilize in
water molecules forming a lipid semipermeable membrane [208]. The lipid bilayer mem- brane formed is 6
− 10 nm thick and act as potential barrier to the diffusion of polar so- lutes, with the associated embedded proteins and cholesterol providing the pathways for
the charge core of reverse micelle resulting in, Fig. 25: a organized water molecules and ions on the articular surfaces, b stabilization of charged particles and elimination of floc-
culation, c facilitation of the electrostatic attachment of polyelectrolyte molecules to the hydrophilic surface and enabling PLs to organize into a double layer of electrostatic charges
during cartilage-to-cartilage contact, d carry out the selective transfer of certain molecular substances through the lipid barrier, and e facilitate the transfer of mechanical information
from the extracellular matrix ECM into the interior of the cell within the cartilage matrix. These bilayers or sheets lie in widely separated parallel planes loosely held together by a
weak physical force, thus allowing, them to slide over one another with minimal friction. The lipids in AC are composed of cholesterol, triglicerides, and PLs from 0.3 to 4 [209].
Furthermore, the electrostatic charges have been identified as a powerful intermediary in the manipulation of the properties of the complex joint fluid system [123, 207].
Characteristics of joint fluid-surfactant system - Of importance is the finding that the
glycoprotein GlyPr with MW of 227 , 000, namely “lubricin” exhibited remarkable lubri-
cating capabilities when combined with PLs. It is also known that water-soluble glycopro- tein macromolecules are a carrier for other highly water-insoluble small PL molecules MW
approximately 730. Lubricin, a component of the SF, was identified to contain 86 of gly- coprotein and 12 PLs with 2 remaining unknown [156]. Being a lubricant, lubricin is an
active macro-ion in SF which deposits or adsorbs the oligolamellar layer of PLs that pos- sess the capability to bear high loads [205, 210, 211]. Phospholipid molecules bind amino
acid groups that contain the glycoprotein chains forming lubricin. It has also been proposed that self-lubrication of cartilage which is characterized with low lubricity will occur regard-
less of the type of fluid between contacting cartilage surfaces [206, 211]. The hydrophilicity of the surface molecular groups, e.g. lipid head-groups is affected by the electrolyte ions in
solutions; such that between negatively charged surfaces, short range-hydration-repulsion increases as more cations are adsorbed [212]. A few molecular layers or 1
− 2 nm of water in 0
.01 M KCl solution act as a protective layer against adhesion-induced damage during sliding and a low friction coefficient of 0
.02 is maintained under loads of up to 20 MPa
70 A. Gadomski, I. Santamaria-Holek, N. Kruszewska et al.
[212]. A leading argument regarding the biofluids involved in the biolubrication of AC is that the glycoprotein lubricin on hydrophilic surface active PLs, supported by the hyaluro-
nan that are held together by protoglycans is responsible for the ultra-low friction in the joint in certain pH and surface tension [204, 208, 212, 209, 213, 214].
The pH value of SF can distinguish normal from osteoarthritic condition. In previous studies of samples of aspirated SF, the pH of normal SF was found to be between 7
.3 and 7
.43 [209]. In contrast the pH values of SF in various inflammatory conditions from joints with osteoarthritis OA and rheumatoid arthritis RA were 7
.4 − 8.1 mean of 7.9 for 16 joints with OA, and 7
.4 − 7.6 7.5 for the six joints with RA [213]. It is known that multi- layer film prepared by sequential electrostatic adsorption of polyL-lysine and hyaluronic
acid, PLLHA onto charged silicon surfaces can provide an insight into the understanding of surface friction and wettability. In particular, studies have shown that surface friction
can be altered by a factor of 10 and the degree of swelling by a factor of 8 for films com- posed of the two polyelectrolytes, by simply varying the pH [215]. Synovial fluid surface
tension ST, free energy measure in surface layer was measured for inflammatory joint diseases. The ST values of synovial fluid in various inflammatory conditions from joints
with seronegative spandylarthropathies Spa and rheumatoid arthritis RA were mean of 42
.42 mNm for 6 joints with Spa, and mean of 47.99 mNm for the 19 joints with RA. It was connected with significantly higher concentration of total proteins 5
.0 gdL for Spa and 3
.9 gdL for ST [214].
3.3. On the Role of Reverse Micelles Other Aggregates in the System
