An indentation-based framework for probing the glycosaminoglycan-mediated interactions of collagen fibrils

Abstract

Microscale deformation processes, such as reorientation, buckling, and sliding of collagen fibrils, determine the mechanical behavior and function of collagenous tissue. While changes in the structure and composition of tendon have been extensively studied, the deformation mechanisms that modulate the interaction of extracellular matrix (ECM) constituents are not well understood, partly due to the lack of appropriate techniques to probe the behavior. In particular, the role of glycosaminoglycans (GAGs) in modulating collagen fibril interactions has remained controversial. Some studies suggest that GAGs act as crosslinkers between the collagen fibrils, while others have not found such evidence and postulate that GAGs have other functions. Here, we introduce a new framework, relying on orientation-dependent indentation behavior of tissue and computational modeling, to evaluate the shear-mediated function of GAGs in modulating the collagen fibril interactions at a length scale more relevant to fibrils compared to bulk tests. Specifically, we use chondroitinase ABC to enzymatically deplete the GAGs in tendon; measure the orientation-dependent indentation response in transverse and longitudinal orientations; and infer the microscale deformation mechanisms and function of GAGs from a microstructural computational model and a modified shear-lag model. We validate the modeling approach experimentally and show that GAGs facilitate collagen fibril sliding with minimal crosslinking function. We suggest that the molecular reconfiguration of GAGs is a potential mechanism for their microscale, strain-dependent viscoelastic behavior. This study reveals the mechanisms that control the orientation-dependent indentation response by affecting the shear deformation and provides new insights into the mechanical function of GAGs and collagen crosslinkers in collagenous tissue.

Graphical Abstract

Introduction

Biological processes such as aging and pregnancy, and diseases like tendonosis and liver fibrosis, influence the mechanical properties of tissue at different length scales by altering the structure, composition, and deformation mechanisms. Collagen, among other tissue constituents, plays a central role in regulating the mechanical properties of tissue (Fratzl, 2008). Collagen crosslinkers, GAGs, elastin, and other biomolecules modulate the interactions of collagen fibrils and contribute to the mechanical response. Through these interactions, the strain is transferred from the tissue level to the molecular level, engaging both non-collagen ECM and collagen fibrils. The transferred strains typically become progressively smaller at the lower levels of hierarchy, but the exact distribution of strain and the role of different tissue constituents in load transfer between collagen fibrils is not well-understood (Fratzl, 2008).

Tendon is a collagenous connective tissue that transmits force generated in muscle, to bone. It is composed of water (55–70%), collagen (60–85% dry mass), cartilage oligomeric matrix protein (~3% dry mass), elastin (~2% dry mass), decorin (~1% dry mass), and other small leucine rich proteoglycans (PGs, ~0.5% dry mass) (Taye et al., 2020). Decorin constitutes more than 90% of the PGs in tendon (Fessel and Snedeker, 2009). The most important collagen types in tendon are types I and III and these make up approximately 60–80% and 0–10% of the collagen content, respectively (Taye et al., 2020). Collagen molecules assemble into fibrils, fibers, and then fascicles to form a hierarchical structure (Fratzl, 2008). Complex structural features and composition of tendon determine its mechanical behavior and facilitate optimal function. For example, the longitudinal crimping pattern of the collagen fibers (10–100 µm length scale (Fratzl, 2008)) contributes to the nonlinear, J-shaped strain-stress curve observed in tensile tests and gives rise to a toe region distinct from the linear and failure regions (Fang and Lake, 2016; Kastelic et al., 1980; Wang, 2006).

Characterizing the mechanical behavior of the tendon at the fibril and fiber level helps to interpret and understand the behavior of tendon at larger length scales, and will help to understand similar deformation mechanisms in other tissues. Different techniques have been used to evaluate the contribution of crimping, sliding, and fiber superstructure to the fiber-level mechanical behavior of tendon. Confocal microscopy and mechanical testing have shown that the larger helical pitch angle in energy-storing tendons gives rise to more fiber rotation and less sliding during stress-relaxation, compared to positional tendons with smaller pitch angles (Thorpe et al., 2013). Polarized light microscopy, combined with tensile testing, has revealed that the uncrimping of collagen fibers is involved in the nonlinear mechanical behavior of tendon and the formation of the toe region (Fang and Lake, 2017a; Franchi et al., 2007). Second-harmonic generation (SHG) microscopy of the elastase-treated tendon has suggested that the elastic fibers are likely involved in modulating the crimping and recoiling of collagen fibers (Grant et al., 2015). The sliding of collagen fibers at the microscale has also been evaluated by imaging the strained tendon; two-photon microscopy, combined with shear and compression tests, has shown that sliding significantly contributes to the shear response, while other mechanisms, e.g., reorganization, are more dominant in the compression mode of deformation (Fang and Lake, 2015). PGs and GAGs are suggested to contribute to the aforementioned deformation processes.

PGs are composed of a core protein covalently linked to one or more GAG side chains (Varki et al., 1999). GAGs are large linear polysaccharides consisting of repeating disaccharides (King, 2014) that constitute an important group of ECM molecules (Chen et al., 2022). Heparin/heparan sulfate, chondroitin/dermatan sulfate, keratan sulfate, and hyaluronic acid are the main classes of GAGs (Casale and Crane, 2019) and the number and type of GAG side chains attached to PGs help to classify different types of PGs. Researchers have established that GAGs control formation and growth of collagen fibrils during tissue development (Kalamajski and Oldberg, 2010; Parry et al., 1982); for example, tissues rich in hyaluronic acid have small-diameter collagen fibrils (~60 nm) while those rich in dermatan sulfate have larger-diameter fibrils (~200 nm) (Parry et al., 1982). Their mechanical function in mature tissue, however, has remained controversial (Ahmadzadeh et al., 2013; Chen et al., 2022).

Some studies suggest that GAG-PG complexes contribute to load transfer during deformation in tissues like tendon and ligament (Cribb and Scott, 1995; Liao and Vesely, 2007; Redaelli et al., 2003; Sasaki and Odajima, 1996; Scott, 1990) because they create a bridge between aligned, adjacent collagen fibrils, meaning that they bind to adjacent fibrils and could transfer force (Watanabe et al., 2016a). In agreement with this hypothesis, the failure stress of mature tendon with a higher concentration of PG is higher than the immature tendon with lower PG concentration (Cribb and Scott, 1995; Pins et al., 1997). Moreover, the distal portion of tendon has a higher shear modulus compared to the proximal region with lower PG content (Fang et al., 2014; Fang and Lake, 2017a, 2017b, 2016, 2015). Several constitutive and computational models have supported the feasibility of this load transfer mechanism, e.g., (Ahmadzadeh et al., 2015; Ciarletta et al., 2008; Fang and Lake, 2016; Fessel and Snedeker, 2011; Redaelli et al., 2003; Vesentini et al., 2005).

Other studies, however, do not generally support this load transfer hypothesis. Enzymatic depletion of GAGs, for example, shows little to no measurable change in the quasi-static mechanical properties of the tendon and ligament (Al Makhzoomi et al., 2022; Eisner et al., 2022; Fang and Lake, 2017b; Legerlotz et al., 2013; Lujan et al., 2007; Rigozzi et al., 2009; Svensson et al., 2011). Molecular modeling has shown that crosslinking forces generated by GAGs are not sufficiently large to facilitate load transfer between the fibrils (Vesentini et al., 2005, p. 200). At a larger length scale, computational modeling has suggested that GAGs can only contribute to the load transfer when the fibril length is greater than a characteristic length scale related to the microstructural parameters such as GAG spacing and stiffness (Ahmadzadeh et al., 2013). GAG knock-out studies, e.g., (Ahmadzadeh et al., 2013; Dourte et al., 2012; Robinson et al., 2017, 2004b; Zhang et al., 2006), have also been used, but the active involvement of GAGs during fibril formation confounds the results. Regardless of their limitations, the knock-out studies also do not generally support the load transfer function of GAGs (Eisner et al., 2022). Beyond their load transfer, or crosslinking function, a number of studies propose other mechanical functions for the GAGs, e.g., modulating the viscoelastic behavior and fibril sliding (Al Makhzoomi et al., 2021; Ciarletta et al., 2008; Dourte et al., 2013; Legerlotz et al., 2013; Rigozzi et al., 2013; Robinson et al., 2017, 2004b). Despite significant efforts towards understanding the mechanical function of GAGs, the role of these polysaccharides in mature tissue is debated and their structure-function relationship remains elusive (Eisner et al., 2022).

While informative, the previous studies relied on macroscale mechanical tests to infer the deformation mechanisms at the microscale; this approach likely contributes to the inconclusive data and controversy surrounding the mechanical function of GAGs. In this paper, we extend the computational-experimental approach of (Moghaddam et al., 2023) to investigate the role of GAGs in modulating the microscale deformation mechanisms of tendon. Specifically, we use an enzymatic treatment to deplete GAGs and disturb the deformation mechanisms in a controlled way; measure the indentation response in orthogonal orientations; and use a microstructural finite element model, introduced in (Moghaddam et al., 2023), to deduce the deformation mechanisms that produce the trends in experimental data. This work provides a novel framework for the characterization of deformation mechanisms and gives new insights into the mechanical function of GAGs in tendon and other collagenous tissues. Computational modeling reveals previously unknown mechanisms by which GAGs modulate the viscoelastic behavior. While we focused on the mechanical function of GAGs, our new computational/experimental approach is broadly applicable to other tissues and tissue constituents.

Methods

Sample preparation

All procedures involving animals were approved by the Institutional Animal Care and Use Committee at the University of Illinois at Urbana-Champaign. Nine pig feet were acquired from a local grocer and stored at -80°C. The feet were thawed at 4°C for 24 h immediately before harvesting the digital flexor tendons. The tendons were cut into 5 mm segments, 1 cm away from the natural bifurcation. Samples were then embedded in Optimal Cutting Temperature (OCT) compound and frozen at -20°C. Using a cryostat (Leica Biosystems, Wetzlar, Germany), the samples were cut either parallel (longitudinal) or perpendicular (transverse) to the long axis of tendon; GAG depletion experiments used n=6 tendons per orientation while glutaraldehyde experiments used n=3 per orientation. The control and treated sections were harvested from the same location along the length of tendon to ensure similar properties. The final thickness of the cryosectioned tendons was larger than 3 mm in all samples. OCT was washed out after sectioning using deionized water and PBS. Samples were stored in 4°C PBS immediately.

SHG imaging

A laser scanning confocal microscope (Zeiss LSM 710, Oberkochen, Germany) imaged the samples using a 70-fs laser centered at 780 nm to illuminate the tissue, and a 20x 0.8 NA objective lens to capture images. A motorized stage imaged larger fields of view and Zeiss’s Zen software (Zeiss, Oberkochen, Germany) stitched the images. Previous publications (Lee et al., 2021, 2020; Ostadi Moghaddam et al., 2022) describe the SHG image quantification and co-registration of the SHG and nanoindentation (NI) data.

Glutaraldehyde treatment

Tendon samples (n=3) were treated with 0.01% glutaraldehyde (G5882, Sigma-Aldrich, St. Louis MO) in PBS for 24 hr at 4°C. The 24-hour incubation time ensured a more uniform diffusion compared to a treatment with higher glutaraldehyde concentration and shorter incubation time. The control samples (n=3) were kept in PBS at the same temperature and for the same duration. The samples were cryosectioned a second time after treatment to ensure smooth indentation surfaces for NI. SHG images of one representative sample were compared before and after glutaraldehyde treatment to confirm that the collagen microstructure remained unaffected. The spatial heterogeneity of the tissue microstructure was used to find the same imaging location before and after the treatment. Glutaraldehyde creates both inter- and intrafibrillar crosslinkers in tissue, but the intrafibrillar crosslinking density is higher (Chandran et al., 2012; Hansen et al., 2009). This non-uniform crosslinking action provided a great platform to test the accuracy of the computational model.

Chondroitinase treatment

The tendon samples (n=6) were treated with 0.3 unit/ml chondroitinase ABC (ChABC) from Proteus vulgaris (C2905, Sigma-Aldrich, St. Louis MO) in 50 mM Tris, 60 mM sodium acetate, 0.02% bovine serum albumin, at pH=8 for 14 hours at 37°C. The control samples (n=6) were incubated similarly in a buffer without ChABC. The digestion of sulfated GAGs was evaluated by Alcian Blue staining (H-3501, Vector Laboratories, Burlingame, CA, USA), following the standard protocol provided by the manufacturer. SHG images of one representative sample were compared before and after ChABC treatment to confirm that the collagen microstructure remained unchanged.

Nanoindentation

Cyanoacrylate glued the tissue to the bottom of a Petri dish and prevented the movement of the 3 mm thick sample that can be caused by buoyancy forces when the sample is in fluid. While samples were submerged in PBS (room temperature), a Piuma nanoindenter (Optics11, Amsterdam, Netherlands) measured the force and displacement of the probe in the displacement-controlled mode. The prescribed displacement included loading up to 3 µm depth (5 μm/s), a 90 second hold at 3 µm, and unloading at the same rate. The spherical probe radius was 52.5 μm and the cantilever stiffness was 0.46 N/m. A general anisotropic contact model (Swadener and Pharr, 2001) was used to calculate the indentation modulus from the loading portion of the force-indentation curve (Eq.1).

$$F=\frac{4\text{E}{R}^{1/2}}{3}{h}^{3/2}$$ (Eq.1)

where F is the indentation force, h is the indentation depth, E is the indentation modulus and R is the tip radius. Here, the indentation modulus (E) is a complex function of all of the components of the elasticity tensor, i.e., shear moduli, Poisson’s ratios, and Young’s moduli, as well as the orientation of the material relative to the indentation axis (Moghaddam et al., 2020; Swadener and Pharr, 2001). The approximate analytical solution of this contact model can be obtained by solving three integral equations iteratively. To simplify the analysis and avoid imposing constraints on the anisotropic behavior, we only measure the indentation modulus in this study.

To obtain the viscoelastic parameters, the elastic constants in the contact equation were substituted by viscoelastic operators (Mattice et al., 2006)

$$F(t)=\frac{8\sqrt{R}}{3}{\int }_0^{t}G(t-\tau )\left[\frac{d}{d\tau }{h}^{3/2}(\tau )\right]d\tau$$ (Eq.2)

where F(t) is indentation force, t is time, R is the probe radius, G(t) is the relaxation function, and h(t) is the indentation depth. The parameter h(τ)is a function of τ in Eq.2.

Assuming a relaxation function with the following form,

$$\left.G(t)=C_0+C_1\exp \left(-t/T_1\right)+C_2\exp \left(-t/T_2\right)\right)$$ (Eq.3)

The numerical integration of Eq.2 yields

$$F(t)=B_0+B_{1}exp\left(-t/T_1\right)+B_{2}exp\left(-t/T_2\right)$$ (Eq.4)

where B₀, B₁are fitting parameters and T₁, and T₂ are the material time constants. The coefficients of the material relaxation function (Eq.3) are

$$C_k=\frac{B_k}{\left(RC{F}_k\right)h_{max}^{3/2}(8\sqrt{R}/3)}$$ (Eq.5)

where k = 1, 2, and RCF_k are the ramp correction factors to consider the ramping deformations before the hold period

$$RC{F}_k=\frac{T_k}{t_R}\left[\exp \left(t_R/T_k\right)-1\right]$$ (Eq.6)

where t_R is the rise time. The instantaneous and equilibrium shear moduli were calculated from the coefficients of the material relaxation function, as shown below

$$G_0=\frac{C_0+C_1+C_2}{2}\text{\hspace{1em}and\hspace{1em}}{G}_{\text{inf}}=\frac{C_0}{2}$$ (Eq.7)

The instantaneous (E₀) and equilibrium (E_inf ) moduli were calculated as follows

$$E_0=3G_0\text{\hspace{1em}and\hspace{1em}}{E}_{\text{inf}}=3G_{inf}$$ (Eq.8)

Statistical analyses

R 2021 software (R Foundation for Statistical Computing, Vienna, Austria (Team, 2014)) was used for statistical analyses and a Welch two sample t-test compared the control and treated groups. P-values less than 0.05 were considered significant and are shown in figures and given in the text. A two-way ANOVA examined how the combination of treatment and sample to sample variation influenced the mean of moduli and time constants.

Computational modeling

Both microstructural and shear-lag models were developed in COMSOL Multiphysics V 5.6 (COMSOL AB, Stockholm, Sweden). Compared to other modeling approaches such as the Gasser-Ogden-Holzapfel model (Holzapfel and Gasser, 2001), the discrete models used in this study were more suitable for evaluating the deformation mechanisms since they allowed for studying the interactions of the tissue constituents.

Microstructural model:

A previous publication (Moghaddam et al., 2023) describes the microstructural model in detail. Briefly, a 2D plain strain model consisting of a rigid spherical indenter and a sample with stiff fibrils (linear elastic and isotropic), embedded in a soft matrix (linear elastic and orthotropic), was used to simulate the indentation of tendon. The soft matrix regulated the interaction of the individual collagen fibrils and represented all non-collagen ECM components. While both fibril and non-collagen matrix are often modeled as isotropic materials at the microscale, e.g., (Ahmadzadeh et al., 2013), an orthotropic matrix in our model allowed for capturing the influence of the crosslinkers on the deformation process. We simulated the influence of interfibrillar crosslinkers on the mechanical behavior of tissue by changing the shear modulus of the orthotropic non-collagen matrix. To this end, we chose a shear modulus higher than that of the isotropic material to capture the influence of crosslinkers. A parametric study confirmed that the results from this approach correlated with those from an equivalent model with spring crosslinkers (Supplementary, Fig. S1). We simulated the influence of intrafibrillar crosslinkers by changing the modulus of the fibrils. Previous molecular dynamics simulations have confirmed that crosslinks generally increase the elastic modulus of collagen fibrils (Depalle et al., 2015; Kwansa et al., 2016). In this work, the influence of the viscoelastic properties of the non-collagen ECM on the overall indentation response was also investigated. To calculate the material time constants, the relaxation curves from indentation relaxation simulations were fit into a one-term exponential relaxation function. A strain-dependent function (Eq.9) was used to describe the material time constant of the non-collagen matrix and to model the dynamic interactions of collagen fibrils. In this formulation, the time constant did not change with strain in compression, or after a critical tensile strain$\left({\epsilon }_c\right)$, but increased linearly between 0 and${\epsilon }_c$. This strain-dependent formulation for the material time constant, to our knowledge, has not been suggested in previous studies; this format described a possible deformation mechanism and was proposed because the results between the simulation and experiments agreed, which was not the case using a conventional strain-independent function. A sequential search was used to find the unknown parameters (t_a, t_b,ε_c) of this function, based on the trends in experimental data.

$$f(\epsilon )=\left\{\begin{array}{cc}{t}_a& \epsilon <0\\ \left(t_b-t_a\right)\frac{\epsilon }{{\epsilon }_c}+t_a& 0<\epsilon <{\epsilon }_c\\ t_b& \epsilon >{\epsilon }_c\end{array}\right.$$ (Eq.9)

Importantly, the sequential search determined the parameters that captured the trends in the experimental data rather than the best-fit parameters from a comprehensive search (inverse analysis); the latter approach would not provide additional information for probing the deformation mechanisms due to high sample to sample variation. The bassline values for fibril diameter and spacing, fibril and non-collagen matrix Young’s moduli, and Poisson’s ratios were 200 nm, 100 nm, 1 GPa, 5 MPa, and 0.3, respectively. Similar to the model in (Moghaddam et al., 2023), the sample dimensions and indenter radius were 25 µm² and 50 µm, respectively.

Shear-lag model:

A 2D plain strain shear-lag model was used to represent a group of staggered fibrils. The unit cell of the model consisted of two fibrils (linear elastic) connected by a soft, linear viscoelastic matrix. Common nodes and shared boundaries separated the fibril-matrix interface. The loading and boundary conditions are described in Fig.1.

Figure 1.

Geometry and boundary conditions of the shear-lag model

Structured quadrilateral elements meshed the sample (800 total), and a standard linear solid model produced viscoelastic behavior in the matrix. Since we only attempted to capture the trends in the experimental results, this simple model was sufficient for describing the viscoelastic behavior. More sophisticated models would be required to capture the exact experimental values. However, without having a deep understanding of the viscoelastic behavior of crosslinkers, more advanced models would simply fit the data better with more parameters without necessarily providing additional insights into the deformation mechanisms. To interpret the spherical indentation data from the shear-lag model, the equivalent boundary condition, i.e., the prescribed shear displacement, was calculated from the microstructural model. This preliminary analysis informed the shear-lag model and ensured that the matrix experienced the same orientation-dependent shear strain in both microstructural and shear-lag models. To this end, the average shear strain in the matrix, ${\epsilon }_{x{y}_{ave}}=\iint {\epsilon }_{xy}dxdy/A$, was calculated from the microstructural model in both transverse and longitudinal orientations. Using the results, the prescribed shear displacement in the shear-lag model of transverse indentation was set to be 1.8 times higher than the longitudinal orientation to differentiate indentation in orthogonal planes.

Like the microstructural model, a sequential search was performed to find the parameters in Eq.9 that roughly captured the experimental data, without attempting to find the best-fit parameters. Table 1 reports the material and geometric properties in the shear-lag model. The material properties are normalized relative to the Young’s modulus of fibril, and the lengths are normalized relative to the fibril diameter.

Table 1:

Material and geometric properties in the shear-lag model

Property	Selected value (normalized)	Typical values
Fibril diameter	100 nm (1)	100–200 nm (Gupta, 2008; Redaelli et al., 2003; Robinson et al., 2004a)
Fibril spacing	50 nm (0.5)	50–200 nm (Ahmadzadeh et al., 2013; Redaelli et al., 2003)
Fibril Young’s modulus	1 GPa (1)	1 GPa (Ahmadzadeh et al., 2013; Svensson et al., 2012; Wu et al., 2018)
Poisson’s ratio (matrix and fibril)	0.3	0.3 (Reese et al., 2010; Topçu et al., 2022)
Fibril length	5 µm (50)	NA
Matrix Young’s modulus	5 MPa (0.005)	NA

Results

Influence of the glutaraldehyde and ChABC treatment on the tissue microstructure

Alcian Blue staining, counterstained with nuclear fast red per manufacturer’s instructions, confirmed the successful digestion of sulfated GAGs, which were stained blue (Fig.2. top). The combination of pink (background) and blue (GAGs) could have contributed to the deviation of color from pure blue in the control group. The chromaticity plots quantitatively illustrated the distribution of different colors in each image relative to a reference (Fig.2, bottom). The points on the curved boundary of the reference chromaticity plot were unique spectral colors, while the colors inside the diagram represented different mixtures of colors. The chromaticity coordinates (x and y) can be calculated based on spectral power distribution at each wavelength. The chromaticity diagrams showed a preferred distribution towards blue in the control group. SHG microscopy confirmed that the collagen microstructure did not change significantly after glutaraldehyde or ChABC treatment (Fig.3).

Figure 2.

Representative brightfield images of the control (A) and chondroitinase treated (B) tendon samples in the longitudinal orientation. C and E show the chromaticity plots corresponding to A and B, respectively, and D shows the reference color distribution. X and Y are chromaticity coordinates that serve to compare the colors present in the images to a reference plot that includes all visible colors

Figure 3.

SHG images of tendon sample in the longitudinal (top row) and transverse (bottom row) planes before and after ChABC treatment (left panel) and glutaraldehyde treatment (right panel).

Microstructural modeling differentiates the inter and intrafibrillar crosslinkers

We first investigated the potential crosslinking function of the GAGs, i.e., their ability to transfer force between the fibrils. To this end, we extended the microstructural model introduced in (Moghaddam et al., 2023) to evaluate the influence of inter (between fibril) and intrafibrillar (sub-fibril) crosslinkers on the orientation-dependent indentation response. The interfibrillar crosslinkers bridged the space between the collagen fibrils while the intrafibrillar crosslinkers bridged sub-fibrillar collagen structures. The interfibrillar crosslinkers were represented by the shear modulus of the matrix; by changing the shear modulus, we limited how much the fibrils could move relative to one another for a given applied shear force without affecting the stiffness of matrix in other modes of deformation, i.e., tension and compression. Considering the size of the fibrils (100–200 nm diameter) relative to the indentation contact diameter (~32 µm for an indentation depth of 5 µm), we used the fibril modulus as a measure of intrafibrillar crosslinking density; in other words, we considered the homogenized material properties and the effective response of crosslinkers that acted on any structure smaller than the fibrils and did not model crosslinkers at the sub-fibrillar scale.

We performed a parametric study to assess the potential dependence of each type of crosslinker, inter or intra, on the orientation-dependent normalized indentation force (Fig.4, top panel). We evaluated the indentation force for matrix shear modulus at 1x, 5x, and 20x relative to the isotropic baseline in order to simulate interfibrillar crosslinking and found that this crosslinker type influenced the reaction force in longitudinal indentation more than in the transverse indentation (Fig.4 A and B). We then changed the Young’s modulus of the fibrils by 0.5x, 0.75x, or 1x of the baseline to simulate the variation of intrafibrillar crosslinking and found that these crosslinkers only affected the reaction force in the transverse indentation (Fig.4 C and D). A higher indentation modulus is equivalent to a higher reaction force at the same indentation depth for a given tip radius (see Eq. 1)

Figure 4.

Influence of the inter (between fibrils) and intrafibrillar (sub-fibril) crosslinkers on the orientation-dependent indentation response of collagenous tissue. Normalized reaction force vs normalized displacement is shown for a model with A: interfibrillar crosslinkers indented in the longitudinal plane, and B: transverse plane; and with intrafibrillar crosslinkers indented in C: longitudinal and D: transverse plane. Interfibrillar crosslinkers have a more pronounced effect in the longitudinal indentation, while intrafibrillar crosslinkers affect the reaction force only in the transverse indentation. E: Results from a model with both inter- and intrafibrillar crosslinkers indented in the longitudinal and F: transverse plane. G: Influence of glutaraldehyde crosslinking on the indentation modulus (E) of tendon when indented in the longitudinal and transverse planes (E ~ Reaction force). The increase in E was more pronounced in transverse indentation, compared to the longitudinal indentation, agreeing with the predictions of the model. The schematics show the dominant orientation of fibrils relative to the indentation axis. Target crosslinker type is highlighted in red. The force-displacement curves are normalized relative to the stiffest sample in each group.

In the longitudinal indentation, the matrix dominated the response and increasing the intrafibrillar crosslinking (higher fibril modulus) did not increase the reaction force since the fibrils remained mostly strain-free. The interfibrillar crosslinkers, however, engaged the fibrils in the deformation process and increased the reaction force. In the transverse indentation, the crosslinked fibrils always contributed to the indentation response, regardless of the low stiffness of the matrix in tension and compression. Increasing intrafibrillar crosslinking, therefore, significantly influenced the indentation reaction force in the transverse orientation and the interfibrillar crosslinkers became less influential. This nonuniform, orientation-dependent increase in the reaction force was used to differentiate the type of crosslinkers.

To experimentally validate the model, we performed indentation experiments on glutaraldehyde-treated tendon. Glutaraldehyde is known to create both inter- and intrafibrillar crosslinkers in tissue, though the induced crosslinking density is higher within (intra) a single fibril (Chandran et al., 2012; Hansen et al., 2009). From the simulation, when the density of both inter- and intrafibrillar crosslinkers increased, the increase in indentation reaction force was more pronounced in the transverse indentation (Fig.4 E and F). The experimental results confirmed the predictions of the model (Fig.4 G); the increase in the indentation modulus after treatment was 3.4x in the longitudinal-plane indentation compared to a 5.3x increase in the transverse-plane indentation.

GAGs facilitate collagen fibril sliding, but have minimal crosslinking function

We experimentally investigated the influence of GAGs on fibril-fibril interactions by using an enzymatic treatment (Chondroitinase ABC) that degrades chondroitin sulfate GAGs (see Methods). We performed indentation-relaxation tests in orthogonal orientations, in the transverse and longitudinal planes, and obtained the instantaneous (E₀) and equilibrium (E_inf) moduli and short and long material time constants (T₁ and T₂ ). We expected to see a reduced stiffness after GAG depletion, considering the understood interfibrillar arrangement of the GAGs that bridged the neighboring fibrils (Watanabe et al., 2016b). Contrary to our prediction, we found that GAG depletion did not significantly change the instantaneous or equilibrium modulus of tendon in either orientation (Fig.5 A and B). We only observed a non-significant decrease (>10%) in the mean equilibrium modulus (E_inf). The material time constants (T₁ and T₂), on the other hand, significantly increased (p<0.01) after GAG depletion in both orientations (Fig.5 C and D). The increase, however, was not uniform across the orientations; the average time constant increased 67.19% (T₁) and 122.94% (T₂) in the longitudinal indentation, and 12.11% (T₁) and 19.28% (T₂) in the transverse indentation. In other words, GAG depletion influenced the material time constants in the longitudinal indentation more than the transverse indentation.

Figure 5.

Influence of GAG depletion on viscoelastic properties of tendon. GAG depletion leads to a significant increase in material time constants, but does not affect the instantaneous (E0) or equilibrium (Einf) modulus. A: E0, B: Einf, C and D: material time constants (T1<T2) of the control (gray) and ChABC treated (red) groups in the longitudinal and transverse indentation.

After identifying the changes of viscoelastic properties due to GAG depletion, we used our computational model to infer the fibril-level deformation mechanisms from the experimental data. Our model showed that both inter- and intrafibrillar crosslinkers give rise to an increased indentation reaction force (RF), as discussed in the previous section and shown in Fig.6 A and B (different representation of data in Fig.4 A–D with RF at the maximum depth). This increase was orientation-dependent and varied with crosslinker type and density. The experimental normalized reaction force, calculated from the equilibrium modulus (E_inf), however, did not change significantly after GAG depletion (Fig.6 C, different representation of the average values in Fig.5 B). Therefore, we could not conclude that the GAGs have a strong crosslinking function. However, the nonsignificant decrease in the reaction force may point to a weak interfibrillar crosslinking function; depletion of the crosslinkers decreased the reaction force in our model.

Figure 6.

Crosslinking and fibril sliding functions of GAGs in tendon. GAGs facilitate collagen fibril sliding but their crosslinking function is minimal. Top row: GAG crosslinking function. Bottom row: GAG fibril sliding function. A: Normalized reaction force (RF) from a model with interfibrillar and B: Intrafibrillar crosslinkers. The legend in A also applies to B. C: Experimental normalized reaction force calculated from the equilibrium modulus (Reaction force ~ E). D: Normalized relaxation time constant from a model in which GAGs have strain-independent and E: strain-dependent time constants. F: Normalized material time constant (T1) from experiments.

Next, we considered the potential role of GAGs in facilitating fibril sliding. We observed that the material time constants (T₁ and T₂) increased significantly after GAG depletion and hypothesized that this increase was caused by friction and intermolecular Van der Waals forces between neighboring fibrils. To simulate these fibril interactions, we considered an increased material time constant (f in Eq.9, where f=t_a=t_b for the strain-independent formulation) for the non-collagen matrix after GAG depletion. Simulation of indentation-relaxation experiments showed that increasing the time constant (t_a) of the matrix generated a uniform increase in the indentation relaxation time in transverse and longitudinal orientations (Fig.6 D). This result, however, did not agree with our experimental observations in which the normalized time constant (T₁) changed more substantially in the longitudinal indentation (Fig.6 F, different representation of the average values in Fig.5 C). We then hypothesized that the increase in time constants T₁ and T₂ arose from the strain-dependent molecular arrangement of the GAGs that bridged the neighboring fibrils. To test this hypothesis, we used a strain-dependent function to describe the time constant of the non-collagen matrix ($f(\epsilon )$ in Eq.9 where t_a ≠ t_b for the strain-dependent formulation) in healthy tendon. The central assumption was that GAGs can only separate the fibrils effectively when stretched below a threshold. After a critical strain , GAGs partially lose their ability to separate the fibrils and the relaxation time (characterized by T₁ and T₂) increases.

We found that this strain-dependent model (Eq.9) could capture the trends in the experimental data (Fig.6 E). For the control (intact) tendon, , t_a, and t_b were 0.05, 0.5 s, and 1 s, respectively. For the GAG-depleted tendon, a strain-independent time constant (f in Eq.9, where f=ta=tb) of 1 s adequately captured the experimental results. The time constants from the simulation were only compared to the short material time constant (T₁) from the experiments since T₁and T₂ were highly correlated. This observation confirmed our proposed hypothesis for the deformation mechanism.

The shear-lag model verifies the strain-dependent role of GAGs in regulating the viscoelastic behavior

We also used a simplified shear-lag model (Fig.7), a well-established and computationally efficient approach for investigating the fibril interactions (Ahmadzadeh et al., 2015), to infer the role of GAGs in modulating the microscale deformation mechanisms. We first established the equivalent boundary conditions that represented the spherical indentation in orthogonal orientations in the shear-lag model. While it was not possible to fully capture the complex deformation of tissue under the spherical indenter, particular modes of deformation could still be investigated. We focused on the shear component of the strain tensor because of its important role in regulating the fibril interactions. As illustrated in (Moghaddam et al., 2023), spherical indentation induced a higher level of shear strain in the transverse indentation, compared to the longitudinal indentation; we applied a prescribed displacement in the shear-lag model that yielded similar, orientation-specific total strains in the matrix. We then used the same strain-dependent function (Eq.9) to describe the behavior of matrix (representing GAGs) in the shear-lag model. Results showed that the shear-lag model could also capture the experimental indentation results when used with the boundary and loading conditions described above (Fig.7 B and C). The unknown parameters of Eq.9, ε_c, t_a, and t_b, that captured the experimental results were 0.05, 0.2 s, and 2.5 s, respectively, for the control (intact) tendon and 0.05, 2.25 s, 2.75 s, respectively, for the GAG-depleted tendon.

Figure 7.

Shear-lag model for GAG sliding function. A: model in the reference configuration. B: Representative shear strain corresponding to transverse spherical indentation in the microstructural model. C: Normalized relaxation time constant calculated from the shear-lag model. The matrix was assumed to have a strain-dependent time constant as described in Eq.9. All values are normalized relative to the control (intact) tendon indented in the longitudinal plane.

Both modeling approaches, while very different in length scale and boundary conditions, confirmed our hypothesis regarding the strain-dependent role of GAGs in regulating the viscoelastic behavior of tendon. While the shear-lag model lacked the complex multiaxial deformation modes induced by spherical indentation, the shear mode alone, as an important aspect of deformation, could provide an explanation for the deformation mechanisms related to GAGs that agreed with those obtained from the more complex microstructural model.

Discussion

We used orientation-dependent indentation and computational modeling to examine the deformation mechanisms of collagenous tissue. Leveraging the distinct deformation modes introduced by transverse and longitudinal spherical indentation, we showed that a microstructural model can differentiate the inter- and intrafibrillar crosslinkers and capture the deformation mechanisms related to fibril interactions (Fig.4). Focusing on the function of GAGs in tendon, we found that GAGs facilitate collagen fibril sliding and reduce the stress relaxation time (Fig.5 C and D, Fig.6 D–F), while having minimal crosslinking function (Fig.5 A and B, Fig.6 A–C). We suggested that the molecular reconfiguration of GAGs is a potential mechanism for their microscale, strain-dependent viscoelastic behavior.

Consistent with several previous studies (Eisner et al., 2022; Legerlotz et al., 2013; Lujan et al., 2007; Rigozzi et al., 2009; Svensson et al., 2011), we did not find a significant difference in tissue stiffness after enzymatic depletion of GAGs (Fig.5 A and B). This observation provided further evidence against the crosslinking function of GAGs in tissue and confirmed that the load transfer between collagen fibrils is likely facilitated by other mechanisms that do not involve GAGs. Unlike several previous studies (Connizzo et al., 2013; Dourte et al., 2013; Fessel and Snedeker, 2009; Lujan et al., 2009), though, we found that the GAGs play a major role in modulating the fibril sliding and viscoelastic behavior of tendon (Fig.5 C and D, Fig.6 D–F). In agreement with our findings, Rigozzi et al. (Rigozzi et al., 2013) reported that GAG depletion led to an increased D-period at high strain levels, indicating more fibril stretch and less fibril sliding. Some previous work at larger length scales also supported the role of GAGs in modulating the viscoelastic response of tendon (Legerlotz et al., 2013; Robinson et al., 2017, 2004b). Compared to previous studies, our work used a more direct approach to probe the function of GAGs at the scale of fibrils. Our novel multi-directional indentation approach, combined with computational modeling, allowed us to infer the potential underlying mechanisms that contributed to the observations in mechanical tests.

The strain-dependent modulation of fibril interactions by GAGs has functional benefits for the tissue; at small strains, close to homeostasis, the fast relaxation response of ECM promotes proliferation, spreading, and differentiation of the cells (Chaudhuri et al., 2016). It also supports the mechanical function of connective tissues such as tendon by keeping the tissue deformations in phase with dynamic periodic loads. At large strains, however, the same fast relaxation response may lead to tissue damage; in response to dynamic loads, the strains would increase excessively due to the reduced reaction forces from the tissue, which might possibly go beyond the failure limits. The interfibrillar configuration of GAGs that forms bridges between collagen fibrils, therefore, may serve to protect the tissue by generating a strain-dependent relaxation response instead of transferring force between the fibrils. Consistent with this finding, Legerlotz et al. (Legerlotz et al., 2013) reported that GAG depletion leads to partially reversible increased stress relaxation and reduction in failure stress, and suggested that GAGs might have a protective role against fatigue by increasing the tissue hydration.

Tendon diseases such as tendinitis (Riley et al., 1994) and Dupuytren disease (Flint et al., 1982), and prescription drugs, e.g., ciprofloxacin (Juras et al., 2015) and statins (de Oliveira et al., 2015), as well as other factors such as age and loading conditions (Riley et al., 1994) can influence the GAG content of the tissue, and thus almost certainly the mechanical behavior. The successful use of constitutive models for explaining and predicting the mechanical behavior of healthy and diseased tissue relies on the ability of these models to not only capture the mechanical response, but also the underlying mechanisms that contribute to the mechanical behavior of tissue. It is therefore necessary to understand the mechanical function of GAGs, as well as other less abundant tissue constituents, and incorporate the related microscale deformation processes in constitutive models. This approach may enable new clinical applications of mechanobiology and targeted treatments.

The shear-lag model has been previously used to examine the interactions of collagen fibrils through GAGs and crosslinkers in the tensile mode of deformation (Ahmadzadeh et al., 2015, 2013; Szczesny and Elliott, 2014; Wu et al., 2018). Compared to the microstructural model, the shear-lag model is more well-suited to illustrate the combined influence of GAGs, crosslinkers, fibril length, fibril distance, and other geometric parameters on the mechanical behavior. We demonstrated an approach to use this model for interpretation of spherical indentation data. Our method relied on determining the equivalent boundary conditions for the shear-lag model from a microstructural model involving fibrils and matrix. Results showed that when the shear deformations are central to the mechanical response, the shear-lag model can be used to interpret the spherical indentation experiments (Fig. 7). To our knowledge, this is the first use of the shear-lag model for interpretation of indentation data.

While we focused on the mechanical function of GAGs and crosslinkers in the tendon, our approach is broadly applicable to other tissues and tissue constituents. For example, the mechanical function of elastin, another key component of ECM, can be identified similarly; elastase enzymes selectively digest elastin (Janoff, 1985), and an orthogonal indentation approach can reveal how elastin is involved in the anisotropic and microscale deformation mechanisms. Similarly, the mechanical function of different types of GAGs, e.g., hyaluronic acid (Chen et al., 2022), can be identified using appropriate enzymatic degradations, e.g., hyaluronidase (Meyer, 1947). Knock-out animal models can be used instead of, or complementary to, the enzymatic treatments with a similar study design.

There were several limitations to this study, besides the limitations of computational model, e.g., 2D modeling instead of 3D modeling, discussed in (Moghaddam et al., 2023). First, we observed sample to sample variations in the mechanical properties, possibly due to the variations in the age of animals; yet the influence of treatment was consistent across the samples; our conclusions remained valid when we considered the sample-to-sample variations (Supplementary, Table S.1). Considering the potential interactions of treatment and individual differences in ANOVA also did not alter the conclusions of this analysis (data not shown). Second, we did not directly confirm our conclusions regarding deformation processes; the influence of GAG molecular reconfiguration on the viscoelastic behavior was only inferred from the mechanical data and computational model, not from direct observation. Imaging the GAGs in their native microenvironment during deformation could further strengthen our findings, but, currently, such a technique does not exist to our knowledge. Our indentation-based approach, therefore, could serve as an excellent alternative for understanding the deformation mechanisms involved in collagen fibril interactions. Finally, we did not investigate the potentially different function of different types of GAGs and limited our scope to sulfated GAGs digested by chondroitinase ABC. Future studies could refine the experimental approach of this work and use enzymes that selectively target particular types of GAGs.

This paper provides new insights into the mechanical function of GAGs in the collagenous tissue and presents a framework for probing the underlying physical mechanisms related to collagen fibril interactions. It may resolve conflicting hypotheses regarding the mechanical role of GAGs in mature tissue and help to improve the accuracy of constitutive microstructural models. Beyond GAGs, this general experimental-computational framework can be used to identify the tissue-specific role of other ECM components in regulating the microscale deformation processes.

Data availability

The data that support the findings and plots of this study are available from the corresponding author upon reasonable request.