Estimating the 3D Pore Size Distribution of Biopolymer Networks from Directionally Biased Data

The pore size of biopolymer networks governs their mechanical properties and strongly impacts the behavior of embedded cells. Confocal reflection microscopy and second harmonic generation microscopy are widely used to image biopolymer networks; however, both techniques fail to resolve vertically oriented fibers. Here, we describe how such directionally biased data can be used to estimate the network pore size. We first determine the distribution of distances from random points in the fluid phase to the nearest fiber. This distribution follows a Rayleigh distribution, regardless of isotropy and data bias, and is fully described by a single parameter—the characteristic pore size of the network. The bias of the pore size estimate due to the missing fibers can be corrected by multiplication with the square root of the visible network fraction. We experimentally verify the validity of this approach by comparing our estimates with data obtained using confocal fluorescence microscopy, which represents the full structure of the network. As an important application, we investigate the pore size dependence of collagen and fibrin networks on protein concentration. We find that the pore size decreases with the square root of the concentration, consistent with a total fiber length that scales linearly with concentration.     

Estimating the 3D Pore Size Distribution of Biopolymer Networks from Directionally Biased Data

The pore size of biopolymer networks governs their mechanical properties and strongly impacts the behavior of embedded cells. Confocal reflection microscopy and second harmonic generation microscopy are widely used to image biopolymer networks; however, both techniques fail to resolve vertically oriented fibers. Here, we describe how such directionally biased data can be used to estimate the network pore size. We first determine the distribution of distances from random points in the fluid phase to the nearest fiber. This distribution follows a Rayleigh distribution, regardless of isotropy and data bias, and is fully described by a single parameter—the characteristic pore size of the network. The bias of the pore size estimate due to the missing fibers can be corrected by multiplication with the square root of the visible network fraction. We experimentally verify the validity of this approach by comparing our estimates with data obtained using confocal fluorescence microscopy, which represents the full structure of the network. As an important application, we investigate the pore size dependence of collagen and fibrin networks on protein concentration. We find that the pore size decreases with the square root of the concentration, consistent with a total fiber length that scales linearly with concentration.     

A Blind Spot in Confocal Reflection Microscopy: The Dependence of Fiber Brightness on Fiber Orientation in Imaging Biopolymer Networks

We investigate the dependence of fiber brightness on three-dimensional fiber orientation when imaging biopolymer networks with confocal reflection microscopy (CRM) and confocal fluorescence microscopy (CFM). We compare image data of fluorescently labeled type I collagen networks concurrently acquired using each imaging modality. For CRM, fiber brightness decreases for more vertically oriented fibers, leaving fibers above ∼50° from the imaging plane entirely undetected. As a result, the three-dimensional network structure appears aligned with the imaging plane. In contrast, CFM data exhibit little variation of fiber brightness with fiber angle, thus revealing an isotropic collagen network. Consequently, we find that CFM detects almost twice as many fibers as are visible with CRM, thereby yielding more complete structural information for three-dimensional fiber networks. We offer a simple explanation that predicts the detected fiber brightness as a function of fiber orientation in CRM.     

Parameter-free binarization and skeletonization of fiber networks from confocal image stacks

We present a method to reconstruct a disordered network of thin biopolymers, such as collagen gels, from three-dimensional (3D) image stacks recorded with a confocal microscope. The method is based on a template matching algorithm that simultaneously performs a binarization and skeletonization of the network. The size and intensity pattern of the template is automatically adapted to the input data so that the method is scale invariant and generic. Furthermore, the template matching threshold is iteratively optimized to ensure that the final skeletonized network obeys a universal property of voxelized random line networks, namely, solid-phase voxels have most likely three solid-phase neighbors in a 3 x 3 x 3 neighborhood. This optimization criterion makes our method free of user-defined parameters and the output exceptionally robust against imaging noise.     

Structure-Function Relations and Rigidity Percolation in the Shear Properties of Articular Cartilage

Among mammalian soft tissues, articular cartilage is particularly interesting because it can endure a lifetime of daily mechanical loading despite having minimal regenerative capacity. This remarkable resilience may be due to the depth-dependent mechanical properties, which have been shown to localize strain and energy dissipation. This paradigm proposes that these properties arise from the depth-dependent collagen fiber orientation. Nevertheless, this structure-function relationship has not yet been quantified. Here, we use confocal elastography, quantitative polarized light microscopy, and Fourier-transform infrared imaging to make same-sample measurements of the depth-dependent shear modulus, collagen fiber organization, and extracellular matrix concentration in neonatal bovine articular cartilage. We find weak correlations between the shear modulus |G^∗| and both the collagen fiber orientation and polarization. We find a much stronger correlation between |G^∗| and the concentration of collagen fibers. Interestingly, very small changes in collagen volume fraction v_c lead to orders-of-magnitude changes in the modulus with |G^∗| scaling as (v_c – v₀)^ξ. Such dependencies are observed in the rheology of other biopolymer networks whose structure exhibits rigidity percolation phase transitions. Along these lines, we propose that the collagen network in articular cartilage is near a percolation threshold that gives rise to these large mechanical variations and localization of strain at the tissue’s surface.     

Structure-Function Relations and Rigidity Percolation in the Shear Properties of Articular Cartilage

Among mammalian soft tissues, articular cartilage is particularly interesting because it can endure a lifetime of daily mechanical loading despite having minimal regenerative capacity. This remarkable resilience may be due to the depth-dependent mechanical properties, which have been shown to localize strain and energy dissipation. This paradigm proposes that these properties arise from the depth-dependent collagen fiber orientation. Nevertheless, this structure-function relationship has not yet been quantified. Here, we use confocal elastography, quantitative polarized light microscopy, and Fourier-transform infrared imaging to make same-sample measurements of the depth-dependent shear modulus, collagen fiber organization, and extracellular matrix concentration in neonatal bovine articular cartilage. We find weak correlations between the shear modulus |G^∗| and both the collagen fiber orientation and polarization. We find a much stronger correlation between |G^∗| and the concentration of collagen fibers. Interestingly, very small changes in collagen volume fraction v_c lead to orders-of-magnitude changes in the modulus with |G^∗| scaling as (v_c – v₀)^ξ. Such dependencies are observed in the rheology of other biopolymer networks whose structure exhibits rigidity percolation phase transitions. Along these lines, we propose that the collagen network in articular cartilage is near a percolation threshold that gives rise to these large mechanical variations and localization of strain at the tissue’s surface.     

A microstructurally based continuum model of cartilage viscoelasticity and permeability incorporating measured statistical fiber orientations

The remarkable mechanical properties of cartilage derive from an interplay of isotropically distributed, densely packed and negatively charged proteoglycans; a highly anisotropic and inhomogeneously oriented fiber network of collagens; and an interstitial electrolytic fluid. We propose a new 3D finite strain constitutive model capable of simultaneously addressing both solid (reinforcement) and fluid (permeability) dependence of the tissue’s mechanical response on the patient-specific collagen fiber network. To represent fiber reinforcement, we integrate the strain energies of single collagen fibers—weighted by an orientation distribution function (ODF) defined over a unit sphere—over the distributed fiber orientations in 3D. We define the anisotropic intrinsic permeability of the tissue with a structure tensor based again on the integration of the local ODF over all spatial fiber orientations. By design, our modeling formulation accepts structural data on patient-specific collagen fiber networks as determined via diffusion tensor MRI. We implement our new model in 3D large strain finite elements and study the distributions of interstitial fluid pressure, fluid pressure load support and shear stress within a cartilage sample under indentation. Results show that the fiber network dramatically increases interstitial fluid pressure and focuses it near the surface. Inhomogeneity in the tissue’s composition also increases fluid pressure and reduces shear stress in the solid. Finally, a biphasic neo-Hookean material model, as is available in commercial finite element codes, does not capture important features of the intra-tissue response, e.g., distributions of interstitial fluid pressure and principal shear stress.     

On the Presence of Affine Fibril and Fiber Kinematics in the Mitral Valve Anterior Leaflet

In this study, we evaluated the hypothesis that the constituent fibers follow an affine deformation kinematic model for planar collagenous tissues. Results from two experimental datasets were utilized, taken at two scales (nanometer and micrometer), using mitral valve anterior leaflet (MVAL) tissues as the representative tissue. We simulated MVAL collagen fiber network as an ensemble of undulated fibers under a generalized two-dimensional deformation state, by representing the collagen fibrils based on a planar sinusoidally shaped geometric model. The proposed approach accounted for collagen fibril amplitude, crimp period, and rotation with applied macroscopic tissue-level deformation. When compared to the small angle x-ray scattering measurements, the model fit the data well, with an r² = 0.976. This important finding suggests that, at the homogenized tissue-level scale of ∼1 mm, the collagen fiber network in the MVAL deforms according to an affine kinematics model. Moreover, with respect to understanding its function, affine kinematics suggests that the constituent fibers are largely noninteracting and deform in accordance with the bulk tissue. It also suggests that the collagen fibrils are tightly bounded and deform as a single fiber-level unit. This greatly simplifies the modeling efforts at the tissue and organ levels, because affine kinematics allows a straightforward connection between the macroscopic and local fiber strains. It also suggests that the collagen and elastin fiber networks act independently of each other, with the collagen and elastin forming long fiber networks that allow for free rotations. Such freedom of rotation can greatly facilitate the observed high degree of mechanical anisotropy in the MVAL and other heart valves, which is essential to heart valve function. These apparently novel findings support modeling efforts directed toward improving our fundamental understanding of tissue biomechanics in healthy and diseased conditions.     

The effects of aging on the intimal region of the human saphenous vein: insights from multimodal microscopy and quantitative image analysis

We hypothesized that structural remodeling associated with advancing age occurs in human saphenous veins. To address this hypothesis, we have identified structural remodeling in human saphenous veins by applying histochemistry, fluorescence staining and quantitative image analysis to specifically assess intimal area, intimal cellularity and intimal collagen content and organization. Saphenous veins were collected from patients undergoing coronary artery bypass graft surgery. Area measurements and cellularity were quantified using the image analysis software Stereo Investigator, employing planimetry and counting frames, respectively. Collagen content and organization were quantified in MetaMorph image analysis software based on measurements of color (hue, saturation, and intensity) from polarized light images. Intimal area and cellularity showed no statistically significant increases with age; in contrast, total collagen content showed a significant decrease with advancing age. Furthermore, collagen fiber types also demonstrated a statistically significant alteration with age; increases in age resulted in decreases in larger collagen fibers. No significant changes in small collagen fibers were identified. These results raise the possibility that age-associated structural alterations in total collagen content, specifically collagen fiber size, could be a factor in the etiology of age-associated venous diseases.     

Objective threshold selection procedure (OTS) for segmentation of scanning laser confocal microscope images

The determination of volumes and interface areas from confocal laser scanning microscopy (CLSM) images requires the identification of component objects by segmentation. An automated method for the determination of segmentation thresholds for CLSM imaging of biofilms was developed. The procedure, named objective threshold selection (OTS), is a three-dimensional development of the approach introduced by the popular robust automatic threshold selection (RATS) method. OTS is based on the statistical properties of local gray-values and gradients in the image. By characterizing the dependence between a volumetric feature and the intensity threshold used for image segmentation, the former can be determined with an arbitrary confidence level, with no need for user intervention. The identification of an objective segmentation procedure renders the possibility for the full automation of volume and interfacial area measurement. Images from two distinct biofilm systems, acquired using different experimental techniques and instrumental setups were segmented by OTS to determine biofilm volume and interfacial area. The reliability of measurements for each case was analyzed to identify optimal procedure for image acquisition. The automated OTS method was shown to reproduce values obtained manually by an experienced operator.     

Macroscopic-microscopic characterization of the passive mechanical properties in rat soleus muscle

The purpose of the study was to investigate changes in passive mechanical properties of the soleus muscle of the rat during the first year of life. These mechanical changes were quantified at a macroscopic (whole muscle) and a microscopic level (fiber) and were correlated with biochemical and morphological properties. Three passive mechanical tests (a relaxation test, a ramp stretch test and a stretch release cycle test) with different amplitudes and velocities were performed on isolated soleus muscles and fibers in rats at ages 1 (R1), 4 (R4) and 12 (R12) months. Mechanical parameters (dynamic and static forces, stresses and normalized stiffness) were recorded and measured. The morphological properties (size of fibers and muscles) for the three groups of rats were assessed by light microscopy which allowed us to observe the evolution of the fiber type (I, IIc and IIa) in the belly region and along the longitudinal axis of the muscle. In addition, biochemical analyses were performed at the level of the whole muscle in order to determine the collagen content. The results of the passive mechanical properties between the macroscopic (muscle) and microscopic (fiber) levels showed a similar evolution. Thus, an increase of the dynamic and static forces appeared between 1 and 4 months while a decrease of the passive tension occurred between 4 and 12 months. These mechanical changes were correlated to the morphological properties. In addition, the size of the three fibers type which grew with age could explain the increase of forces between 1 and 4 months. Furthermore, the biochemical analysis showed an increase of the collagen content during the same period which could also be associated with the increase of the passive forces. After 4 months, the passive tension decreased while the size of the fiber continued to increase. The biochemical analysis showed a decrease of the collagen content after 4 months, which could explain the loss of passive tension in the whole muscle. Concerning the similar loss at the fiber level, other assumptions are required such as a myofibril loss process and an increase of intermyofibrillar spaces. The originality of this present study was to compare the passive mechanical properties between two different levels of anatomical organization within the soleus muscle of the rat and to explain these mechanical changes in terms of biochemical and morphological properties.     

Functional Grading of Mineral and Collagen in the Attachment of Tendon to Bone

Attachment of dissimilar materials is a major challenge because high levels of localized stress may develop at their interfaces. An effective biologic solution to this problem exists at one of nature's most extreme interfaces: the attachment of tendon (a compliant, structural “soft tissue”) to bone (a stiff, structural “hard tissue”). The goal of our study was to develop biomechanical models to describe how the tendon-to-bone insertion derives its mechanical properties. We examined the tendon-to-bone insertion and found two factors that give the tendon-to-bone transition a unique grading in mechanical properties: 1), a gradation in mineral concentration, measured by Raman spectroscopy; and 2), a gradation in collagen fiber orientation, measured by polarized light microscopy. Our measurements motivate a new physiological picture of the tissue that achieves this transition, the tendon-to-bone insertion, as a continuous, functionally graded material. Our biomechanical model suggests that the experimentally observed increase in mineral accumulation within collagen fibers can provide significant stiffening of the partially mineralized fibers, but only for concentrations of mineral above a “percolation threshold” corresponding to formation of a mechanically continuous mineral network within each collagen fiber (e.g., the case of mineral connectivity extending from one end of the fiber to the other). Increasing dispersion in the orientation distribution of collagen fibers from tendon to bone is a second major determinant of tissue stiffness. The combination of these two factors may explain the nonmonotonic variation of stiffness over the length of the tendon-to-bone insertion reported previously. Our models explain how tendon-to-bone attachment is achieved through a functionally graded material composition, and provide targets for tissue engineered surgical interventions and biomimetic material interfaces.     

Rapid Quantification of 3D Collagen Fiber Alignment and Fiber Intersection Correlations with High Sensitivity

Metastatic cancers aggressively reorganize collagen in their microenvironment. For example, radially orientated collagen fibers have been observed surrounding tumor cell clusters in vivo. The degree of fiber alignment, as a consequence of this remodeling, has often been difficult to quantify. In this paper, we present an easy to implement algorithm for accurate detection of collagen fiber orientation in a rapid pixel-wise manner. This algorithm quantifies the alignment of both computer generated and actual collagen fiber networks of varying degrees of alignment within 5°°. We also present an alternative easy method to calculate the alignment index directly from the standard deviation of fiber orientation. Using this quantitative method for determining collagen alignment, we demonstrate that the number of collagen fiber intersections has a negative correlation with the degree of fiber alignment. This decrease in intersections of aligned fibers could explain why cells move more rapidly along aligned fibers than unaligned fibers, as previously reported. Overall, our paper provides an easier, more quantitative and quicker way to quantify fiber orientation and alignment, and presents a platform in studying effects of matrix and cellular properties on fiber alignment in complex 3D environments.     

Arterial Extracellular Matrix: A Mechanobiological Study of the Contributions and Interactions of Elastin and Collagen

The complex network structure of elastin and collagen extracellular matrix (ECM) forms the primary load bearing components in the arterial wall. The structural and mechanobiological interactions between elastin and collagen are important for properly functioning arteries. Here, we examined the elastin and collagen organization, realignment, and recruitment by coupling mechanical loading and multiphoton imaging. Two-photon excitation fluorescence and second harmonic generation methods were performed with a multiphoton video-rate microscope to capture real time changes to the elastin and collagen structure during biaxial deformation. Enzymatic removal of elastin was performed to assess the structural changes of the remaining collagen structure. Quantitative analysis of the structural changes to elastin and collagen was made using a combination of two-dimensional fast Fourier transform and fractal analysis, which allows for a more complete understanding of structural changes. Our study provides new quantitative evidence, to our knowledge on the sequential engagement of different arterial ECM components in response to mechanical loading. The adventitial collagen exists as large wavy bundles of fibers that exhibit fiber engagement after 20% strain. The medial collagen is engaged throughout the stretching process, and prominent elastic fiber engagement is observed up to 20% strain after which the engagement plateaus. The fiber orientation distribution functions show remarkably different changes in the ECM structure in response to mechanical loading. The medial collagen shows an evident preferred circumferential distribution, however the fiber families of adventitial collagen are obscured by their waviness at no or low mechanical strains. Collagen fibers in both layers exhibit significant realignment in response to unequal biaxial loading. The elastic fibers are much more uniformly distributed and remained relatively unchanged due to loading. Removal of elastin produces similar structural changes in collagen as mechanical loading. Our study suggests that the elastic fibers are under tension and impart an intrinsic compressive stress on the collagen.     

Mechanisms of Plastic Deformation in Collagen Networks Induced by Cellular Forces

Contractile cells can reorganize fibrous extracellular matrices and form dense tracts of fibers between neighboring cells. These tracts guide the development of tubular tissue structures and provide paths for the invasion of cancer cells. Here, we studied the mechanisms of the mechanical plasticity of collagen tracts formed by contractile premalignant acinar cells and fibroblasts. Using fluorescence microscopy and second harmonic generation, we quantified the collagen densification, fiber alignment, and strains that remain within the tracts after cellular forces are abolished. We explained these observations using a theoretical fiber network model that accounts for the stretch-dependent formation of weak cross-links between nearby fibers. We tested the predictions of our model using shear rheology experiments. Both our model and rheological experiments demonstrated that increasing collagen concentration leads to substantial increases in plasticity. We also considered the effect of permanent elongation of fibers on network plasticity and derived a phase diagram that classifies the dominant mechanisms of plasticity based on the rate and magnitude of deformation and the mechanical properties of individual fibers. Plasticity is caused by the formation of new cross-links if moderate strains are applied at small rates or due to permanent fiber elongation if large strains are applied over short periods. Finally, we developed a coarse-grained model for plastic deformation of collagen networks that can be employed to simulate multicellular interactions in processes such as morphogenesis, cancer invasion, and fibrosis.     

Arterial Extracellular Matrix: A Mechanobiological Study of the Contributions and Interactions of Elastin and Collagen

The complex network structure of elastin and collagen extracellular matrix (ECM) forms the primary load bearing components in the arterial wall. The structural and mechanobiological interactions between elastin and collagen are important for properly functioning arteries. Here, we examined the elastin and collagen organization, realignment, and recruitment by coupling mechanical loading and multiphoton imaging. Two-photon excitation fluorescence and second harmonic generation methods were performed with a multiphoton video-rate microscope to capture real time changes to the elastin and collagen structure during biaxial deformation. Enzymatic removal of elastin was performed to assess the structural changes of the remaining collagen structure. Quantitative analysis of the structural changes to elastin and collagen was made using a combination of two-dimensional fast Fourier transform and fractal analysis, which allows for a more complete understanding of structural changes. Our study provides new quantitative evidence, to our knowledge on the sequential engagement of different arterial ECM components in response to mechanical loading. The adventitial collagen exists as large wavy bundles of fibers that exhibit fiber engagement after 20% strain. The medial collagen is engaged throughout the stretching process, and prominent elastic fiber engagement is observed up to 20% strain after which the engagement plateaus. The fiber orientation distribution functions show remarkably different changes in the ECM structure in response to mechanical loading. The medial collagen shows an evident preferred circumferential distribution, however the fiber families of adventitial collagen are obscured by their waviness at no or low mechanical strains. Collagen fibers in both layers exhibit significant realignment in response to unequal biaxial loading. The elastic fibers are much more uniformly distributed and remained relatively unchanged due to loading. Removal of elastin produces similar structural changes in collagen as mechanical loading. Our study suggests that the elastic fibers are under tension and impart an intrinsic compressive stress on the collagen.     

Light scattering from collagen fiber networks: micro-optical properties of normal and neoplastic stroma

Development of epithelial precancer and cancer leads to well-documented molecular and structural changes in the epithelium. Recently, it has been recognized that stromal biology is also altered significantly with preinvasive disease. We used the finite-difference time-domain method, a popular technique in computational electromagnetics, to model light scattering from heterogeneous collagen fiber networks and to analyze how neoplastic changes alter stromal scattering properties. Three-dimensional optical images from the stroma of fresh normal and neoplastic oral-cavity biopsies were acquired using fluorescence confocal microscopy. These optical sections were then processed to create realistic three-dimensional collagen networks as model input. Image analysis revealed that the volume fraction of collagen fibers in the stroma decreases with precancer and cancer progression, and fibers tend to be shorter and more disconnected in neoplastic stroma. The finite-difference time-domain modeling results showed that neoplastic fiber networks have smaller scattering cross sections compared to normal networks. Computed scattering-phase functions indicate that high-angle scattering probabilities tend to be higher for neoplastic networks. These results provide valuable insight into the micro-optical properties of normal and neoplastic stroma. Characterization of optical signals obtained from epithelial tissues can aid in development of optical spectroscopic and imaging techniques for noninvasive monitoring of early neoplastic changes.     

Elastic anisotropy of articular cartilage is associated with the microstructures of collagen fibers and chondrocytes

Chondrocyte shape and volumetric concentration change as a function of depth in articular cartilage. A given chondrocyte shape produces different effects on the global material properties depending on the structure of the collagen fiber network. The shape and volumetric concentration of chondrocytes in articular cartilage appear to be related to the mechanical stability of the matrix. The present study was aimed to investigate, theoretically, the effects of the structural arrangement of the collagen fiber network, and the shape and distribution of chondrocytes, on the global material behavior of articular cartilage. Articular cartilage was assumed to be a four-phasic composite comprised of a matrix (associated with the properties of the proteoglycan structure), vertically and horizontally distributed collagen fibers, and spheroidal inclusions representing chondrocytes. A solution for composite materials was used to estimate the global, effective material properties of cartilage. Only the elasticity of the solid phase was investigated in the present study. Our simulations suggest that a soft, spheroidal cell inclusion in a fiber-reinforced proteoglycan matrix affects the material properties differently depending on the shape of the spheroidal inclusions. If the long axis of the inclusions is parallel to the collagen fibers, as in the deep zone, the soft inclusions increase the stiffness of the composite in the fiber direction, and reduce the stiffness of the composite in the direction normal to the fibers. Furthermore, we found that Young's modulus normal to the contact surface increases from the superficial to the deep zone in articular cartilage by a factor of 10-50, a finding that agrees well with experimental observations. Our analysis suggests that the combination of proteoglycan matrix, fiber orientation, and shape of chondrocytes are intimately related and are likely adapted to optimize the mechanical stability and load carrying capacity of the structure.     

Mechanical interactions between collagen and proteoglycans: implications for the stability of lung tissue.

Collagen and elastin are thought to dominate the elasticity of the connective tissue including lung parenchyma. The glycosaminoglycans on the proteoglycans may also play a role because osmolarity of interstitial fluid can alter the repulsive forces on the negatively charged glycosaminoglycans, allowing them to collapse or inflate, which can affect the stretching and folding pattern of the fibers. Hence, we hypothesized that the elasticity of lung tissue arises primarily from 1) the topology of the collagen-elastin network and 2) the mechanical interaction between proteoglycans and fibers. We measured the quasi-static, uniaxial stress-strain curves of lung tissue sheets in hypotonic, normal, and hypertonic solutions. We found that the stress-strain curve was sensitive to osmolarity, but this sensitivity decreased after proteoglycan digestion. Images of immunofluorescently labeled collagen networks showed that the fibers follow the alveolar walls that form a hexagonal-like structure. Despite the large heterogeneity, the aspect ratio of the hexagons at 30% uniaxial strain increased linearly with osmolarity. We developed a two-dimensional hexagonal network model of the alveolar structure incorporating the mechanical properties of the collagen-elastin fibers and their interaction with proteoglycans. The model accounted for the stress-strain curves observed under all experimental conditions. The model also predicted how aspect ratio changed with osmolarity and strain, which allowed us to estimate the Young's modulus of a single alveolar wall and a collagen fiber. We therefore identify a novel and important role for the proteoglycans: they stabilize the collagen-elastin network of connective tissues and contribute to lung elasticity and alveolar stability at low to medium lung volumes.