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Fibrillar collagens in connective tissues are organized into complex and diverse hierarchical networks. In dermis, bone and tendon, one common phenomenon at the micrometer scale is the organization of fibrils into bundles. Previously we have reported that collagen fibrils in these tissues exhibit a 10 nm width distribution of D-spacing values. This study expands the observation to a higher hierarchical level by examining fibril D-spacing distribution in relation to the bundle organization. We used Atomic Force Microscopy (AFM) imaging and two dimensional Fast Fourier Transform (2D FFT) analysis to investigate dermis, tendon and bone tissues. We found that in each tissue type, collagen fibril D-spacings within a single bundle were nearly identical, and frequently differing by less than 1 nm. The full 10 nm range in D-spacing values arises from different values found in different bundles. The similarity in D-spacing was observed to persist for up to 40 µm in bundle length and width. A nested mixed model analysis of variance examining 107 bundles and 1710 fibrils from dermis, tendon and bone indicated that fibril D-spacing differences arise primarily at the bundle level (~76%), independent of species or tissue types.
Non-cartilaginous connective tissues, including dermis, tendon and bone, are predominantly composed of type I fibrillar collagen in the organic phase of their extracellular matrix (ECM). As the main ECM building block, collagen fibrils play pivotal roles in maintaining tissue integrity, providing the basis for mechanical properties, and influencing cell activities. Collagen fibrils have an exceptionally long half-life in vivo, which is estimated to be 15–95 years. 1, 2They are resistant to common proteases since the tightly packed fibrillar structure prevents access to cleavage sites.3 Collagen fibrils are mechanically tough; 4 as a structural network, they enhance cell attachment, migration and differentiation.5, 6
The properties of ECM derive in part from the hierarchical structure of collagen molecules, fibrils, fibril bundles, and higher levels of organization (Figure 1). The fibril-forming collagen molecules (type I, III, V, XI, etc.) share similar structural motifs. Each of the three α-helices contains Gly-X-Y repeating triplets with proline and hydroxyproline being the most common X and Y residues.7 The molecular packing of collagen fibril was studied by X-ray in the 1960s to 1980s.8–15 The fibrils are composed of five-stranded microfibrils that are quasi-hexagonally packed in the equatorial plane8, 9, 12–14, 16 and supertwisted in the axial direction3. Within a fibril, as the Hodge-Petruska model depicts, collagen molecules are aligned in a parallel staggered manner resulting in a repeating Gap/Overlap pattern, resulting in the observed D-spacing. 3, 17
The next level of collagen hierarchy in ECM is the organization of fibrils into bundles, which occurs at micrometer to millimeter scale (Figure 1). Qualitatively, a bundle is a group of parallel fibrils that are generally associated with each other via interfibrillar cross-links.18 In dermis and tendon, a bundle is frequently referred to as a fiber; while in bone it is a lamella sheet of parallel collagen fibrils. The micrometer-scale organization of fibril bundles varies dramatically among tissues. As shown in Figure 1, in the dermis, bundles of collagen fibrils with a lateral size ranging from tens of microns to a few hundred microns are randomly oriented in a three dimensional meshwork.19, 20 Tendon has an overall uniaxial structure where collagen fibrils are aligned in parallel arrays 21, 22 Bone adapts a twisted plywood structure constructed by lamellae of collagen fibrils with alternating fibril angles among different lamella sheets.23–25 Despite the significantly different ECM organizations described above, the grouping of collagen fibrils into micrometer-scale bundles is ubiquitous among collagenous tissues.26–28
Characterization of fibril bundles in connective tissues has been limited to qualitative descriptions. For example, scanning electron microscopy (SEM), transmission electron microscopy (TEM) and circularly polarized light microscopy imaging have been used for visualization of dermal fibril bundles and bone lamellae.19, 24, 29, 30 We have recently developed a quantitative method for D-spacing analysis at the micrometer to sub-micrometer scale, using Atomic Force Microscopy (AFM) imaging and two-dimensional Fast Fourier Transform (2D FFT) analysis.31, 32 Using this method, we have shown that a distribution of nanometer-scale D-spacings is present in a variety of type I collagen based connective tissues, including bone, tooth, tendon and dermis, from a number of species, including murine, ovine, and human.31, 33, 34 An example of D-spacing distribution is shown in Figure 2. The chemical and physical significance of the distribution of D-periodic axial spacing or ”D-spacing” values, first characterized by electron microscopy in 1942,35 has been largely overlooked for seven decades. Only a few publications have quantitatively described collagen D-spacing as a distribution of values to date.35–38 The majority of publications have adopted the view, largely derived from X-ray scattering data,39–41 that D-spacing is a single value of about 67 nm and values deviating from this have generally been attributed to tissue dependent differences,39, 42 and/or artifacts of sample preparation methods such as dehydration.36, 40, 43 However, we found that the D-spacing distributions were altered as a function of disease including estrogen deprivation induced osteopenia and Osteogenesis Imperfecta, suggesting the biological significance of the D-spacing distribution.33, 34, 44
In this study, the connection between the nanometer-scale collagen fibril D-spacing distribution and the micrometer-scale fibril bundle organization is explored. By comparing fibril D-spacings within a bundle and across different bundles, we wanted to test the two following hypotheses:
We then discuss potential models of collagen fibril structure that describe the origin of the D-spacing morphology as well as the implications for currently proposed mechanisms of fibrillogenesis.
Collagen fibril bundles in healthy adult ovine bone and dermis, human dermis and lamb tendon were imaged and analyzed. Typically a fibril bundle was captured in one 3.5 µm × 3.5 µm AFM scan. In the case of ovine dermis and lamb tendon bundles, we collected images from multiple regions on a bundle (Figure 5 and and6).6). For all the bundle data included in this study, the angular orientations of fibrils within a bundle varied by 10° or less in the XY plane; most fibrils in tendon bundles varied by 3° or less; most fibrils in dermis or bone bundles varied by 5° or less. The small differences of fibril angular orientation represent the laterally ordered organization in a fibril bundle, which serves as a primary criterion for selecting the bundles for quantitative analyses.
Occasionally two or more bundles were captured in one frame. Examples of these bundle interfaces are shown in Figure 3. Interestingly, even though the fibrils are spatially close to each other and captured by the same AFM tip in the same image, fibrils from different bundles exhibit distinctively different D-spacings; fibrils measured from the same bundle share similar D-spacing. Figures 3a and 3b illustrate a typical example of two lamella layers in ovine bone: in this instance the underlying bundle has a mean D-spacing of 64.3 ± 1.3 nm, while the top bundle’s D-spacing mean is 66.9 ± 0.8 nm. Another example of ovine bone is shown in Figure 3c and 3d, where the two bundles have D-spacing means of 63.2 ± 0.6 nm and 59.4 ± 0.6 nm. In addition to aligned fibril bundles, we observed additional interesting structures in bone. Examples of broom-like and interwoven fibril organizations are shown in Supporting Figure S1. Figure 3e shows a set of fibril bundles from human dermis, two of which were captured in Figure 3f, with D-spacings of 60.3 ± 1.3 nm and 62.8 ± 0.6 nm. Similarly, Figure 3g and 3h are from human dermis, and figure 3h is a zoomed-in region of figure 3g that captured three fibril bundles in one scan. The D-spacings are 58.9 ±0.9 nm, 63.4 ±0.6 nm, and 61.1 ± 0.2 nm. Average D-spacing and angular orientations of individual bundles are summarized in Table 1. In every case, differences among the bundles were statistically significant (p < 0.001).
To illustrate how bundle D-spacings contribute to tissue scale D-spacing distributions, we color coded the distribution histogram to show the contribution from different bundles (Figure 4). Taking ovine bone as an example, when plotted in a single histogram (Figure 4a and 4b), fibril bundle D-spacings range from 58 nm to 69 nm; however, within each fibril bundle, D-spacing generally spans 1~3 nm. Meanwhile, fibrils from different bundles exhibited independently variant D-spacings that contribute to the full ~10 nm distribution range in these tissues. The narrow intra-bundle D-spacing distribution along with a wide tissue distribution was found for both ovine and human tissues and for both mineralized (bone) and non-mineralized (dermis, tendon) tissue types (Figure 4).
When comparing fibril D-spacings from ovine and human dermis, the overall D-spacing averages of 63.0 nm and 62.5 nm, respectively, are not significant different (p = 0.24). Upon employing a nested analysis of variance (mixed model ANOVA) to evaluate the contributions of the fibril, bundle and animal variance to the range of D-spacing values, we found that bundle-to-bundle variance was the largest component, accounting for 78% of overall variance. The standard deviation (STD, symbol σ) between bundles is 1.3 nm and the overall STD is 1.5 nm. The bundle STD is significantly different from 0 (p < 0.0001). In addition, bundle and fibril level variance are not different between ovine and human by likelihood ratio chi-square test (p>0.999 and p = 0.86, respectively). The data set exhibited a skewness on the low end of the distribution contributed by bundles with D-spacings as low as 58 nm. As a result, 4.8 % of fibrils were found below μ0 + τ − 2σ and none above μ0 + τ + 2σ.
The fibril D-spacings averages from ovine dermis, bone and tendon, 62.9 nm, 63.8 nm and 64.0 nm, respectively, are not significantly different from each other (p = 0.12). Similar to human/ovine dermis comparison, the nested analysis indicates the bundle level variance component differed from 0 (p<0.0001), and it accounts for 76% of overall variance. The bundle level and overall STD are 1.6 and 1.8 nm, respectively. Interestingly, bundle variance differs substantially among the three tissues. For dermis, bone and tendon, the estimated are 1.8, 3.8 and 1.4, respectively (p = 0.074 by likelihood ratio chi-square test). Similarly, the fibril variance is also largest in bone and smallest in tendon. The estimated are 0.4, 0.5, 0.2 for dermis, bone and tendon, respectively (p <0.0001). A summary of the statistical analysis is provided in Table 2. Additional detail of the nested analysis of variance mixed model ANOVA can be found in supporting information (Table S1).
Next, we investigated the persistence length of bundle D-spacings in lamb tendon fascicles and ovine dermis. Figure 5a shows two fascicles (A and B) of lamb tendon on the 50 µm-scale. D-spacings were obtained from six 3.5µm × 3.5 µm regions spaced over 20 µm for fascicle A and 40 µm for fascicle B. Fascicles A and B have statistically different D-spacings (p < 0.001) of 64.0 ± 0.9 nm, and 66.2 ± 0.9 nm, respectively. D-spacings have a 3.3 nm range in fascicle A and 2.9 nm in fascicle B. Within each fascicle, variations from region to region over a 50 µm-scale are larger than variations within a 3.5µm region. For example, region 1A has a mean D-spacing of 64.9 ± 0.3 nm whereas region 6A has a mean D-spacing of 62.8 ± 0.3 nm. In another example, regions spaced over 40 µm length of a tendon fascicle give a 4.4 nm range of D-spacing values, with an overall mean of 64.1 ± 0.9 nm (Supporting information, Figure S2). Nevertheless, the region-to-region variation is small compared to the full D-spacing width distribution. Nested model ANOVA estimates that region-to-region variance in lamb tendon is 0.4, which is significantly lower than that of bundle-to-bundle variance, (p = 0.0013 by likelihood ratio chi-square test). We also imaged perpendicular to the axial direction of one or more fascicles (Supporting information, Figure S3). In this case, the range of D-spacings is 4 nm, and the region-to-region variance is 0.3. Finally, Figure 6 shows a fibril bundle of ovine dermis on the 50 µm scale. Six 3.5 µm × 3.5 µm regions spaced over 30 µm give a set of D-spacings for each region ranging from 61.8 ± 0.6 nm to 62.9 ± 0.4 nm with an overall average of 62.4 ± 0.7 nm. Nested model ANOVA estimates region-to-region variance for ovine dermis is 0.1, significantly lower than bundle-to-bundle variance, (p = 0.0102 by likelihood ratio chi-square test).
We have observed that collagen fibrils in a single bundle share similar D-spacings (±1 nm), and the full ~10 nm D-spacing distribution found in tissues31, 33, 34, 44 results from differences in bundle-level D-spacing. This observation is supported by nested mixed model ANOVA analysis. When we evaluate the effect of tissue types, species, animals, bundles nested within animals, and fibrils nested within bundles and animals, the largest component of variance comes from the bundle-to-bundle variance. It accounts for over 76% of total variance, independent of tissue types (bone, dermis and tendon) and species (ovine vs. human). Based on these results, we propose a quantitative definition of a collagen bundle as a bundle of collagen fibrils characterized by identical D-spacing (with ±1 nm STD), and we will refer to fibril bundles with this property as D-bundles. Estimated from 107 D-bundles, STD within a D-bundle is 0.6 nm (see Table 2), which is within the error associated with AFM analysis;31, 32 therefore the fibrils in each bundle have similar, if not identical, D-spacings. The bundle-to-bundle variations, as small as 1.3 nm STD in tendon and as large as 1.9 nm STD in bone, are the major component that give rise to the full distribution of 8–10 nm width and 1.5–2 nm STD, typically seen for tissue samples (an example is shown in Figure 2). These observations are consistent with hypothesis H2 and inconsistent with H1.
The bundle size, typically on the order of tens of microns, varies among tissues. As observed by AFM, the fibril bundle width in lamb tendon is 20 microns and larger; ovine and human dermis tend to have bundle width of a few microns in papillary dermis, and 50 microns or larger in reticular dermis (similar observations in refs. 38, 45); fibril bundles in ovine cortical bone, in contrast to all the other tissues used in this study, are less frequently observed and are usually of 1–5 µm in lateral size.
The question of persistence length of D-bundles is particularly interesting in tissues such as tendon, where fascicles can extend to millimeters in length. We evaluated the persistence length of D-bundles by taking D-spacing measurements across 40–50 µm axial and perpendicular directions of tendon fascicles. As shown in Figure 5 and Supporting Figure S2–3, D-spacings from regions of a tendon fascicle vary in a range of 4–5 nm. This range is in between that of a D-bundle (1–3 nm range; 0.6 nm STD) and that of a tissue-scale D-spacing distribution (10 nm range; 1.5–2 nm STD). Based on nested ANOVA analysis, the region-to-region variance in the axial direction in lamb tendon is 0.4 (σ = 0.6 nm) and that of perpendicular direction is 0.3 (σ = 0.6 nm), which is significantly smaller than variance of different tendon bundles, 1.3 (σ = 1.2 nm). It suggests regions within a tendon fascicle vary to a lesser extent than do different D-bundles in tissue consisting of multiple fascicles, and thus are more likely to be related with each over. In ovine dermis, the data in Figure 6 indicate that D-bundles can maintain a persistent D-spacing up to 30 µm in the axial direction, which is in agreement with the nested ANOVA analysis since the estimated region-to-region variance is 0.1(σ = 0.4 nm).
Knowing the physical and/or biochemical origins of tissue scale D-spacing distribution and narrow D-bundle D-spacing range is imperative to our understanding of fibrillogenesis. Although this question remains to be answered, this section is devoted to discussing potential factors that could influence fibril D-spacing. First and foremost, it should be mentioned that biomineralization is not a determinant for the tissue scale distribution of D-spacings, since the 10 nm range of D-spacing and narrow D-spacing range in D-bundles are observed in both mineralized bone and non-mineralized dermis and tendon tissues.31, 34
Mutations in the collagen composition can change the D-spacing. Based on a previous AFM study using an Osteogenesis Imperfecta (OI) mice model and molecular dynamics (MD) simulation, single substitution of glycine to cystein in collagen amino acid composition destabilizes the collagen triple helical structure,46 and D-spacing distribution in the OI model showed significant shift from the control model.44
Some studies have shown D-spacing elongation as a function of strain47–49. However, elongation of D-spacing accounts only a small fraction of tissue level strain in the elastic deformation regime. Sasaki47, Puxkandl48, and Gupta et al49. have all shown in their studies that fibril strain tends to be on the order of 1–2 nm in tendon and bone. In our study, no external stress was applied to the tissues and we observed ~ 10 nm range difference in bundles D-spacings. Therefore it is very unlikely that strain alone is causing the bundle D-spacing differences.
Another hypothesis is that covalent cross-linking is responsible for D-bundle formation. It is possible that hydroxylysine sites are matched between adjacent fibrils during enzymatic cross-linking process, resulting in overlapping gap zones and overlap zones. 50 In addition to enzymatic cross-linking, nonenzymatic glycation (NEG) such as cross-linking between collagen and sugar occurs with ageing and diabetes.51 However we have found no effect of NEG on collagen fibril D-spacings using ovine bones treated with D-ribose in vitro (supplementary figure 4). Similar results have been reported by Odetti and others.37
Other factors known to interact with collagen during formation and maturation include type V and XI collagen 52, 53; SLRPs such as decorin and lumican50, 54, 55; and fibronectin56–58. Knockout studies on collagen V or decorin have shown irregular fibril formation and in some cases early embryonic death55, 59–61, suggesting indispensible roles that the minor collagen types and SLRPs play in regulating collagen fibril formation. However, little is known about whether these small proteins play a role in changing collagen fibril D-spacing.
In summary, the simplest form of the Hodge-Petruska model shown in Figure 1 does not address the variations of D-spacings reported here. In particular, this data indicates the need for collagen fibril growth and structural models to account for the collagen fibril D-spacings being organized at the hierarchical level of fibril bundles. As we understand more about the structural complexity of collagen and its dynamic interactions with other ECM components, it becomes increasingly important that we adopt a more sophisticated model of collagen fibril structure that also reflects D-spacing distribution. This model will allow us to better understand normal collagen hierarchy and changes in collagen structure induced by ageing, diseases and mechanical failures.
The mechanism of D-bundle formation is still an open question, competing theories offer different views on the nucleation and growth of collagen fibrils.
EM studies by Birk’s and Kadler’s groups suggest a nucleation, growth and coalescence model for the formation of collagen fibrils and fibril bundles (NGC model, Figure 7). In chick embryonic tendon, single or small groups of fibrils were found in membrane protrusions or depressions near fibroblast cell surfaces, which are called fibripositors.62–64 Based on this observation, it is hypothesized that single collagen fibrils nucleate in these fibripositors and grow in the axial direction. Side-to-side fusion 26, 30, 65,62 as well as tip-to-tip fusion55, 66 of fibrils has been observed, which could explain the D-bundle formation. Our quantitative data on fibril D-spacing and their relationship to bundle structure place two interesting constraints on the NGC model. First, if D-spacing is determined by extracellular factors such as binding with proteoglycans and/or mechanical stress, then it is plausible that a bundle could share similar D-spacing if these factors exert uniform effect within a bundle. An alternative hypothesis is that D-spacing is determined at the fibripositor stage, which implies bundle-dependent D-spacing is also cell-dependent. Although there is clear evidence indicating that intracellular information such as genetic coding can play a vital role in fibril D-spacing formation,44 further experiments are required to clarify the relationship between collagen fibril D-spacing and the cells that produce collagen.
Driven by the observation of liquid crystalline properties in type I collagen67–69 in vitro, Giraud-Guille and others have proposed that collagen precursors (procollagen or tropocollagen) are pre-aligned in concentrated local environments, which aids in the alignment, undulations and twists in the packing of collagen fibrils (LC model, Figure 7).70 It is also interesting to note that the plywood structure of human compact bone osteons is analogous to the organization of cholesteric liquid crystals, as the direction of fibrils rotates by a constant angle from one lamallar layer to the next.24, 29, 68 This model provides a simple physical explanation for the collagen structural organization in collective tissues, and offers the intriguing possibility that D-bundle spacing is synchronized by liquid crystalline alignment. Although aspects of this model are compelling, the liquid crystallinity of collagen has not been demonstrated directly in vivo.
In conclusion, we observed a narrow distribution of D-spacings within D-bundles (±1 nm). In addition, large variations in D-spacings among different bundles contribute to the full distribution (10 nm range) at the tissue scale in bone, dermis, and tendon. The measurements and statistical analysis support the hypothesis that differences at the bundle level cause the full range of D-spacing values, whereas D-spacings within a bundle are similar (H2) and are inconsistent with fibril D-spacing being random with respect to the higher level bundle structure (H1). The formation of D-bundles has important implications in terms of how collagen fibrils are assembled; however, the mechanisms of D-bundle formation and D-spacing variations are poorly understood. Mechanistic pathways for both the NGC and LC models can be proposed that are consistent with the data presented here for the relationship between fibril D-spacing and bundle structure. Future research efforts are needed to answer many questions raised by these studies including: how are cells and/or extracellular proteins involved in forming collagen fibril bundles? What contributes to a heterogeneous D-spacing distribution? Is the tight distribution of D-spacings within a D-bundle disrupted by disease? Do D-bundles with different D-spacings play varying roles under mechanical stresses? We are pursuing a number of these challenging questions and we hope that these new quantitative observations regarding type I collagen structure can be employed by the broader scientific community to promote a better understanding of collagen fibrillogenesis and ultimately how collagenous tissues are established and maintained.
Ovine bone and dermis specimens were collected from sham-operated Columbia-Rambouillet ovine, as previously described.33 Bone specimens were acquired from the mid-diaphysis of the left radius, while dermis specimens were harvested from the dorsal midline, in the thoracolumbar region. Procurement of human skin samples was approved the University of Michigan Institutional Review Board, and conducted according to the Declaration of Helsinki principles. All subjects provided written informed consent. Full-thickness human skin biopsies were taken from sun-protected buttock skin from human donors ranging in age from 20 to 40 years old. Lamb tendons were from 6-month-old rambouillet-dorset ovine, provided by a local butcher. Ovine bone data were collected from 15 animals; ovine dermis data were collected from 4 animals, human dermis data were collected 6 donors; lamb tendon data were collected from 4 animals. We analyzed 32 bundles in ovine bone, 26 in ovine dermis, 32 in human dermis and 17 in lamb tendon for a total of 107 bundles and 1710 fibrils.
Combined tissue sectioning and AFM analysis was highlighted in Graham’s recent report.71 First, skin biopsies were embedded in Tissue-Tek optimal cutting temperature (OCT) solution (Sakura Finetek Inc., Torrance, CA, USA) and frozen at −20 °C. 10 µm thick thin-sections of dermis were obtained using Microm HM550 Cryostat (Thermo Scientific Inc., Walldorf, Germany) and transferred onto glass slides. Due to the random meshwork nature of dermis collagen bundles, sections parallel to the skin surface and perpendicular to the skin surface (cross-section) are both suited for AFM imaging. The dermal sections were rinsed with ultrapure water for 5 minutes and kept at −20 °C prior to the AFM study. Tendon specimens were sectioned in a similar manner and the cutting plane was set to be parallel with the long axis of tendon. No artificial stretching was imposed on tissue samples during sample preparation.
Ovine bones were mounted to a steel disk using cyanoacrylate glue, and a flat surface was polished as described previously.33 The bones were demineralized using 0.5 M EDTA at a PH of 8.0 for 1 hour with 5 min sonication at every 20 min interval. The bones were then vigorously rinsed with ultrapure water and preserved at 4 oC before AFM study.
All imaging was carried out in air dry condition using a PicoPlus 5500 AFM (Agilent); dermis and tendon specimens were imaged in contact mode using SNL-10 AFM probes (Bruker AFM probes, nominal tip radius 2 nm, force constant 0.25 N/m). Ovine bones were imaged using tapping mode with VistaProves T300R probes (NanoScience, AZ; nominal radius 10 nm, force constant 40 N/m, resonance frequency 300 kHz). Line scan rates were set at 2 Hz or lower at 512 lines per frame. Random locations on tissue samples were imaged by AFM in search of fibril bundles. Image analysis and measurements were performed using SPIP software (V5.0.8, Image Metrology; Horsholm, Denmark). Collagen fibril D-spacings were measured using 2D fast Fourier Transform (FFT) toolkit of SPIP software, detailed description and validation can be found in previous studies.31, 33
One concern associated with AFM imaging is the effect of thermal drift and tip convolution which may differ from scan to scan. We have carefully examined the effect of thermal drifting and ruled out the possibility of thermal drifting causing an artificial D-spacing distribution.32 Furthermore, finding two or more fibril bundles with different D-spacings in single AFM scans (figure 3) rules out the concern that the differences in D-spacings may be caused by using different AFM tips or scanning on different days. All fibril bundle D-spacings were measured within individual 50 µm × 50 µm area. The limited AFM scan size may underestimate lateral bundle size and persistence length. In addition, due to the cylindrical geometry of bone lamellae, polishing and imaging on a flat surface may cause underestimation in the bundle size and length of fibril bundles in bone tissues.
Mean D-spacings (± standard deviation) from individual bundles were tested using one way ANOVA.
A nested analysis of variance was employed (mixed model ANOVA72) to determine the hierarchical level of the sources of variance in the overall D-spacing distribution (Eq. a–e). Arranged by their hierarchical order, fibrils were nested within bundles, and bundles were nested within animals.
μ0 - D-spacing mean; τ- fixed effect (described in the analyses below); ai - random effect of ith animal; bij – random effect of jth bundle nested within ith animal; εijk – random effect of kth fibril nested in jth bundle and in ith animal.
Two sets of mixed model ANOVA analyses were performed based on the model above:
We thank Electron Microscopy & Image Analysis Laboratory at U of M for the technical assistance on cryostat sectioning. The procurement of human skin samples was supported by NIH grant AG025186.
Supporting Information Available: Supporting Figure S1: Diverse fibril organization in bone; S2 and S3: longitudinal and lateral persistence length of D-spacings in lamb tendon bundles; S4: experimental data of in vitro Non-enzymatic Glycation treatment. Supporting Equations S.Eq a–f: The nested ANOVA model for bundle persistence length assessment. Table S1: Summary of nested ANOVA. This material is available free of charge via the Internet at http://pubs.acs.org.