Elastic moduli of collagen gels can be predicted from two-dimensional confocal microscopy

Abstract

We quantitatively compare data obtained from imaging two-dimensional slices of three-dimensional unlabeled and fluorescently labeled collagen gels with confocal reflectance microscopy (CRM) and/or confocal fluorescence microscopy (CFM). Different network structures are obtained by assembling the gels over a range of concentrations at various temperatures. Comparison between CRM and CFM shows that the techniques are not equally sensitive to details of network structure, with CFM displaying higher fidelity in imaging fibers parallel to the optical axis. Comparison of CRM of plain and labeled collagen gels shows that labeling itself induces changes in gel structure, chiefly through inhibition of fibril bundling. Despite these differences, image analyses carried out on two-dimensional CFM and CRM slices of collagen gels reveal identical trends in structural parameters as a function of collagen concentration and gelation temperature. Fibril diameter approximated from either CRM or CFM is in good accord with that determined via electron microscopy. Two-dimensional CRM images are used to show that semiflexible polymer theory can relate network structural properties to elastic modulus successfully. For networks containing bundled fibrils, it is shown that average structural diameter, rather than fibril diameter, is the length scale that sets the magnitude of the gel elastic modulus.

Figure 1

CRM images of unlabeled collagen (first column), fibrils identified from CRM images in the first column by the fiber-finding algorithm (second column), and CRM/CFM (third/fourth column) images of FITC-labeled collagen formed at 37°C. Collagen concentration is 0.5 mg/mL (first row), 2.0 mg/mL (second row), and 5.0 mg/mL (third row). In the second column, found fibers are either 1 pixel (in red, online) or 2 pixels (in blue and pink, online) in width. Scale bar = 50 μm.

Figure 2

Fibril and network structure as shown by image analysis for gels formed at 37°C. (a) Characteristic mesh size ξ_cha (solid symbols) and average mesh size ξ_av (open symbol; only shown for unlabeled collagen), (b) fibril number, (c) distribution of fibril diameter measured from SEM images, d_fibril,SEM, at 0.5 mg/mL (bars with horizontal lines) and 5.0 mg/mL (hatched bars), and (d) d_fibril,SEM (★) and fibril diameter, d_fibril (= d_structure). In all panels, parameters quantified from CRM images of unlabeled collagen are represented by circles, those from CRM images of FITC-labeled collagen are triangles, and those from CFM images of FITC-labeled collagen are squares.

Figure 3

CRM images of plain collagen (first column), fibers identified from CRM images in the first column by the fiber-finding algorithm (second column), and CRM/CFM (third column/fourth column) images of FITC-labeled collagen of 2 mg/mL. Collagen gels formed at 22°C (first row), 27°C (second row), and 32°C (third row). In the second column, found fibers are either 1 pixel (in red, online), 2 pixels (in blue, online), or 4, 6, or 8 pixels (in pink, online) in width. Scale bar = 50 μm.

Figure 4

Fiber and network structure as revealed by image analysis as a function of gelation temperature for 2 mg/mL collagen gels. (a) Characteristic mesh size ξ_cha (solid symbols) and average mesh size ξ_av (open symbols; only presented for unlabeled collagen). (b) Number of identified structures. In a and b, parameters quantified from CRM images of unlabeled collagen are represented by circles, those from CRM images of FITC-labeled collagen are triangles, and those from CFM images of FITC-labeled collagen are squares. (c) Distribution of fibril diameter measured from SEM images of 2 mg/mL collagen gelled at 22°C (bars with horizontal lines) and 37°C (hatched bars). (d) Fibril diameter measured from SEM, d_fibril,SEM, (★) as well as various measures of structural diameter from CRM images of unlabeled collagen: fibril diameter (d_fibril) (●), structural diameter (d_structure) (▵), and fiber diameter (d_fiber,mixed, ○; d_fiber,calc, ☆).

Figure 5

(a) Storage moduli, G′, of unlabeled collagen as a function of concentration for gels formed at 37°C (●) and 22°C (▴). G′ scales with collagen concentration as G′ ∼ c^2.1 at 37°C (solid curve) and as G′ ∼ c^2.8 at 22°C (dotted curve). (b) Storage modulus of 2 mg/mL collagen as a function of gelation temperature. (c–f) Scaling relationship between storage modulus and characteristic mesh size and structural diameter. Comparison to the (c and e) MacKintosh and (d and f) Morse models. Fits use ξ_av together with d_fibril,SEM (squares, diamonds, triangles, and stars, all within circles) and (c and d) d_structure (■♦▴), or (e,f) d_fiber,mixed (■♦▴). Data are obtained from 0.5, 1.0, 2.0, 4.0, and 5.0 mg/mL collagen gelled at 37°C (star within a circle) and 22°C (solid squares, and open squares within circles), and 2.0 mg/mL collagen gelled at 32°C (solid triangle, and open triangle within a circle) and 27°C (solid diamond, and open diamond within a circle). Fits for data points using (c) d_structure and (e) d_fiber,mixed for comparison with the MacKintosh (m = 0.79, R² = 0.89 and m = 0.87, R² = 0.91, respectively) model are shown as solid lines.