Structure–mechanics relationships of collagen fibrils in the osteogenesis imperfecta mouse model

The collagen molecule, which is the building block of collagen fibrils, is a triple helix of two α1(I) chains and one α2(I) chain. However, in the severe mouse model of osteogenesis imperfecta (OIM), deletion of the COL1A2 gene results in the substitution of the α2(I) chain by one α1(I) chain. As this substitution severely impairs the structure and mechanics of collagen-rich tissues at the tissue and organ level, the main aim of this study was to investigate how the structure and mechanics are altered in OIM collagen fibrils. Comparing results from atomic force microscopy imaging and cantilever-based nanoindentation on collagen fibrils from OIM and wild-type (WT) animals, we found a 33% lower indentation modulus in OIM when air-dried (bound water present) and an almost fivefold higher indentation modulus in OIM collagen fibrils when fully hydrated (bound and unbound water present) in phosphate-buffered saline solution (PBS) compared with WT collagen fibrils. These mechanical changes were accompanied by an impaired swelling upon hydration within PBS. Our experimental and atomistic simulation results show how the structure and mechanics are altered at the individual collagen fibril level as a result of collagen gene mutation in OIM. We envisage that the combination of experimental and modelling approaches could allow mechanical phenotyping at the collagen fibril level of virtually any alteration of collagen structure or chemistry.


S1 Acquisition of force-displacement curves
Data acquisition in this study is based in a recently developed standardized methodology (Andriotis, Manuyakorn et al. 2014).
Briefly, an AFM image of about 10 μm x 10 μm is recorded to discriminate individual collagen fibrils lying on the stiff substrate from fibril bundles. Subsequently a number of collagen fibrils are then individually tested after performing another AFM image which includes one collagen fibril. Depending on the size of the collagen fibril the image scale ranges from 1 μm x 1 μm to 3 μm x 3 μm. AFM cantilever-based nanoindentation is then performed by Force Volume (FV) map. The FV map resolution ranges from 30 lines x 30 points to 50 lines x 50 points. the choice of the FV map resolution depends on that force-displacement curves must be recorded on the fibril crest, which is necessary to eliminate inaccuracy arising from invalid contact between the AFM tip and the collagen fibril due to the cylindrical fibril geometry (Andriotis, Manuyakorn et al. 2014). To allow user friendly data collection the AFM fast scan direction was aligned to the fibril longitudinal axis.
In air dried samples about 50 indents per collagen fibril across 2μm of each length were performed. In total, 12 and 16 collagen fibrils were tested from OIM and WT tail tendons, respectively. The mean elastic modulus per condition was determined from the mean elastic modulus per collagen fibril.
All nanoindentation experiments were carried out under load control with maximum applied load of 150 nN for the air dried samples, 2 nN for the hydrated samples in PBS and PBS/EtOH solutions and 14 nN for the samples tested in 100% EtOH (table S1).

S2 Determination of the projected area of contact
The acquisition of projected area function of contact between the indenter and the sample is required for the calculation of indentation modulus data when performing the Oliver-Pharr analysis method (Oliver and Pharr 2004).
For the NSC15 and AC200 cantilever the projected area of contact was acquired similarly to a recently proposed method (Andriotis, Manuyakorn et al. 2014). Briefly, we initially imaged a silicon spike from the calibration grating TGT1 (NT-MDT). The resulting image is an envelope image of the reference TGT1 spike and the AFM tip. Subsequently, we generate an image of the AFM tip by applying a reconstruction algorithm, programmed in Matlab 7.10.0 (R2010a), as proposed by Keller et al. (Keller and Franke 1993). We assumed the spikes to be cones with an opening angle of 50 degrees and a tip radius of 5 nm (as provided by the manufacturer). The contact area is expressed with the second order polynomial: where, Ac is the projected area (μm 2 ) at a given height h, α and b are the fitting parameters. Figure S1 shows the a three dimensional perspective of the reconstructed AFM tip and the corresponding projected area function.

Figure S1
Typical reconstructed projected area of contact of an AFM tip. Inset shows a three dimensional perspective of the reconstructed AFM tip apex.
For the AFM cantilevers used to test the hydrated samples, i.e. the PNP-TR and PNP-DB, it was not possible to apply the aforementioned approach due to the small tip height and aspect ratio. We therefore used a geometrical approach.
The projected area of contact was estimated by assuming a pyramidal geometry (SEM images) with a round tip of radius R and half opening angle α. A graphical representation of the side view of a rounded pyramidal tip is illustrated in Figure S2. The projected area of contact, Ac, is given by: where h is the indentation depth in nanometers, ξ is the correction distance in nanometers that accounts for the rounded tip apex and α is the half opening angle of the AFM tip. The correction factor ξ is a function of the AFM tip radius, R, and the half opening angle, α: For R=10 nm and α=35 degrees we have ξ=51.34 nm.
As illustrated in Figure S2, for indentation depths where R is the radius of the sphere as illustrated in Figure S2. Assuming a 10 nm tip radius and 35 deg half opening angle (suggested by the manufacturer), the factor R(1-sinα) is 4.3 nm. In this study, the minimum indentation depth during AFM cantilever-based nanoindentation with the PNP cantilevers was about 10 nm.
Therefore, Equation 2 was used for the determination of the projected area of contact.

Figure S2
Determination of correction factor ξ or a 4-sided pyramidal tip with half opening angle α and tip radius R.
The contact area is finally a function of the contact depth. The contact depth was determined according to Oliver-Pharr analysis method (Oliver and Pharr 2004): where the ε is a constant that depends on the indenter geometry and is 0.75 for a Berkovich tip, 1 for a flat punch, and 0.73 for cone shaped indenters. The AFM tips are cone shaped indenters and thus ε was taken equal to 0.73 (Fischer-Cripps 2002, Oliver andPharr 2004).

S3 Swelling measurements
Collagen fibrils swell, i.e. increase in fibril diameter, when hydrated with an aqueous solution, such as phosphate buffered saline solution (PBS). Swelling was measured by comparing the change in height of collagen fibrils when they were subsequently images first in air and then in PBS. For swelling measurements we assumed that only the diameter of collagen fibrils increases during hydration while their length remains unchanged. Figure S3 shows AFM images of collagen fibrils from male WT mouse dried in air (panel (a)) and hydrated in PBS (panel (b)). Panel (c) of Figure

S4 Estimation of collagen fibril density based on swelling measurements and the results gained from the in silico study
Assuming that the collagen fibril is geometrically characterized by a cylinder, the volume of the fibril is simply given as: where d is the diameter and L is length of the fibril. Assuming the mass, m, of the fibril remains the same before and after hydration and because the swelling is described here as the fold-change in fibril diameter, we can describe the density ( m / V ρ = ) of the hydrated and the dry fibril as a function of the volume, V and therefore as a function of swelling, S: Given that the normalized volume of air-dried WT collagen fibril is  (2.2 ± 0.6) MPa. No statistical differences were found between samples of the same health state but of different gender (P > 0.05, when using either parametric or non-parametric statistics). However, the indentation modulus of collagen fibrils from female OIM (EOIM_lsmean = 21.5 MPa) was about five-fold higher compared to the one of WT (EWT_lsmean = 3.7 MPa) with P < 0.001. Similarly, the indentation modulus of collagen fibrils from male OIM (EOIM-♂_lsmean = 9.4 MPa) was about four-fold higher compared to the one of WT (EWT_lsmean = 1.9 MPa) with P < 0.001.

Figure S4
Box plots of indentation modulus results comparing male vs. female animals.