High-Speed Nanomechanical Mapping of the Early Stages of Collagen Growth by Bimodal Force Microscopy

High-speed atomic force microscopy (AFM) enabled the imaging of protein interactions with millisecond time resolutions (10 fps). However, the acquisition of nanomechanical maps of proteins is about 100 times slower. Here, we developed a high-speed bimodal AFM that provided high-spatial resolution maps of the elastic modulus, the loss tangent, and the topography at imaging rates of 5 fps. The microscope was applied to identify the initial stages of the self-assembly of the collagen structures. By following the changes in the physical properties, we identified four stages, nucleation and growth of collagen precursors, formation of tropocollagen molecules, assembly of tropocollagens into microfibrils, and alignment of microfibrils to generate microribbons. Some emerging collagen structures never matured, and after an existence of several seconds, they disappeared into the solution. The elastic modulus of a microfibril (∼4 MPa) implied very small stiffness (∼3 × 10–6 N/m). Those values amplified the amplitude of the collagen thermal fluctuations on the mica plane, which facilitated microribbon build-up.


Supplementary
. HS-bimodal AFM topography data to generate the iso-time maps The images were obtained at 100 Hz, 3 µm scan size, 512 x 512 pixels and 0.2 fps. The san time was of 512 seconds. The cantilever used was a USC-F0.3-k0. 3. The cantilever parameters were f 1 = 132 kHz, k 1 = 0.18 nN/nm, Q 1 = 2.4 for the first mode and f 2 = 1045 kHz, k 2 = 12 nN/nm, Q 2 = 5.7 for the second mode. The measurement was performed with a free amplitude A 01 = 10 nm, A 02 = 1.5 nm and A 1 = 9 nm. The maximum force F peak exerted on the collagen was of 1 nN. The measurements were performed on the same collagen sample. The images were obtained at 1µm scan size and 512x512 pixels. The cantilever parameters (USC-F0.3-k0.3, NanoAndMore). were f 1 = 137 kHz, k 1 = 0.33 nN/nm, Q 1 = 2.1 for the first mode and f 2 = 1083 kHz, k 2 = 20 nN/nm, Q 2 = 5.6 for the second mode. The measurement was performed with a free amplitude A 01 = 5.7 nm, A 02 = 0.3 nm and A 1 = 4.4 nm. The maximum force F peak exerted on the collagen was of 2 nN. Figure 5: HS-Bimodal AFM Imaging of collagen fibrils acquired at 5 fps (96x368 pixels at a scanline rate of 543 Hz, see video S4 in SI). The bimodal AFM parameters were A 01 = 11.0 nm, A 1 = 8.5 nm, A 2 = 1.0 nm and F max = 1 nN. Images were obtained with a USC-F1.2-k0.15 cantilever (f 01 = 647 kHz, k 1 = 0.08 N m -1 , Q 1 = 1.5, f 02 = 5.6 MHz, k 2 = 8 N m -1 ). Experiment performed in liquid.

Elastic modulus and loss tangent values from bimodal AFM data (AM-open loop)
The expression to determine the compressive elastic modulus and the loss tangent from bimodal AFM were deduced by applying energy balance and virial theorem considerations to the tip's motion. The general process was developed previously for a semi-spherical tip of radius R. [1][2][3][4][5] The elastic modulus was determined by We assumed that the energy dissipation process is detected by the first mode. The loss tangent represents the ratio between the energy dissipated in sample and the energy store in the cantilever-tip system in one cycle. 6 It was calculated by where E dis is the energy dissipated and V 1 is the virial of mode 1. We note that Eq. s3 and s4 provide accurate determination of the loss tangent and the energy dissipated for high quality factor cantilevers. In liquid, the first mode might lose energy through different processes, interaction with the sample, the liquid and energy losses to higher harmonics. 7 The latter processes were not been taking into account in the above expressions. This effect is particular relevant when comparing loss tangent values between mica (~50 GPa) and collagen (~5 MPa). The tip-sample interaction force on mica will generate higher harmonics components. The amplitudes of those harmonics will be significantly larger than the amplitudes of the harmonics generated on collagen. However, Eq, s3 provides a good approximation to estimate the dissipative properties of the collagen structures because the change in Young's modulus is of a few MPa. Those differences do not generate significant changes in the high harmonic components.

Tip's radius determination
The elastic modulus depends on the tip's radius as defined in equation s1. We have applied an in situ process to determine the tip's radius based on the spatial resolution given by the bimodal AFM image. Fig. S2a shows a HS-bimodal AFM image (topography) of a microribbon split in two. The tip's radius is determined by finding the best fit to the cross-section (Fig. S2b). The points selected to perform the fitting are marked in red in Fig. S2b (the minimum and the tangent points). A radius R=33 nm was obtained for Fig. S2a.

Bottom-effect correction for the determination of nanomechanical properties
The force exerted by an AFM on a soft and very thin material such as collagen microfibrils bears the influence of the elastic properties of the solid support. 8 To account for this effect in the determination of the elastic modulus of the collagen we have used the following expression for the force exerted by the tip, 7 δ is the deformation (indentation) and h the thickness of the undeformed collagen. Equation s7 was introduced in the virials 4 of modes 1 and 2 to determine the elastic modulus and the indentation.

Cantilever calibration
The cantilever parameters were calibrated after the experiment. An extensive explanation of the fitting procedure has already been described. 3 The inverse optical lever sensitivity (nm V −1 ) of the first mode was calibrated by acquiring a deflectiondistance curve on a stiff surface (muscovite mica). With a measurement of the power spectral density (PSD) the spring constant of the first mode was calibrated, fitting it with the single harmonic oscillator (SHO) model. Thus, the resonance frequency of the second mode, , is measured from the PSD and the corresponding force constant is 2 calculated with the stiffness-frequency power law relationship given by, 9 (s9) 2 = 1( 2 1 ) assuming . Once is known, the PSD is fitted with the SHO where the peak of = 2