The role of confined collagen geometry in decreasing nucleation energy barriers to intrafibrillar mineralization

Mineralization of collagen is critical for the mechanical functions of bones and teeth. Calcium phosphate nucleation in collagenous structures follows distinctly different patterns in highly confined gap regions (nanoscale confinement) than in less confined extrafibrillar spaces (microscale confinement). Although the mechanism(s) driving these differences are still largely unknown, differences in the free energy for nucleation may explain these two mineralization behaviors. Here, we report on experimentally obtained nucleation energy barriers to intra- and extrafibrillar mineralization, using in situ X-ray scattering observations and classical nucleation theory. Polyaspartic acid, an extrafibrillar nucleation inhibitor, increases interfacial energies between nuclei and mineralization fluids. In contrast, the confined gap spaces inside collagen fibrils lower the energy barrier by reducing the reactive surface area of nuclei, decreasing the surface energy penalty. The confined gap geometry, therefore, guides the two-dimensional morphology and structure of bioapatite and changes the nucleation pathway by reducing the total energy barrier.

. Non-collagenous proteins (NCP) and other small acidic molecules exist in human blood plasma, and would influence the σ values. However, in this proof of concept calculation, we limited the input parameters to the major ionic compounds used for SBF solutions. Figure 1: Experimental setup for in situ SAXS measurements during collagen mineralization. a Design of a custom-made sample polytetrafluoroethylene (PTFE) frame containing two collagen matrices (thickness, t = 2.38 mm; diameter, d = 3 mm). t was chosen to collect enough scattering intensity signals, and d was chosen to scan multiple positions for averaging the data. b Mineralization of collagen matrices held in the frame, using a flow-through reaction system on a hot-plate maintaining the reactor at 37 ± 1 o C. c Experimental setup for SAXS measurements. ki and kf are the incident and scattered wave vectors, respectively. The scattering vector, q, is given by ki -kf, and 2θf is the exit angle of the X-rays.

Supplementary Figure 2:
Comparison of interfacial energy relationships for confined nucleation models with different exposed surfaces. The free energy change per molecule (∆G) is the sum of the bulk and surface energy terms (∆Gb and ∆Gs, respectively). A typical ∆G profile shows a maximum (i.e., energy barrier, ∆Gn) at a critical radius (rc). r and h are the length and height of nuclei. For the volume per molecule of nucleus, vm, 5 × 10 -23 cm 3 and 2.63 × 10 -22 cm 3 are used for ACP 3 and for HA 4 , respectively. kB is the Boltzmann constant (1.38 × 10 -23 J K -1 ). T is the temperature of the reactor (310 K). σ is the supersaturation (ln(IAP/Ksp), where IAP is the ion activity product and Ksp is the solubility product. α is the interfacial energy between nuclei and solution.

Supplementary Note 2: Intra-and extrafibrillar mineralization controlled by polyaspartic acid
Without pAsp, spherical particles at the outer surface of fibrils were observed on collagen films mineralized in both 2.65× and 2.85×SBF solutions, as shown in scanning electron microscope (SEM) images ( Supplementary Fig. 3c,d). In 2.65×SBF, relatively small spheres ( Supplementary Fig. 3c, radius, r = 67.1 ± 13.4 nm) were observed at extrafibrillar collagen spaces, showing a low Ca/P molar ratio of around 1.05 as analyzed by energy-dispersive x-ray spectroscopy (EDS). The rough surface texture also indicated that these spheres were aggregates of smaller primary particles ( Supplementary Fig. 3c, inset). In 2.85×SBF, microscale aggregates of thin crystals were more frequently observed at the extrafibrillar spaces after 11 hr of mineralization ( Supplementary Fig. 3d). These aggregates showed an increased Ca/P molar ratio = 1.62 ( Supplementary Fig. 3d, inset). These properties of extrafibrillar spheres formed without pAsp correspond well to an early stage of CaP development under a pathway involving aggregation of prenucleation clusters, which has been observed in environments without nanoscale confinement 3,5,6 . The increase in the Ca/P molar ratio is one characteristic of this pathway, which shows a transition from 0.67 to 1.67 during the transformation from amorphous spheres to aggregates of apatite plates 3 Fig. 3e,f). The periodic banding patterns (~67 nm, Supplementary  Fig. 3a,b) disappeared with mineralization by the deposition of bioapatite crystals, which aligned perpendicular to the bands of fibrils 7 . The Ca/P molar ratio obtained from intrafibrillarmineralized fibrils was relatively constant, at around 1.35, which is somewhat lower than the theoretical value for hydroxyapatite (1.67). Similar Ca/P molar ratios, mainly due to CaP phase transformation from amorphous to crystalline, have been reported for early stage development of intrafibrillar mineralized fibrils 6,8 . With 10 mg l -1 pAsp, we did not observe any aggregated extrafibrillar particles of larger size (as shown in Supplementary Fig. 3c,d) in all SBF solutions.
Therefore, we assumed that the influence of extrafibrillar mineralization is not significant in the presence of pAsp.

Supplementary Figure 4:
Exposed surface model to evaluate the solubility of platelike CaP nucleus in a confined space, using the Kelvin equation. The model assumes that the Kelvin effects on the overall solubility of the nucleus is proportional to the fraction of the plate-like nucleus' surface exposed to the SBF solution. In addition, the two exposed edge surfaces of the plate-like CaP nucleus (red faces of plate; also refer to our confined model in Fig. 1b Fig.3 a,b in the main text). Error ranges for αHA values for EM and IM are standards errors of the estimates for regressions between ln(J) and 1/σ 2 , and between ln(J) and 1/σ, respectively. Figure 7: Energy barriers to HA nucleation at different σHA. a ∆Gn for three different nucleation models: Unconfined nucleation without pAsp (representing extrafibrillar mineralization, blue line), confined nucleation with pAsp (representing intrafibrillar mineralization, red line), and unconfined nucleation with pAsp (IM calculation with no confinement effect, black line). b ∆G profiles at σHA = 22.7, which corresponds to human blood plasma (yellow bar in Supplementary Fig. 7 a).