Hierarchical pattern of microfibrils in a 3D fluorapatite–gelatine nanocomposite: simulation of a bio-related structure building process

The shape development of a biomimetic fluorapatite–gelatine nanocomposite on the μm scale is characterised by a fractal mechanism with the origin being intrinsically coded in a (central) elongated hexagonal-prismatic seed. The 3D superstructure of the seed is distinctively overlaid by a pattern consisting of gelatine microfibrils. The orientation of the microfibrils is assumed to be controlled by an intrinsic electrical field generated by the nanocomposite during development and growth of the seed. In order to confirm this assumption and to get more detailed information on orientational relations of the complex nanocomposite we simulated the pattern formation process up to the μm scale. The results from experimental studies and simulation results on an atomistic level support a model scenario wherein the elementary building blocks for the aggregation are represented by elongated hexagonal-prismatic objects (A-units), with the embedded collagen triple-helices in their centers. The interactions of the A-units are consequently modelled by three contributions: the crystal energy part (originating from the pair-wise interactions of the “apatite shells” of the prismatic units), the electrostatic interaction (originating from the unit charges located at the ends of the collagen triple helices), and the interaction energy of the A-units mediated by the solvent. The next level of complexity is related to the fact that micro fibrils were found in the fluorapatite–gelatine nanocomposites. They consist of bundles of triple helical protein molecules, which are embedded within the 3D-hexagonal prismatic arrangement of the A-units. In our approach we consider the microfibrils as chains of flexible dipoles with effective dipole moments. The crystal growth processes is modelled as an energetically controlled stepwise association of elementary building blocks of different kind on a 3D-grid. The remarkable and excellent qualitative agreement between the simulated fibril patterns and the observations made by SEM and TEM support the concept of an intrinsic electric field driven morphogenesis of the fluorapatite–gelatine nanocomposite. The simulated fibril pattern also bears the chance to make fresh attempts in order to find explanations for experimental observations which are not understood up to now.