Phase-field collagen fibrils: Coupling chirality and density modulations

To describe the interaction between longitudinal density modulations along collagen fibrils (the D band) with a radial twist field of molecular orientation (double twist), we couple a phase-field crystal (PFC) with liquid-crystalline free energies to obtain a hybrid model of equilibrium collagen fibril structure. We numerically compute the resulting axial and radial structure. We find two distinct fibrillar phases, L and C, with a coexistence line that ends in an Ising-like critical point. We propose that the coexistence between these phases can explain the bimodal distribution of fibril radii that has been widely reported within tendon tissues. Tensile strain applied to our model fibrils straightens the average fibrillar twist and flattens the D-band modulation. Our PFC approach should apply directly to other longitudinally modulated chiral filaments, such as fibrin and intermediate filaments.