Theoretical Platform for Liquid-Crystalline Self-Assembly of Collagen-Based Biomaterials

Abstract

The collagen triple helix is a ubiquitous biomacromolecule used in acidic aqueous solutions as precursor in the fabrication of artificial compact bone and cornea and in tissue engineering. The primary architecture of these highly structured solid tissues is formed during the cholesteric liquid-crystalline stage of their morphogenesis. The theoretical platform that describes the coupled dynamics of phase-ordering and mass transfer developed, implemented and validated here can be used for optimal material design and plays a significant complementary role to future experimental studies. Based on uniaxiality assumption, we have recently developed and validated a theory for the free energy tailored for acidic collagenous dispersions. Here we significantly expand and generalize our previous study, by including biaxiality since cholesteric phases must have a degree of biaxiality. In this work, we first modify the proposed interchain interaction and excluded-volume contribution by use of the addition theorem for spherical harmonics. Then, the Euler-Lagrange minimization followed by expansion around I/N* transition allows us to construct the free energy of ordering in terms of the phenomenological Landau–de Gennes formulation. Finally, we use the time-dependent Ginzburg-Landau equations to study the non-Fickian evolution of a single two dimensional cholesteric tactoid through a shallow quench from the isotropic to biphasic region of the phase diagram. Although equilibrium biaxiality is considerably low for these long-pitch cholesterics, we found that during self-assembly the biaxial order parameter achieves significant larger values than the equilibrium value. Additionally, the relaxed director field becomes both onion-like and defect-less, which is consistent with the twisted bipolar structure observed experimentally. The self-assembly simulations demonstrate that the formulated theoretical platform is not only consistent with previous theoretical and experimental studies but also able to be used to explore new routes for non-equilibrium collagen self-assembly. Taken together, this study deepens our understanding of cholesteric (chiral nematic N*) mesophase in acidic solutions of tropocollagen, and suggests a systematic spatio-temporal model that is capable of being used to extract the engineering principles for processing of these sought-after biomaterials.