Nematic ordering pattern formation in the process of self-organization of microtubules in a gravitational field

Papaseit et al. (Proc. Natl. Acad. Sci. U.S.A. 97, 8364, 2000) showed the decisive role of gravity in the formation of patterns by assemblies of microtubules in vitro. By virtue of a functional scaling, the free energy for MT systems in a gravitational field was constructed. The influence of the gravitational field on MT's self-organization process, that can lead to the isotropic to nematic phase transition, is the focus of this paper. A coupling of a concentration gradient with orientational order characteristic of nematic ordering pattern formation is the new feature emerging in the presence of gravity. The concentration range corresponding to a phase coexistence region increases with increasing g or MT concentration. Gravity facilitates the isotropic to nematic phase transition leading to a significantly broader transition region. The phase transition represents the interplay between the growth in the isotropic phase and the precipitation into the nematic phase. We also present and discuss the numerical results obtained for local MT concentration change with the height of the vessel, order parameter and phase transition properties.