The formation of labyrinths, spots and stripe fragments: Applications to cardiovascular calcification and bone regeneration

Calcification and mineralization are fundamental physiological processes, yet the mechanisms of calcification, in trabecular bone and in calcified lesions in atherosclerotic calcification, are unclear. Recently, it was shown in in vitro experiments that vascular-derived mesenchymal stem cells can display self-organized calcified patterns. These patterns were attributed to activator/inhibitor dynamics in the style of Turing, with bone morphogenetic protein 2 (BMP-2) acting as an activator, and matrix GLA protein (MGP) acting as an inhibitor. Different pattern morphologies were produced by external application of the inhibitor MGP. Motivated by this qualitative activator-inhibitor dynamics, we study here a bistable form of the Gierer-Meinhardt model, with autocatalytic saturation. Through a detailed analysis in one and two dimensions, we explore the pattern formation mechanisms of steady state patterns, including their dependence on initial conditions. These patterns range from localized holes to labyrinths and localized peaks, or in other words, from dense to sparse activator distributions (respectively). We believe that an understanding of the wide spectrum of activator-inhibitor patterns discussed here is prerequisite to their biochemical control. The mechanisms of pattern formation suggest therapeutic strategies applicable to bone formation in atherosclerotic lesions in arteries (where it is pathological) and to the regeneration of trabecular bone (recapitulating normal physiological development).