  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 acting as an activator, and matrix GLA protein acting as an
inhibitor. Motivated by this qualitative activator-inhibitor dynamics, we
employ a prototype Gierer-Meinhardt model used in the context of
activator-inhibitor based biological pattern formation. Through a detailed
analysis in one and two spatial 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).
