Abstract
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).
Highlights
Cardiovascular calcification, in atherosclerosis or valvular stenosis, is considered one of the most notorious cardiac diseases [1]
The morphology of the patterns was experimentally altered by applying external matrix GLA protein (MGP); MGP molecules bind to active bone morphogenetic protein 2 (BMP-2), disabling their functionality
Since: (i) the cell migration occurs at much slower time scales than the chemical diffusion, (ii) cell proliferation is relatively low [40], and (iii) neither BMP-2 nor MGP are consumed by the cells, we can neglect, to leading order, other contributions such as cell density, which indicate contributions of further, albeit minor, spatiotemporal changes of chemotactic distributions
Summary
Cardiovascular calcification, in atherosclerosis or valvular stenosis, is considered one of the most notorious cardiac diseases [1]. The morphology of the patterns was experimentally altered by applying external matrix GLA protein (MGP) (see figure 1); MGP molecules bind to active BMP-2, disabling their functionality Alan Turing, in his seminal work on morphogenesis [7], suggested that the formation of biological patterns can be understood by means of biochemistry, that is, in the reaction-diffusion framework. In this scenario, chemicals produced by cells interact as activators or inhibitors, and diffuse through the medium at distinct rates.
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