The formation of labyrinths, spots and stripe patterns in a biochemical approach to cardiovascular calcification

TL;DR

This paper models biochemical pattern formation in cardiovascular calcification using activator-inhibitor dynamics, revealing diverse steady-state patterns that could inform therapeutic strategies for bone regeneration and vascular calcification.

Contribution

It applies a Gierer-Meinhardt model to explain pattern formation in calcification, linking biochemical dynamics to diverse spatial patterns in cardiovascular tissues.

Findings

Patterns range from holes to labyrinths and peaks.

Pattern formation depends on initial conditions.

Insights could guide therapeutic strategies.

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).