Burgos-Flórez F J, Gavilán-Alfonso M E, Garzón-Alvarado D A
Biomimetics Laboratory, Instituto de Biotecnología, Universidad Nacional de Colombia, Bogotá, Colombia; Mathematical Modelling and Numerical Methods Research Group (GNUM), Universidad Nacional de Colombia, Bogotá, Colombia.
Mathematical Modelling and Numerical Methods Research Group (GNUM), Universidad Nacional de Colombia, Bogotá, Colombia.
J Theor Biol. 2016 Mar 21;393:127-44. doi: 10.1016/j.jtbi.2016.01.006. Epub 2016 Jan 15.
The processes of flat bones growth, sutures formation and interdigitation in the human calvaria are controlled by a complex interaction between genetic, biochemical and environmental factors that regulate bone formation and resorption during prenatal development and infancy. Despite previous experimental evidence accounting for the role of the main biochemical factors acting on these processes, the underlying mechanisms controlling them are still unknown. Therefore, we propose a mathematical model of the processes of flat bone and suture formation, taking into account several biological events. First, we model the growth of the flat bones and the formation of sutures and fontanels as a reaction diffusion system between two proteins: TGF-β2 and TGF-β3. The former is expressed by osteoblasts and allows adjacent mesenchymal cells differentiation on the bone fronts of each flat bone. The latter is expressed by mesenchymal cells at the sutures and inhibits their differentiation into osteoblasts at the bone fronts. Suture interdigitation is modelled using a system of reaction diffusion equations that develops spatio-temporal patterns of bone formation and resorption by means of two molecules (Wnt and Sclerostin) which control mesenchymal cells differentiation into osteoblasts at these sites. The results of the computer simulations predict flat bone growth from ossification centers, sutures and fontanels formation as well as bone formation and resorption events along the sutures, giving rise to interdigitated patterns. These stages were modelled and solved by the finite elements method. The simulation results agree with the morphological characteristics of calvarial bones and sutures throughout human prenatal development and infancy.
人类颅骨中扁骨生长、缝线形成和相互交错的过程受遗传、生化和环境因素之间复杂相互作用的控制，这些因素在产前发育和婴儿期调节骨形成和吸收。尽管先前的实验证据说明了主要生化因素在这些过程中的作用，但控制它们的潜在机制仍然未知。因此，我们提出了一个扁骨和缝线形成过程的数学模型，考虑了几个生物学事件。首先，我们将扁骨的生长以及缝线和囟门的形成建模为两种蛋白质（TGF-β2和TGF-β3）之间的反应扩散系统。前者由成骨细胞表达，使相邻间充质细胞在每个扁骨的骨前沿分化。后者由缝线处的间充质细胞表达，并抑制它们在骨前沿分化为成骨细胞。缝线相互交错是通过一个反应扩散方程组来建模的，该方程组借助两种分子（Wnt和硬化蛋白）形成骨形成和吸收的时空模式，这两种分子控制这些部位间充质细胞分化为成骨细胞。计算机模拟结果预测了从骨化中心开始的扁骨生长、缝线和囟门的形成以及沿缝线的骨形成和吸收事件，从而产生相互交错的模式。这些阶段通过有限元方法进行建模和求解。模拟结果与人类产前发育和婴儿期整个颅骨和缝线的形态特征一致。
