Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138, USA.
Phys Biol. 2013 Aug;10(4):046001. doi: 10.1088/1478-3975/10/4/046001. Epub 2013 Jun 5.
We model the formation of periodic patterns of gene expression in epithelial cell sheets driven by autocrine signaling coupled to juxtacrine lateral inhibition. The mathematical model is based on a continuous description of the extracellular matrix and a discrete cell-level description of the layer of cells, coupling the dynamics of diffusible ligands to the threshold-controlled cell-autonomous regulation with randomly fluctuating production rates. The results of numerical simulations indicate that propagating signaling waves emerge in a certain parametric domain, leading to the formation of a variety of either periodic or irregular patterns. For some selections of parameters, a propagating stripe of uniform expression leaves in its wake stationary periodic arrays. Coupling of autocrine and juxtacrine cell communication is essential for the pattern regularity and for the selection of expression patterns. Moreover, weak but non-vanishing noise levels are essential for the formation of regular patterns. Additional autocrine and cell-autonomous regulatory interactions can be introduced to increase the spacing of a periodic pattern.
我们建立了一个数学模型，研究了由自分泌信号驱动的上皮细胞片层中基因表达的周期性模式的形成，该信号与旁分泌横向抑制有关。该数学模型基于对细胞外基质的连续描述和对细胞层的离散细胞级描述，将可扩散配体的动力学与具有随机波动产生率的阈值控制的细胞自主调节耦合起来。数值模拟的结果表明，在一定的参数域中会出现传播信号波，从而导致各种周期性或不规则模式的形成。对于某些参数选择，传播的均匀表达条纹会在其后面留下静止的周期性阵列。自分泌和旁分泌细胞通讯的耦合对于模式的规则性和表达模式的选择至关重要。此外，较弱但非零的噪声水平对于形成规则模式是必不可少的。可以引入额外的自分泌和细胞自主调节相互作用来增加周期性模式的间距。
