In Arabidopsis, lateral roots originate from pericycle cells deep within the primary root. New lateral root primordia (LRP) have to emerge through several overlaying tissues. Here, we report that auxin produced in new LRP is transported towards the outer tissues where it triggers cell separation by inducing both the auxin influx carrier LAX3 and cell-wall enzymes. LAX3 is expressed in just two cell files overlaying new LRP. To understand how this striking pattern of LAX3 expression is regulated, we developed a mathematical model that captures the network regulating its expression and auxin transport within realistic three-dimensional cell and tissue geometries. Our model revealed that, for the LAX3 spatial expression to be robust to natural variations in root tissue geometry, an efflux carrier is required--later identified to be PIN3. To prevent LAX3 from being transiently expressed in multiple cell files, PIN3 and LAX3 must be induced consecutively, which we later demonstrated to be the case. Our study exemplifies how mathematical models can be used to direct experiments to elucidate complex developmental processes.

中文翻译：

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生长素流出和流入载体的顺序诱导调节侧根的出现。

在拟南芥中，侧根起源于初生根深处的周轮细胞。新的侧根原基 (LRP) 必须通过几个覆盖组织出现。在这里，我们报告新 LRP 中产生的生长素被转运到外部组织，在那里它通过诱导生长素流入载体 LAX3 和细胞壁酶来触发细胞分离。LAX3 仅在两个覆盖新 LRP 的单元文件中表示。为了了解这种 LAX3 表达的惊人模式是如何被调节的，我们开发了一个数学模型，该模型捕获了在现实的三维细胞和组织几何形状中调节其表达和生长素转运的网络。我们的模型显示，为了使 LAX3 空间表达对根组织几何形状的自然变化具有鲁棒性，需要一个外排载体——后来被确定为 PIN3。为了防止 LAX3 在多个单元格文件中瞬时表达，必须连续诱导 PIN3 和 LAX3，我们后来证明是这种情况。我们的研究举例说明了如何使用数学模型来指导实验来阐明复杂的发育过程。