Plant hormone auxin has critical roles in plant growth, dependent on its heterogeneous distribution in plant tissues. Exactly how auxin transport and developmental processes such as growth coordinate to achieve the precise patterns of auxin observed experimentally is not well understood. Here we use mathematical modelling to examine the interplay between auxin dynamics and growth and their contribution to formation of patterns in auxin distribution in plant tissues. Mathematical models describing the auxin-related signalling pathway, PIN and AUX1 dynamics, auxin transport, and cell growth in plant tissues are derived. A key assumption of our models is the regulation of PIN proteins by the auxin-responsive ARF-Aux/IAA signalling pathway, with upregulation of PIN biosynthesis by ARFs. Models are analysed and solved numerically to examine the long-time behaviour and auxin distribution. Changes in auxin-related signalling processes are shown to be able to trigger transition between passage- and spot-type patterns in auxin distribution. The model was also shown to be able to generate isolated cells with oscillatory dynamics in levels of components of the auxin signalling pathway which could explain oscillations in levels of ARF targets that have been observed experimentally. Cell growth was shown to have influence on PIN polarisation and determination of auxin distribution patterns. Numerical simulation results indicate that auxin-related signalling processes can explain the different patterns in auxin distributions observed in plant tissues, whereas the interplay between auxin transport and growth can explain the ‘reverse-fountain’ pattern in auxin distribution observed at plant root tips.

中文翻译：

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植物组织中生长素转运的数学模型：通量满足信号和生长

植物激素生长素在植物生长中具有关键作用，这取决于其在植物组织中的异质分布。植物生长素运输和发育过程（如生长）如何协调以达到实验观察到的生长素的精确模式尚不清楚。在这里，我们使用数学建模来检查生长素动力学和生长之间的相互作用以及它们对植物组织中生长素分布模式形成的贡献。衍生出描述植物组织中生长素相关信号通路、PIN 和 AUX1 动力学、生长素转运和细胞生长的数学模型。我们模型的一个关键假设是通过生长素响应的 ARF-Aux/IAA 信号通路调节 PIN 蛋白，通过 ARF 上调 PIN 生物合成。对模型进行数值分析和求解，以检查长期行为和生长素分布。生长素相关信号传导过程的变化显示能够触发生长素分布中通道型和点型模式之间的转变。该模型还被证明能够产生在生长素信号通路组分水平上具有振荡动力学的分离细胞，这可以解释实验观察到的 ARF 靶标水平的振荡。细胞生长被证明对 PIN 极化和生长素分布模式的确定有影响。数值模拟结果表明，生长素相关的信号传导过程可以解释植物组织中观察到的生长素分布的不同模式，