论文标题
生长素波的缩放关系
Scaling Relations for Auxin Waves
论文作者
论文摘要
我们通过生长素介导的PIN1生长素转运蛋白的偏振蛋白分析了一个“高梯度”模型，用于形成植物激素生长素的传输通道。我们表明，该模型接纳了一个由生长素 - 脉冲高度参数化的流动波解决方案家族。我们发现这些波浪的速度和宽度的比例关系，并通过数值计算验证这些严格的结果。此外，我们为前阶波轮廓提供明确的表达式，这允许很容易鉴定出问题中生物学参数的影响。我们的证明是基于Friesecke和PEGO开发的缩放原理的概括，以构建经典的Fermi-Pasta-ulam-Tsingou模型，该模型描述了一维耦合的非线性弹簧链。
We analyze an 'up-the-gradient' model for the formation of transport channels of the phytohormone auxin, through auxin-mediated polarization of the PIN1 auxin transporter. We show that this model admits a family of travelling wave solutions that is parameterized by the height of the auxin-pulse. We uncover scaling relations for the speed and width of these waves and verify these rigorous results with numerical computations. In addition, we provide explicit expressions for the leading-order wave profiles, which allows the influence of the biological parameters in the problem to be readily identified. Our proofs are based on a generalization of the scaling principle developed by Friesecke and Pego to construct pulse solutions to the classic Fermi-Pasta-Ulam-Tsingou model, which describes a one-dimensional chain of coupled nonlinear springs.
