Department of Physiology, Centre for Nonlinear Dynamics, McGill University, Montréal, Québec, Canada.
PLoS One. 2011 Apr 25;6(4):e18549. doi: 10.1371/journal.pone.0018549.
Turgor generates the stress that leads to the expansion of plant cell walls during cellular growth. This has been formalized by the Lockhart equation, which can be derived from the physical laws of the deformation of viscoelastic materials. However, the experimental evidence for such a direct correlation between growth rate and turgor is inconclusive. This has led to challenges of the Lockhart model. We model the oscillatory growth of pollen tubes to investigate this relationship. We couple the Lockhart equation to the dynamical equations for the change in material properties. We find that the correct implementation of the Lockhart equation within a feedback loop leading to low amplitude oscillatory growth predicts that in this system changes in the global turgor do not influence the average growth rate in a linear manner, consistent with experimental observations. An analytic analysis of our model demonstrates in which regime the average growth rate becomes uncorrelated from the turgor pressure.
膨压在细胞生长过程中产生导致植物细胞壁扩张的力。这一过程已经通过朗哈特方程（Lockhart equation）形式化，该方程可以从粘弹性材料变形的物理定律中推导出来。然而，关于生长速率与膨压之间存在直接相关性的实验证据并不明确，这给朗哈特模型带来了挑战。我们通过模拟花粉管的振荡生长来研究这种关系。我们将朗哈特方程与物质属性变化的动力学方程耦合。我们发现，在一个导致低幅度振荡生长的反馈回路中正确实现朗哈特方程，表明在这个系统中，全局膨压的变化不会以线性方式影响平均生长速率，这与实验观察结果一致。我们模型的解析分析表明，在何种情况下平均生长速率与膨压压力不再相关。
