Reproduction et Développement des Plantes, Université de Lyon, Ecole normale supérieure de Lyon, Université Claude Bernard Lyon 1, Institut national de recherche pour l'agriculture, l'alimentation et l'environnement, CNRS, 69364 Lyon Cedex 07, France.
Laboratoire d'Hydrodynamique, CNRS, Ecole polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France.
Proc Natl Acad Sci U S A. 2024 Jun 4;121(23):e2318481121. doi: 10.1073/pnas.2318481121. Epub 2024 May 30.
Living tissues display fluctuations-random spatial and temporal variations of tissue properties around their reference values-at multiple scales. It is believed that such fluctuations may enable tissues to sense their state or their size. Recent theoretical studies developed specific models of fluctuations in growing tissues and predicted that fluctuations of growth show long-range correlations. Here, we elaborated upon these predictions and we tested them using experimental data. We first introduced a minimal model for the fluctuations of any quantity that has some level of temporal persistence or memory, such as concentration of a molecule, local growth rate, or mechanical property. We found that long-range correlations are generic, applying to any such quantity, and that growth couples temporal and spatial fluctuations, through a mechanism that we call "fluctuation stretching"-growth enlarges the length scale of variation of this quantity. We then analyzed growth data from sepals of the model plant Arabidopsis and we quantified spatial and temporal fluctuations of cell growth using the previously developed cellular Fourier transform. Growth appears to have long-range correlations. We compared different genotypes and growth conditions: mutants with lower or higher response to mechanical stress have lower temporal correlations and longer-range spatial correlations than wild-type plants. Finally, we used theoretical predictions to merge experimental data from all conditions and developmental stages into a unifying curve, validating the notion that temporal and spatial fluctuations are coupled by growth. Altogether, our work reveals kinematic constraints on spatiotemporal fluctuations that have an impact on the robustness of morphogenesis.
活组织表现出波动——组织属性在其参考值周围的随机时空变化——在多个尺度上。人们认为这种波动可能使组织能够感知其状态或大小。最近的理论研究为生长组织中的波动开发了特定的模型，并预测了波动的生长表现出长程相关性。在这里，我们详细阐述了这些预测，并使用实验数据对其进行了测试。我们首先为任何具有一定时间持久性或记忆的数量（如分子浓度、局部生长率或机械性能）的波动引入了一个最小模型。我们发现，长程相关性是通用的，适用于任何这样的数量，并且生长通过我们称之为“波动拉伸”的机制耦合了时间和空间波动——生长扩大了该数量变化的长度尺度。然后，我们分析了来自模式植物拟南芥花萼的生长数据，并使用先前开发的细胞傅里叶变换量化了细胞生长的时空波动。生长似乎具有长程相关性。我们比较了不同的基因型和生长条件：对机械应力响应较低或较高的突变体比野生型植物具有较低的时间相关性和较长的空间相关性。最后，我们使用理论预测将来自所有条件和发育阶段的实验数据合并到一个统一的曲线上，验证了波动的时空变化是由生长耦合的观点。总之，我们的工作揭示了对形态发生的稳健性有影响的时空波动的运动学约束。
