The Intermittent Nature of Leaf Growth Fields
What are the general principles that allow proper growth of a tissue or an organ? A growing leaf is an example of such a system: it increases its area by orders of magnitude, maintaining a proper (usually flat) shape. How can this be achieved without a central control unit? One would think that a combination of uniform growth with viscoelastic rheology would allow that. Here we show that that the exact opposite process is in action: the natural growth of the leaf surface strongly fluctuates in time and position. By combining high resolution measurements and multi-scale statistical analysis, we suggest a paradigm-change in the way leaf growth is viewed. We measure the in-plane tissue growth of Tobacco leaves in Lagrangian coordinates in 3D and study the statistics of three scalar fields associated with the tensorial growth field: The growth rate, its isotropy and directionality. We identify the governing time and length scales of the fluctuations in the growth rate, and capture abundant switching between local area swelling and shrinking, when measured in high resolution. At lower spatio-temporal resolution the growth rate field becomes smooth. In contrast, the anisotropy field increases over time. Finally, we find significant differences between growth measured during day and night. The growth at night is found to be more intermittent, with shorter correlation lengths and no global directionality. Despite its fluctuative nature, growth fields are not random, thus carry information about growth regulation. Indeed, mechanical analysis shows that a growing leaf can stay flat only if the measured fluctuations are regulated/correlated. Our measurements suggest that the entire statistics of growth fields, and not just their means, should be studied. In particular, the regulation of such fields and the link between their characteristics and the global geometry of a leaf should be studied.