Abstract
A growing leaf is a prototypical active solid, as its active units, the cells, locally deform during the out-of-equilibrium process of growth. During this local growth, leaves increase their area by orders of magnitude, yet maintain a proper shape, usually flat. How this is achieved in the lack of a central control, is unknown. Here we measure the in-plane growth tensor of Tobacco leaves and study the statistics of growth-rate, isotropy and directionality. We show that growth strongly fluctuates in time and position, and include multiple shrinkage events. We identify the characteristic scales of the fluctuations. We show that the area-growth distribution is broad and non-Gaussian, and use multiscale statistical methods to show how growth homogenizes at larger/longer scales. In contrast, we show that growth isotropy does not homogenize in time. Mechanical analysis shows that with such growth statistics, a leaf can stay flat only if the fluctuations are regulated/correlated.
Highlights
A growing leaf is a prototypical active solid, as its active units, the cells, locally deform during the out-of-equilibrium process of growth
Out of equilibrium active solids are prevalent in nature and include bio-mechanical systems under development and physiology such as animal epithelium[1,2] and plant tissues[3,4,5]
In-plant lateral organs, such as leaves and petals, cell division is stopped at the early stages of development and most of the increase in volume occurs via cell expansion
Summary
A growing leaf is a prototypical active solid, as its active units, the cells, locally deform during the out-of-equilibrium process of growth. Different genetic and molecular networks in plants are known to participate in growth regulation[17,27,28,29,30], but recently, feedback mechanisms between stress and growth were proposed to be involved as well, in order to achieve desired shapes Such feedbacks are being studied in animals, mainly in Drosophila embryo development, as means to homogenize growth and keep a growing object flat or self-similar, or as a source of instability and creation of complex shapes[4,31,32,33,34,35,36]. It is still not known if and how chemical and mechanical fields are coordinated in a way that leads to the proper growth of leaves
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