Related papers: Leaf growth is conformal
The innumerable shapes of plant leaves present a challenge to the explanatory power of biophysical theory. A model is needed that can produce these shapes with a small set of parameters. This paper presents a simple model of leaf shape…
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…
Plant morphogenesis relies on dynamic growth deformations at the cell and tissue scales driven by osmotic fluxes. A mechanistic understanding of this phenomenon demands a physical framework that integrates cell imbibition, tissue mechanics,…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
The growth of plants is a hydromechanical phenomenon in which cells enlarge by absorbing water, while their walls expand and remodel under turgor-induced tension. In multicellular tissues, where cells are mechanically interconnected,…
How morphogenesis depends on cell properties is an active direction of research. Here, we focus on mechanical models of growing plant tissues, where microscopic (sub)cellular structure is taken into account. In order to establish links…
The spongy mesophyll is a complex, porous tissue found in plant leaves that enables carbon capture and provides mechanical stability. Unlike many other biological tissues, which remain confluent throughout development, the spongy mesophyll…
We propose a two-scale model to resolve essential features of developmental tissue deformations. The model couples individual cellular behavior to the mechanics at tissue scale. This is realized by a multiphase-field model addressing the…
In the statistical analysis of shape a goal beyond the analysis of static shapes lies in the quantification of `same' deformation of different shapes. Typically, shape spaces are modelled as Riemannian manifolds on which parallel transport…
Lotus leaves floating on water usually experience short-wavelength edge wrinkling that decays toward the center, while the leaves growing above water normally morph into a global bending cone shape with long rippled waves near the edge.…
A central question in developmental biology is how size and position are determined. The genetic code carries instructions on how to control these properties in order to regulate the pattern and morphology of structures in the developing…
Mathematical models of biological growth commonly attempt to distinguish deformation due to growth from that due to mechanical stresses through a hypothesised multiplicative decomposition of the deformation gradient. Here we demonstrate…
Growing a flat lamina such as a leaf is almost impossible without some feedback to stabilize long wavelength modes that are easy to trigger since they are energetically cheap. Here we combine the physics of thin elastic plates with feedback…
The remarkable range of biological forms in and around us, such as the undulating shape of a leaf or flower in the garden, the coils in our gut, or the folds in our brain, raise a number of questions at the interface of biology, physics and…
The original problem of phyllotaxis was focused on the regular arrangements of leaves on mature stems represented by common fractions such as 1/2, 1/3, 2/5, 3/8, 5/13, etc. The phyllotaxis fraction is not fixed for each plant but it may…
Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside of…
Optimal embedding in the three-dimensional space of exponentially growing squeezed surfaces, like plants leaves, or 2D colonies of exponentially reproducing cells, is considered in the framework of conformal approach. It is shown that the…
How does growth encode form in developing organisms? Many different spatiotemporal growth profiles may sculpt tissues into the same target 3D shapes, but only specific growth patterns are observed in animal and plant development. In…
This is a review of two-dimensional conformal field theory including some of the relations to integrable models. An effort is made to develop the basic formalism in a way which is as elementary and flexible as possible at the same time.…
Localized deformation patterns are a common motif in morphogenesis and are increasingly finding widespread applications in materials science, for instance as memory devices. Here we describe the emergence of spatially localized deformations…