Final Report Summary - SOFTGROWTH (Growth and Shaping of Soft Tissue)
SoftGrowth was a research project aiming at understanding shaping via growth of soft tissues. It had three main objectives:
1. Developing a theoretical framework that allows quantitative calculation of the three-dimensional shapes of thin sheets that grow non-uniformly.
2. Developing experimental systems that allow the construction of thin soft sheets that undergo non-uniform growth. Using these system to study the geometrical principles of shape selection in growing tissue.
3. Studying if and how the principles mentioned above govern the shaping of growing leaves and other slender plant organs.
The project was extremely successful in fulfilling these objectives. We have completed formulating a theoretical framework, which is an extension of the elastic plate theory, which allows for quantitative calculations of equilibrium configurations of growing sheets. The framework uses a geometrical formulation of both the growth field and the elastic response of the material. It is now being used by several research groups in the world. Experimentally, we developed the method of sheets with “programmable” metric. We constructed discs made of gel that shrinks at high temperature. The gel was not uniform across the disc, leading to non-uniform shrinkage (or growth) when heated. With this system we performed the first studies of the shaping principles of growing sheets. Our work on plants had several major achievements. First, we developed the machinarry and analysis tools to measure the local growth and the three- dimensional shape of leaves and to analyze their shape in proper geometrical way. We also discovered surprising facts on the process of leaf growth. For example, we showed that at each moment during leaf growth, about one third of the cells undergo shrinkage. Finally, we analyzed the process of seed pod opening. This study revealed a new mechanical transition, from twisted configurations to helical ones. Using our theoretical model we could explain the transition. Moreover, we showed that the mechanics that governs seed pod opening is highly relevant to systems that are hundred million times smaller. It turns out that the shape of macromolecules that are built via the self assembly of chiral molecules is determined by the same geometrical and mechanical principles. This surprising result is the subject of current intense study. It is beyond the scope of SoftGrowth, but it is a direct result of its success. The impact of the project indeed goes beyond its initial scope. The techniques and formalism that were developed are highly effective in the study of plasticity, glasses, mechano-transduction and even in industrial design. These research directions will be developed in the near future.
1. Developing a theoretical framework that allows quantitative calculation of the three-dimensional shapes of thin sheets that grow non-uniformly.
2. Developing experimental systems that allow the construction of thin soft sheets that undergo non-uniform growth. Using these system to study the geometrical principles of shape selection in growing tissue.
3. Studying if and how the principles mentioned above govern the shaping of growing leaves and other slender plant organs.
The project was extremely successful in fulfilling these objectives. We have completed formulating a theoretical framework, which is an extension of the elastic plate theory, which allows for quantitative calculations of equilibrium configurations of growing sheets. The framework uses a geometrical formulation of both the growth field and the elastic response of the material. It is now being used by several research groups in the world. Experimentally, we developed the method of sheets with “programmable” metric. We constructed discs made of gel that shrinks at high temperature. The gel was not uniform across the disc, leading to non-uniform shrinkage (or growth) when heated. With this system we performed the first studies of the shaping principles of growing sheets. Our work on plants had several major achievements. First, we developed the machinarry and analysis tools to measure the local growth and the three- dimensional shape of leaves and to analyze their shape in proper geometrical way. We also discovered surprising facts on the process of leaf growth. For example, we showed that at each moment during leaf growth, about one third of the cells undergo shrinkage. Finally, we analyzed the process of seed pod opening. This study revealed a new mechanical transition, from twisted configurations to helical ones. Using our theoretical model we could explain the transition. Moreover, we showed that the mechanics that governs seed pod opening is highly relevant to systems that are hundred million times smaller. It turns out that the shape of macromolecules that are built via the self assembly of chiral molecules is determined by the same geometrical and mechanical principles. This surprising result is the subject of current intense study. It is beyond the scope of SoftGrowth, but it is a direct result of its success. The impact of the project indeed goes beyond its initial scope. The techniques and formalism that were developed are highly effective in the study of plasticity, glasses, mechano-transduction and even in industrial design. These research directions will be developed in the near future.