While in animals there is a distinction between the "growth" of the organism and its "behavior", in the case of plants, which are sessile and move by growing, these two aspects of living are not separable. This implies that plant growth includes behavioral aspects, which essentially involve monitoring of the environment, integration of information and decision-making. How do plant process information and how can their growth be modeled? The lack of a central computation organ (a brain) implies that information is processed within the tissue, affecting and coordinating growth. This makes growing plants a fascinating multidisciplinary system: From the biological side it is a multi-cellular system controlled by the complex bio-chemical network. From the computation aspect, it is a brainless system with "intelligence" embedded in its tissue. Finally, from the physical side, it is an "active solid" – an extended solid system, whose elements (cells) perform mechanical work, which drives the evolving geometry via physical laws. These different views do not contradict each other. Contrarily, they are complementary, as each highlights a different aspect of this inherently multidisciplinary system.
The interdisciplinary approach to plant growth is a rapidly growing field, which gathers researchers from botany, computer sciences, physics and engineering. Several main research directions are distinct in this field: Plant tropism, roots growth and leaf shape evolution. All of these topics involve growth regulation, evolving curved geometries, nonlinear field theories (such as reaction-diffusion and nonlinear elasticity) and solid mechanics.
Plant tropism: Plants are equipped with sensory systems which allow them to sense a variety of directional stimuli such as light, gravity, touch, and gradients of various chemicals. They respond by growing towards or away from that direction, called tropisms. For example plant shoot grow towards light (phototropism) and away from gravity (gravitropism). While the basic cellular sensory systems of these two tropisms have been identified (1) , it is the control mechanisms that process these signals which are still not understood. Recent experimental, computational and analytic studies have led to a new view on these important processes. The resultant dynamical system takes into account growth, distributed sensing, and elasticity (2, 3), however it is not yet completely understood. Most exciting are, perhaps, the clear indications of integration of signals (4), a clear signature of "information processing". This is of particular interest also in the recent field of plant-inspired robotics (5).
Roots are quasi one-dimensional structures with highly non-trivial tasks. They have to penetrate into a highly heterogeneous granular medium, to split and spread in order to provide coupling to the soil. Modeling of roots growth is motivated by biological and agricultural interests and also, more recently, by the robotics community, which seeks biomimetic principles for underground robots (6). The study of root growth revealed that the change in root growth direction stems from a combination of sensing with specialized organs, which results in growth hormone (auxin) redistribution (7) and mechanical response of the root and the medium in which it grows (8). This can give rise to intriguing growth patterns which biological purpose is still under debate (9).
Leaves face a different challenge: how to achieve the "proper" leaf shape. Unlike 1D curves, 2D surfaces require compatibility conditions, expressed by the Gauss-Minardi-Coddazzi equations (10) that link between the surface's metric and curvature. Non-uniform growth would dictate a non-Euclidean metric and the leaf would thus crinkle and crumple due to internal stresses. It is thus not clear how a leaf, which lacks a central control "unit", manages to grow properly (most often flat) despite the highly heterogeneous local growth (11). This requires growth regulation system, embedded within the tissue. From the physical point of view, it can be described as an effective rheology of an active solid sheet (12). First experiments, simulations and models (13) only start to reveal these complex biological-mechanical-geometrical processes.
As reviewed here, plant growth introduces new types of scientific questions that involve biology, physics, control and geometry and span many orders of length and time scales. These must be addressed in a multidisciplinary approach that involves experiments and computation methods which include modeling and basic theoretical study. The proposed conference will be a milestone in this direction.