The Dynamics of Root Growth: A Geometric Model.

A new model for macroscopic root growth based on a dynamical Riemannian geometry is presented. Assuming that the thickness of the root is much less than its length, the model is restricted to growth in one dimension (1D). We treat 1D tissues as continuous, deformable, growing geometries for sizes larger than 1 mm. The dynamics of the growing root are described by a set of coupled tensor equations for the metric of the tissue and velocity field of material transport in non-Euclidean space. These coupled equations represent a novel feedback mechanism between growth and geometry. We compare 1D numerical simulations of these tissue growth equations to two measures of root growth. First, sectional growth along the simulated root shows an elongation zone common to many species of plant roots. Second, the relative elemental growth rate calculated in silico exhibits spatio-temporal dynamics recently characterized in high-resolution root growth studies but which thus far lack a biological hypothesis to explain them. In our model, these dynamics are a direct consequence of considering growth as both a geometric reaction-diffusion process and expansion due to a distributed source of new materials.

Modelling biomechanics of bark patterning in grasstrees.

BACKGROUND AND AIMS: Bark patterns are a visually important characteristic of trees, typically attributed to fractures occurring during secondary growth of the trunk and branches. An understanding of bark pattern formation has been hampered by insufficient information regarding the biomechanical properties of bark and the corresponding difficulties in faithfully modelling bark fractures using continuum mechanics. This study focuses on the genus Xanthorrhoea (grasstrees), which have an unusual bark-like structure composed of distinct leaf bases connected by sticky resin. Due to its discrete character, this structure is well suited for computational studies. METHODS: A dynamic computational model of grasstree development was created. The model captures both the phyllotactic pattern of leaf bases during primary growth and the changes in the trunk's width during secondary growth. A biomechanical representation based on a system of masses connected by springs is used for the surface of the trunk, permitting the emergence of fractures during secondary growth to be simulated. The resulting fracture patterns were analysed statistically and compared with images of real trees. KEY RESULTS: The model reproduces key features of grasstree bark patterns, including their variability, spanning elongated and reticulate forms. The patterns produced by the model have the same statistical character as those seen in real trees. CONCLUSIONS: The model was able to support the general hypothesis that the patterns observed in the grasstree bark-like layer may be explained in terms of mechanical fractures driven by secondary growth. Although the generality of the results is limited by the unusual structure of grasstree bark, it supports the hypothesis that bark pattern formation is primarily a biomechanical phenomenon.