科研之友
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摘要
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.
- 出版日期2017-8
- 单位INRIA
