MODELING OF ROOT-GROWTH AND BENDING IN 2 DIMENSIONS

A special co-ordinate system is developed for modelling the gravitropi c bending of plant roots. It is based on the Local Theory of Curves in differential geometry and describes, in one dimension, growth events that may actually occur in two, or even three, dimensions. With knowle dge of the spatial distributions of relative elemental growth rates (R ELELs) for the upper and lower flanks of a gravistimulated root, and a lso their temporal dependencies, it is possible to compute the develop ment of curvature along the root and hence describe the time-course of gravitropic bending. In addition, the RELEL distributions give inform ation about the velocity field and the basipetal displacement of point s along the root's surface. According to the Fundamental Theorem of Lo cal Curve Theory, the x and y co-ordinates of the root in its bending plane are then determined from the associated values of local curvatur e and local velocity. With the aid of this model, possible mathematica l growth functions that correspond to biological mechanisms involved i n differential growth can be tested. Hence, the model can help not onl y to distinguish the role of various physiological or biophysical para meters in the bending process, but also to validate hypotheses that ma ke assumptions concerning their relative importance. However, since th e model is constructed at the level of the organ and treats the root a s a fluid continuum, none of the parameters relate to cellular behavio ur; the parameters must instead necessarily apply to properties that i mpinge on the behaviour of the external boundary of the root. (C) 1997 Academic Press Limited.