Andrés Chavarría-Krauser

Differential growth curvature rate (DGCR), defined as the spatial derivative of the tropic speed, was derived as a measure of curvature production in cylindrical organs. Its relation to usual concepts, such as curvature (kappa), rate of curvature (dkappa/dt) and differential growth profiles, was determined. A root gravitropism model, testing the hypothesis of one and two motors, exemplified its capabilities.DGCR was derived using cylindrical geometry and its meaning was obtained through a curvature conservation equation. The root gravitropism model was solved using a discrete difference method on a computer.DGCR described curvature production independently of growth, and was superior to dkappa/dt, which underestimated production. Moreover, DGCR profiles were able to differ between one and two motors, while profiles of kappa and dkappa/dt were not. The choice of the measure of curvature production has a large impact on experimental results, in particular when spatial and temporal patterns of differential growth need to be determined. DGCR was shown to fulfill the accuracy needed in the quantification of curvature production and should thus serve as a helpful tool for measurements

Plant hormones control many aspects of plant development and play an important role in root growth. Many plant reactions, such as gravitropism and hydrotropism, rely on growth as a driving motor and hormones as signals. Thus, modelling the effects of hormones on expanding root tips is an essential step in understanding plant roots. Here we achieve a connection between root growth and hormone distribution by extending a model of root tip growth, which describes the tip as a string of dividing and expanding cells. In contrast to a former model, a biophysical growth equation relates the cell wall extensibility, the osmotic potential and the yield threshold to the relative growth rate. This equation is used in combination with a refined hormone model including active auxin transport. The model assumes that the wall extensibility is determined by the concentration of a wall enzyme, whose production and degradation are assumed to be controlled by auxin and cytokinin. Investigation of the effects of auxin on the relative growth rate distribution thus becomes possible. Solving the equations numerically allows us to test the reaction of the model to changes in auxin production. Results are validated with measurements found in literature.