Quantification of curvature production in cylindrical organs, such as roots and hypocotyls

Abstract

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