Schematic comparison of sigmoidal and bi-linear growth profiles. (A) Sigmoidal (blue) and bi-linear (red) model profiles of velocity; zero on the abscissa corresponds to the root tip. (B) Derivatives of the velocity profiles in (A) with respect to position, yielding profiles of elemental elongation rates. The distinct character of the two growth profiles becomes more evident in (B) than in (A). (C) Time-courses of elemental elongation rates calculated from the velocity profiles (A). Time 0 was chosen to correspond to the position at which the two rate profiles cross over for the first time (position 0.155 in (B)). The curves show the elemental elongation rate experienced over time by a point initially located at that position on the root.