Growth Patterns Inferred from Anatomical Records

Abstract

Our objective was to test whether accurate growth analyses can be obtained from anatomical records and some mathematical formulas. Roots of Zea mays L. were grown at one of two temperatures (19°C or 29°C) and were prepared with standard techniques for light microscopy. Positions of cell walls were digitized from micrographs. The digitized data were averaged and smoothed and used in formulas to estimate growth trajectories, Z(t), velocities, v(z), and strain rates, r(z), where Z(t) is the location occupied by the cellular particle at time t; and v(z) and r(z) are, respectively, the fields of growth velocity and strain rate. The relationships tested are: for Z(t), t = n * c; v(z) = l(z) * f; and r(z) = f * (∂/∂z (l(z))). In the formulas, n represents the number of cells between the origin and the position Z(t); l(z) is local cell length; the constant c, named the `cellochron,' denotes the time for successive cells to pass a spatial point distal to the meristem; l(z) is local cell length, and f is cell flux. Growth trajectories and velocity fields from the anatomical method are in good agreement with earlier analyses based on marking experiments at the two different temperatures. Growth strain rate fields show an unexpected oscillation which may be due to numerical artifacts or to a real oscillation in cell production rate.