On the mechanical origins of waving, coiling and skewing patterns in Arabidopsis thaliana roots

We present theory and simulations of the well-known waving, coiling and skewing patterns presented by roots of Arabidopsis thaliana when grown on inclined agar substrates. Our simulations confirm previous intuitions of waving and coiling arising from the combination of active gravitropism and passive root-plane interactions. Skewing is instead related to intrinsic twist due to cell file rotation, and circumnutations. Numerical investigations are outfitted with an analytical framework that consistently relates transitions between straight, waving and coiling patterns, as well as skewing angle, with tilt angle. Simulations are found to corroborate theory, providing a rigorous computational framework for studying interactions of plant organs with their environment.