Waving and skewing of Arabidopsis thaliana roots results from mechanical interactions with the substrate*

We present a novel numerical solver based on a Cosserat rod integrator and a quasi-static integration scheme, which allows to quantitatively investigate how growing rod-like organs mechanically interact with their environment, for the first time.

We use our solver to shed new light on the well-known waving, coiling and skewing patterns presented by roots of Arabidopsis thaliana when grown on agar plates that are tilted with respect to gravity. Although we use simplified models for the roots and the experimental geometry, our simulations are able to test mechanistic assumptions regarding the development of these growth patterns that have been hard to verify until now.

Our simulations confirm previous theories suggesting that waving and coiling result from the combination of gravitropism and mechanical interactions of the root with the tilted plane, while skewing is related to an intrinsic twist profile. We develop analytic models relating skewing angles, and the transition between waving and coiling patterns, to the tilt angle of the substrate. Furthermore, we compare our simulation results regarding skewing angles to quantitative data from a number of published experimental papers and find a good agreement.