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

By masterfully balancing directed growth and passive mechanics, plant roots are remarkably capable of navigating complex heterogeneous environments to find resources. Here we present a theoretical and numerical framework which allows us to interrogate and simulate the mechanical impact of solid interfaces on the growth pattern of plant organs. We focus on the well-known waving, coiling and skewing patterns exhibited by roots of Arabidopsis thaliana when grown on inclined surfaces, serving as a minimal model of the intricate interplay with solid substrates. By modelling growing slender organs as Cosserat rods that mechanically interact with the environment, our simulations verify hypotheses of waving and coiling arising from the combination of active gravitropism and passive root-plane responses. Skewing is instead related to intrinsic twist due to cell file rotation. Numerical investigations are outfitted with an analytical framework that consistently relates transitions between straight, waving, coiling and skewing patterns with substrate tilt angle. Simulations are found to corroborate theory and recapitulate a host of reported experimental observations, thus providing a systematic approach for studying in silico plant organs behavior in relation to their environment. SignificancePlant roots exhibit an exceptional ability to navigate in heterogeneous soil environments while overcoming obstacles. Our study combines theory and experimental observations to interrogate and simulate the mechanical impact of obstacles on organ growth. As a test case we focus on well-known observations of waving, coiling and skewing growth patterns of Arabidopsis thaliana roots grown on inclined substrates. Overall, our study explains a broad set of experimental observations through the minimal ingredients of gravitropism and passive mechanics. Our numerical framework provides an in silico laboratory, yielding quantitative insight into the dynamics of growing organs at the intersection of active processes and passive mechanics, applicable beyond plants to any slender growing system, from neurons or fungal hyphae to novel soft robots.