Plant root growth against a mechanical obstacle: the early growth response of a maize root facing an axial resistance is consistent with the Lockhart model

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 modeling 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.

A quantitative model for spatio-temporal dynamics of root gravitropism

Plant organs adapt their morphology according to environmental signals through growth-driven processes called tropisms. While much effort has been directed towards the development of mathematical models describing the tropic dynamics of aerial organs, these cannot provide a good description of roots due to intrinsic physiological differences. Here we present a mathematical model informed by gravitropic experiments on Arabidopsis thaliana roots, assuming a subapical growth profile and apical sensing. The model quantitatively recovers the full spatio-temporal dynamics observed in experiments. An analytical solution of the model enables us to evaluate the gravitropic and proprioceptive sensitivities of roots, while also allowing us to corroborate the requirement for proprioception in describing root dynamics. Lastly, we find that the dynamics are analogous to a damped harmonic oscillator, providing intuition regarding the source of the observed oscillatory behavior and the importance of proprioception for efficient gravitropic control. In all, the model provides not only a quantitative description of root tropic dynamics, but also a mathematical framework for the future investigation of roots in complex media.

Genotypic differences in systemic root responses to mechanical obstacles

As roots grow through the soil to forage for water and nutrients, they encounter mechanical obstacles such as patches of dense soil and stones that locally impede root growth. Here, we investigated hitherto poorly understood systemic responses of roots to localised root impedance. Seedlings of two wheat genotypes were grown in hydroponics and exposed to impenetrable obstacles constraining the vertical growth of the primary or a single seminal root. We deployed high-resolution in vivo imaging to quantify temporal dynamics of root elongation rate, helical root movement, and root growth direction. The two genotypes exhibited distinctly different patterns of systemic responses to localised root impedance, suggesting different strategies to cope with obstacles, namely stress avoidance and stress tolerance. Shallower growth of unconstrained seminal roots and more pronounced helical movement of unconstrained primary and seminal roots upon localised root impedance characterised the avoidance strategy shown by one genotype. Stress tolerance to localised root impedance, as exhibited by the other genotype, was indicated by relatively fast elongation of primary roots and steeper seminal root growth. These different strategies highlight that the effects of mechanical obstacles on spatiotemporal root growth patterns can differ within species, which may have major implications for resource acquisition and whole-plant growth.