Cell to Organ Modeling of Mechanics of Circumnutation in Rice Roots

Plant roots navigate subterranean terrain via cell division and elongation without the use of a central nervous system. Circumnutation, the helical motion of the root tip, promotes root penetration and exploration [Taylor et al, PNAS 2021]. How cell elongation is coordinated and modulated in different environments is largely unknown. We grew O. sativa rice roots (~ 200 um diameter) in transparent gels of different stiffnesses. Across environments, we observed a negative correlation between amplitude, the root tip angle (spanning from 0.1 to 0.7 mm), and frequency, how often the tip sweeps a full circle (from 0.5 to 1 nutations per hour). To explain this relationship, we constructed a Discrete Element Method (DEM) simulation of the epidermal layer of a growing root (~20,000 cells in 1 cm), treating the particles of the DEM model as individual cells. Interactions between cells are implemented through bonds with time-dependent equilibrium lengths to enable cell elongation. We implement circumnutation via differential elongation where cells in different rows grow at different speeds, inducing global root curvature; this differential elongation is then rotated around the periphery of the root as it grows. Simulations reveal that modulating the rotational speed of the differential elongation zones around the root recapitulates the negative correlation between amplitude and frequency observed in experiments.