Force generation by a cylindrical cell under stationary osmolyte synthesis.

Turgor is the driving force of plant growth, making it possible for roots to overcome soil resistance or for stems to counteract gravity. Maintaining a constant growth rate while avoiding cell content dilution, which would progressively stop the inward water flux, imposes the production or import of osmolytes in proportion to the increase of volume. We coin this phenomenon stationary osmoregulation. The article explores the quantitative consequences of this hypothesis on the interaction of a cylindrical cell growing axially against an obstacle. An instantaneous axial compression of a pressurized cylindrical cell generates a force and a pressure jump, which both decrease towards a lower value once water has flowed out of the cell to reach the water potential equilibrium. In the first part, the article derives analytical formulae for these forces and over-pressure both before and after relaxation. In the second part, we describe how the coupling of the Lockhart growth law with the stationary osmoregulation hypothesis predicts a transient slowdown in growth due to contact before a re-acceleration in growth. We finally compare these predictions with the output of an elastic growth model which ignores the osmotic origin of growth: models only match in the early phase of contact for a high-stiffness obstacle.

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.

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.

Plant root growth is dramatically reduced in compacted soils, affecting the growth of the whole plant. Through a model experiment coupling force and kinematics measurements, we probed the force-growth relationship of a primary root contacting a stiff resisting obstacle, which mimics the strongest soil impedance variation encountered by a growing root. The growth of maize roots just emerging from a corseting agarose gel and contacting a force sensor (acting as an obstacle) was monitored by time-lapse imaging simultaneously to the force. The evolution of the velocity field along the root was obtained from kinematics analysis of the root texture with a particle image velocimetry derived technique. A triangular fit was introduced to retrieve the elemental elongation rate or strain rate. A parameter-free model based on the Lockhart law quantitatively predicts how the force at the obstacle modifies several features of the growth distribution (length of the growth zone, maximal elemental elongation rate and velocity) during the first 10 min. These results suggest a strong similarity of the early growth responses elicited either by a directional stress (contact) or by an isotropic perturbation (hyperosmotic bath).

The helical motions of roots are linked to avoidance of particle forces in soil.

Limitation to root growth results from forces required to overcome soil resistance to deformation. The variations in individual particle forces affects root development and often deflects the growth trajectory. We have developed transparent soil and optical projection tomography microscopy systems where measurements of growth trajectory and particle forces can be acquired in a granular medium at a range of confining pressures. We developed image-processing pipelines to analyse patterns in root trajectories and a stochastic-mechanical theory to establish how root deflections relate to particle forces and thickening of the root. Root thickening compensates for the increase in mean particle forces but does not prevent deflections from 5% of most extreme individual particle forces causing root deflection. The magnitude of deflections increases with pressure but they assemble into helices of conserved wavelength in response linked to gravitropism. The study reveals mechanisms for the understanding of root growth in mechanically impeding soil conditions and provides insights relevant to breeding of drought-resistant crops.

Bending transition in the penetration of a flexible intruder in a two-dimensional dense granular medium.

We study the quasistatic penetration of a flexible beam into a two-dimensional dense granular medium lying on a horizontal plate. Rather than a buckling-like behavior we observe a transition between a regime of crack-like penetration in which the fiber only shows small fluctuations around a stable straight geometry and a bending regime in which the fiber fully bends and advances through series of loading and unloading steps. We show that the shape reconfiguration of the fiber is controlled by a single nondimensional parameter L/L_{c}, which is the ratio of the length of the flexible beam L to L_{c}, a bending elastogranular length scale that depends on the rigidity of the fiber and on the departure from the jamming packing fraction of the granular medium. We show, moreover, that the dynamics of the bending transition in the course of the penetration experiment is gradual and is accompanied by a symmetry breaking of the granular packing fraction in the vicinity of the fiber. Together with the progressive bending of the fiber, a cavity grows downstream of the fiber and the accumulation of grains upstream of the fiber leads to the development of a jammed cluster of grains. We discuss our experimental results in the framework of a simple model of bending-induced compaction and we show that the rate of the bending transition only depends on the control parameter L/L_{c}.

Physical root-soil interactions.

Plant root system development is highly modulated by the physical properties of the soil and especially by its mechanical resistance to penetration. The interplay between the mechanical stresses exerted by the soil and root growth is of particular interest for many communities, in agronomy and soil science as well as in biomechanics and plant morphogenesis. In contrast to aerial organs, roots apices must exert a growth pressure to penetrate strong soils and reorient their growth trajectory to cope with obstacles like stones or hardpans or to follow the tortuous paths of the soil porosity. In this review, we present the main macroscopic investigations of soil-root physical interactions in the field and combine them with simple mechanistic modeling derived from model experiments at the scale of the individual root apex.

Reorganization of a dense granular assembly: the unjamming response function.

We investigate the mechanical properties of a static dense granular assembly in response to a local forcing. To this end, a small cyclic displacement is applied on a grain in the bulk of a two-dimensional disordered packing under gravity and the displacement fields are monitored. We evidence a dominant long range radial response in the upper half part above the solicitation and after a large number of cycles the response is "quasireversible" with a remanent dissipation field exhibiting long range streams and vortexlike symmetry.