To understand spatial and temporal aspects of rhizosphere function, three points of view should be considered. From the point of view of the moving root tip, we see a chemical field surrounding the tip as the tip moves to deeper soil layers. A complementary perspective is the point of view of the stationary soil particle that will eventually lie beside a mature root cell. The fixed soil particle will experience the processes (efflux or uptake) associated with a neighboring root element, so that fluxes corresponding to the different root locations will be encountered in a predictable sequence. Solving for the chemical field around the moving growth zone involves following a slice of soil as it “moves upward,” keeping track of the history of the radial profile and updating the chemical flux and diffusion over time as the soil encounters the older tissue elements. This approach is quite general and is illustrated for the computation of the pH in the soil around the tip of a growing root with known proton fluxes from the root surface. The third perspective is that of a particle attached to a cell initially on the surface of the root tip. This is the Lagrangian specification of root interaction with the soil. With time the cellular particle accelerates away from the tip to reach a displacement velocity equal to the root elongation rate, as the cell decelerates to a final fixed location in the soil profile. Working simultaneously in the moving reference frame attached to the root tip and the stationary reference frame of the soil horizon is essential to understanding rhizosphere development and plant impacts on soil, yet few soil studies in the literature take root growth into account.
The soil-based and cell-based points of view are also important for understanding the hydraulics of root growth. Primary growth is characterized by cell expansion facilitated by water uptake generating hydrostatic (turgor) pressure to inflate the cell, stretching the rigid cell walls. The multiple source theory of root growth hypothesizes that root growth involves transport of water both from the soil surrounding the growth zone and from the mature tissue higher in the root via phloem and protophloem. We used protophloem water sources as boundary conditions in a three-dimensional model of growth-sustaining water potentials in primary roots. The model is based on the Reynolds Transport Theorem for water transport into the expanding, moving cell in response to a water potential differential. The model predicts small radial gradients in water potential, with a significant longitudinal gradient. The results improve the agreement of theory with empirical studies for water potential in the primary growth zone of roots of maize (Zea mays). A sensitivity analysis quantifies the functional importance of apical phloem differentiation in permitting growth and reveals that the presence of phloem water sources makes the growth-sustaining water relations of the root relatively insensitive to changes in root radius and hydraulic conductivity. Adaptation to drought and other environmental stresses is predicted to involve more apical differentiation of phloem and/or higher phloem delivery rates to the growth zone.
References:
Wiegers BS, Cheer AY, Silk WK (2009) Modeling the Hydraulics of Root Growth in Three Dimensions with Phloem Water Sources. Plant Physiology 150 (4):2092-2103.
Dupuy LX, Silk WK (accepted for publication) Mechanisms of early microbial establishment on growing root surfaces. Vadose Zone Journal