Change in hydraulic properties of the rhizosphere of maize under different abiotic stresses

Abstract

Background and aims

Root growth alters the rhizosphere thereby affecting root uptake of water and nutrients. However, the influence of abiotic stress on this process is poorly understood. In this study we investigated the effects of water and salinity stresses (both in isolation and combined) on maize (Zea mays L.).

Methods

Seedlings were grown in pots packed with a loamy sand soil for two weeks and then subjected to water and salinity stresses, together with an unstressed control. After an additional two weeks, plants were removed from the pots and the soil aggregates adhering to the roots were collected and scanned using X-ray Computed Tomography. The ability of the aggregates to conduct water was calculated from pore-scale simulation of water flow using the lattice Boltzmann method.

Results

It was found that both water and salinity stresses reduced the permeability of the rhizospheric aggregates, although the reduction under salinity stress was more significant than under water stress. Combining water and salinity stresses reduced the permeability of the rhizosphere by one order in magnitude compared to the unstressed rhizosphere.

Conclusions

Abiotic stresses work with root-induced activity to reshape the rhizosphere. As water and nutrients need to pass through the rhizosphere before being taken up by roots, understanding such rhizosphere changes has an important implication in plant acquisition of soil resources.

Water flow and solute diffusion through the void space of the segmented images were both simulated by the following lattice Boltzmann model

$$ {f}_i\left(\mathrm{x}+\delta t{\mathrm{e}}_i,t+\delta t\right)={f}_i\left(\mathrm{x},t\right)+{M}^{-1} SM\left[{f}_i^{eq}\left(\mathrm{x},t\right)-{f}_i\left(\mathrm{x},t\right)\right], $$

(A1)

wheref_i(x, t)is the particle distribution function at location x and time t moving at lattice velocity e_i, δx is the size of the image voxels, δt is a time step, ${f}_i^{eq}\left(\mathrm{x},t\right)$ is the equilibrium distribution function, M is a transform matrix and S is the collision matrix. The models for water flow and solute transport differed only in their equilibrium distribution functions, both involving a collision step and a streaming step to advance a time step. In each model, the collision was calculated as $m= SM\left[{f}_i^{eq}\left(\mathrm{x},t\right)-{f}_i\left(\mathrm{x},t\right)\right]$ first and m was then transformed back to particle distribution functions byM⁻¹m. In both models, we used the D3Q19 lattice in which the particles move in 19 directions with velocities: (0, 0, 0), (±δx/δt, ±δx/δt, 0), (0, ±δx/δt, ±δx/δt), (±δx/δt, 0, ±δx/δt)and (±δx/δt, ±δx/δt, ±δx/δt) (Qian et al. 1992).

Model for water flow

The collision matrix in the model for water flow is diagonal (d’Humiers et al. 2002):

$$ {\displaystyle \begin{array}{l}S={\left({s}_0,{s}_1,{s}_2,{s}_3,{s}_4,{s}_5,{s}_6,{s}_7,{s}_8,{s}_9,{s}_{10},{s}_{11},{s}_{12},{s}_{13},{s}_{14},{s}_{15},{s}_{16},{s}_{17},{s}_{18}\right)}^T,\\ {}{s}_0={s}_3={s}_5={s}_7=0,\\ {}{s}_1={s}_2={s}_{9-15}=1/\tau, \\ {}{s}_4={s}_6={s}_8={s}_{16-18}=8\left(2-{\tau}^{-1}\right)/\left(8-{\tau}^{-1}\right),\end{array}} $$

(A2)

and the equilibrium distribution functions are

$$ {\displaystyle \begin{array}{l}{f}_i^{eq}={w}_i\left[\rho +{\rho}_0\left(\frac{3{\mathrm{e}}_i\cdot \mathrm{u}}{s^2}+\frac{9{\left({\mathrm{e}}_i\cdot \mathrm{u}\right)}^2}{2{s}^4}-\frac{3\mathrm{u}\cdot \mathrm{u}}{2{s}^2}\right)\right],\\ {}{w}_0=1/3,\\ {}{w}_i=1/18,\kern2.25em \left\Vert {\mathrm{e}}_{\mathrm{i}}\right\Vert =\delta x/\delta t\\ {}{w}_i=1/36\kern3em \left\Vert {\mathrm{e}}_{\mathrm{i}}\right\Vert =\sqrt{2}\delta x/\delta t\ \end{array}} $$

(A3)

wheres = δx/δtand ρ₀is a reference fluid density to ensure an incompressible fluid at steady state (Zou et al. 1995). The water density ρ and bulk water velocity u are calculated from

$$ {\displaystyle \begin{array}{l}\rho ={\sum}_{i=0}^{18}{f}_i,\\ {}\mathrm{u}={\sum}_{i=1}^{18}{f}_i{\mathrm{e}}_i/{\rho}_0.\end{array}} $$

(A4)

The kinematic viscosity of fluid wasν = δx²(τ − 0.5)/3δt and its pressure is related to fluid density in p = ρδx²/3δt².

Model for solute diffusion

The equilibrium distribution functions for solute diffusion are defined by

$$ {f}_i^{eq}={w}_ic, $$

(A5)

where c is solute concentration and the weighting parameter w_i is the same as those defined in Eq. (A3). The diagonal collision matrix for solute diffusion is uniform:

$$ S={\left({\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0,{\tau}_0\right)}^T, $$

(A6)

The collision can thus be directly calculated from$m={\tau}_0\left[{f}_i^{eq}\left(\mathrm{x},t\right)-{f}_i\left(\mathrm{x},t\right)\right]$ without need of the transform as for fluid flow. The concentration c and the diffusice flux j in each voxel are calculated from

$$ {\displaystyle \begin{array}{l}c={\sum}_{i=0}^{18}{f}_i^{eq},\\ {}\mathrm{j}={\sum}_{i=0}^{18}\left(1-0.5{\tau}_0\right){e}_i{f}_i^{eq},\end{array}} $$

(A7)

The molecular diffusion coefficient in the above model isD₀ = δx²(1/τ₀ − 0.5)/3δt. The effective diffusion coefficient of the image was calculated using the method proposed in our previous work (Zhang et al. 2016a).

Model implementation

For both water flow and solute diffusion, there are two calculations to advance one time step. The first one is to calculate the collisions: ${f}_i^{\ast }={f}_i\left(\mathrm{x},t\right)+{M}^{-1} SM\left[{f}_i^{eq}\left(\mathrm{x},t\right)-{f}_i\left(\mathrm{x},t\right)\right]$ for water and ${f}_i^{\ast }={f}_i\left(\mathrm{x},t\right)+{\tau}_0\left[{f}_i^{eq}\left(\mathrm{x},t\right)-{f}_i\left(\mathrm{x},t\right)\right]$ for solute, and the second step is to move ${f}_i^{\ast }$ to x + δte_i at the end of δt. Whenever${f}_i^{\ast }$ hits a solid voxel during the streaming, it is bounced back to where it emanates to ensure a zero velocity on the water-solid interface for both water flow and solute diffusion.