Using non-equilibrium thermodynamics to model cadmium accumulation by maize

Abstract

Many people around the world are overexposed to cadmium through their consumption of plant products. A model predicting Cd content in crops would improve risk assessment and cultural practices. As no such model exists, we evaluated different methods to simulate the root uptake of Cd and its translocation to the aerial parts of maize.

Using non-equilibrium thermodynamics, the Cd flux ($J_{A,B}$) from one compartment (A) to another (B) was considered to be proportional to the difference in electrochemical potential between the compartments and given by an equation of the type $J_{A,B}={\beta }_{A,B}\ln (K_B{C}_A/K_A{C}_B)$, where ${\beta }_{A,B}$ and $K_B$ are constants and $C_A$ and $C_B$ the actual Cd concentrations in compartments A and B. The compartments considered were rhizosphere solution (Rh), root cortex (Co), xylem sap (X) and aerial tissues. The model was evaluated against the experimental uptake of Cd by maize exposed for 8 h to a constant Cd concentration in the rhizosphere solution.

The formalism made it possible to describe the flow of Cd from the rhizosphere to the root cortex, with ${\beta }_{\mathrm{Rh},\mathrm{Co}}$ = 8.7E-11 mol m⁻² s⁻¹ and $K_{\mathrm{Co}}$ = 73. This questions the common use of Michaelis-Menten kinetics to model root absorption over the long term (throughout the cultivation period). In this case, the apparent validity of the Michaelis-Menten uptake kinetics is probably more closely linked to the root growth than to the Cd internalization mechanisms. To take into account the resistance to the ion transport linked to crossing the root cortex, thermodynamic and diffusion formalisms had to be associated, which enabled the prediction of the Cd flux towards xylem, with $K_X$ = 12.48 and a diffusion coefficient $D_{\mathrm{Co}}$ = 3.44E-11 m² s⁻¹. The Cd flux from xylem to aerial tissues was better predicted by modelling the sap flow due to plant transpiration. This work opens perspectives towards a relatively simple modelling of plant Cd accumulation.