Mathematical Model of Lateral Oxygen Diffusion and Respiration of Roots for Estimating the Diffusion Coefficient and Affinity to Oxygen

We propose herein a mathematical model, for calculating the oxygen diffusion coefficient (D) and K _m value of a cell (M) based on oxygen concentration-respiration rate curve obtained under the condition that oxygen was supplied by lateral diffusion in roots. The model was deductively developed on the assumption that the roots were uniform and cylindrical and that the oxygen concentration and respiration rate were interdependent.

We estimated D and M from the oxygen concentration-respiration curves of rice (cv. Fujisaka 5) and wheat (cv. Chinese Spring) using this model. These values showed a certain range as follows. In rice, 0.003 cm² h^-1 ≤ D < 0.037 cm² h^-1, and 0.55 μmol mL^-1 ≤ M < 0.75 μmol mL^-1, in wheat, 0.016 cm² h^-1 ≤ D < 0.093 cm² h^-1, and 2.1 μmol mL^-1 ≤ M < 2.2 μmol mL^-1. By comparing the values, rice appeared to be more adapted to hypoxia than wheat, because rice had lower D and M values implying the existence of a safeguard mechanism and high affinity to oxygen. Higher oxygen uptake rate under hypoxia in rice was derived from the lower M value, which exceeded the low D.