Mathematical modeling of oxygen diffusion and respiration in legume root nodules

The O₂ permeability of legume root nodules is under physiological control; decreases in permeability are triggered by various forms of stress. Two linked mathematical models were used to explore several hypotheses concerning the physical nature of the variable diffusion barrier in nodules. Respiration and diffusion of dissolved O₂ and oxygenated leghemoglobin were simulated for the nodule cortex and the nodule interior. Measured nodule permeabilities were shown to be inconsistent with the hypothesis that large numbers of air-filled pores penetrate the diffusion barrier. Changes in the affinity of leghemoglobin for O₂ or in the rate of cytoplasmic streaming in diffusion barrier cells did not result in the large changes in O₂ permeability reported for real nodules. The presence or absence, but not the thickness, of aqueous plugs in radial pores through the cortex was found to have a large effect on permeability. Flooding of intercellular spaces, either between layers of cells in the cortex or in the nodule interior, also caused large changes in simulated permeability. The unsteady-state O₂ method for determining nodule permeability was tested using data generated by the model. The accuracy of the method was confirmed, provided that certain assumptions (full oxygenation of leghemoglobin under pure O₂ and uniform conditions in the nodule interior) are met.