A case is presented for progressing from mathematical models of root aeration which assume complete radial homogeneity in respiratory demand and oxygen diffusivity to models which accommodate radial differences between the various tissue cylinders. The described model simulates aeration in submerged roots and allows for axial gas-phase diffusion in the cortex and radial liquid-phase diffusion elsewhere. It also accommodates diffusion into the rhizosphere and axial and radial differences in the root's properties on a tissue cylinder basis.
The results, based on the characteristics of aerenchymatous graminean roots, highlight the potential for stelar anoxia and some wall-layer anoxia in submerged, and even non-submerged, roots. They show that, (1) stelar anoxia should raise oxygen levels elsewhere and enhance root extension; (2) with high and constant oxygen diffusivity in the stele, anoxia should first occur close to the apex and spread basally and laterally with further root extension; (3) there will be competition between the oxygen demands of the root and rhizosphere; (4) extension may be reduced by radial oxygen losses into the rhizosphere, but the subapical decline in root-wall permeability in wetland species safeguards against this effect; (5) differences in critical oxygen pressure for extension growth (COPE) and respiration (COPR) may arise; and (6) survival may be helped by the manner in which anoxia spreads with aerobic conditions persisting in the phloem and pericycle until only traces of oxygen remain in the cortex. Sectional profiles of the roots show how oxygen gradients in the stele and wall layers will increase with increasing subapical impedance in these zones and, in the case of the wall layers, by oxygen throughflux to the rhizosphere.
Some of the results suggest that inner-stele anoxia might account for some of the hypoxic responses found in roots, and it is predicted that declining stelar oxygen diffusivity in subapical regions will raise COPR but not COPE, the inner-stele becoming anoxic subapically and the apical regions remaining wholly aerobic. This implies the possibility that where roots are described in the literature as hypoxic, because of ethanol production, raised alcohol dehydrogenase activity and reduced energy charge, the symptoms may be sometimes indicative only of some subapical stelar anoxia.
The results also serve to illustrate how variable the occurrence and shape of anoxic stelar zones might be. With only a slight alteration in subapical stelar oxygen diffusivity, anoxia could arise simultaneously in two positions along the root, or the first site of anoxia in the growing root might be both subapical and hypobasal. The likelihood of the endodermis in subapical parts being a possible cause of anoxia in roots is also considered.