Tissue stresses and resistance to water flow conspire to uncouple the water potential of the epidermis from that of the xylem in elongating plant stems.

Considerable evidence exists that, in elongating dicot stems such as soybean hypocotyls: (1) the elongation rate is controlled largely by the mechanical properties of the epidermal cell walls; (2) the inner tissue is under compression in the sense that the turgor pressure of the cells is not fully borne by their cell walls; (3) the surplus turgor pressure in this inner tissue generates a force that is transmitted to the epidermis, where it drives irreversible elongation of the cell walls; and (4) the radial flow of water from the xylem to the rest of the tissue, needed to fill the expanding cells, is driven by gradients in water potential. On the basis of these propositions, this paper develops a mathematical description of the biophysical control of elongation rate and the radial distribution of water potential in the growing plant stem. Additional simplifying assumptions are that the osmotic pressure of the cells and their elastic modulus are constant throughout, and that the proportion of the tensile force that is borne by the walls of the inner cells is also constant. We assume, further, that the epidermal cell walls yield plastically in response to the tensile force they experience, as in the Lockhart model of cell expansion. The analysis gives expressions for the strain rate and the radial distribution of water potential as functions of the water potential of the xylem and of various parameters. These parameters include diffusivity of water in the tissue, the radii of the stem and of the cylindrical band of xylem within it, and the extensibility and yield threshold of the Lockhart equation. Aremarkable feature of the water relations of the elongating soybean hypocotyl is that changes in the water potential of the xylem, while they rapidly affect elongation rate, cause little or no change in the water potential of the epidermis, at least for many hours. The analysis shows how such an uncoupling can occur, and, further, predicts that low diffusivity would result in the water potential of the epidermis falling when that of the xylem is raised.