Biophysical Model of Xylem Conductance in Tracheids of the Fern Pteris vittata

Calkin, H. W., Gibson, A. C. and Nobel, P. S. 1986. Biophysicalmodel of xylem conductance in tracheids of the fern Pteris vittata.—J.exp. Bot. 37: 1054–1064. Water movement in the xylem is often analysed with the Hagen-Poiseuilleequation, which applies to capillaries of specific diameters.However, the predicted hydraulic conductances per unit length(K_h) are generally much higher than measured values and importantanatomical details, such as the pits of tracheids, are ignored.Here, a previous model based on the Hagen-Poiseuille analysisfor water flow in the stipes of Pteris vittata is improved byincorporating the actual lumen transectional shape (usuallyelliptical or ovate) and the tapering that occurs at the endsof its tracheids, as well as using a better method for analysingthe electrical circuit analogues for the pits (pit cavitiesplus pit membranes). The measured K_h was similar to that predictedby the Hagen-Poiseuille equation for narrow stipes with theirsmall tracheids, but was only about half the measured K^h forlarge stipes. Correcting for the actual shape changed K^h 2-to 3-fold for tracheids with elliptic and ovate transections.For the smaller diameter tracheids, most of the flow resistancewas from the lumens but for the larger tracheids most was fromthe pit membranes. For all stipes the pit cavities accountedfor 12–22% of the total resistance. When the pit membraneswere partially digested away with cellulase, K^h increased about66%, consistent with the deduced resistance of this part ofthe pathway. The present model incorporating realistic anatomicaldetails allowed reasonable predictions of the hydraulic conductanceper unit length over a wide size range of stipes for this fern. Key words: Hydraulic conductance, pit, tracheid, xylem