Biophysical Model of Xylem Conductance in Tracheids of the FernPteris vittata

Abstract

Calkin, H. W., Gibson, A. C. and Nobel, P. S. 1986. Biophysical model 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-Poiseuille equation, 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 important anatomical details, such as the pits of tracheids, are ignored. Here, a previous model based on the Hagen-Poiseuille analysis for water flow in the stipes of Pteris vittata is improved by incorporating the actual lumen transectional shape (usually elliptical or ovate) and the tapering that occurs at the ends of its tracheids, as well as using a better method for analysing the electrical circuit analogues for the pits (pit cavities plus pit membranes). The measured K_h was similar to that predicted by the Hagen-Poiseuille equation for narrow stipes with their small tracheids, but was only about half the measured K^h for large 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 resistance was from the lumens but for the larger tracheids most was from the pit membranes. For all stipes the pit cavities accounted for 12–22% of the total resistance. When the pit membranes were partially digested away with cellulase, K^h increased about 66%, consistent with the deduced resistance of this part of the pathway. The present model incorporating realistic anatomical details allowed reasonable predictions of the hydraulic conductance per unit length over a wide size range of stipes for this fern.