Phloem Mobility of Xenobiotics

A passive diffusion model has been developed which simultaneously accounts for the dependence of phloem mobility on permeability and acid dissociation. The model is consistent with the observation that the addition of an acid moiety to an otherwise phloem immobile compound may enhance that compound's ability to move in the phloem. However, acid trapping in the basic phloem is not the only enhancement factor. Acid functionalization also lowers the effective permeability usually towards its optimum value. The unified theory predicts that for a given acid dissociation constant there is an optimum permeability and conversely for a given permeability there is an optimum dissociation constant. According to one theory, the phloem mobility of a compound depends upon the presence of a weak acid functionality within that compound (2). Another theory deals with compounds which are nonelectrolytes at physiological pH and ascribes efficient phloem mobility to compounds whose membrane permeabilities fall within some optimum range (6, 8). The optimum range is determined by attributes such as plant length, leaf size, phloem sap velocity, etc. The latter theory has been developed into a mathematical model (8). Neither of these theories invokes a carrier mechanism and the two theories are not necessarily in opposition. This paper describes an extension of the mathematical model (8) that unifies the two theories. The extended model explains in a straightforward fashion the enhanced phloem mobility of weakly acidic compounds without invoking a carrier mechanism. While the model provides for acid trapping within the sieve tubes, the mobility of weak acids is in large part due to their intermediate permeability. THEORY The model used is an extension of that of Tyree et al. (8). It consists of a linear plant of length LI (Fig. 1). A xenobiotic is assumed to have been applied over a length l* of the leaf whose length is 1. The length of the leaf, petiole, and stem is 0.5L, while the root system accounts for the other half of the plant's length. Phloem sap is assumed to flow through a sieve tube of radius r. The velocity of the phloem sap is assumed to rise linearly from near zero at the leaf tip until it reaches a maximum value of v -which is maintained throughout the petiole and stem. Xenobiotic is assumed to enter the sieve tubes in the leaf zone by passive diffusion driven by a concentration gradient. For an acidic I A complete list of abbreviations and symbols appears in Table I. Table I. Abbreviations and Symbols Used in the Text L: Length of plant in m 1: Length of leaf in m 1*: Length of leaf in m over which compound is applied r: Radius of sieve tube in m v: Maximum velocity of phloem sap in m/s s: Distance from leaf tip in m HA: An undissociated acid A -: Conjugate base of HA [HA]L: Concentration of HA (M) in apoplast [HA],: Concentration of HA (M) within sieve tube at a distance s from leaf tip [A l Concentration of A (M) in apoplast [A -],: Concentration of A (M) within sieve tube at a distance s from leaf tip C,.O: Total concentration of xenobiotic (M) in leaf apoplast; total of [HA]L and [A C,(s): Concentration of xenobiotic (M) within the sieve tube at a distance s from the leaf tip; total of [HA], and [A -] Cf: Concentration factor (unitless); the ratio of C, (0.9 L) to C,,0 [H +i: Hydrogen ion concentration (M) within sieve tube [H + ]o: Hydrogen ion concentration (M) within apoplast PHA: Permeability of HA in m/s PA: Permeability of Ain m/s Ka: Acid dissociation constant of HA (M) pKa: Log (1/Ka) KO,,: Octanol-water partition coefficient nHA. Number of moles of HA nA : Number of moles of AQ: Area of cylindrical sieve tube element (m2) v': Flow velocity (m/s) of phloem sap at a distance s from leaf tip substance, HA, the total concentration of xenobiotic in the leaf apoplast, C,O, is defined as the sum of the concentrations of HA and Awhere Ais the conjugate base of HA. All concentrations may be assumed to be in mol/L. Analogously, C,(s) is defined as the total concentration of xenobiotic at point s in the leaf sieve tube. Generally, C,,O will exceed C,(s) for s < 1, that is within the leaf. Hence, within the leaf portion of the plant there is a net flow of xenobiotic into the sieve tube. In the stem and petiole, the concentration of xenobiotic in the apoplast surrounding the sieve tube (including the xylem) is assumed to be zero. Hence, some of the xenobiotic leaks into the apoplast as the phloem sap carries the remaining portion towards the root. The xenobiotic which leaks into the apoplast is assumed 803 www.plantphysiol.org on January 16, 2018 Published by Downloaded from Copyright © 1988 American Society of Plant Biologists. All rights reserved. Plant Physiol. Vol. 86, 1988 B. VELOCITY PROFILE: 0.0 *.I --------------; -----0.5 L