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Previous attempts to model steady state Munch pressure flow in phloem (Christy and Ferrier. [19731. Plant Physiol. 52: 531-538; and Ferrier et al. [19741. Plant Physiol. 54: 589-600) lack sufficient equations, and results were produced which do not represent correct mathematical solutions. Additional equations for the present closed form model were derived by assuming that unloading of a given solute is dependent upon the concentration of that solute in the sieve tube elements. Examples As no unique steady state mathematical solution could be found, the above models were used to approximate steady state sieve tube transport by a judicious choice of initial concentrations and convergence criteria, in a quasi-time-dependent iteration procedure. It is unlikely that such inconsistencies occur in real phloem, and thus, another equation must exist which would provide a unique, closed form solution at a given loading rate.The above problem did not arise in the mechanical analogue model of Eschrich et al. (4). In this system, a given, initial amount of sugar was placed within an open or closed tubular, semipermeable membrane. In the absence of continuous loading and/or unloading of solute, their mathematical model correctly predicted the velocity of the solute front, the lack of equilibrium in the open tube, and the equilibrium condition when the front reached the end of the closed tube. Therefore, the necessary additional equations for a closed form mathematical model of steady state phloem translocation may lie with the assumptions regarding the loading and/or unloading of solutes. These considerations can best be illustrated by examining the existing equations as they apply to all of the individual elements of a sieve tube.REVIEW OF GENERAL THEORY The standard water potential terminology (9,15,16) Water potentials of the xylem-apoplast continuum will be denoted by the subscript x, and those of the sieve tube elements as i. The flux of water through the peripheral membrane (J,i, see Table I for units) of the ith sieve element would be a function of the water potential difference, and the hydraulic conductivity (La) and reflection coefficient (c-) of membranes, i

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Summary. An integrated approach to study the effects of environmental factors on plants is described. The central theme of the system is the use of CO2 labelled with 11C supplied continuously to the plant and following the emitted radiation in vivo in the leaf, the phloem and the various sinks. The system consists of six components and with minor changes can be used for other tracers such as 13N for nitrogen fixation studies. Because of the short half life of the isotope, several experiments can be carried out on the same plant under the same environmental conditions without disturbing the plant. A host of ecologically, agriculturally and genetically important questions can be answered using this technique.

Extended square-wave traeer kinetics using "CO2 were used to measure the speed of transport and activity level (proportional to concentration) in the phloem at high and low loading rates in six species of plants. In all cases, increased loading rates resulted in inereased concentration. In most cases speed also increased, however, in two cases speed was lower and tracer activity was much higher at the higher loading rate. All the responses are consistent with the Milnch-Horwitz theory of phloem transport, depending upon the equation used to represent the unloading mechanism as described in a previous paper (Goeschl & Magnuson, 1986). For example, the latter two cases are consistent with the assumption that the unloading rate was limited by a process with saturable kinetics (enzyme-like).