Modeling xylem and phloem water flows in trees according to cohesion theory and Münch hypothesis

Abstract

Water and solute flows in the coupled system of xylem and phloem were modeled together with predictions for xylem and whole stem diameter changes. With the model we could produce water circulation between xylem and phloem as presented by the Münch hypothesis. Viscosity was modeled as an explicit function of solute concentration and this was found to vary the resistance of the phloem sap flow by many orders of magnitude in the possible physiological range of sap concentrations. Also, the sensitivity of the predicted phloem translocation to changes in the boundary conditions and parameters such as sugar loading, transpiration, and hydraulic conductivity were studied. The system was found to be quite sensitive to the sugar-loading rate, as too high sugar concentration, (approximately 7 MPa) would cause phloem translocation to be irreversibly hindered and soon totally blocked due to accumulation of sugar at the top of the phloem and the consequent rise in the viscosity of the phloem sap. Too low sugar loading rate, on the other hand, would not induce a sufficient axial water pressure gradient. The model also revealed the existence of Münch "counter flow", i.e., xylem water flow in the absence of transpiration resulting from water circulation between the xylem and phloem. Modeled diameter changes of the stem were found to be compatible with actual stem diameter measurements from earlier studies. The diurnal diameter variation of the whole stem was approximately 0.1 mm of which the xylem constituted approximately one-third.T. Hölttä ( ) · T. Vesala · S. Sevanto

Linking phloem function to structure: Analysis with a coupled xylem–phloem transport model

“…Additionally, sugar loading and unloading rates must be equal to the photosynthesis rate in steady state. The phloem will be close to water potential equilibrium with the xylem (Daudet et al, 2002;Hölttä et al, 2006a), differing in only by the amount needed to exchange water radially with the xylem. …”

“…Theoretically, hydraulic coupling to the xylem is significant as phloem is close to water potential equilibrium with the surrounding apoplast (Thompson and Holbrook, 2003b) and also with the surrounding xylem (Daudet et al, 2002;Hölttä et al, 2006a). Any changes in xylem water potential will therefore be transmitted to the phloem.…”

“…While the structural scaling of xylem has received a great deal of attention lately (e.g., West et al, 1999) hardly any consideration has been given to phloem morphology. As the carbohydrate transport in most plants takes place in the form of sugars forming viscous solutions at high concentrations, this poses a real problem for transport (Hölttä et al, 2006a;Lang, 1978). In a way, this task of constraining solution viscosity within physiological limits to allow transport of concentrated sugar concentration, could even be compared to the task of constraining xylem tensions to avoid xylem cavitation.…”

“…(7)) and higher sugar concentrations are needed in the phloem to draw water in osmotically from the xylem. In a dynamic scenario, short-term changes in xylem water potential could be temporarily buffered (Hölttä et al, 2006a), but in steady state, the effects of continuous differences in xylem water potential could be clearly seen on phloem translocation. Large investment in xylem conductance to maintain high xylem water potential for a given transpiration rate reduced the need for phloem conductance for a given assimilation rate.…”

Osmotically driven flows in microchannels separated by a semipermeable membrane

“…However, many theoretical and numerical studies of the sugar translocation in plants have used the pressure-flow hypothesis [6,7,8] with good results. To verify that these results are indeed valid, we believe that it is of fundamental importance to conduct a systematic survey of osmotically driven flows at the micrometer scale.…”