Scaling Phloem Transport: Water Potential Equilibrium and Osmoregulatory Flow

Abstract

In this work, the common assumption that phloem sap is in water potential equilibrium with the surrounding apoplast was examined. With a dimensionless model of phloem translocation that scales with just two dimensionless parameters ((R) over cap and (F) over cap), a 'map' of phloem behaviour as a function of these parameters was produced, which shows that the water potential equilibrium assumption ((R) over cap(F) over cap >> 1) is valid for essentially all realistic values of the relevant scales. When in water potential equilibrium, a further parameter reduction is possible that limits model dependence to a single parameter ((F) over cap), which describes the ratio of the solution's osmotic strength to its axial pressure drop. Due to the locally autonomous nature of individual sieve element/companion cell complexes, it is argued that long-distance integrative control is most efficient when is large ( that is, when the pressure drop is relatively small), permitting the sieve tube to regulate solute loading in response to global changes in turgor. This mode of transport has been called 'osmoregulatory flow.' Limitations on the pressure drop within the transport phloem could require that sieve tubes be shorter than the long axis of the plant, and thus arranged in series and hydraulically isolated from one another.