Leaf hydraulics I: scaling transport properties from single cells to tissues

In leaf tissues, water may move through the symplast or apoplast as a liquid, or through the airspace as vapor, but the dominant path remains in dispute. This is due, in part, to a lack of models that describe these three pathways in terms of experimental variables. We show that, in plant water relations theory, the use of a hydraulic capacity in a manner analogous to a thermal capacity, though it ignores mechanical interactions between cells, is consistent with a special case of the more general continuum mechanical theory of linear poroelasticity. The resulting heat equation form affords a great deal of analytical simplicity at a minimal cost: we estimate an expected error of less than 12%, compared to the full set of equations governing linear poroelastic behavior. We next consider the case for local equilibrium between protoplasts, their cell walls, and adjacent air spaces during isothermal hydration transients to determine how accurately simple volume averaging of material properties (a 'composite' model) describes the hydraulic properties of leaf tissue. Based on typical hydraulic parameters for individual cells, we find that a composite description for tissues composed of thin walled cells with air spaces of similar size to the cells, as in photosynthetic tissues, is a reasonable preliminary assumption. We also expect isothermal transport in such cells to be dominated by the aquaporin-mediated cell-to-cell path. In the non-isothermal case, information on the magnitude of the thermal gradients is required to assess the dominant phase of water transport, liquid or vapor.