Generalized Münch Coupling between Sugar and Water Fluxes for Modelling Carbon Allocation as Affected by Water Status

A model of within-plant carbon allocation is proposed which makes a generalized use of the Münch mechanism to integrate carbon and water functions and their involvement in growth limitations. The plant is envisioned as a branched network of resistive pathways (phloem and xylem) with nodal organs acting as sources and sinks for sucrose. Four elementary organs (leaf, stem, fruit, root) are described with their particular sink functions and hydraulic attributes. Given the rates of photosynthesis and transpiration and the hydraulic properties of the network as inputs, the model calculates the internal fluxes of water and sucrose. Xylem water potential (Ψ), phloem sucrose concentration (C) and turgor pressure (P) are calculated everywhere in the network accounting for osmotic equilibrium between apoplasm and symplasm and coupled functioning of xylem and phloem. The fluxes of phloem and xylem saps are driven by the gradients of P and Ψ, respectively. The fruit growth rate is assumed as turgor pressure dependent. To demonstrate its ability to address within-plant competition, the model is run with a simple-branched structure gathering three leaves, eight stem segments, three competing growing fruits and one root. The model was programmed with P-SpiceTM, a software specifically designed for simulating electrical circuits but easily adaptable to physiology. Simulations of internal water fluxes, sucrose concentrations and fruit growth rates are given for different conditions of soil water availability and hydraulic resistances (sensitivity analysis). The discussion focuses on the potential interest of this approach in functional–structural plant models to address water stress-induced effects.