A Biophysical Analysis of Stem and Root Diameter Variations in Woody Plants

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Abstract
A comprehensive model of stem and root diameter variation was developed. The stem (or root) was represented using two coaxial cylinders corresponding with the mature xylem and the extensible tissues. The extensible tissues were assumed to behave as a single cell separated from the mature xylem by a virtual membrane. The mature xylem and the extensible tissues are able to dilate with temperature and grow. Moreover, the extensible tissues are able to shrink and swell according to water flow intensity. The model is mainly based on the calculation of water volume flows in the “single cell” that are described using the principles of irreversible thermodynamics. The elastic response to storage volume and plastic extension accompanying growth are described. The model simulates diameter variation due to temperature, solute accumulation, and xylem, water potential. The model was applied to the peach (Prunus persica) stem and to the plum (Prunus domestica × Prunus spinosa) root. The simulation outputs corresponded well with the diameter variation observed. The model predicts that variations of turgor pressure and osmotic potential are smaller than the variations of xylem water potential. It also demonstrates correlations between the xylem water potential, the turgor pressure, the elastic modulus, and the osmotic potential. The relationship between the diameter and the xylem water potential exhibits a subtential hysteresis, as observed in field data. A sensitivity analysis using the model parameters showed that growth and shrinkage were highly sensitive to the initial values of the turgor pressure and to the reflection coefficient of solutes. Shrinkage and growth were sensitive to elastic modulus and wall-yielding threshold pressure, respectively. The model was not sensitive to changes in temperature.